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The median always represents the data better than the mean because the mean can be affect by outliers.

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A four-step process is the best way to organize a statistical problem. the four-step process is state, plan, do, and conclude.

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The probabilities describes only what happens in long run. A few times are not enough to calculate the probabilities.

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A simulation is an imitation of chance behavior.

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Extrapolation is the use of a regression line for prediction far outside the interval of values of the explanatory variable x used to obtain the line.

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Table A help us to find out the possibility by using z score.

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The SRS means a simple random sample.

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The scatterplot shows the relationship between quantitative variables on the same individuals.

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The mean point of a density curve is the balance point, at which the curve would balance if made of solid material.

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0_<P(A)_<1 .... This is in any event A

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The median of a density curve is the equal-areas point, the point that divides the area under the curve in half.

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Following these 4 steps can help solve problems within statistics: State, plan, do, conclude

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Bias and variability relate to precision and accuracy.

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Sample size matters

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Informed consent is important so that subjects refrain from taking legal action against the study.

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An institutional review board protects the safety and well-being of the subjects

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Correlation r shows the direction and strength of two variables

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Causation can be established by considering data from other studies

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In a matched pairs design, there is randomized blocking which has a matching pair of units

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Lurking variables are variables that are not included like explanatory and response variables

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Statistically significant is an observed effect big enough that it randomly occurs by chance

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Pie charts should not be used when percentages do not add up to 100%

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A block is a group of similar units that will react uniquely to a response

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A binomial random variable is the number of successes in a binomial setting

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Statistics are used throughout life and can help predict events whether it be sports, the weather, or any other event.

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Binomial settings have a binary and are independent

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Random variables are numbers that describe a potential outcome

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Statistic can be used in many ways. It can be used to describe a type of math and describe a number within a word problem.

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charts, graphs, and other representations of data can be described through various things such as shape, variance, etc.

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A probability distribution is a list of all possible outcomes and their probabilties

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Voluntary response and convenience samples are not reliable due to the bias they carry.

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When an experiment is double blind the person giving the treatment doesn’t know which treatment is being given to who and the person receiving the treatment doesn’t know which treatment they are getting either.

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The four step process:
state
plan
do
conclude

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To use a confidence interval the situation must be random, normal, and independent.

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You can check to see if a sample is normal by np>/(is greater than or equal to)10 and n(1-p)>/(is greater than or equal to) 10

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Higher sample sizes reduces the variability of the sampling distribution

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A bias is when a statistic consistently over estimates or underestimates a parameter

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The mean of the sampling distribution is equal to the parameter mean

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If there is a high bias then you’ll be farther away from the center or true value

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A statistic used to estimate a parameter is unbiased if the mean of its sampling distribution is equal to the true value of the parameter being estimated.

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P(A^c) Is the probability that A does NOT happen)

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If something is mutually exclusive, it means that one event can not occur if the other event happens. They cannot happen together.

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Sample Space is the set of all possible outcomes

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The law of large numbers says that the more we repeat a simulation, the closer it will get to the true number

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If something is statistically significant it means that would rarely occur by chance

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BITS stands for:
Binomial
Independent
Trials
Same Probability

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BINS stands for:
Binomial
Independent
Number
Same Probability

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Statistics talks about samples
Parameters talk about the whole population

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There are different terms /symbols for the mean and standard deviation of a population and a sample

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Correlation does not equal causation

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Non-response occurs when an individual chosen for a sample can't be contacted or refuses to participate and is a hindrance on the experiment.

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A systematic pattern of incorrect responses in a sample survey leads to response bias.

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Under-coverage occurs when some groups in the population are left out of the process of choosing the sample

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Choosing individuals who are the easiest to reach is considered a convenience sample and may not be the best representation of the population.

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The population is the entire group studied but in statistics we use a sample of the population to find averages in mean.

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Association does not imply causation.

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All normal distributions fit the 68-95-99.7 rule.

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The mean and median are equal for symmetric density curves.

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The five number summary consists of the median, the 1st and 3rd quartiles, and the minimum and maximum values.

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The mean and the median describe the center of a distribution.

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Adding a constant to a random variable increases or decreases the mean of the random variable by the value of the constant but doesn't affect its standard deviation or shape of the probability distribution.

