# data[].attributes.body
Discrete data is a count that involves integers only limited number of value is possible

# data[].attributes.body
Continuous data is data which can be data which can be divided into smaller parts, being able to be decimals or fractions.

# data[].attributes.attachment_link.title
Discrete vs. Continuous Data: Differences & Examples

# data[].attributes.attachment_link.description
Discrete vs continuous data are two broad categories of numeric variables. You count discrete data but measure continuous.

# data[].attributes.body
Discrete data refers to specific, distinct values or outcomes, often derived from countable items or events.

https://en.m.wikipedia.org/wiki/Continuous_or_discrete_variable

# data[].attributes.attachment_link.title
Continuous or discrete variable - Wikipedia

# data[].attributes.attachment_link.description
In mathematics and statistics, a quantitative variable may be continuous or discrete if it is typically obtained by measuring or counting, respectively.[1] If it can take on two particular real values such that it can also take on all real values between them (including values that are arbitrarily or infinitesimally close together), the variable is continuous in that interval.[2] If it can take on a value such that there is a non-infinitesimal gap on each side of it containing no values that the variable can take on, then it is discrete around that value.[3] In some contexts, a variable can be discrete in some ranges of the number line and continuous in others.

# data[].attributes.body
Continuous data is a type of numerical data that can take any value.

https://whatagraph.com/blog/articles/discrete-vs-continuous-data

# data[].attributes.attachment_link.title
Discrete vs. Continuous Data: What Is The Difference?

# data[].attributes.attachment_link.description
Learn the similarities and differences between discrete and continuous data.

# data[].attributes.body
Continuous refers to a type of data that can take any value within a given range. In statistics and data analysis, continuous data is crucial for various applications, including statistical modeling, data visualization, and hypothesis testing.

# data[].attributes.body
Discrete data is a type of quantitative data that includes nondivisible figures and statistics you can count. You typically write discrete data points as numbers that represent exact values. You can often describe discrete data by using the phrase "the number of," such as the number of customers in a store.Discrete data usually represents single events that have already occurred. When reviewing discrete data, you can analyze exact figures like units sold on a specific day or the hours an employee worked during a certain week.

# data[].attributes.body
Ordinal data is data which is placed into some kind of order or scale.

# data[].attributes.attachment_link.title
What Is Ordinal Data? | Examples & Definition

# data[].attributes.attachment_link.description
Ordinal data is classified into categories within a variable that have a natural rank order. However, the distances between the categories are uneven or

# data[].attributes.body
Data which has 2 or more categories, which has clear ordering of the categories.

# data[].attributes.attachment_link.title
What is the difference between categorical, ordinal and interval variables?

# data[].attributes.attachment_link.description
In talking about variables, sometimes you hear variables being described as categorical
(or sometimes nominal), or ordinal, or interval. Below we will define these
terms and explain why they are important.

# data[].attributes.body
Continuous data is information that could be meaningfully divided into finer levels. It can be measured on a scale or continuum and can have almost any numeric value. For example, you can measure your height at very precise scales — meters, centimeters, millimeters and etc.

# data[].attributes.body
Nominal data is a type of qualitative data which groups variables into categories. You can think of these categories as nouns or labels; they are purely descriptive, they don’t have any quantitative or numeric value, and the various categories cannot be placed into any kind of meaningful order or hierarchy.

# data[].attributes.body
Continuous data is data that has an infinite number of possible values. A good example of this is height. If you were recording everyone’s height in a classroom, you can round the height to the nearest centimetre. However, you could record the true value because it can be recorded to an infinite accuracy. You could record it to the nearest millimetre or maybe even micrometre… You could go on forever. Other examples of this are time or temperature.

https://www.twinkl.co.uk/parenting-wiki/continuous-data

# data[].attributes.attachment_link.readable_text
Continuous data is data that has an infinite number of possible values. A good example of this is height. If you were recording everyone's height in a classroom, you can round the height to the nearest centimetre. However, you could record the true value because it can be recorded to an infinite accuracy. You could record it to the nearest millimetre or maybe even micrometre... You could go on forever. Other examples of this are time or temperature.

