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Preliminary Information

On the next page you'll be asked to select an Implicit Association Test (IAT) from a list of possible topics . We will also ask you (optionally) to report your attitudes or beliefs about these topics and provide some information about yourself.

We ask these questions because the IAT can be more valuable if you also describe your own self-understanding of the attitude or stereotype that the IAT measures. We would also like to compare differences between people and groups.

On the IAT, you may find it easier to pair certain attributes with one group of people compared to another. Your IAT results may depart from your personal beliefs.

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Important disclaimer: In reporting to you results of any IAT test that you take, we will mention possible interpretations that have a basis in research done (at the University of Washington, University of Virginia, Harvard University, and Yale University) with these tests. However, these Universities, as well as the individual researchers who have contributed to this site, make no claim for the validity of these suggested interpretations. If you are unprepared to encounter interpretations that you might find objectionable, please do not proceed further. You may prefer to examine general information about the IAT before deciding whether or not to proceed.

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On the next page you'll be asked to select an Implicit Association Test (IAT) from a list of possible topics . We will also ask you (optionally) to report your attitudes or beliefs about these topics and provide some information about yourself.

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The danger of predictive algorithms in criminal justice

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The danger of predictive algorithms in criminal justice

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The danger of predictive algorithms in criminal justice | Hany Farid | TEDxAmoskeagMillyard

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How Is the Use of Predictive Analytics in the Criminal Justice System Negatively Impacting Black Defendants?

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How Is the Use of Predictive Analytics in the Criminal Justice System Negatively Impacting Black Defendants?

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Introduction
There has been an increasing trend in the public sector to use predictive analytics to predict and solve some of society's biggest policy challenges. Governments are using predictive analytics tools to try to help build more effective programs and policies before they...

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How Is the Use of Predictive Analytics in the Criminal Justice System Negatively Impacting Black...

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Introduction There has been an increasing trend in the public sector to use predictive analytics to predict and solve some of society's biggest policy challenges. Governments are using predictive analytics tools to try to help build more effective programs and policies before they...

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Unit Plans

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Understanding by Design: Complete Collection | Understanding by Design | Trinity University

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These units were written during the Summer Curriculum Writing Institute* (SCWI) at Trinity University beginning in 2005 and are added to at the close of the Institute each year. They use the Understanding by Design framework developed by Grant Wiggins and Jay McTighe.

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Introduction to Linear Regression

Author(s)
David M. Lane

Prerequisites
Measures of Variability, Describing Bivariate Data

Learning Objectives

1. Define linear regression

2. Identify errors of prediction in a scatter plot with a regression line

In simple linear regression, we predict scores on one variable from the scores on a second variable. The variable we are predicting is called the criterion variable and is referred to as Y. The variable we are basing our predictions on is called the predictor variable and is referred to as X. When there is only one predictor variable, the prediction method is called simple regression. In simple linear regression, the topic of this section, the predictions of Y when plotted as a function of X form a straight line.

The example data in Table 1 are plotted in Figure 1. You can see that there is a positive relationship between X and Y. If you were going to predict Y from X, the higher the value of X, the higher your prediction of Y.

Table 1. Example data.

X

Y

1.00

1.00

2.00

2.00

3.00

1.30

4.00

3.75

5.00

2.25

Figure 1. A scatter plot of the example data.

Linear regression consists of finding the best-fitting straight line through the points. The best-fitting line is called a regression line. The black diagonal line in Figure 2 is the regression line and consists of the predicted score on Y for each possible value of X. The vertical lines from the points to the regression line represent the errors of prediction. As you can see, the red point is very near the regression line; its error of prediction is small. By contrast, the yellow point is much higher than the regression line and therefore its error of prediction is large.

Figure 2. A scatter plot of the example data. The black line consists of the predictions, the points are the actual data, and the vertical lines between the points and the black line represent errors of prediction.

The error of prediction for a point is the value of the point minus the predicted value (the value on the line). Table 2 shows the predicted values (Y') and the errors of prediction (Y-Y'). For example, the first point has a Y of 1.00 and a predicted Y (called Y') of 1.21. Therefore, its error of prediction is -0.21.

Table 2. Example data.

You may have noticed that we did not specify what is meant by "best-fitting line." By far, the most commonly-used criterion for the best-fitting line is the line that minimizes the sum of the squared errors of prediction. That is the criterion that was used to find the line in Figure 2. The last column in Table 2 shows the squared errors of prediction. The sum of the squared errors of prediction shown in Table 2 is lower than it would be for any other regression line.

The formula for a regression line is

Y' = bX + A

where Y' is the predicted score, b is the slope of the line, and A is the Y intercept. The equation for the line in Figure 2 is

Y' = 0.425X + 0.785

For X = 1,

Y' = (0.425)(1) + 0.785 = 1.21.

For X = 2,

Y' = (0.425)(2) + 0.785 = 1.64.

Computing the Regression Line

In the age of computers, the regression line is typically computed with statistical software. However, the calculations are relatively easy, and are given here for anyone who is interested. The calculations are based on the statistics shown in Table 3. M X is the mean of X, M Y is the mean of Y, s X is the standard deviation of X, s Y is the standard deviation of Y, and r is the correlation between X and Y.

Formula for standard deviation
Formula for correlation

Table 3. Statistics for computing the regression line.

The slope (b) can be calculated as follows:

b = r s Y/s X

and the intercept (A) can be calculated as

A = M Y - bM X.

For these data,

b = (0.627)(1.072)/1.581 = 0.425

A = 2.06 - (0.425)(3) = 0.785

Note that the calculations have all been shown in terms of sample statistics rather than population parameters. The formulas are the same; simply use the parameter values for means, standard deviations, and the correlation.

Standardized Variables

The regression equation is simpler if variables are standardized so that their means are equal to 0 and standard deviations are equal to 1, for then b = r and A = 0. This makes the regression line:

Z Y' = (r)(Z X)

where Z Y' is the predicted standard score for Y, r is the correlation, and Z X is the standardized score for X. Note that the slope of the regression equation for standardized variables is r.

A Real Example

The case study " SAT and College GPA" contains high school and university grades for 105 computer science majors at a local state school. We now consider how we could predict a student's university GPA if we knew his or her high school GPA.

Figure 3 shows a scatter plot of University GPA as a function of High School GPA. You can see from the figure that there is a strong positive relationship. The correlation is 0.78. The regression equation is

University GPA' = (0.675)(High School GPA) + 1.097

Therefore, a student with a high school GPA of 3 would be predicted to have a university GPA of

University GPA' = (0.675)(3) + 1.097 = 3.12.

Figure 3. University GPA as a function of High School GPA.

Assumptions

It may surprise you, but the calculations shown in this section are assumption-free. Of course, if the relationship between X and Y were not linear, a different shaped function could fit the data better. Inferential statistics in regression are based on several assumptions, and these assumptions are presented in a later section of this chapter.

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Introduction to Linear Regression Author(s) David M. Lane Prerequisites Measures of Variability, Describing Bivariate Data Learning Objectives Define linear regression Identify errors of prediction in a scatter plot with a regression line In simple linear regression, we predict scores on one variable from the scores on a second variable.

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How to Calculate and Interpret a Correlation (Pearson's r)

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As you fit regression models, you might need to make a choice between linear and nonlinear regression models. The field of statistics can be weird. Despite their names, both forms of regression can fit curvature in your data. So, how do you choose? In this blog post, I show you how to choose between linear and nonlinear regression models.

This blog post covers the basics of choosing between linear and nonlinear regression models. However, I've written more in-depth posts about some of the relevant issues. Please follow the links as needed.

First off, let's cover a few basics. If the two types of regression models are not named based on their ability to fit curves, what is the difference between them?

In a nutshell, linear models must follow one very particular form:

Dependent variable = constant + parameter * IV + ... + parameter * IV

The form is linear in the parameters because all terms are either the constant or a parameter multiplied by an independent variable (IV). A linear regression equation simply sums the terms. While the model must be linear in the parameters, you can raise an independent variable by an exponent to fit a curve. For instance, you can include a squared or cubed term.

Nonlinear regression models are anything that doesn't follow this one form.

While both types of models can fit curvature, nonlinear regression is much more flexible in the shapes of the curves that it can fit. After all, the sky is the limit when it comes to the possible forms of nonlinear models. See the related post below for more details.

Related posts: The Difference Between Linear and Nonlinear Regression Models and When Should I Use Regression Analysis?

Guidelines for Choosing Between Linear and Nonlinear Regression

The general guideline is to use linear regression first to determine whether it can fit the particular type of curve in your data. If you can't obtain an adequate fit using linear regression, that's when you might need to choose nonlinear regression.

Linear regression is easier to use, simpler to interpret, and you obtain more statistics that help you assess the model. While linear regression can model curves, it is relatively restricted in the shapes of the curves that it can fit. Sometimes it can't fit the specific curve in your data.

Nonlinear regression can fit many more types of curves, but it can require more effort both to find the best fit and to interpret the role of the independent variables. Additionally, R-squared is not valid for nonlinear regression, and it is impossible to calculate p-values for the parameter estimates.

Linear and Nonlinear Regression Examples

Let's fit an example dataset using both linear and nonlinear regression. With these regression examples, I'll show you how to determine whether linear regression provides an unbiased fit and then how to fit a nonlinear regression model to the same data. Our goal is to develop an unbiased model. These data are freely available from the NIST and pertain to the relationship between density and electron mobility. Download the CSV data file to try it yourself: ElectronMobility.

Example of a linear regression model

First, I'll attempt to fit the curve using a linear model. Because there is only one independent variable, I can use a fitted line plot. This plot is handy because you can graph the estimated relationship along with the data. In this model, I use a cubed term to fit the curvature.

The fitted relationship in the graph follows the data fairly close and produces a high R-squared of 98.5%. Those sound great, but look more closely and you'll notice that various places along the regression line consistently under and over-predict the observed values. This model is biased, and it illustrates a point that I make in my post about R-squared. By themselves, high R-squared values don't necessarily indicate that you have a good model.

Because we have only one independent variable, we can plot the relationship on the fitted line plot. However, when you have more than one independent variable, you can't use a fitted line plot and you'll need to rely on residual plots to check the regression assumptions. For our data, the residual plots display the nonrandom patterns very clearly. You want to see random residuals.

Our linear regression model can't adequately fit the curve in the data. There's nothing more we can do with linear regression. Consequently, it's time to try nonlinear regression.

Related posts: Linear Regression and Seven Classical Assumptions of OLS Linear Regression

Example of a nonlinear regression model

Now, let's fit the same data but using nonlinear regression. As I mentioned earlier, nonlinear regression can be harder to perform. The fact that you can fit nonlinear models with virtually an infinite number of functional forms is both its strength and downside.

The main positive is that nonlinear regression provides the most flexible curve-fitting functionality. The downside is that it can take considerable effort to choose the nonlinear function that creates the best fit for the particular shape of the curve. Unlike linear regression, you also need to supply starting values for the nonlinear algorithm. Some datasets can require substantial effort to find acceptable starting values. For instance, some starting values can cause the algorithm to fail to converge on a solution or to converge on an incorrect solution. It's for these reasons that I always recommend fitting linear models first.

Our example dataset is one that the NIST uses to illustrate a hard-to-fit nonlinear relationship. So, it's no surprise that the linear model was insufficient. Because this blog post focuses on the basics of choosing between linear and nonlinear models, I'm not going to cover how the researchers chose the optimal functional form of the nonlinear model. Instead, I'll jump to the solution and not show all the work to get there, much like a cooking show! I want you to see how the following nonlinear model compares to the linear model based on the best solution.

For our data, a rational function provides the best nonlinear fit. A rational function is the ratio of two polynomial functions. For electron mobility, the model is:

Y = (B1 + B2*x + B3*x^2 + B4*x^3) / (1 + B5*x + B6*x^2 + B7*x^3)

The equation for the nonlinear regression analysis is too long for the fitted line plot:

Electron Mobility = (1288.14 + 1491.08 * Density Ln + 583.238 * Density Ln^2 + 75.4167 * Density Ln^3) / (1 + 0.966295 * Density Ln + 0.397973 * Density Ln^2 + 0.0497273 * Density Ln^3)

Comparing the Regression Models and Making a Choice

In the fitted line plot, the nonlinear relationship follows the data almost exactly. The residual plot displays the randomness that we want to see for an unbiased model. R-squared does not appear because it is invalid for nonlinear regression. However, we can compare the standard error of the regression (S) for the two models. You want S to be smaller because it indicates that the data points are closer to the fitted line. For the linear model, S is 72.5 while for the nonlinear model it is 13.7. The nonlinear model provides a better fit because it is both unbiased and produces smaller residuals.

Nonlinear regression is a powerful alternative to linear regression but there are a few drawbacks. Fortunately, it's not difficult to try linear regression first.

For more information about fitting curves with both linear and nonlinear regression, and comparing the results, read my post: Curve Fitting Using Linear and Nonlinear Regression. There are numerous other types of regression analysis that you can use. Read my post to learn how to choose the correct type of regression for your data.

If you're learning regression, check out my Regression Tutorial!