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Random assignment is when experimental units are assigned to treatments at random using some kind of chance process in an experiment.

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A residual plot is a scatter plot of the residuals against the explanatory variable. They help assess how well a regression line fits the data.

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Correlation is the variable r. It measures the strength and direction of the linear association between two quantitative variables. R only measures straight-line relationships.

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A scatterplot shows how two quantitative variables are related when measured on the same individuals. One variable goes on the x axis, one variable on the y axis. Each individual in the data is represented by a point in the graph.

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Table A is a table of areas under the standard Normal curve. For each value z, the table entry is the area under the curve to the left of z.

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Histograms are most useful for quantitative data. Bar graphs are most useful for categorical data. Relative frequency histograms are most useful for comparing different size data sets.

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A categorical variable places all individuals intro categories, while quantitative variables have numerical values that measure characteristics of individuals. Categorical variable example - male/female? Quantitative variable example - height.

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There are three principles of experimental design:
Control for lurking variables that can change responses
Random Assignment uses chance to assign experimental units to treatments
Replication uses sufficient experimental units in each group so differences in treatment effects can be distinguishes from chance differences between the groups.

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An observational study simply observes individuals and measures variables of interest but doesn't try to influence the responses. An experiment tries to influence responses by imposing some treatment on individuals.

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In a matched-pairs design, two very similar individuals are paired and each receives one of two treatments. Twins are especially helpful for this design. Another way to carry out a matched-pairs experiment is to assign both treatments in random order to each subject.

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Stratified random samples are the most representative of the total population.

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Cluster sampling is often preferred over other sampling methods because it is easier and less time-consuming.

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A null hypothesis predicts that the outcome of an experiment will not be affected by the manipulation of a variable.

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An outcome is considered statistically significant if it is unlikely enough to occur due to chance.

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Experiments are usually repeated many times to reduce or eliminate confounding and lurking variables.

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There are three main methods for assigning treatments:
Random assignment
Random block assignment
Matched-pairs assignment

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There are three main sampling methods:
Stratified
SRS
Cluster

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The population is the entire group of individuals an experiment is designed to represent.

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50% of the data falls between the first and third quartiles.

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All bars/bins in a histogram has to be the same size. You cant use pictures or shapes as bars/bins.

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In all experiments, the subjects must be randomly selected. If not, there is an opportunity for bias to alter the results.

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To find if something is binomial use BINS - Binary - yes or no outcome (2)
Independent - Does not effect result
Number - Fixed number of trials
Success - probability pf success is included

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to find if something is geometric use BITS
Binary - yes or no outcome (2)
Independent - does no effect results
Trial - repeat until you get outcome, no set limit of trials
Success - provability of success is included

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The gamblers fallacy is the belief that the more times you do something, the probability of getting it smaller and the likelihood goes up. This is incorrect because no matter what, you still have the same probability of getting it.

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To find IQR we must take Q3 and subtract it by Q1

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Categorical - mostly of questions that do not pertain to numbers
Quantitative - has to do with numbers and data

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Placebos help eliminate bias. This is especially used in physiological experiments and medical experiments. This eliminated the self concision part of the experiment and gets rid of bias

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You need to be careful when using a venn diagram because you could put the same person in two boxes, messing up your data.

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SOCS - Shape Outlier Center Spread

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Conditional probability is the probability that Event A occurs, given that Event B has occurred

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Resistance in statistics represents how the data is not affected by any outliers.

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An observational study draws inferences from a sample to a population, and the researcher has no control over the variables in an observational study. An experiment is where treatments are applied to a group and the effects are recorded.

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Cluster sampling refers to selecting groups of individuals who are similar yet different from the total population.

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Inferences can be drawn about a larger population and cause and effect can be established if a sample is selected randomly and assigned treatments randomly.

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Binomial random variables require a fixed number of trials while a geometric random variable continues in trials until success is reached.

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When 2 events are mutually exclusive both events cannot occur at the same time.

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A z-score provides us with a fractional number of standard deviations from the mean.

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A regression line tells us what the predicted values of Y may be given X in a linear relationship because Y is dependent on X.

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A trend or association between two sets of data doesn't imply that one causes the other.