Download FREE teacher-made resources covering 'Continuous Data'

Why does my child need to be aware of continuous data?

Continuous data comes into maths lessons when your child learns about statistics. They'll need an understanding of the type of data they're dealing with so they can make an appropriate choice as to how to present the data. It also comes in handy to know the type of data when interpreting it and drawing any conclusions.

How can I support my child with their understanding of continuous data?

Take a look at this PowerPoint which explains the difference between continuous and discrete data. Your child might also find these posters handy as support. Think about examples of continuous data - can your child write a list? Start off with height and length - what could they measure in this way?

# data[].attributes.attachment_link.description
Continuous data is data that has an infinite number of possible values. A good example of this is height. If you were recording everyone's height in a classroom, you can round the height to the nearest centimetre. However, you could record the true value because it can be recorded to an infinite accuracy.

# data[].attributes.body
Nominal data is a type of qualitative data that categorised variable into groups without providing numeric values

https://www.simplilearn.com/what-is-nominal-data-article

# data[].attributes.attachment_link.title
What is Nominal Data? Definition, Examples, Variables & Analysis | Simplilearn

# data[].attributes.attachment_link.description
In this article we'll define what nominal data is, look at the characteristics of nominal data, examples of nominal data, how to analyze nominal data, and nominal vs. ordinal data.

# data[].attributes.body
Ordinal data is a type of categorical data that has a meaningful order among its categories but lacks numerical values or fixed intervals between them¹. This means that while the categories can be ranked or ordered, the precise difference between the ranks is not known. For example, in a customer satisfaction survey, respondents might rate their satisfaction on a scale from "Dissatisfied" to "Satisfied." Here, the order is apparent, but the exact variance between each category is not¹.

# data[].attributes.body
Ordinal data classifies data while introducing an order, or ranking. For instance, measuring economic status using the hierarchy: ‘wealthy’, ‘middle income’ or ‘poor.’ However, there is no clearly defined interval between these categories.

https://careerfoundry.com/en/blog/data-analytics/what-is-ordinal-data/

# data[].attributes.attachment_link.title
What Is Ordinal Data? [Definition, Analysis & Examples]

# data[].attributes.attachment_link.description
What is ordinal data and how is it analyzed? What are some examples of ordinal data, and how is it different from nominal data? Learn more here.

# data[].attributes.body
data which 2 or more categories, with no intrinsic ordering.

# data[].attributes.attachment_link.title
What is the difference between categorical, ordinal and interval variables?

# data[].attributes.attachment_link.description
In talking about variables, sometimes you hear variables being described as categorical
(or sometimes nominal), or ordinal, or interval. Below we will define these
terms and explain why they are important.

# data[].attributes.body
Categorical data classifies information into distinct groups or categories, lacking a specific numerical value. It is a type of qualitative data that can be stored and identified based on names or labels¹. Categorical data is mainly divided into two types: Nominal Data and Ordinal Data.

Types of Categorical Data

# data[].attributes.body
In statistics, nominal data (also known as nominal scale) is a type of data that is used to label variables without providing any quantitative value. It is the simplest form of a scale of measure. Unlike ordinal data, nominal data cannot be ordered and cannot be measured.

https://corporatefinanceinstitute.com/resources/data-science/nominal-data/

# data[].attributes.attachment_link.description
In statistics, nominal data (also known as nominal scale) is a type of data that is used to label variables without providing any quantitative value.

# data[].attributes.body
Categorical data means data that can be stored into a groups or categories. Examples of categorical variables are race, sex, age groups

https://www.fullstory.com/blog/categorical-vs-quantitative-data/#:~:text=Categorical%20data%20is%20a%20type,a%20method%20known%20as%20matching.

# data[].attributes.attachment_link.title
Categorical vs. Quantitative Data: The Difference | Fullstory

# data[].attributes.attachment_link.description
Learn the differences between categorical and quantitative data and their value in analytics with Fullstory’s comprehensive guide for optimal decision-making.