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How to Choose Between Linear and Nonlinear Regression

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As you fit regression models, you might need to make a choice between linear and nonlinear regression models. The field of statistics can be weird. Despite their names, both forms of regression can fit curvature in your data. So, how do you choose?

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Chi-square tests for count data: Finding the p-value

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Chi Square Calculator - Up To 5x5, With Steps

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A Chi-Square Test calculator for a contingency table that has up to five rows and five columns

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View the current State of Homelessness in America Report

Download archived State of Homelessness Reports

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The State of Homelessness in America 2013-2016 - National Alliance to End Homelessness

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The State of Homelessness in America is a yearly report that charts progress in ending homelessness in the United States. It uses the most recently available data to present national and state trends in homelessness, trends in populations at risk of homelessness and trends in the types and utilization of assistance available to people experiencing homelessness.

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Contingency Tables

Author(s)
David M. Lane
Prerequisites
Chi Square Distribution, One-Way Tables

Learning Objectives

1. State the null hypothesis tested concerning contingency tables

2. Compute expected cell frequencies

3. Compute Chi Square and df

This section shows how to use Chi Square to test the relationship between nominal variables for significance. For example, Table 1 shows the data from the Mediterranean Diet and Health case study.

Table 1. Frequencies for Diet and Health Study.

The question is whether there is a significant relationship between diet and outcome. The first step is to compute the expected frequency for each cell based on the assumption that there is no relationship. These expected frequencies are computed from the totals as follows. We begin by computing the expected frequency for the AHA Diet/Cancers combination. Note that 22/605 subjects developed cancer. The proportion who developed cancer is therefore 0.0364. If there were no relationship between diet and outcome, then we would expect 0.0364 of those on the AHA diet to develop cancer. Since 303 subjects were on the AHA diet, we would expect (0.0364)(303) = 11.02 cancers on the AHA diet. Similarly, we would expect (0.0364)(302) = 10.98 cancers on the Mediterranean diet. In general, the expected frequency for a cell in the ith row and the jth column is equal to

where Ei,j is the expected frequency for cell i,j, Ti is the total for the ith row, Tj is the total for the jth column, and T is the total number of observations. For the AHA Diet/Cancers cell, i = 1, j = 1, Ti = 303, Tj = 22, and T = 605. Table 2 shows the expected frequencies (in parenthesis) for each cell in the experiment.

Table 2. Observed and Expected Frequencies for Diet and Health Study.

Outcome

AHA

15
(11.02)

24
(19.03)

25
(16.53)

239
(256.42)

303

Mediterranean

7
(10.98)

14
(18.97)

8
(16.47)

273
(255.58)

302

The significance test is conducted by computing Chi Square as follows.

The degrees of freedom is equal to (r-1)(c-1), where r is the number of rows and c is the number of columns. For this example, the degrees of freedom is (2-1)(4-1) = 3. The Chi Square calculator can be used to determine that the probability value for a Chi Square of 16.55 with three degrees of freedom is equal to 0.0009. Therefore, the null hypothesis of no relationship between diet and outcome can be rejected.

A key assumption of this Chi Square test is that each subject contributes data to only one cell. Therefore, the sum of all cell frequencies in the table must be the same as the number of subjects in the experiment. Consider an experiment in which each of 16 subjects attempted two anagram problems. The data are shown in Table 3.

Table 3. Anagram Problem Data.

Anagram 1

Anagram 2

Solved

10

4

Did not Solve

6

12

It would not be valid to use the Chi Square test on these data since each subject contributed data to two cells: one cell based on their performance on Anagram 1 and one cell based on their performance on Anagram 2. The total of the cell frequencies in the table is 32, but the total number of subjects is only 16.

The formula for Chi Square yields a statistic that is only approximately a Chi Square distribution. In order for the approximation to be adequate, the total number of subjects should be at least 20. Some authors claim that the correction for continuity should be used whenever an expected cell frequency is below 5. Research in statistics has shown that this practice is not advisable. For example, see:

Bradley, D. R., Bradley, T. D., McGrath, S. G., & Cutcomb, S. D. (1979) Type I error rate of the chi square test of independence in r x c tables that have small expected frequencies. Psychological Bulletin, 86, 1200-1297.

The correction for continuity when applied to 2 x 2 contingency tables is called the Yates correction. The simulation 2 x 2 tables lets you explore the accuracy of the approximation and the value of this correction.

Please answer the questions:

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Contingency Tables Author(s) David M. Lane Prerequisites Chi Square Distribution, One-Way Tables Learning Objectives State the null hypothesis tested concerning contingency tables Compute expected cell frequencies Compute Chi Square and df This section shows how to use Chi Square to test the relationship between nominal variables for significance.

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Contents
Click to skip to a section Definitions

1. What is a Chi Square Test?

2. What is a Chi-Square Statistic?

3. Chi Square P-Values.

4. The Chi-Square Distribution & Chi Distribution

Calculations:

1. How to Calculate a Chi-Square Statistic:

2. How To Test a Chi Square Hypothesis (with video)

See also:
There are two types of chi-square tests. Both use the chi-square statistic and distribution for different purposes:

A chi-square goodness of fit test determines if a sample data matches a population. For more details on this type, see: Goodness of Fit Test.

A chi-square test for independence compares two variables in a contingency table to see if they are related. In a more general sense, it tests to see whether distributions of categorical variables differ from each another.

A very small chi square test statistic means that your observed data fits your expected data extremely well. In other words, there is a relationship.

A very large chi square test statistic means that the data does not fit very well. In other words, there isn't a relationship.

The formula for the chi-square statistic used in the chi square test is:

The subscript "c" are the degrees of freedom. "O" is your observed value and E is your expected value. It's very rare that you'll want to actually use this formula to find a critical chi-square value by hand. The summation symbol means that you'll have to perform a calculation for every single data item in your data set. As you can probably imagine, the calculations can get very, very, lengthy and tedious. Instead, you'll probably want to use technology:

A chi-square statistic is one way to show a relationship between two categorical variables. In statistics, there are two types of variables: numerical (countable) variables and non-numerical (categorical) variables. The chi-squared statistic is a single number that tells you how much difference exists between your observed counts and the counts you would expect if there were no relationship at all in the population.

There are a few variations on the chi-square statistic. Which one you use depends upon how you collected the data and which hypothesis is being tested. However, all of the variations use the same idea, which is that you are comparing your expected values with the values you actually collect. One of the most common forms can be used for contingency tables:

Where O is the observed value, E is the expected value and "i" is the "ith" position in the contingency table.

A low value for chi-square means there is a high correlation between your two sets of data. In theory, if your observed and expected values were equal ("no difference") then chi-square would be zero - an event that is unlikely to happen in real life. Deciding whether a chi-square test statistic is large enough to indicate a statistically significant difference isn't as easy it seems. It would be nice if we could say a chi-square test statistic >10 means a difference, but unfortunately that isn't the case.

You could take your calculated chi-square value and compare it to a critical value from a chi-square table. If the chi-square value is more than the critical value, then there is a significant difference.

You could also use a p-value. First state the null hypothesis and the alternate hypothesis. Then generate a chi-square curve for your results along with a p-value (See: Calculate a chi-square p-value Excel). Small p-values (under 5%) usually indicate that a difference is significant (or "small enough").

Tip: The Chi-square statistic can only be used on numbers. They can't be used for percentages, proportions, means or similar statistical value. For example, if you have 10 percent of 200 people, you would need to convert that to a number (20) before you can run a test statistic.
Back to Top

A chi square test will give you a p-value. The p-value will tell you if your test results are significant or not. In order to perform a chi square test and get the p-value, you need two pieces of information:

1. Degrees of freedom. That's just the number of categories minus 1.

2. The alpha level(α). This is chosen by you, or the researcher. The usual alpha level is 0.05 (5%), but you could also have other levels like 0.01 or 0.10.

In elementary statistics or AP statistics, both the degrees of freedom(df) and the alpha level are usually given to you in a question. You don't normally have to figure out what they are. You may have to figure out the df yourself, but it's pretty simple: count the categories and subtract 1.

Degrees of freedom are placed as a subscript after the chi-square (Χ ²) symbol. For example, the following chi square shows 6 df:
Χ ² ₆.
And this chi square shows 4 df:
Χ ² ₄.
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The chi-square distribution (also called the chi-squared distribution) is a special case of the gamma distribution; A chi square distribution with n degrees of freedom is equal to a gamma distribution with a = n / 2 and b = 0.5 (or β = 2).

Let's say you have a random sample taken from a normal distribution. The chi square distribution is the distribution of the sum of these random samples squared . The degrees of freedom (k) are equal to the number of samples being summed. For example, if you have taken 10 samples from the normal distribution, then df = 10. The degrees of freedom in a chi square distribution is also its . In this example, the mean of this particular distribution will be 10. Chi square distributions are always right skewed. However, the greater the degrees of freedom, the more the chi square distribution looks like a normal distribution.

Uses

The chi-squared distribution has many uses in statistics, including:

Chi Distribution

A similar distribution is the chi distribution. This distribution describes the square root of a variable distributed according to a chi-square distribution.; with df = n > 0 degrees of freedom has a probability density function of:

For values where x is positive.

The cdf for this function does not have a closed form, but it can be approximated with a series of integrals, using calculus.

A chi-square statistic is used for testing hypotheses. Watch this video, How to calculate a chi square, or read the steps below. Still having difficulty? Chegg.com will match you with a tutor, and your first 30 minutes is free!

The chi-square formula is a difficult formula to deal with. That's mostly because you're expected to add a large amount of numbers. The easiest way to solve the formula is by making a table.
Sample question: 256 visual artists were surveyed to find out their zodiac sign. The results were: Aries (29), Taurus (24), Gemini (22), Cancer (19), Leo (21), Virgo (18), Libra (19), Scorpio (20), Sagittarius (23), Capricorn (18), Aquarius (20), Pisces (23). Test the hypothesis that zodiac signs are evenly distributed across visual artists.

Step 1: Make a table with columns for "Categories," "Observed," "Expected," "Residual (Obs-Exp)", "(Obs-Exp) ²" and "Component (Obs-Exp) ² / Exp." Don't worry what these mean right now; We'll cover that in the following steps.

Step 2: Fill in your categories. Categories should be given to you in the question. There are 12 zodiac signs, so:

Step 6: Square your results from Step 5 and place the amounts in the (Obs-Exp) ² column.

Step 8: Add up (sum) all the values in the last column.

This is the chi-square statistic: 5.094.

Like the explanation? Check out the Practically Cheating Statistics Handbook, which has hundreds more step-by-step explanations, just like this one!

You'll find the chi square test in SPSS under "Crosstabs".

Sample problem: Run a chi square test in SPSS.

Note:in order to run a chi-square test in SPSS you should already have written a hypothesis statement. See: How to state the null hypothesis.

Watch the video or read the steps below:

Step 1: Click "Analyze," then click "Descriptive Statistics," then click "Crosstabs."

Step 3: Click "Chi Square" to place a check in the box and then click "Continue" to return to the Crosstabs window.

Step 4: Select the variables you want to run (in other words, choose two variables that you want to compare using the chi square test). Click one variable in the left window and then click the arrow at the top to move the variable into "Row(s)." Repeat to add a second variable to the "Column(s)" window.

Step 5: Click "cells" and then check "Rows" and "Columns". Click "Continue."

Step 6: Click "OK" to run the Chi Square Test. The Chi Square tests will be returned at the bottom of the output sheet in the "Chi Square Tests" box.

Step 7: Compare the p-value returned in the chi-square area (listed in the Asymp Sig column) to your chosen alpha level.

Check out our YouTube channel for more help with stats. Find dozens of videos on basic stats principles plus how to calculate stats using Microsoft Excel.

Watch the video, or read the steps below:

A chi-square test for independence shows how categorical variables are related. There are a few variations on the statistic; which one you use depends upon how you collected the data. It also depends on how your hypothesis is worded. All of the variations use the same idea; you are comparing the values you expect to get ( expected values) with the values you actually collect (observed values). One of the most common forms can be used in a contingency table.

The chi square hypothesis test is appropriate if you have:

For example, you could have a clinical trial with blood sugar outcomes of hypoglycemic, normoglycemic, or hyperglycemic.

Test a Chi Square Hypothesis: Steps

Sample question: Test the chi-square hypothesis with the following characteristics:

1. 11 Degrees of Freedom

2. Chi square test statistic of 5.094

Note: Degrees of freedom equals the number of categories minus 1.

Step 1: Take the chi-square statistic. Find the p-value in the chi-square table. If you are unfamiliar with chi-square tables, the chi square table link also includes a short video on how to read the table. The closest value for df=11 and 5.094 is between .900 and .950.
Note: The chi square table doesn't offer exact values for every single possibility. If you use a calculator, you can get an exact value. The exact p value is 0.9265.

Step 2: Use the p-value you found in Step 1. Decide whether to support or reject the null hypothesis. In general, small p-values (1% to 5%) would cause you to reject the null hypothesis. This very large p-value (92.65%) means that the null hypothesis should not be rejected.

Like the explanation? Check out the Practically Cheating Statistics Handbook, which has hundreds more step-by-step explanations, just like this one!

Reference

Johns Hopkins.
Kenney, J. F. and Keeping, E. S. Mathematics of Statistics, Pt. 2, 2nd ed. Princeton, NJ: Van Nostrand, 1951.

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Chi-Square Statistic: How to Calculate It / Distribution - Statistics How To

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Click to skip to a section Definitions What is a Chi Square Test? What is a Chi-Square Statistic? Chi Square P-Values. The Chi-Square Distribution & Chi Distribution Calculations: How to Calculate a Chi-Square Statistic: How To Test a Chi Square Hypothesis (with video) See also: There are two types of chi-square tests.

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Chi Squared Table

The chi squared table below is used in hypothesis testing. It helps you to decide whether to accept or reject the null hypothesis. The following chi squared table has the most common values for chi squared. You can find exact figures by using Excel ( how to calculate a chi square p value Excel), SPSS ( How to perform a chi square in SPSS) or other technology. However, in the vast majority of cases, the chi squared table will give you the value you need.

Watch the video showing how to read critical values on chi squared table. The video includes examples of problems with chi square random variables.

Can't see the video? Click here.

Chi Squared Table

Right tail areas for the Chi-squared Distribution

Sample problem using the chi squared table

Sample question: You work for a seed manufacturer. You want to find out if there is a link between hybrid plants and how many deviations (i.e. unwanted plants) that crop up. There are two corn types: blue and yellow. The probability that deviations would happen by chance is about 5%. Find the critical chi-square value using the chi squared table.

Step 1: Subtract 1 from the number of categories to get the degrees of freedom. Categories are blue corn and yellow corn, so df = 2-1 = 1.

Step 2: Look up your degrees of freedom and probability in the chi squared table. The probability is given to you in the question (5% or 0.05).

One degree of freedom and 5 percent probability is 3.84 in the chi squared table. This is your critical chi-square value.

Tip: A small value from the chi squared table means that there isn't much of a relationship between the two variables. A larger value indicates a greater relationship between your two variables.

References

Beyer, W. (2017). Handbook of Tables for Probability and Statistics 2nd Edition. CRC Press.

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The chi squared table below is used in hypothesis testing. It helps you to decide whether to accept or reject the null hypothesis. The following chi squared table has the most common values for chi squared.

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Centering Racial Equity throughout Data Integration

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The beauty of data visualization - David McCandless

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Hypothesis testing: step-by-step, p-value, t-test for difference of two means - Statistics Help

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Compare the means of two or more variables or groups in the data

The compare means t-test is used to compare the mean of a variable in one group to the mean of the same variable in one, or more, other groups. The null hypothesis for the difference between the groups in the population is set to zero. We test this hypothesis using sample data.

We can perform either a one-tailed test (i.e., less than or greater than) or a two-tailed test (see the 'Alternative hypothesis' dropdown). We use one-tailed tests to evaluate if the available data provide evidence that the difference in sample means between groups is less than (or greater than ) zero.

Example: Professor salaries

We have access to the nine-month academic salary for Assistant Professors, Associate Professors and Professors in a college in the U.S (2008-09). The data were collected as part of an on-going effort by the college's administration to monitor salary differences between male and female faculty members. The data has 397 observations and the following 6 variables.

rank = a factor with levels AsstProf, AssocProf, and Prof

discipline = a factor with levels A ("theoretical" departments) or B ("applied" departments)

yrs.since.phd = years since PhD

yrs.service = years of service

sex = a factor with levels Female and Male

salary = nine-month salary, in dollars

The data are part of the CAR package and are linked to the book: Fox J. and Weisberg, S. (2011) An R Companion to Applied Regression, Second Edition Sage.

Suppose we want to test if professors of lower rank earn lower salaries compared to those of higher rank. To test this hypothesis we first select professor rank and select salary as the numerical variable to compare across ranks. In the Choose combinations box select all available entries to conduct pair-wise comparisons across the three levels. Note that removing all entries will automatically select all combinations. We are interested in a one-sided hypothesis (i.e., less than).

The first two blocks of output show basic information about the test (e.g., selected variables and confidence levels) and summary statistics (e.g., mean, standard deviation, margin or error, etc. per group). The final block of output shows the following:

Null hyp. is the null hypothesis and Alt. hyp. the alternative hypothesis

diff is the difference between the sample means for two groups (e.g., 80775.99 - 93876.44 = -13100.45). If the null hypothesis is true we expect this difference to be small (i.e., close to zero)

p.value is the probability of finding a value as extreme or more extreme than diff if the null hypothesis is true

If we check Show additional statistics the following output is added:

Pairwise mean comparisons (t-test)
Data      : salary
Variables : rank, salary
Samples   : independent
Confidence: 0.95
Adjustment: None

      rank        mean   n n_missing         sd        se        me
  AsstProf  80,775.985  67         0  8,174.113   998.627 1,993.823
 AssocProf  93,876.438  64         0 13,831.700 1,728.962 3,455.056
      Prof 126,772.109 266         0 27,718.675 1,699.541 3,346.322

 Null hyp.              Alt. hyp.              diff      p.value se       t.value df      0%   95%
 AsstProf = AssocProf   AsstProf < AssocProf   -13100.45 < .001  1996.639  -6.561 101.286 -Inf  -9785.958 ***
 AsstProf = Prof        AsstProf < Prof        -45996.12 < .001  1971.217 -23.334 324.340 -Inf -42744.474 ***
 AssocProf = Prof       AssocProf < Prof       -32895.67 < .001  2424.407 -13.569 199.325 -Inf -28889.256 ***

Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

se is the standard error (i.e., the standard deviation of the sampling distribution of diff)

t.value is the t statistic associated with diff that we can compare to a t-distribution (i.e., diff / se)

df is the degrees of freedom associated with the statistical test. Note that the Welch approximation is used for the degrees of freedom

0% 95% show the 95% confidence interval around the difference in sample means. These numbers provide a range within which the true population difference is likely to fall

Testing

There are three approaches we can use to evaluate the null hypothesis. We will choose a significance level of 0.05. ¹ Of course, each approach will lead to the same conclusion.

Multiple comparison adjustment

The more comparisons we evaluate the more likely we are to find a "significant" result just by chance even if the null hypothesis is true. If we conduct 100 tests and set our significance level at 0.05 (or 5%) we can expect to find 5 p.values smaller than or equal to 0.05 even if the are no associations in the population.

Bonferroni adjustment ensures the p.values are scaled appropriately given the number of tests conducted. This XKCD cartoon expresses the need for this type of adjustments very clearly.

Stats speak

This is a comparison of means test of the null hypothesis that the true population difference in means is equal to 0. Using a significance level of 0.05, we reject the null hypothesis for each pair of ranks evaluated, and conclude that the true population difference in means is less than 0.

The p.value for the test of differences in salaries between assistant and associate professors is < .001. This is the probability of observing a sample difference in means that is as or more extreme than the sample difference in means from the data if the null hypothesis is true. In this case, it is the probability of observing a sample difference in means that is less than (or equal to) -13100.45 if the true population difference in means is 0.

The 95% confidence bound is -9785.958. If repeated samples were taken and the 95% confidence bound computed for each one, the true population mean would be below the lower bound in 95% of the samples

¹ The significance level, often denoted by \(\alpha\), is the highest probability you are willing to accept of rejecting the null hypothesis when it is actually true. A commonly used significance level is 0.05 (or 5%)

Report > Rmd

Add code to to (re)create the analysis by clicking the icon on the bottom left of your screen or by pressing ALT-enter on your keyboard.

If a plot was created it can be customized using ggplot2 commands (e.g., plot(result, plots = "scatter", custom = TRUE) + labs(title = "Compare means")). See Data > Visualize for details.

R-functions

For an overview of related R-functions used by Radiant to evaluate means see Basics > Means

The key function from the stats package used in the compare_means tool is t.test.

Video Tutorials

Copy-and-paste the full command below into the RStudio console (i.e., the bottom-left window) and press return to gain access to all materials used in the hypothesis testing module of the Radiant Tutorial Series:

usethis::use_course("https://www.dropbox.com/sh/0xvhyolgcvox685/AADSppNSIocrJS-BqZXhD1Kna?dl=1")
Compare Means Hypothesis Test

This video shows how to conduct a compare means hypothesis test

Topics List:

Calculate summary statistics by groups

Setup a hypothesis test for compare means in Radiant

Use the p.value and confidence interval to evaluate the hypothesis test

© Vincent Nijs (2019)

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Compare the means of two or more variables or groups in the data The compare means t-test is used to compare the mean of a variable in one group to the mean of the same variable in one, or more, other groups. The null hypothesis for the difference between the groups in the population is set to zero.

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Difference between Two Means (Independent Groups)

Author(s)
David M. Lane
Prerequisites
Sampling Distribution of Difference between Means, Confidence Intervals, Confidence Interval on the Difference between Means, Logic of Hypothesis Testing, Testing a Single Mean

Learning Objectives

1. State the assumptions for testing the difference between two means

2. Estimate the population variance assuming homogeneity of variance

3. Compute the standard error of the difference between means

4. Compute t and p for the difference between means

5. Format data for computer analysis

It is much more common for a researcher to be interested in the difference between means than in the specific values of the means themselves. This section covers how to test for differences between means from two separate groups of subjects. A later section describes how to test for differences between the means of two conditions in designs where only one group of subjects is used and each subject is tested in each condition.

We take as an example the data from the " Animal Research" case study. In this experiment, students rated (on a 7-point scale) whether they thought animal research is wrong. The sample sizes, means, and variances are shown separately for males and females in Table 1.

Table 1. Means and Variances in Animal Research study.

Group

n

Mean

Variance

Females

17

5.353

2.743

Males

17

3.882

2.985

As you can see, the females rated animal research as more wrong than did the males. This sample difference between the female mean of 5.35 and the male mean of 3.88 is 1.47. However, the gender difference in this particular sample is not very important. What is important is whether there is a difference in the population means.

In order to test whether there is a difference between population means, we are going to make three assumptions:

1. The two populations have the same variance. This assumption is called the assumption of homogeneity of variance.

2. The populations are normally distributed.

3. Each value is sampled independently from each other value. This assumption requires that each subject provide only one value. If a subject provides two scores, then the scores are not independent. The analysis of data with two scores per subject is shown in the section on thecorrelated t test later in this chapter.

The consequences of violating the first two assumptions are investigated in the simulation in the next section. For now, suffice it to say that small-to-moderate violations of assumptions 1 and 2 do not make much difference. It is important not to violate assumption 3.

We saw the following general formula for significance testing in the section on testing a single mean:

In this case, our statistic is the difference between sample means and our hypothesized value is 0. The hypothesized value is the null hypothesis that the difference between population means is 0.

We continue to use the data from the "Animal Research" case study and will compute a significance test on the difference between the mean score of the females and the mean score of the males. For this calculation, we will make the three assumptions specified above.

The first step is to compute the statistic, which is simply the difference between means.

M ₁ - M ₂ = 5.3529 - 3.8824 = 1.4705

Since the hypothesized value is 0, we do not need to subtract it from the statistic.

The next step is to compute the estimate of the standard error of the statistic. In this case, the statistic is the difference between means, so the estimated standard error of the statistic is ( ). Recall from the relevant section in the chapter on sampling distributions that the formula for the standard error of the difference between means is:

In order to estimate this quantity, we estimate σ ² and use that estimate in place of σ ². Since we are assuming the two population variances are the same, we estimate this variance by averaging our two sample variances. Thus, our estimate of variance is computed using the following formula:

where MSE is our estimate of σ ². In this example,

MSE = (2.743 + 2.985)/2 = 2.864.

Since n (the number of scores in each group) is 17,

= = = 0.5805.

The next step is to compute t by plugging these values into the formula:

t = 1.4705/.5805 = 2.533.

Finally, we compute the probability of getting a t as large or larger than 2.533 or as small or smaller than -2.533. To do this, we need to know the degrees of freedom. The degrees of freedom is the number of independent estimates of variance on which MSE is based. This is equal to (n ₁ - 1) + (n ₂ - 1), where n ₁ is the sample size of the first group and n ₂ is the sample size of the second group. For this example, n ₁ = n ₂ = 17. When n ₁ = n ₂, it is conventional to use "n" to refer to the sample size of each group. Therefore, the degrees of freedom is 16 + 16 = 32.

Once we have the degrees of freedom, we can use the t distribution calculator to find the probability. Figure 1 shows that the probability value for a two-tailed test is 0.0164. The two-tailed test is used when the null hypothesis can be rejected regardless of the direction of the effect. As shown in Figure 1, it is the probability of a t < -2.533 or a t > 2.533.

Figure 1. The two-tailed probability.

The results of a one-tailed test are shown in Figure 2. As you can see, the probability value of 0.0082 is half the value for the two-tailed test.

Figure 2. The one-tailed probability.

Online Calculator: t distribution
Formatting Data for Computer Analysis

Most computer programs that compute t tests require your data to be in a specific form. Consider the data in Table 2.

Table 2. Example Data.

Group 1

Group 2

3

2

4

6

5

8

Here there are two groups, each with three observations. To format these data for a computer program, you normally have to use two variables: the first specifies the group the subject is in and the second is the score itself. The reformatted version of the data in Table 2 is shown in Table 3.