# data[].attributes.body
Categorical data refers to a type of information that can be stored and identified based on their names or labels. It is a form of qualitative data that can be grouped into categories rather than being measured numerically. This data type consists of categorical variables that indicate things like a person’s gender, hometown, and so on. Categorical measurements are not provided as numbers but rather as natural language descriptions.

https://www.questionpro.com/blog/categorical-data/

# data[].attributes.attachment_link.title
Categorical Data: Definition, Types, Features + Examples

# data[].attributes.attachment_link.description
Categorical Data is a form of qualitative data that can be grouped into categories rather than being measured numerically.

# data[].attributes.body
Nominal data is labelled into mutually exclusive categories within a variable. These categories cannot be ordered in a meaningful way.

For example, preferred mode of transportation is a nominal variable, because the data is sorted into categories: car, bus, train, tram, bicycle, etc.

# data[].attributes.body
A smaller set of a larger population.

# data[].attributes.attachment_link.readable_text
Populations

In statistics the term "population" has a slightly different meaning from the one given to it in ordinary speech. It need not refer only to people or to animate creatures - the population of Britain, for instance or the dog population of London. Statisticians also speak of a population of objects, or events, or procedures, or observations, including such things as the quantity of lead in urine, visits to the doctor, or surgical operations. A population is thus an aggregate of creatures, things, cases and so on.

Although a statistician should clearly define the population he or she is dealing with, they may not be able to enumerate it exactly. For instance, in ordinary usage the population of England denotes the number of people within England's boundaries, perhaps as enumerated at a census. But a physician might embark on a study to try to answer the question "What is the average systolic blood pressure of Englishmen aged 40-59?" But who are the "Englishmen" referred to here? Not all Englishmen live in England, and the social and genetic background of those that do may vary. A surgeon may study the effects of two alternative operations for gastric ulcer. But how old are the patients? What sex are they? How severe is their disease? Where do they live? And so on. The reader needs precise information on such matters to draw valid inferences from the sample that was studied to the population being considered. Statistics such as averages and standard deviations, when taken from populations are referred to as population parameters. They are often denoted by Greek letters: the population mean is denoted by μ(mu) and the standard deviation denoted by ς (low case sigma)

Samples

A population commonly contains too many individuals to study conveniently, so an investigation is often restricted to one or more samples drawn from it. A well chosen sample will contain most of the information about a particular population parameter but the relation between the sample and the population must be such as to allow true inferences to be made about a population from that sample.

Consequently, the first important attribute of a sample is that every individual in the population from which it is drawn must have a known non-zero chance of being included in it; a natural suggestion is that these chances should be equal. We would like the choices to be made independently; in other words, the choice of one subject will not affect the chance of other subjects being chosen. To ensure this we make the choice by means of a process in which chance alone operates, such as spinning a coin or, more usually, the use of a table of random numbers. A limited table is given in the Table F (Appendix), and more extensive ones have been published.(1-4) A sample so chosen is called a random sample.The word "random" does not describe the sample as such but the way in which it is selected.

To draw a satisfactory sample sometimes presents greater problems than to analyse statistically the observations made on it. A full discussion of the topic is beyond the scope of this book, but guidance is readily available(1)(2). In this book only an introduction is offered.

Before drawing a sample the investigator should define the population from which it is to come. Sometimes he or she can completely enumerate its members before beginning analysis - for example, all the livers studied at necropsy over the previous year, all the patients aged 20-44 admitted to hospital with perforated peptic ulcer in the previous 20 months. In retrospective studies of this kind numbers can be allotted serially from any point in the table to each patient or specimen. Suppose we have a population of size 150, and we wish to take a sample of size five. contains a set of computer generated random digits arranged in groups of five. Choose any row and column, say the last column of five digits. Read only the first three digits, and go down the column starting with the first row. Thus we have 265, 881, 722, etc. If a number appears between 001 and 150 then we include it in our sample. Thus, in order, in the sample will be subjects numbered 24, 59, 107, 73, and 65. If necessary we can carry on down the next column to the left until the full sample is chosen.