Table 3. Reformatted Data.

G

Y

1

3

1

4

1

5

2

2

2

6

2

8

To use Analysis Lab to do the calculations, you would copy the data and then

1. Click the "Enter/Edit Data" button. (You may be warned that for security reasons you must use the keyboard shortcut for pasting data.)

2. Paste your data.

3. Click "Accept Data."

4. Set the Dependent Variable to Y.

5. Set the Grouping Variable to G.

6. Click the "t-test/confidence interval" button.

The t value is -0.718, the df = 4, and p = 0.512.

Computations for Unequal Sample Sizes (optional)

The calculations are somewhat more complicated when the sample sizes are not equal. One consideration is that MSE, the estimate of variance, counts the group with the larger sample size more than the group with the smaller sample size. Computationally, this is done by computing the sum of squares error (SSE) as follows:

where M ₁ is the mean for group 1 and M ₂ is the mean for group 2. Consider the following small example:

Table 4. Unequal n.

Group 1

Group 2

3

2

4

4

5

M ₁ = 4 and M ₂ = 3.

SSE = (3-4) ² + (4-4) ² + (5-4) ² + (2-3) ² + (4-3) ² = 4

Then, MSE is computed by: MSE = SSE/df

where the degrees of freedom (df) is computed as before:
df = (n ₁ - 1) + (n ₂ - 1) = (3 - 1) + (2 - 1) = 3.
MSE = SSE/df = 4/3 = 1.333.

The formula

=

is replaced by

=

where n h is the harmonic mean of the sample sizes and is computed as follows:

n h = = = 2.4.
and

= = 1.054.

Therefore,

t = (4-3)/1.054 = 0.949

and the two-tailed p = 0.413.

Data file
data=read.csv(file="animal.csv")
t.test(data$WRONG ~ data$GENDER,var.equal=TRUE)

Two Sample t-test

data: data$WRONG by data$GENDER
t = 2.5335, df = 32, p-value = 0.01639
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
0.2882231 2.6529534
sample estimates:
mean in group 1 mean in group 2
5.352941 3.882353

Please answer the questions:

feedback

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Difference between Two Means (Independent Groups) Author(s) David M.

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Data Analysis Resources: Compare Means, Correlation, Chi Squared

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Data Analysis Resources: Compare Means, Correlation, Chi Squared

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Worldmapper | rediscover the world as you’ve never seen it before

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Mapping our place in the world: The atlas for the 21st century. Worldmapper is a collection of world maps where countries are resized according to a broad range of global issues. Our cartograms are unique visualisations that show the world as you’ve never seen it before. Explore them all!

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The Truth in Numbers: Redefining Data Journalism Through Art

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Journalist Mona Chalabi uses hand-drawn sketches to break down complex data and challenge mainstream misconceptions.

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We begin this chapter with a discussion of statistical inference and statistical thinking. Next we explore what we feel every data scientist should do once they've gotten data in hand for any data-related project: exploratory data analysis (EDA).

From there, we move into looking at what we're defining as the data science process in a little more detail. We'll end with a thought experiment and a case study.

Big Data is a vague term, used loosely, if often, these days. But put simply, the catchall phrase means three things. First, it is a bundle of technologies. Second, it is a potential revolution in measurement. And third, it is a point of view, or philosophy, about how decisions will be-and perhaps should be-made in the future.

Steve Lohr, The New York Times

When you're developing your skill set as a data scientist, certain foundational pieces need to be in place first-statistics, linear algebra, some programming. Even once you have those pieces, part of the challenge is that you will be developing several skill sets in parallel simultaneously-data preparation and munging, modeling, coding, visualization, and communication-that are interdependent. As we progress through the book, these threads will be intertwined. That said, we need to start somewhere, and will begin by getting grounded in statistical inference.

We expect the readers of this ...

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We begin this chapter with a discussion of statistical inference and statistical thinking. Next we explore what we feel every data scientist should do once they've gotten data in hand for any data-related project: exploratory data analysis (EDA). From there, we move into looking at what we're defining as the data science process in a little more detail.

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Social Justice Standards: The Teaching Tolerance Anti-bias Framework is a set of 20 anchor standards and 80 grade-level outcomes organized into four domains-Identity, Diversity, Justice and Action-that reflect the desired impact of successful anti-bias and multicultural education on student personal and social development. The standards provide a common language and organizational structure. Teachers can use them to guide curriculum development, and administrators can use them to make schools more just, equitable and safe.

The four unique anti-bias perspectives and the standards that accompany them are labeled throughout the meaningful and complex texts found in our Perspectives text library. Teachers and students are able to further develop their understanding of these standards through examination of the examples highlighted in the texts.

The following professional development modules are aimed to help teachers understand the standards and identify how to use them to engage students in a range of anti-bias, multicultural and social justice issues.

Four Professional Development Modules

Social Justice Standards: Unpacking Identity
Understand the five Identity anchor standards, and relate how identity has many characteristics and affects relationships within the school building and the classroom.

Social Justice Standards: Unpacking Diversity
Develop respectful ways to discuss similarities and differences with others through the five Diversity anchor standards, and begin to think about how diversity affects relationships within the school building and the classroom.

Social Justice Standards: Understanding Justice
Understand the difference between personal stereotypes and systemic discrimination, and explore how privilege impacts discrimination and justice, and understand the five Justice anchor standards.

Social Justice Standards: Unpacking Action
Understand the five Action anchor standards and how they can be used to move students from prejudice reduction to collective action.

# data[].attributes.attachment_link.description
Social Justice Standards: The Teaching Tolerance Anti-bias Framework is a set of 20 anchor standards and 80 grade-level outcomes organized into four domains-Identity, Diversity, Justice and Action-that reflect the desired impact of successful anti-bias and multicultural education on student personal and social development.

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Amid the COVID-19 pandemic that is disproportionately killing Black people, more than 20 cities, at least 3 states, the American Public Health Association, and the American Medical Association have declared racism a public health emergency. Public health data glaringly highlight these disparities. The maternal mortality rate is three times higher for Black women than for white women, a reality that could worsen under COVID-19. And the average life expectancy for Black people is four years lower than for white people, in part because of medical racism and police targeting of Black communities.

In their statements, jurisdictions note that such declarations encourage doctors, public officials, and communities to center racial health disparities in their collaborative work. But a surprising amount of national data, especially at granular levels, are not disaggregated by race or ethnicity. To tackle racism as a public health emergency, the field needs to address limitations in health data, such as morbidity and disease prevalence, and the social determinants of health, such as employment, wealth, education, and housing. Advocates, researchers, policymakers, health professionals, and others should work together to fill information gaps todisrupt how structural oppression operates. The first step to doing so is disaggregating data by race and ethnicity to enable access to key data to inform public policy decisions that can transform lives. Here are three ways to advance this goal.

1. Require race and ethnicity data in ongoing data collection

COVID-19 has widened racial and ethnic disparities, underscoring how violently and quickly anti-Blackness and structural racism can shorten Black and brown lives. Black, Indigenous, and Latinx people are two to three times more likely to die from COVID-19 and are more likely to experience adverse economic effects during the pandemic than white people.

Without cross-sector advocacy at the beginning of the pandemic, we would have been in the dark about the extent of the pandemic's disparate impacts. In March and April, US researchers, doctors, and policymakers (PDF) suggested that an egregious lack of racial and ethnic data on COVID-19 cases and deaths was likely masking disproportionate case and death rates among communities of color. Thanks to their efforts, the Trump administration provided new guidance in June on COVID-19 case and death reporting, requiring all state and public health departments to report racial, ethnic, and other demographic data. These data, albeit incomplete, allowed organizations like Data for Black Lives and the Urban Institute's Racial Equity Analytics Lab to produce maps and visualizations that validated targeted efforts to improve COVID-19 outcomes in BIPOC communities.

The work is not done. Research shows that this guidance had less-than-perfect compliance in several states, suppressing reported racial and ethnic health disparities in COVID-19 cases and deaths. Expanding major racial identifiers to more closely match our population's diversity would help better serve populations' needs. For example, the racial category of "Asian American and Pacific Islander" contains more than 27 ethnicities.

2. Advocate for new research questions about racism

Thanks to the momentum built by declarations of racism as a public health crisis, Mariko Toyoji, an epidemiologist at Public Health Seattle and King County's Assessment, Policy Development, and Evaluation Unit, was a part of a recent successful campaign to include new questions about experiences with racial discrimination in the Washington State Behavioral Risk Factor Surveillance System module. Toyoji helped build a coalition of county health jurisdictions united by their interest in better understanding racial discrimination in their state. "We wanted to add the questions so we could have an idea of the prevalence of racial discrimination and link health disparities and outcomes, whether physical and mental, back to the experiences of discrimination among BIPOC," Toyoji said. Answers to these questions will help inform funding and resources in local health equity and social justice initiatives.

3. Advance ethical use of data

When collecting demographic data is not practical in the short term, researchers can adopt alternative estimation methods, such as data imputation, or the practice of replacing missing values with predicted ones. This method requires statistical estimation (PDF) and may not be accessible to all data practitioners. But it can help close reporting gaps. Nearly a quarter of confirmed COVID-19 cases nationally are missing race and ethnicity data, and a study by the Virginia Department of Health (PDF) estimated race and ethnicity for more than 85 percent of those missing values.

Urban's Racial Equity Analytics Lab is exposing patterns of structural racism against BIPOC communities by imputing race and ethnicity onto credit bureau data. This will help policymakers and practitioners identify, monitor, and build tools that address racial disparities in wealth and financial well-being and dismantle institutions that perpetuate oppressive systems. Before jumping into the statistical methods, however, the team is assessing the ethical implications of imputation and related methods, exploring the benefits and potential harms to BIPOC and developing tools to help researchers and data scientists avoid these harms. This work will help answer new questions about the wealth and financial health gaps, especially post pandemic, and highlight the institutions that perpetuate oppressive systems.

All approaches to data analysis should apply an equity lens

These three approaches to data collection and analysis alone will not disrupt racial and ethnic health disparities. Absent a commitment to equity, they could even perpetuate racist outcomes. Careless data collection could cause harmful violations of informed consent, privacy, and confidentiality; machine learning used in data imputation could replicate stereotypes through algorithm bias; and reporting racial disparities could cause racist data interpretations, as we have seen with the blaming of Black communities for their disproportionate number of COVID-19 cases and deaths.

To ensure disaggregated data inform responses that mitigate, rather than further entrench, racial and ethnic disparities, researchers, policymakers, and health professionals should apply an equity lens to their data practice. This involves centering the people who bear the greatest risks, primarily BIPOC communities, in research design, implementation and policy advocacy. With a multipronged strategy on data collection, data advocacy, and the latest data science guided by equity principles, we can make significant progress on the data available to combat structural racism.

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Three Steps to Improving Data to Help Combat the Public Health Emergency of Structural Racism

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Amid the COVID-19 pandemic that is disproportionately killing Black people, more than 20 cities, at least 3 states, the American Public Health Association, and the American Medical Association have declared racism a public health emergency. Public health data glaringly highlight these disparities.

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Data Analysis and Statistics Resources for Teaching - e.g. online textbooks and problems

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Data Analysis and Statistics Resources for Teaching - e.g. online textbooks and problems

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What is Data Storytelling? Plus 5 Great Examples

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Storytelling is the watchword in content marketing. To communicate with humans on an emotional level, you should tell stories using the same techniques that we all grew up with. We learn from an early age through stories and there is a practical method to storytelling that you can employ in your content marketing.

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Online Statistics Education: An Interactive Multimedia Course of Study

Developed by Rice University (Lead Developer), University of Houston Clear Lake, and Tufts University

OnlineStatBook Project Home
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Table of Contents

Rice Virtual Lab in Statistics

This is the original classic with all the simulations and case studies.
Version in PDF
Partial support for this work was provided by the National Science Foundation's Division of Undergraduate Education through grants DUE-9751307, DUE-0089435, and DUE-0919818. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

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Online Statistics Education: A Free Resource for Introductory Statistics

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Online Statistics Education: An Interactive Multimedia Course of Study Developed by Rice University (Lead Developer), University of Houston Clear Lake, and Tufts University OnlineStatBook Project Home This work is in the public domain. Therefore, it can be copied and reproduced without limitation. However, we would appreciate a citation where possible.

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1. Who are the stakeholders in the data? (and who is excluded)
2. Who created this data set/visualization? What was their purpose?
3. What do you notice about the data?
4. What other variables impact this data set?
5. How has this data impacted you? your mindset? your future actions?

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1. Who is benefiting from this data?
2. What is this data not showing or not telling?
3. Are there any variables that would change the story the author is trying to tell with this data?
4. How does this data effect your community?

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1. What motivations/biases may the publisher of this data have?

2. What patterns in this data set could you tell in order to prove your hypothesis?

3. Does the story this data is telling reflect your community? What is missing that the data cannot tell you?

4. What questions do you have for the group that put together this data visualization?

5. How could you use this data to make a difference in your community?

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1. Who is excluded from the data? 2. Who benefits vs. negatively impacted by the dissemination of data? 3. Who does the data serve and support? 4. Prompt: What does this data (x) tell you about communities it represents? 5. Prompt: Do you agree or disagree? Humans are data.