The use of random numbers in this way is generally preferable to taking every alternate patient or every fifth specimen, or acting on some other such regular plan. The regularity of the plan can occasionally coincide by chance with some unforeseen regularity in the presentation of the material for study - for example, by hospital appointments being made from patients from certain practices on certain days of the week, or specimens being prepared in batches in accordance with some schedule.

As susceptibility to disease generally varies in relation to age, sex, occupation, family history, exposure to risk, inoculation state, country lived in or visited, and many other genetic or environmental factors, it is advisable to examine samples when drawn to see whether they are, on average, comparable in these respects. The random process of selection is intended to make them so, but sometimes it can by chance lead to disparities. To guard against this possibility the sampling may be stratified.This means that a framework is laid down initially, and the patients or objects of the study in a random sample are then allotted to the compartments of the framework. For instance, the framework might have a primary division into males and females and then a secondary division of each of those categories into five age groups, the result being a framework with ten compartments. It is then important to bear in mind that the distributions of the categories on two samples made up on such a framework may be truly comparable, but they will not reflect the distribution of these categories in the population from which the sample is drawn unless the compartments in the framework have been designed with that in mind. For instance, equal numbers might be admitted to the male and female categories, but males and females are not equally numerous in the general population, and their relative proportions vary with age. This is known as stratified random sampling.For taking a sample from a long list a compromise between strict theory and practicalities is known as a systematic random sample.In this case we choose subjects a fixed interval apart on the list, say every tenth subject, but we choose the starting point within the first interval at random.

Unbiasedness and precision

The terms unbiased and precision have acquired special meanings in statistics. When we say that a measurement is unbiased we mean that the average of a large set of unbiased measurements will be close to the true value. When we say it is precise we mean that it is repeatable. Repeated measurements will be close to one another, but not necessarily close to the true value. We would like a measurement that is both accurate and precise. Some authors equate unbiasedness with accuracy,but this is not universal and others use the term accuracy to mean a measurement that is both unbiased and precise. Strike (5) gives a good discussion of the problem.

An estimate of a parameter taken from a random sample is known to be unbiased. As the sample size increases, it gets more precise.

Randomisation

Another use of random number tables is to randomise the allocation of treatments to patients in a clinical trial. This ensures that there is no bias in treatment allocation and, in the long run, the subjects in each treatment group are comparable in both known and unknown prognostic factors. A common method is to use blocked randomisation. This is to ensure that at regular intervals there are equal numbers in the two groups. Usual sizes for blocks are two, four, six, eight, and ten. Suppose we chose a block size of ten. A simple method using Table F (Appendix) is to choose the first five unique digits in any row. If we chose the first row, the first five unique digits are 3, 5, 6, 8, and 4. Thus we would allocate the third, fourth, fifth, sixth, and eighth subjects to one treatment and the first, second, seventh, ninth, and tenth to the other. If the block size was less than ten we would ignore digits bigger than the block size. To allocate further subjects to treatment, we carry on along the same row, choosing the next five unique digits for the first treatment. In randomised controlled trials it is advisable to change the block size from time to time to make it more difficult to guess what the next treatment is going to be.

It is important to realise that patients in a randomised trial are not a random sample from the population of people with the disease in question but rather a highly selected set of eligible and willing patients. However, randomisation ensures that in the long run any differences in outcome in the two treatment groups are due solely to differences in treatment.

Variation between samples

Even if we ensure that every member of a population has a known, and usually an equal, chance of being included in a sample, it does not follow that a series of samples drawn from one population and fulfilling this criterion will be identical. They will show chance variations from one to another, and the variation may be slight or considerable. For example, a series of samples of the body temperature of healthy people would show very little variation from one to another, but the variation between samples of the systolic blood pressure would be considerable. Thus the variation between samples depends partly on the amount of variation in the population from which they are drawn.

Furthermore, it is a matter of common observation that a small sample is a much less certain guide to the population from which it was drawn than a large sample. In other words, the more members of a population that are included in a sample the more chance will that sample have of accurately representing the population, provided a random process is used to construct the sample. A consequence of this is that, if two or more samples are drawn from a population, the larger they are the more likely they are to resemble each other - again provided that the random technique is followed. Thus the variation between samples depends partly also on the size of the sample. Usually, however, we are not in a position to take a random sample; our sample is simply those subjects available for study. This is a "convenience" sample. For valid generalisations to be made we would like to assert that our sample is in some way representative of the population as a whole and for this reason the first stage in a report is to describe the sample, say by age, sex, and disease status, so that other readers can decide if it is representative of the type of patients they encounter.