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1) How does the data impact decisions being made for students in the classroom?
2) How will students interpret the data? What reactions, responses, etc. can I anticipate from my scholars?
3) What does "equitable" and "fair" data look like?
4) How has collecting data changed with the use of new technology?

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1. What factors effect this data that are not included?
2. What is the intended story for this data?
3. Who is this data about and who is this data for?
4. Is the visualization proportional? (if comparing two data visualizations)

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1. Who made this data visualization, and who benefits from it?
2.  What variables would affect this data that aren't included? (What's missing?)
3. What story was the author trying to create, and does it make sense?
4. How independent are the factors considered in the data? How interconnected?
5. How many constraints were put on the data? (How accurate will the data be for very specific questions? Is this data aimed for generalizations or specific interpretations?)

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1. Who is the intended audience for this data?
2. What is excluded from the data?
3. What is the intention of creating this data visualization?
4. Which populations are excluded from the sample?
5. What other factors could provide a better understanding of the data as a whole

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The Opportunity Atlas is an initial release of social mobility data, the result of a collaboration between researchers at the Census Bureau, Harvard University, and Brown University. While the estimates in the Opportunity Atlas are not provisional, we are still testing aspects of the research product, including census.gov integration, planned annual data refreshes, and variable additions. Any opinions and conclusions expressed herein are those of the authors and do not necessarily reflect the views of the U.S. Census Bureau. All results have been reviewed to ensure that no confidential information is disclosed. The statistical summaries reported in this paper have been cleared by the Census Bureau's Disclosure Review Board release authorization number CBDRB-FY18-319.

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Map the childhood roots of social mobility

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Essential Questions to Ask of Data and Data Visualizations as Anti-Racist Educators

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Essential Questions to Ask of Data and Data Visualizations as Anti-Racist Educators

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Pose questions, reflection prompts, resources, etc... that you think are important for anti-racist educators to consider when gathering data, analyzing data, and visualizing data.

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In today's era of technological innovation, students need to gain knowledge and skills in order to solve difficult problems, gather and evaluate evidence, make sense of information they study, and be prepared for the careers and challenges of the 21 st century and beyond. Students can develop and strengthen these skills by studying science, technology, engineering, and mathematics (STEM) subjects, including computer science (CS). [1] STEM education is embedded in the U.S. Department of Education's (the Department) mission. Learn more about the focus on STEM education.

Mathematics has been called the "language" of STEM because students need a strong mathematics foundation to succeed in STEM fields and to make sense of STEM-related topics in their daily lives. [2] This story focuses on Algebra I within K-12 education because it is seen as a gatekeeper course: Students normally need to complete Algebra I in order to take higher level mathematics and science courses.[3] Taking the course earlier in their academic careers allows students sufficient time to take the more advanced courses that are often prerequisites for postsecondary STEM majors. However, we see in this data story that only 24 percent of all 8 th graders are enrolled in Algebra I. See what the research says about why this matters.

This data story explores both access to and enrollment in Algebra I in K-12 public schools using the 2015-16 Civil Rights Data Collection (CRDC). [4] The data story looks at the types of schools that offer Algebra I classes and further explores the students who actually enroll in these classes, particularly in 8 th grade. The Department is encouraging both access to and enrollment in STEM courses. Both aspects are important because, as we will see through the story, even where access to Algebra I classes are available students do not necessarily enroll in them.

When students take Algebra I matters, but many students do not have early access.

Despite the benefits of early access to Algebra I, we see that only 59 percent of schools that serve 8 th graders offer Algebra I. A typical math course sequence would start with Algebra I and continue with Geometry, Algebra II, Pre-Calculus, and Calculus. Students who do not have access to Algebra I until high school are unlikely to have the opportunity to take any Calculus courses before they graduate.

Only 59 percent of schools offer Algebra I in 8th grade. Access to Algebra I in high school grades is more common, but still not universal.

Since high-level mathematics and high-level science courses are frequently taken together, students who have the opportunity to take more advanced math courses are also more likely to take advanced science courses. When schools don't offer Algebra I to 8 th graders, it can reduce the amount of all STEM courses - not just math courses - they can take before graduation.

Access to Algebra I in 8th grade is uneven across the country.

Schools that offer Algebra I in 8 th grade provide their students with an opportunity to reach more advanced math and science courses in high school. However, there is a wide variation in students' access to Algebra I in 8 th grade based on where the school is located and the type of school that a student attends. Given the importance of early access to Algebra I, the remainder of this story focuses only on 8 th grade students and the schools that serve them.

About 30 percent of school districts across the nation did not offer Algebra I in 8 th grade.

For districts that serve 8 th grade students, this map allows us to dig deeper to see the percentage of schools offering Algebra I in 8 th grade in each district. Despite wide variations across the country, there are many states across the Northeast and along the Atlantic coast where a high percentage of students had access.

Overall, 80 percent of 8th grade students had access to Algebra I, however access varied widely by the type of school the student attended. Students enrolled in magnet or traditional public schools were more likely to have access to Algebra I in 8th grade.

While 59 percent of schools offered Algebra I in 8 th grade, these schools served 80 percent of 8 th grade students overall, meaning that four-fifths of all 8 th graders attended a school that offered Algebra I. The percentage of 8 th graders who had access to Algebra I was largest for students attending magnet schools, with nearly 90 percent of students having access to Algebra I in 8 th grade, and lowest for students attending a special education school with nearly 20 percent of students having access to Algebra I in 8 th grade. This wide variation shows that students' access to STEM education can be greatly affected by the type of school they attend.

Differences in early access to algebra by urbanicity were small. Even in rural schools, 75% of 8th graders could take Algebra I.

About 86 percent of students in suburban areas (where the largest percentage of students are enrolled) had access to Algebra I in 8 th grade, compared to about 75 percent of students in all other areas.

Next we will explore how access to Algebra I differs from enrollment in Algebra I in 8 th grade.

Enrollment lags behind access. Even when they can take Algebra I, many 8th graders do not.

While access to Algebra I is important, access alone is not enough. Students will not reap the benefits of access to more STEM courses if they are not actually enrolled in the courses.

There are many factors within a school that may affect how many, and which, students are enrolled in Algebra I in 8 th grade. For example, some students have access to Algebra I in 7 th grade, some students may not be ready to take Algebra I in 8 th grade, and others may not be interested in accelerated mathematics. See what the research says about why this matters.

Overall, only 24 percent of all 8th graders were enrolled in Algebra I. Looking further at the data suggests a complicated story of opportunity for different types of students.

Previously, we saw that 80 percent of 8 th grade students had access to Algebra I in 8 th grade; however, only 24 percent of 8 th grade students across the country were actually enrolled in the course. Furthermore, not all students were enrolled at the same rate. Students who are Asian were the most likely to be enrolled in Algebra I in 8 th grade with 34 percent of all 8 th graders who are Asian enrolled in the course. Comparatively, only 12 percent of 8 th graders who are black enrolled in Algebra I in 8 th grade. In addition, a slightly higher percentage of female students (25 percent) than male students (22 percent) were enrolled in Algebra I in 8 th grade. See what the research says about why this matters.

We also see geographic trends in where 8 th graders are enrolled in Algebra I across the country.

Across the country, there were 75 districts that had all 8 th graders enrolled in Algebra I.

Although over 8,000 districts offered access to Algebra I, in almost 90 percent of districts, less than half of all 8 th graders were enrolled in the course. We also see differences in enrollment by state, with Minnesota and Pennsylvania, for example, standing out as states with broad enrollment. Learn more about how States are focusing on Algebra I.

We know that a strong STEM education is a path to successful career and we know that the need for STEM knowledge and skills will continue to grow in the future. [5] Taking Algebra I before high school, such as in 8 th grade, can set students up for a strong foundation of STEM education and open the door for various college and career options.

The data explored in this story highlight both successes and areas for improvement, as school leaders, teachers and parents across the country, work to ensure equal access to a strong STEM education for all students.

Civil Rights Data Collection

The data explored in this story comes from the Civil Rights Data Collection (CRDC). Since 1968, the U.S. Department of Education (ED) has conducted the CRDC to collect data on key education and civil rights issues in our nation's public schools. The CRDC collects a variety of information including student enrollment and educational programs and services, most of which is disaggregated by race/ethnicity, sex, limited English proficiency, and disability. The CRDC informs the Office of Civil Rights' overall strategy for administering and enforcing the civil rights statutes for which it is responsible. The CRDC collects data only from public schools and does not include data from private schools. To directly download the CRDC data files, click here (34MB).

Data Exclusion Rules

Data included in this story may differ slightly from other published reports due to certain data decisions. For the purposes of these analyses, schools with incomplete or inconsistent data values were excluded as follows:

1. Less than 1% of schools were excluded from all analyses because they reported inconsistent data for Algebra I enrollment for the same grade level.

2. An additional 6% of schools serving 8 th grade students were excluded from all enrollment analyses due to missing 8 th grade enrollment data or the 8 th grade Algebra I enrollment count being larger than the 8 th grade overall enrollment.

3. Fewer than 10 schools were excluded from the enrollment by urbanicity (locale) analysis due to missing data.

4. Schools with an 8 th grade Algebra I enrollment count larger than the 8 th grade enrollment for either the male or female subgroup (1% of schools serving 8th-grade students) were excluded from the enrollment by gender analysis.

5. Schools with an 8 th grade Algebra I enrollment count larger than the 8 th grade enrollment for at least one race/ethnicity subgroup (16% of schools serving 8 th grade students) were excluded from the enrollment by race/ethnicity analysis.

References

[3] Noonan, R. (2017). STEM jobs: 2017 Update. Washington, DC: Office of the Chief Economist, Economics and Statistics Administration, U.S. Department of Commerce.

[5] Noonan, R. (2017). STEM jobs: 2017 Update. Washington, DC: Office of the Chief Economist, Economics and Statistics Administration, U.S. Department of Commerce.

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A Leak in the STEM Pipeline: Taking Algebra Early

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In today's era of technological innovation, students need to gain knowledge and skills in order to solve difficult problems, gather and evaluate evidence, make sense of information they study, and be prepared for the careers and challenges of the 21 st century and beyond.

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Eating Out in the Time of Corona - Social Explorer

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Even with a pandemic raging for much of 2020, the nation's capital (not known for its food scene until recently) was the capital of take-out and dine-in food, accordin...Social Explorer provides easy access to demographic information about the United States. We provide thousands of interactive data maps going back to 1790.

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Explore and run machine learning code with Kaggle Notebooks | Using data from Palestine Body Count

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Dollar Street

Dollar Street is a Gapminder project - free for anyone to use.
Today we feature 469 families in 67 countries, with 46070 photos and 8586 videos and counting!

Want to add a home? There are still lots of places in the world not represented on Dollar Street. You can find all the resources for documenting a home here.

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Dollar Street - photos as data to kill country stereotypes

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Imagine the world as a street. Everyone lives on Dollar Street. The poorest to the left and the richest on the right. Every else live somewhere in between. Where would you live? Visit Dollar Street and see homes from hundreds of homes from all over the World.

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Below are 6 examples of data visualization stories

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Data.gov is the United States government's open data website. It provides access to datasets published by agencies across the federal government. Data.gov is intended to provide access to government open data to the public, achieve agency missions, drive innovation, fuel economic activity, and uphold the ideals of an open and transparent government.

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NYC Open Data helps New Yorkers use and learn about City data

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This guide will help you locate data for New York City's boroughs and neighborhoods. The data may be organized in profiles (several pieces of data for one place) or comparative tables (one piece of data for many places). When looking for data, you will often have to balance geographic availability with currency and data format. Most of the sources in this guide are publicly available; the US Census Bureau and various City and State agencies are the main sources.

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Research Guides: New York City Data: Intro to NYC Data

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This guide will help you locate data for New York City's boroughs and neighborhoods. The data may be organized in profiles (several pieces of data for one place) or comparative tables (one piece of data for many places). When looking for data, you will often have to balance geographic availability with currency and data format.

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Three Steps to Improving Data to Help Combat the Public Health Emergency of Structural Racism

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Amid the COVID-19 pandemic that is disproportionately killing Black people, more than 20 cities, at least 3 states, the American Public Health Association, and the American Medical Association have declared racism a public health emergency. Public health data glaringly highlight these disparities. The maternal mortality rate is three times higher for Black women than for white women, a reality that could worsen under COVID-19. And the average life expectancy for Black people is four years lower than for white people, in part because of medical racism and police targeting of Black communities.

In their statements, jurisdictions note that such declarations encourage doctors, public officials, and communities to center racial health disparities in their collaborative work. But a surprising amount of national data, especially at granular levels, are not disaggregated by race or ethnicity. To tackle racism as a public health emergency, the field needs to address limitations in health data, such as morbidity and disease prevalence, and the social determinants of health, such as employment, wealth, education, and housing. Advocates, researchers, policymakers, health professionals, and others should work together to fill information gaps todisrupt how structural oppression operates. The first step to doing so is disaggregating data by race and ethnicity to enable access to key data to inform public policy decisions that can transform lives. Here are three ways to advance this goal.