Standard error of the mean

If we draw a series of samples and calculate the mean of the observations in each, we have a series of means. These means generally conform to a Normal distribution, and they often do so even if the observations from which they were obtained do not (see Exercise 3.3). This can be proven mathematically and is known as the "Central Limit Theorem". The series of means, like the series of observations in each sample, has a standard deviation. The standard error of the mean of one sample is an estimate of the standard deviation that would be obtained from the means of a large number of samples drawn from that population.

A general practitioner in Yorkshire has a practice which includes part of a town with a large printing works and some of the adjacent sheep farming country. With her patients' informed consent she has been investigating whether the diastolic blood pressure of men aged 20-44 differs between the printers and the farm workers. For this purpose she has obtained a random sample of 72 printers and 48 farm workers and calculated the mean and standard deviations, as shown in Table 3.1.

To calculate the standard errors of the two mean blood pressures the standard deviation of each sample is divided by the square root of the number of the observations in the sample.

These standard errors may be used to study the significance of the difference between the two means, as described in successive chapters

Standard error of a proportion or a percentage

Just as we can calculate a standard error associated with a mean so we can also calculate a standard error associated with a percentage or a proportion. Here the size of the sample will affect the size of the standard error but the amount of variation is determined by the value of the percentage or proportion in the population itself, and so we do not need an estimate of the standard deviation. For example, a senior surgical registrar in a large hospital is investigating acute appendicitis in people aged 65 and over. As a preliminary study he examines the hospital case notes over the previous 10 years and finds that of 120 patients in this age group with a diagnosis confirmed at operation 73 (60.8%) were women and 47 (39.2%) were men.

If p represents one percentage, 100 p represents the other. Then the standard error of each of these percentages is obtained by (1) multiplying them together, (2) dividing the product by the number in the sample, and (3) taking the square root:

which for the appendicitis data given above is as follows:

Problems with non-random samples

In general we do not have the luxury of a random sample; we have to make do with what is available, a " convenience sample ". In order to be able to make generalisations we should investigate whether biases could have crept in, which mean that the patients available are not typical. Common biases are:

hospital patients are not the same as ones seen in the community;

volunteers are not typical of non-volunteers;

patients who return questionnaires are different from those who do not.

In order to persuade the reader that the patients included are typical it is important to give as much detail as possible at the beginning of a report of the selection process and some demographic data such as age, sex, social class and response rate.

Common questions

Given measurements on a sample, what is the difference between a standard deviation and a standard error?

A standard deviation is a sample estimate of the population parameter; that is, it is an estimate of the variability of the observations. Since the population is unique, it has a unique standard deviation, which may be large or small depending on how variable the observations are. We would not expect the sample standard deviation to get smaller because the sample gets larger. However, a large sample would provide a more precise estimate of the population standard deviation than a small sample.

A standard error, on the other hand, is a measure of precision of an estimate of a population parameter. A standard error is always attached to a parameter, and one can have standard errors of any estimate, such as mean, median, fifth centile, even the standard error of the standard deviation. Since one would expect the precision of the estimate to increase with the sample size, the standard error of an estimate will decrease as the sample size increases.

When should I use a standard deviation to describe data and when should I use a standard error?

It is a common mistake to try and use the standard error to describe data. Usually it is done because the standard error is smaller, and so the study appears more precise. If the purpose is to describe the data (for example so that one can see if the patients are typical) and if the data are plausibly Normal, then one should use the standard deviation (mnemonic D for Description and D for Deviation). If the purpose is to describe the outcome of a study, for example to estimate the prevalence of a disease, or the mean height of a group, then one should use a standard error (or, better, a confidence interval; see Chapter 4) (mnemonic E for Estimate and E for Error).