1. Require race and ethnicity data in ongoing data collection

COVID-19 has widened racial and ethnic disparities, underscoring how violently and quickly anti-Blackness and structural racism can shorten Black and brown lives. Black, Indigenous, and Latinx people are two to three times more likely to die from COVID-19 and are more likely to experience adverse economic effects during the pandemic than white people.

Without cross-sector advocacy at the beginning of the pandemic, we would have been in the dark about the extent of the pandemic's disparate impacts. In March and April, US researchers, doctors, and policymakers (PDF) suggested that an egregious lack of racial and ethnic data on COVID-19 cases and deaths was likely masking disproportionate case and death rates among communities of color. Thanks to their efforts, the Trump administration provided new guidance in June on COVID-19 case and death reporting, requiring all state and public health departments to report racial, ethnic, and other demographic data. These data, albeit incomplete, allowed organizations like Data for Black Lives and the Urban Institute's Racial Equity Analytics Lab to produce maps and visualizations that validated targeted efforts to improve COVID-19 outcomes in BIPOC communities.

The work is not done. Research shows that this guidance had less-than-perfect compliance in several states, suppressing reported racial and ethnic health disparities in COVID-19 cases and deaths. Expanding major racial identifiers to more closely match our population's diversity would help better serve populations' needs. For example, the racial category of "Asian American and Pacific Islander" contains more than 27 ethnicities.

2. Advocate for new research questions about racism

Thanks to the momentum built by declarations of racism as a public health crisis, Mariko Toyoji, an epidemiologist at Public Health Seattle and King County's Assessment, Policy Development, and Evaluation Unit, was a part of a recent successful campaign to include new questions about experiences with racial discrimination in the Washington State Behavioral Risk Factor Surveillance System module. Toyoji helped build a coalition of county health jurisdictions united by their interest in better understanding racial discrimination in their state. "We wanted to add the questions so we could have an idea of the prevalence of racial discrimination and link health disparities and outcomes, whether physical and mental, back to the experiences of discrimination among BIPOC," Toyoji said. Answers to these questions will help inform funding and resources in local health equity and social justice initiatives.

3. Advance ethical use of data

When collecting demographic data is not practical in the short term, researchers can adopt alternative estimation methods, such as data imputation, or the practice of replacing missing values with predicted ones. This method requires statistical estimation (PDF) and may not be accessible to all data practitioners. But it can help close reporting gaps. Nearly a quarter of confirmed COVID-19 cases nationally are missing race and ethnicity data, and a study by the Virginia Department of Health (PDF) estimated race and ethnicity for more than 85 percent of those missing values.

Urban's Racial Equity Analytics Lab is exposing patterns of structural racism against BIPOC communities by imputing race and ethnicity onto credit bureau data. This will help policymakers and practitioners identify, monitor, and build tools that address racial disparities in wealth and financial well-being and dismantle institutions that perpetuate oppressive systems. Before jumping into the statistical methods, however, the team is assessing the ethical implications of imputation and related methods, exploring the benefits and potential harms to BIPOC and developing tools to help researchers and data scientists avoid these harms. This work will help answer new questions about the wealth and financial health gaps, especially post pandemic, and highlight the institutions that perpetuate oppressive systems.

All approaches to data analysis should apply an equity lens

These three approaches to data collection and analysis alone will not disrupt racial and ethnic health disparities. Absent a commitment to equity, they could even perpetuate racist outcomes. Careless data collection could cause harmful violations of informed consent, privacy, and confidentiality; machine learning used in data imputation could replicate stereotypes through algorithm bias; and reporting racial disparities could cause racist data interpretations, as we have seen with the blaming of Black communities for their disproportionate number of COVID-19 cases and deaths.

To ensure disaggregated data inform responses that mitigate, rather than further entrench, racial and ethnic disparities, researchers, policymakers, and health professionals should apply an equity lens to their data practice. This involves centering the people who bear the greatest risks, primarily BIPOC communities, in research design, implementation and policy advocacy. With a multipronged strategy on data collection, data advocacy, and the latest data science guided by equity principles, we can make significant progress on the data available to combat structural racism.

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Three Steps to Improving Data to Help Combat the Public Health Emergency of Structural Racism

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Amid the COVID-19 pandemic that is disproportionately killing Black people, more than 20 cities, at least 3 states, the American Public Health Association, and the American Medical Association have declared racism a public health emergency. Public health data glaringly highlight these disparities.

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Toolkit Activity 1:
Who Should Be at the Table? (page 34)

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The Opportunity Atlas is an initial release of social mobility data, the result of a collaboration between researchers at the Census Bureau, Harvard University, and Brown University. While the estimates in the Opportunity Atlas are not provisional, we are still testing aspects of the research product, including census.gov integration, planned annual data refreshes, and variable additions. Any opinions and conclusions expressed herein are those of the authors and do not necessarily reflect the views of the U.S. Census Bureau. All results have been reviewed to ensure that no confidential information is disclosed. The statistical summaries reported in this paper have been cleared by the Census Bureau's Disclosure Review Board release authorization number CBDRB-FY18-319.

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Map the childhood roots of social mobility

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Social Explorer uses cookies to allow us to better understand how the site is used and to improve your experience. By continuing to use this site, you consent to this policy. About cookies

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How can I use Justice Map?

1. Visualize race and income data for your neighborhood, county, state, or the entire US.

2. Share a custom map with your friends.

3. Journalists, bloggers, activists, and others can create maps for their online or print publications.

4. Map makers can add race and income layers to their maps.

5. Who Lives Nearby. Advanced mode lets you compare who lives within 1 vs 5 miles of a location (and more!).

Get Support: Email Aaron with your questions and suggestions.

What data layers do you have?
We have several race layers and income layers (three different representations of median household income). The race layers are available at the county, census tract, block group, and block level. The income layers are available at the county and census tract level. This provides greater detail when you zoom in.

What are open map tile layers?
We have 100 GB of map tiles that we are sharing. Similar to open software anyone can use them on their website. This saves map makers the time required to deal with large datasets and tile production.

What is the data source?
Our information comes from the Census Bureau - the 2010 Census and the latest American Community Survey (five year summary).

How did you create the map?
We imported the census data into a postgis database and generated the tiles with TileMill.

Who is behind this project?
The website was developed by Aaron Kreider - as a project for Energy Justice Network and Sunlight Foundation. Further development has been supported by the Energy Justice Network and Aaron Kreider (volunteer hours).

Justice Map - open map tile layers for race and income powered by Census Data.
I want you to use the layers on your own map!

Updates
Sept 19, 2021. If you are using our API, please contact us. Otherwise, as I haven't heard from anyone who is - the API is going to be revised and the old version will break (We might replace justicemap-api.org with another domain). Also if you have been using our tile layers with javascript - this might stop working (though you can easily switch to the newer 2020 layers, and we'll continue to support the 2010 layers just with a different url that you'll need to update).

Sept 18, 2021. Early release of Census 2020 race data. Income needs to be updated as does the API.

Jan. 14-16, 2020. We updated the income data to use the 2014-2018 American Community Survey.

Jan. 13, 2019. We updated the income data from the 2012-2016 American Community Survey to the 2013-2017 data. This applies to tile layers, clicking on the map, and the API. Puerto Rico is included in the update! An even bigger change is that we updated the income categories (for the first time), and started controlling for inflation in the Income Change layer.

Aug 30, 2018. Redesigned the user interface to support mobile phones.

Jan. 9, 2018. We updated the income data from the 2011-2015 American Community Survey to the 2012-2016 data. This applies to tile layers, clicking on the map, and the API. This time Puerto Rico is included in the update!

Dec. 30, 2016. Try the Spatial Justice Test. It's a tool to identify environmental injustice (and more). You can test how race and income varies at different distances from a set of points. Use our power plant data or upload your own!

Dec. 20, 2016. We added a visualization that estimates Income at the Block Level. It can be used as an index that combines race and income to give a micro-level view of environmental injustice (or other forms of spatial injustice).

Dec. 13, 2016. We updated the income data from the 2010-2014 American Community Survey to the 2011-2015 data. This applies to tile layers, clicking on the map, and the API. Puerto Rico is still using the old data (2007-2011).

More Information
API - Include the map or data layers on your website

Categorization Methods

Data and Downloads

Terms of Use

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Justice Map - Visualize race and income data for your community.

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High resolution map of race and income in the US. Also includes a set of open map layers, an API, tools to build your own maps, and more.

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Data Visualizations and Data American Panorama Visualizations

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Data Visualizations and Data American Panorama Visualizations

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American Panorama is created by the Digital Scholarship Lab at the University of Richmond. Robert K. Nelson and Edward L. Ayers serve as editors. Justin Madron manages the project's spatial data. Nathaniel Ayers leads the design work. Scott Nesbit served as associate editor until 2017.

The Andrew W. Mellon Foundation and the University of Richmond have generously provided funding for American Panorama. Stamen Design developed the software for this project.

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American Panorama is created by the Digital Scholarship Lab at the University of Richmond. Robert K. Nelson and Edward L. Ayers serve as editors. Justin Madron manages the project's spatial data. Nathaniel Ayers leads the design work. Scott Nesbit served as associate editor until 2017. The Andrew W.

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Click on a city to zoom in to it's map.

Zoom in and tap on a city to see it's map.

How do we calculate place inequality?

1. Data

Our anonymous data contains billions of visits to locations in the Boston Metro Area from October 2016 to March 2017. We analyze mobility patterns of about 150,000 anonymous users, provided through Cuebiq's Data for Good initiative, in the whole Boston Metro area (around 3% of the population). MIT Media Lab coupled Cuebiq's anonymous location data with census information to determine user income groups and identify user visitation patterns to places. We use the census-based core-based statistical areas s to define metro areas. This definition encompasses the cities, suburbs, and commuting zones that are economically tied to a central city of interest. In the Boston case, it contains large areas in New Hampshire and down the Massachusetts coast. Finally, we have used the public Foursquare API to get the list of the 30,000 places that users visit.

2. Estimating home and income

Using the same anonymous data, we determine users' home location at the level of Census Block Groups, a statistical subarea of census tracts that each contain between 600 and 3,000 people. To determine a user's home census block group, we compute the most common block group that a user spends time in between 8:00 pm and 4:00 am. We then assign each user an income using the median household income of their "home" census block group from the 5-year American Community Survey for 2012-2016. Users were then clustered in 4 different quantile groups of annual income: low ($10,000 - $67,000), medium ($67,000 - $90,000), upper medium ($90,000 - $114,000), and high (over $114,000). Each income group contains exactly 1/4 of the users in our dataset.

3. Detecting where people visit

Using location data as described above, we determine when users stop for more than 5 minutes in a particular place. If a user stops for more than 5 minutes within 20 meters from a place, we treat them as having visited that place.

We consider a user as having visited a place if they stop within 20 meters of its location for more than 5 minutes.

We consider a user as having visited a place if they stop within 20 meters of its location for more than 5 minutes

4. Measuring inequality in a place

To measure inequality in a place, we first compute the total time each user spends in a venue, and then sort all users by their income group. Then, we compute the total time each income group spends in each place in our dataset. The end result is a chart for each place that shows how likely you are to see people from each income quartile if you visit.

To measure the inequality of a place, we use a city-wide normalized measure. Because income groups correspond to exactly 25% of the users in the area, a totally equal place would be visited by each income group 25% of the time. This corresponds to a flat chart, like the one on the left. We consider any deviation from that flat profile to contribute to inequality. For example, a totally segregated place would show a chart more like the one on the right, with 100% of the users coming from a single income group. Mathematically, we calculate the absolute deviation of a place's income distribution from that flat ideal:

and normalize it to be between 0% (flat distribution) to 100% (only one group is present).

5. Limitations

There are several limitations with our approach that could mean our results are incomplete. First, we select users based on having consistent home locations during the 6 months of our dataset. This excludes smartphone users who are homeless, in transition, or those users who work non-normative work shifts (between 8pm and 4am). Second, the venues we consider are limited to those available via the Foursquare API. Third, our approach to determing whether a user visits a place does not account for GPS noise, and so some of our records of users visiting places could be wrong. See the FAQ for more about data representativeness.

Additionally, it is important to note that the Atlas records income inequality, not class inequality. The lowest income quantile we use encompasses a huge range of both income and socioeconomic difference, covering neighborhoods with median household incomes between $10,000 and $67,000 per year. The qualitative class differences (lifestyle, opportunity, etc) between a household with $20,000 of annual income and $60,000 of annual income are extremely large in the Boston area. Income is also known to be an imperfect proxy for class; many highly wealthy households have little annual income.

Places with economically diverse visitors can be only a few feet away from places where only the wealthiest spend their time. The way we experience economic inequality in cities is impacted by where we go, not just by where we live.

When you want to grab a cup of coffee, where do you go? Does it depend on whether you're at home or at work? How many other coffee shops do you pass on the way to your favorite spot?

We all have our own preferences and needs -- like choosing a latte or a simple cup of black coffee. When we head out into our cities and towns, we use our preferences to decide where to spend our time. Through these choices, we build our habits and routines.

The fact that our routines decide where we spend our time also means that they decide who we spend our time with. Although we may get our daily coffee on the same city block, the specific places we're in -- and the people around us -- can be radically different.

In Boston, like in other cities, coffee shops can occupy places as close as a few feet apart. The two coffee in the figure above are on the same city block. Although they are within 2 minute walk of one another, the incomes of the people who visit them are very different.

Coffeehouse 2 is visited almost exclusively by people we've identified as being in Boston's lowest income bracket, while Coffeehouse 1 has visitors more representative of all incomes. The choice of which coffee shop to visit can contribute significantly to income segregation.

It's important to note that these choices that people make are usually constrained by things like affordability, location, and social groups. But a place where people of all different incomes come together can be on the same block as a place where only the poorest -- or the wealthiest -- spend their time. This means that socio-economic inequality in cities is encoded in part by these choices, not just where people live.

Papers

The segregated places of United States cities

E. Moro, D. Calacci, X. Dong, and A. Pentland, forthcoming (2019).

Segregated interactions in urban and online spaces

X. Dong, A. J. Morales, E. Jahani, E. Moro, B. Lepri, B. Bozkaya, C. Sarraute, Y. Bar-Yam and A. Pentland, arXiv 2019

Posters

High resolution visuals of our Atlas for different cities (pdf format)

Talks

Places

How are the places selected?

The places are extracted using the Foursquare API. We have only considered places that are verified (claimed by the owners) or that have at least 5 check-ins within six months.To preserve the anonymity of users, we only consider places where we detected at least 20 different users within the six-month period.

There is a place I know that isn't included, why?

This could happen for many reasons: it might not be included in the public Foursquare API, or we might have discarded it for privacy or statistical reasons. If you know the actual location of the place, we can possibly include it! Please send us an email specifying the name of the place, its location, and any other details for us to add it to the atlas.

Is your data representative?

In general, yes. To test if our sample of users is representative, we've run several analyses comparing the incomes of people in our dataset to census reports, and the average income of our user sample is only 8.6% higher than the census data. To test if our method of detecting when a person spends time in a place is accurate, we use our data to estimate attendance at professional sports games (NFL, NBA, and the NHL). Estimates of attendance computed using our data are extremely close to official attendance counts, which suggests that the data we use here can describe visits to a specific place quite well (generally within a few thousand of the official attendance counts).

Inequality

What do you mean when you say a place is "65% unequal"?

A place is unequal if it is not visited by the four different income quartiles we've identified in the city. A high value of inequality in a place means that most of its visitors come from one or two of these income groups. You can find more information about how the inequality score is computed in the Methods section.

I visit place X a lot, and know that X is more/less unequal than you reported, why?

We determine that a user has spent time in a place when our data shows that they've spent more than five minutes within 20 meters of it. We've tried our best to be careful in assigning user locations to places, but our method isn't perfect. When places are very close to each other (less than 20 meters), or where places are on different floors of the same building, our data is a little more noisy. Please let us know about the specific place in question by sending us an email, and we will investigate it.

Privacy

Where did you obtain the data about visits at locations? Is this legal?

The anonymous location data come from collaboration with Cuebiq through their Data for Good program. Cuebiq is a location intelligence company that collects data through its proprietary software-development-kit technology integrated in more than 200 mobile apps, reaching a diverse user base of millions of anonymous users who have opted in to share location data. Cuebiq is fully compliant with the GDPR in the EU; its privacy-compliant methodology is at the forefront of industry standards and has earned the company membership status with the Network Advertising Initiative (NAI), the leading industry association dedicated to responsible data collection and its use for digital advertising.

Are you singling out individuals?

No. We are not interested in individual behavior and are not using individual behavior in our analysis. We anonymize our data before analysis by aggregating by neighborhoods, and we are only interested in aggregated trends about the economic diversity of locations visited. Our final data consists of aggregations (counts) at the level of places, not individuals. To ensure privacy and help prevent de-anonymization and re-identification, we only consider places in which we detected at least 20 different users within the six-month period.

The Atlas of Inequality is a project from the Human Dynamics group at the MIT Media Lab and the Department of Mathematics at Universidad Carlos III de Madrid.

It is part of a broader initiative to understand human behavior in our cities and how large-scale problems like transportation, housing, segregation or inequality depend in part on the emergent patterns of people's individual opportunities and choices.

Comments, questions? Contact us by email

Researchers:

Xiaowen Dong
MIT + Oxford

Acknowledgments:

With thanks to:

Cuebiq is a location intelligence and consumer insights company that maps and measures the offline consumer journey. Cuebiq's platform analyzes anonymous location patterns to allow researchers to glean actionable insights on human mobility. Through its Data for Good Program, Cuebiq provides access to location-based intelligence for academic research and humanitarian initiatives related to urban development, economic mobility, transportation, disaster response, and epidemiology, among other use cases.

From smartphones to connected cars, location data is changing the way we live and the way business happens. CARTO is the platform that turns location data into more efficient delivery routes, better behavioural marketing, strategic store placements, and much more. Business analysts, developers and data scientists use CARTO's software and data to understand where and why things happen, optimize business processes, and predict future outcomes.

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Click on a city to zoom in to it's map. Zoom in and tap on a city to see it's map. How do we calculate place inequality? Our anonymous data contains billions of visits to locations in the Boston Metro Area from October 2016 to March 2017.

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Explore and run machine learning code with Kaggle Notebooks | Using data from 500 Greatest Songs of All Time

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Discover what actually works in AI. Join millions of builders, researchers, and labs evaluating agents, models, and frontier technology through crowdsourced benchmarks, competitions, and hackathons.

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R: The R Project for Statistical Computing

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In this interactive K-12 dashboard example, the Jackson Kenneth School District is tracking several educational KPIs in a single screen. Each school's data lives side by side, giving a comprehensive view of the performance of each institution and student body. Using interactive intelligence, the end user can see education assessment scores, enrollment trends, and student to faculty ratio by clicking on the school of interest. The donut chart on the right of the dashboard details data regarding students in accelerated programs, and features several layers of drilldowns by subject of study, class level, and individual student performance.

Scroll down to interact with this school district dashboard example.

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K-12 Education Dashboard Example | iDashboards Software

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In this interactive K-12 dashboard example, the Jackson Kenneth School District is tracking several educational KPIs in a single screen. Each school's data lives side by side, giving a comprehensive view of the performance of each institution and student body.

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Data for Black Lives is a movement of activists, organizers, and mathematicians committed to the mission of using data science to create concrete and measurable change in the lives of Black people. Our blog aims to provide insights into our work by highlighting our research, organizing, and policy updates across all branches of our organization.
COVID-19 Vaccination Data

COVID-19 highlights the already existing racial disparities in our healthcare system. With the distribution of COVID-19 vaccines now underway, it's imperative to turn our focus to the delivery of care. Additionally, we must identify how Black people are still negatively impacted by poor U.S. health infrastructure and racist narratives. We know that public health data must continually be interpreted in the proper historical context, considering the various elements of structural racism that shape the American public health ecosystem.

The availability of vaccines has introduced discussions of pandemic recovery and a return to "normalcy", however, we must ask: Are Black people, who remain overrepresented among COVID-19 deaths, receiving sufficient access to the vaccines?

Below is a chart containing data from a number of states and Washington, D.C. to help visualize the gap between how many Black people are dying from COVID-19 and how many are receiving the vaccine. U.S. states and the percentages of Black people are respectively on the y- and x-axes. For each location, there are 3 data points:

1. Percent of State's Black Population (Pct Population Black/AA): How many residents of the state identify as Black/African-American. Displayed as the blue dot.

2. Percent of State's Vaccinated Population that are Black (Pct Vaccinations Black/AA): How many residents of the state have received at least one vaccine dose and identify as Black/African-American. Displayed as the gray dot.

3. Percent of State's COVID-19 Deaths that are Black (Pct COVID Deaths Black/AA): How many residents of the state who died from COVID-19 identified as Black/African-American. Displayed as the orange dot.

Hover over points for each state to explore the data or go to the legend at the bottom of the chart titled "Measure Names" and click the orange, blue, or gray squares to explore each series individually. As an example, notice that for Georgia the distance between the gray and orange dots is large. This means a lot of Black people in the state are dying from the virus but proportionally, not nearly as many people are getting the vaccine.
Data collected through February 22, 2021. Some states differ in their decision to classify Unknown Race-Black and Hispanic-Black into Black/AA categories.
States have expressed the importance of racial equity in their COVID-19 vaccine distribution plans, but many are failing to reach their Black residents who are still disproportionately affected by the virus. In Maryland, for example, Black residents comprise roughly 30% of Marylands's population while accounting for 35% of Maryland's COVID-19 related deaths and only 15% of Maryland's COVID-19 vaccinated population. This large disparity illustrates how Maryland's Black residents are overrepresented in COVID-19 related deaths and yet severely underrepresented in vaccinations. A common occurrence across numerous Black communities in the U.S., these states must immediately acknowledge this gap in care and remediate the problem.

When encountering a state that does not yet breakdown their vaccination data by race and/or ethnicity, we explored vaccination rates across the state's predominantly Black counties and cities. Although these locations are largely Black, the number of vaccinations administered in those locations does not tell us how much of the respective Black population have received a vaccine.

Michigan, for example, as of February 22 has reported nearly 2 million COVID-19 vaccine doses administered. Michigan does not provide COVID-19 vaccine distribution data by race or ethnicity. They do, however, provide a vaccine distribution map by county. Black residents account for 14% of Michigan's population and approximately 11% of Michigan's COVID-19 cases and 21% of Michigan's COVID-19 related deaths. Exploring Michigan's vaccination data, they define vaccination coverage as "the percentage of people receiving one or more doses" and they rank the coverage of the state's counties on a scale from Low-Moderate-High.

When exploring areas in Michigan with the largest Black populations, Detroit was assigned a vaccination coverage level of "Low" while the wider Wayne County along with Genesee and Saginaw County were assigned levels of "Low to Moderate." Further investigation is required to understand why the vaccination rate is so low given the relatively high density of Black people and the state's overall overrepresentation of Black fatalities as a result of COVID-19. We need more data into who exactly is receiving the vaccine in these counties and if any measures are being taken by Michigan to prioritize the distribution of vaccines to Black people and reduce COVID-19 disparities.

Adding more historical context

Our research compliments existing work that highlights consistent health disparities and systemic racism within our healthcare system related to COVID-19. Black people are underrepresented in vaccinations, and with Black, Native American, Asian, and Hispanic COVID-19 patients still dying at disproportionately alarming rates, this is unacceptable. While some states have highlighted the need for equity in vaccine distribution, not all states are releasing vaccine distribution data disaggregated by race/ethnicity.

There are a variety of reasons why: 1) Black people are not properly prioritized in state vaccine distribution plans and 2) Black people are hesitant to receive the vaccine. It is important to acknowledge the historical context of anti-Black racism within the U.S. public health system in this discussion. The truth is, Black people have every right to legitimately fear and be skeptical of the U.S. healthcare system as it has continually failed to provide Black patients with the assurance that their health and safety is a concern, much less a priority. Additionally, the narrative circulating online that Black people are dubious of vaccines due to conspiracy theories is misleading and oversimplifies valid distrust. Historically, medical research and vaccine trials are quite familiar with racism (see the story of Henrietta Lacks and the unethical Tuskegee Syphilis Study) and it does not help that distrust in the healthcare system is accompanied by barriers to access to health information and the fact that Black patients may be less likely to have access to health insurance and health care services. These barriers are felt at an institutional level as much as they are at an individual one. As we also may unfortunately recall our own personal experiences with condescending and racist health professionals who jeopardize the lives of our loved ones due to substandard care.

We have observed that more work and infrastructure is required to keep Black people safe through the remainder of the pandemic and beyond. We'll keep our network updated as more data is made available. Remember to contact your state health department for information on its COVID-19 vaccination plan.
This research is an ongoing component of our earlier COVID-19 work. In June 2020, Data for Black Lives established a team of volunteer data scientists to track state data on rates of COVID-19 cases and deaths in Black populations. The methods and results of our work can be referred to here: At Data for Black Lives, we will continue to monitor the vaccine distribution data and how Black communities are continuing to be impacted by this global pandemic. https://d4bl.org/covid19-data.html.
Want to stay connected to our movement?

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Black Health in America: Exploring Racial Disparities in COVID-19 Vaccination Data

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Data for Black Lives is a movement of activists, organizers, and mathematicians committed to the mission of using data science to create concrete and measurable change in the lives of Black people. Our blog aims to provide insights into our work by highlighting our research, organizing, and policy updates across all branches of our organization.

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DataWrapper - create maps, scatterplots, charts

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DataWrapper - create maps, scatterplots, charts

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Mapping

We strive to map Indigenous territories, treaties, and languages across the world in a way that goes beyond colonial ways of thinking in order to better represent how Indigenous people want to see themselves.

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Native Land is a resource to learn more about Indigenous territories, languages, lands, and ways of life. We welcome you to our site.

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Baltimore | Open Data | Open Baltimore | City of Baltimore's Open Data Catalog

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Fighting Systemic Racism in K-12 Education: Helping Allies Move From the Keyboard to the School Board

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The surge of new allies in the Black Lives Matter movement for racial justice presents a welcome opportunity to implement systemic changes in the U.S. K-12 education system-and allies should start by following the lead of communities that are Black, Indigenous, and people of color.