References

1. Altman DG. Practical Statistics for Medical Research.London: Chapman & Hall, 1991

2. Armitage P, Berry G. Statistical Methods in Medical Research.Oxford: Blackwell Scientific Publications, 1994.

3. Campbell MJ, Machin D. Medical Statistics: A Commonsense Approach.2nd ed. Chichester: John Wiley, 1993.

4. Fisher RA, Yates F. Statistical Tables for Biological, Agricultural and Medical Research,6th ed. London: Longman, 1974.

5. Strike PW. Measurement and control. Statistical Methods in Laboratory Medicine.Oxford: Butterworth-Heinemann, 1991:255.

Exercises

Exercise 3.1

The mean urinary lead concentration in 140 children was 2.18 mol/24 h, with standard deviation 0.87. What is the standard error of the mean?

Exercise 3.2

In Table F (Appendix), what is the distribution of the digits, and what are the mean and standard deviation?

Exercise 3.3

For the first column of five digits in Table F take the mean value of the five digits and do this for all rows of five digits in the column.

What would you expect a histogram of the means to look like?

What would you expect the mean and standard deviation to be?

# data[].attributes.attachment_link.description
Populations In statistics the term "population" has a slightly different meaning from the one given to it in ordinary speech. It need not refer only to people or to animate creatures - the population of Britain, for instance or the dog population of London. Statisticians also speak of a population

# data[].attributes.body
Data sampling is a statistical analysis technique used to select, manipulate and analyze a representative subset of data points to identify patterns and trends in the larger data set being examined.

# data[].attributes.attachment_link.readable_text
Gathering data for research projects can seem overwhelming and complex. There are many types of data available, and understanding the differences between them is critical to conducting effective research. In this guide, we'll be focusing on two main types: population and sample data.

Population data consists of information collected from every individual in a particular population. Meanwhile, sample data consists of information taken from a subset-or sample -of the population.

In this guide, we'll discuss the differences between population and sample data, the advantages and disadvantages of each, how to collect data from a sample and a population, and common sampling techniques. By the end, you'll have a better understanding of the differences between population and sample data and when to use them.

What is "population" in research?

Population data is the total number of measurements taken from every individual within a group. For example, if you were measuring the heights of all humans on Earth, you'd include all 7 billion people in your population data set.

When analyzing population data, researchers use statistics such as the population mean, median, and standard deviation.

Types of populations

Finite population

A finite population is a population in which all the members are known and can be counted. Examples of this type of population include all the employees of a company, all the students in a school, or the entire population of a city. When working with a finite population, you can calculate the exact population mean, median, and standard deviation.

Infinite population

An infinite population is a population that is too large to be measured or counted. This could be the entire human population on Earth or the number of stars in the sky. Because it's impossible to measure or count these populations, it isn't possible to calculate their exact mean, median, and standard deviation.

Closed population

A closed population is one in which you allow no new members to join. An example of a closed population would be a country's citizens over the age of 18 who have been living there for more than 10 years. As no new members can join, the population remains constant and can easily be measured and analyzed.

Open population

An open population is one in which new members can join. For example, all people living in a certain city are considered an open population because new members can move into the city and become part of the population. This type of population is constantly changing, so it isn't possible to measure and analyze its exact characteristics.

Advantages of population data

Representative

It offers a complete representation of all elements in the population, which can increase the generalizability of findings.

High quality

Population data is usually very accurate and detailed because standardized data collection methods and quality control measures are in place to provide data from every element in the population.

Large sample size

The sample size is large, which can increase the statistical power of a study and help detect small but meaningful differences.

Can address rare events

You can use population data to study rare events or diseases that wouldn't be feasible to study through other methods.

Allows for subgroup analysis

You can use population data to examine subgroups of the population, which can help identify disparities and inform interventions.

Disadvantages of population data

Time and cost constraints

Collecting data from a large population is expensive and time-consuming, especially when it comes to data cleaning and preparation before using it for analysis.

Limited access

Depending on the source of population data, it can be difficult to get access to the population or convince people to participate, especially when there are privacy concerns or restrictions on the use of data.