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Last week, IBM, Amazon, and Microsoft announced they would pause or end sales of their face recognition technology to police in the United States. The announcement caught many by surprise. For years, racial justice and civil rights advocates had been warning that this technology in law enforcement hands would be the end of privacy as we know it. It would supercharge police abuses, and it would be used to harm and target Black and Brown communities in particular.

But the companies ignored these warnings and refused to get out of this surveillance business. It wasn't until there was a national reckoning over anti-Black police violence and systemic racism, and these companies getting caught in activists' crosshairs for their role in perpetuating racism, that the tech giants conceded - even if only a little.

But why did IBM, Amazon, and Microsoft's sale of face recognition to cops make them a target of the Black Lives Matter movement? How is face surveillance an anti-Black technology?

Face surveillance is the most dangerous of the many new technologies available to law enforcement. And while face surveillance is a danger to all people, no matter the color of their skin, the technology is a particularly serious threat to Black people in at least three fundamental ways.

First, the technology itself can be racially biased. Groundbreaking research conducted by Black scholars Joy Buolamwini, Deb Raji, and Timnit Gebru snapped our collective attention to the fact that yes, algorithms can be racist. Buolamwini and Gebru's 2018 research concluded that some facial analysis algorithms misclassified Black women nearly 35 percent of the time, while nearly always getting it right for white men. A subsequent study by Buolamwini and Raji at the Massachusetts Institute of Technology confirmed these problems persisted with Amazon's software.

Late last year, the federal government released its own damning report on bias issues in face recognition algorithms, finding that the systems generally work best on middle-aged white men's faces, and not so well for people of color, women, children, or the elderly. The federal government study concluded the rates of error tended to be highest for Black women, just as Buolamwini, Gebru, and Raji found. These error-prone, racially biased algorithms can have devastating impacts for people of color. For example, many police departments use face recognition technology to identify suspects and make arrests. One false match can lead to a wrongful arrest, a lengthy detention, and even deadly police violence.

Second, police in many jurisdictions in the U.S. use mugshot databases to identify people with face recognition algorithms. But using mugshot databases for face recognition recycles racial bias from the past, supercharging that bias with 21st century surveillance technology.

Across the U.S., Black people face arrest for a variety of crimes at far higher rates than white people. Take cannabis arrests, for just one example. Cannabis use rates are about the same for white and Black people, but Black people are nearly four times more likely to be arrested for marijuana possession than white people. Each time someone is arrested, police take a mugshot and store that image in a database alongside the person's name and other personal information. Since Black people are more likely to be arrested than white people for minor crimes like cannabis possession, their faces and personal data are more likely to be in mugshot databases. Therefore, the use of face recognition technology tied into mugshot databases exacerbates racism in a criminal legal system that already disproportionately polices and criminalizes Black people.

Third, even if the algorithms are equally accurate across race, and even if the government uses driver's license databases instead of mugshot systems, government use of face surveillance technology will still be racist. That's because the entire system is racist. As journalist Radley Balko has carefully documented, Black people face overwhelming disparities at every single stage of the criminal punishment system, from street-level surveillance and profiling all the way through to sentencing and conditions of confinement.

Surveillance of Black people in the U.S. has a pernicious and largely unaddressed history, beginning during the antebellum era. Take 18th century lantern laws, for example. As scholar Simone Browne observed: "Lantern laws were 18th century laws in New York City that demanded that Black, mixed-race and Indigenous enslaved people carry candle lanterns with them if they walked about the city after sunset, and not in the company of a white person. The law prescribed various punishments for those that didn't carry this supervisory device."

Today, police surveillance cameras disproportionately installed in Black and Brown neighborhoods keep a constant watch.

The white supremacist, anti-Black history of surveillance and tracking in the United States persists into the present. It merely manifests differently, justified by the government using different excuses. Today, those excuses generally fall into two categories: spying that targets political speech, too often conflated with "terrorism," and spying that targets people suspected of drug or gang involvement.

In recent years, we learned of an FBI surveillance program targeting so-called "Black Identity Extremists," which appears to be the bureau's way of justifying domestic terrorism investigations of Black Lives Matter activists. Local police are involved in anti-Black political surveillance, too. In Boston, documents revealed the police department was using social media surveillance technology to track the use of the phrase "Black Lives Matter" online. In Memphis, police have spied on Black activists and journalists in violation of a 1978 consent decree. The Memphis Police Department's surveillance included the use of undercover operations on social media targeting people engaged in First Amendment-protected activity. In New York, the police spent countless hours monitoring Black Lives Matter protesters, emails show. And in Chicago, activists suspect the police used a powerful cell phone spying device to track protesters speaking out against police harassment of Black people.

These are just a few examples of a trend that dates back to the surveillance of Black people during slavery, extending through the 20th century when the FBI's J. Edgar Hoover instructed his agents to track the political activity of every single Black college student in the country. It continues to this day, with Attorney General Bill Barr reportedly temporarily expanding the U.S. Drug Enforcement Administration's surveillance authorities that could easily be abused to spy on individuals protesting the police killing of George Floyd.

The war on drugs and gangs is the other primary justification for surveillance programs that overwhelmingly target Black and Brown people in the U.S. From wiretaps to sneak-and-peak warrants, the most invasive forms of authorized government surveillance are typically deployed not to fight terrorism or investigate violent criminal conspiracies like murder or kidnapping, but rather to prosecute people for drug offenses. Racial disparities in the government's war on drugs are well documented.

To avoid repeating the mistakes of our past, we must read our history and heed its warnings. If government agencies like police departments and the FBI are authorized to deploy invasive face surveillance technologies against our communities, these technologies will unquestionably be used to target Black and Brown people merely for existing. That's why racial justice organizations like the Center for Media Justice are calling for a ban on the government's use of this dystopian technology, and why ACLU advocates from California to Massachusetts are pushing for bans on the technology in cities nationwide.

We are at a pivotal moment in our nation's history. We must listen to the voices of the protesters in the streets and act now to make systemic change. Banning face surveillance won't stop systemic racism, but it will take one powerful tool away from institutions that are responsible for upholding it.

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How is Face Recognition Surveillance Technology Racist? | News & Commentary | American Civil Liberties Union

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Last week, IBM, Amazon, and Microsoft announced they would pause or end sales of their face recognition technology to police in the United States. The announcement caught many by surprise. For years, racial justice and civil rights advocates had been warning that this technology in law enforcement hands would be the end of privacy as we know it.

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Link: https://docs.google.com/document/d/1br_qzANieYYE3s58DwfU4ABaiUg2LhTExM3L2jjgFrg/edit?usp=sharing

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https://docs.google.com/document/d/1Y-5QJuJPtZ76okABx1-nTN81tUzwkvfbEjRElg9SpG0/edit?usp=sharing

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Link- https://docs.google.com/document/d/1-mzseQz9xGB8GAjlTC3n3PGJYfXq-6qiUdgXEYb1290/edit?usp=sharing

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(Reflecting on some data about safe streets and neighborhoods)

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Earlier this summer, activists in Washington, D.C.'s Ward 8 held two vigils on the same day-one for a pedestrian killed in a hit-and-run and the other for a young man lost to gun violence. In placing the two vigils one after another, they drew a poignant connection between the high rates of traffic fatalities and gun violence in their neighborhood and left a resounding message for city leaders: It's time to broaden what we mean by "safe streets."

As the summer continues, so have traffic and gun violence-with the city's Wards 7 and 8 (home to the highest concentration of low-income households and black residents) bearing a disproportionate share of the harm. Just earlier this month, another Southeast D.C. resident was killed by a hit-and-run, and the next day, two more Southeast residents were lost to gun violence within the span of an hour.

Community members are grieving, and even those who have come to expect a level of gunfire in the neighborhood are caught off-guard by the repeated traffic fatalities and poor street conditions that enable them. As Southeast residents paint their own cross-walks in poorly-maintained intersections and care for community members shot outside of neighborhood schools and recreation centers, they are bringing to the forefront issues of racism, poverty, and place-based inequities that have long divided the District. And they are demanding that city leaders take action to make their streets safe.

Nationally, street safety is dictated by race and class

Place-based disparities in pedestrian casualties and gun violence are not unique to the nation's capital. Across the nation, street safety is dictated by race, class, and place. The lower a metro area's median household income, the more dangerous its streets are for people walking. And similar trends persist for gun violence: a small set of high-poverty neighborhoods, typically born out of decades of racial segregation, experience disproportionate clusters of violence that concentrate fatalities among marginalized groups.

Although the overlap in places affected by car and gun violence is clear, disciplinary siloes often prevent solutions from being discussed in tandem. Pedestrian fatalities are typically addressed with calls to increase sidewalks, crosswalks, and speed limits, whereas gun fatalities are met with increased policing (despite the negative effects criminal justice interventions can bring to communities of color).

A small set of high-poverty neighborhoods, typically born out of decades of racial segregation, experience disproportionate clusters of violence that concentrate fatalities among marginalized groups.

To some, this bifurcation might make sense, as the two forms of violence seem unrelated at a glance. Yet, they stem from the same historical inequities in how our cities were designed and built, in which intentional decisions by planners and policymakers divided our nation's physical landscape along racial lines. As the New York Times recently reminded readers, our nation's highways were often very purposefully constructed in the middle of black communities, drawing explicit racial barriers between white and black neighborhoods in places like Buffalo, N.Y., Hartford, Conn., Kansas City, Mo., Milwaukee, Pittsburgh, and St. Louis. Federally-commissioned redlining housing maps allowed place and race to dictate the types of infrastructure, lending, and housing that neighborhoods could receive, explicitly marking minority neighborhoods as unworthy of investment. These decisions, coupled with a long legacy of segregation and disinvestment, left entire neighborhoods without proper infrastructure, amenities, or access to economic opportunity.

By dividing communities with roads, refusing to invest in infrastructure, and restricting economic growth, such decisions fueled the spatialized patterns of safety we see today-leaving communities to cope with physically unsafe streets and dire socioeconomic conditions that spur other forms of violence.

Toward a holistic model of street safety

Investments in infrastructure and street design-like those included in Vision Zero campaigns across the country-are critical to building safe streets. But data increasingly show that these efforts alone might not be enough to reduce pedestrian fatalities in low-income neighborhoods, nor can they address safety concerns stemming from decades of historical disinvestment.

Alongside investments in physical infrastructure, low-income neighborhoods require place-based investments that integrate economic and community development strategies with equity at their core.

Alongside investments in physical infrastructure, low-income neighborhoods require place-based investments that integrate economic and community development strategies with equity at their core. Such investments are not a simple fix to the challenges these communities face, but they begin to take seriously residents' calls-to-action for a more holistic approach to street safety.

Openly acknowledge that in disadvantaged communities, safety is intertwined with every aspect of development. A first step for urbanists is to recognize that street safety has more than one meaning, particularly for those living amid structural disadvantage. For those who are vulnerable to victimization when engaging in everyday tasks-like walking to buy snacks or to work-concerns about safety impact nearly every aspect of their lives. And while we often point to place-based gaps in access to food, transportation, and neighborhood amenities, we don't always acknowledge that these disparities can be a matter of life and death for some communities. Community development organizations, like LISC, are beginning to make this shift, embedding principles of safety and justice within all of their work. Others can learn from this approach, and recognize how services and amenities, like grocery stores, are about more than increasing access to food-they are about giving community members safe places to meet, engage, and access economic opportunity.

Ask community residents what they want from their streets, and recognize that it might be more than bike lanes. Traditionally, cities have relied on 311 requests to identify residents' concerns about their streets. But as pilot demonstration projects in cities like Pittsburgh are finding, such methods of engagement are not effective at reaching low-income communities of color. Through the Safe Streets, Smart Cities Academy, the city of Pittsburg analyzed data on neighborhoods with high crashes and demographic factors like income, race, English proficiency, and educational attainment to reach the most vulnerable members of the city and engage them through community forums. Such concerted efforts to listen to hard-to-reach populations are critical for understanding street safety from a holistic perspective, providing residents a chance to voice concerns about the specific geographic inequities that impact them.

Support and invest in locally-led safety strategies that are already working. Finally, it is critical to acknowledge that communities may already hold the answer to advancing safety in their streets. As the NYU sociologist Patrick Sharkey says, "We should be investing in the residents and community organizations that have always had the capacity to control violence, but have never had the resources to do so in a sustainable way." Whether this be through community-planned plazas aimed at improving flawed intersections, neighborhood basketball leagues that help keep crime down, accessible public spaces that promote positive programming, or other spaces for community healing, it is important to identify which neighborhood assets are already keeping streets safe and ensure such assets are preserved and adequately resourced.

Advancing street safety is about improving roads, but it is also about investing in communities. Only after we broaden our understanding of safety to encompass multiple, interlocking sources of place-based disadvantage can we begin to build truly safe and thriving streets.

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To build safe streets, we need to address racism in urban design

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Earlier this summer, activists in Washington, D.C.'s Ward 8 held two vigils on the same day-one for a pedestrian killed in a hit-and-run and the other for a young man lost to gun violence.