Limited variables

Population data may have limited variables or lack information on important factors, which may not allow one to answer a particular research question if the data wasn't originally collected for that purpose.

Difficult to analyze

Population data can be large, complex, and contain a wide variety of data or even missing data which demands advanced analytical skills and high computational requirements.

Population data may become outdated, especially if it was collected some time ago, which can limit its relevance to current research questions.

What is a sample in research?

Sampling is the process of selecting individuals from a larger population and is used to generate representative information about the population of interest. There are two forms of sampling: non-probability.

Probability sampling is from a randomly selected small subset and provides statistical inferences about the whole population without bias. Non-probability sampling collects data from a selected subset chosen for its convenience or, sometimes, to control and manipulate the data collected.

Types of probability sampling

Random sampling

This type of sampling is completely by chance. Each member of the population has an equal chance of being selected for the sample, and the results of a random sample will be statistically representative of the whole population.

For example, if you wanted to know how people felt about a new product, you could use a random number generator to select members from a population for the study.

Stratified sampling

Stratified sampling is when the population is split into different subgroups, or strata, based on one or more characteristics. The researcher then randomly selects members from each stratum to represent the population. This allows the researcher to accurately compare data between different groups because it ensures that all subgroups are represented in the sample.

For example, if you wanted to measure the opinion of people in different age groups, you could divide your population into groups based on age and then take random samples from each stratum.

Cluster sampling

This type of sampling divides the population into clusters or groups and then further takes a sample from each cluster. This method is often used when it isn't possible to access the entire population.

For example, if you wanted to measure public opinion on an issue in a large city, it wouldn't be feasible to survey every single person. Instead, you could divide the city into neighborhoods and take random samples from each one.

Systematic sample

Systematic sampling involves selecting items from a population based on a set pattern or system. This type of sampling is useful when it's impossible or impractical to create a list of all items in a population. It's similar to random sampling in that it helps eliminate any bias from the selection process, but it's more efficient because it requires fewer samples to be taken.

If a researcher can only select 10 members from a population of 200 people, they could use systematic sampling by selecting every 20th person in the list to eliminate bias.

Types of non-probability sampling

Convenience sampling

This form of sampling involves selecting participants based on availability and willingness to take part. This can lead to volunteer bias, meaning that individuals who are more motivated or have more time may be more likely to participate.

Quota sampling

A method of selecting participants from a larger population to match certain criteria is referred to as quota sampling. For example, market researchers might use quota sampling to select a certain number of individuals within specific age groups.

Judgemental sampling

This technique is also referred to as purposive sampling or authoritative sampling. You can use it to target specific individuals who possess a certain set of qualities like age, ethnicity, or religious beliefs. It can help researchers access important information from people with specific knowledge or experience.

However, this kind of sampling can also lead to selection bias, which is the distortion of results due to the non-random selection of participants.

Snowball sampling

Snowball sampling is often used to reach individuals who may be difficult to access through traditional means. This type of sampling involves asking participants to refer others who fit the same criteria. It's often used in social sciences research to identify people within a certain community or social group. For example, researchers may conduct a survey offering a reward to participants who refer their close friends or family and get them to participate.

While this technique can be useful in reaching underserved or underrepresented populations, it also carries the risk of selection bias.

Advantages of sample data

Cost-effective

Collecting data from a sample is typically less expensive and time-consuming than collecting data from an entire population.

Higher quality

Collecting data from a smaller subset of a population can often result in higher-quality data when more resources are dedicated to ensuring the accuracy and completeness of the data.

Feasibility

In some cases, it may be impossible or impractical to collect data from an entire population, making sample data a more feasible option.

Manageable

Sample data is usually smaller and more manageable than population data, which makes it easier to analyze.

Reduced sampling bias

With appropriate sampling methods, sample data can be representative of the large population and provide valuable insights for research.

Disadvantages of using sample data

Generalizability

The quality of the data depends on the quality of the sample selection process. If the sample isn't representative of the population, it leads to skewed results.

Sampling bias

A sample may not provide a complete picture of an entire population when certain groups are overrepresented or underrepresented in the sample.

Sampling error

Because sample data is drawn from a subset of a larger population, there is always a risk of sampling error. It occurs when the sample doesn't accurately represent the larger population, which can lead to inaccurate results.

Statistical power

A small sample size can limit the statistical power of the data analysis, making it more difficult to detect meaningful differences or relationships between studied variables.

Limited score

Sample data may be limited in scope and may not capture the full range of variables present in an entire population. This can limit the depth and breadth of the findings.

Differences between population and sample

When discussing research and data analysis, it's important to understand the differences between population and sample data. Here are some key points to consider when distinguishing between the two:

Population vs. sample

A population is a set of all individuals or objects that share a common characteristic, while a sample is a subset of that population used to draw conclusions about the entire population.

For example, if you wanted to research the opinions of all people living in the United States, the population would be all citizens in the US, while the sample would be a smaller subset of people surveyed to represent the opinion of the entire population.

Sample vs. population mean

The sample mean is an average of a sample's values, while the population mean is an average of all values in a population. For example, if you're researching the average income of households in America, the sample mean would be an average of incomes from a smaller group of households selected from the population of all households in the US.

Sample vs. population standard deviation

Standard deviation measures the variation of a set of values from their mean. The sample standard deviation is based on the variation within a sample, while the population standard deviation is based on the variation within a population.

For example, if you were researching the variation in test scores for students at a particular school, the sample standard deviation would be based on the scores of a smaller subset of students from the school, while the population standard deviation would be based on all scores from every student at the school.

How to collect and use data from a sample

1. Choose the right sampling technique

The most common sampling techniques include random, stratified, convenience, and cluster sampling. Selecting the right technique for your research will depend on your specific needs, resources, goals, and objectives.

2. Decide the sample size

Determining the sample size will vary depending on the goal of your research. Generally speaking, the larger the sample size, the more reliable your results will be. However, there are tradeoffs, such as the cost and resources required to collect data from larger samples.

3. Design an instrument for collecting data

Once you've chosen your sampling technique and decided on the sample size, you'll need to design an instrument for collecting data. This could include surveys, interviews, or experiments. Make sure that the instrument is valid and reliable so that it provides accurate results.

4. Determine a sample frame

Decide who you'll include in the sample by selecting the population or subpopulation you want to study. Consider factors like location, age, gender, behavior, and so on when choosing your sample frame.

5. Execute the sample selection process

In this step, you'll select individuals to form your sample. To ensure accuracy, it's best to use random sampling techniques to guarantee a representative sample.

6. Collect data from a sample

Once you've selected the sample, you can begin collecting data. Depending on the method you chose (e.g., survey, interview, experiment), you may need to do some additional steps before you can begin collecting data:

For example, if you're collecting data through a survey, you may need to obtain permission to conduct the survey from relevant authorities, such as a workplace or community group.

If you plan to conduct interviews as your data collection method, ensure your questions are well-formed and that your interviewees are comfortable answering them. Before the interview, you may also want to send a pre-interview questionnaire to participants to collect basic information to make the interview process more efficient.﻿﻿

Most experiments require a significant amount of planning and preparation to ensure that data is collected in a controlled and systematic manner. Additionally, you may need to consider the ethical implications of conducting the experiment, such as obtaining informed consent from participants and ensuring their safety throughout the experiment.

7. Analyze the data

After you've collected data from the sample, analyze it to find meaningful patterns and trends that you can use to draw conclusions about the population. Remember, since you're working with a sample, your conclusions may not apply to the entire population.

By following these steps, you can easily collect data from a sample to gain insights about a population without having to analyze all of the data from the population itself. When used correctly, sample data can provide valuable insights that can help shape your research conclusions.

How to collect and use data from a population

1. Define the population

Before collecting data from a population, it's important to first clearly define what population you're looking to collect data from. This definition should be as specific as possible and include any relevant behavioral characteristics (e.g., shopping frequency, product use, or commute options) or demographic characteristics (e.g., age, gender, and geography).

2. Create a comprehensive list

After identifying the population in terms of traits, past experiences, outlooks, or other components, create a comprehensive list of the population you'll be studying. Depending on the purpose of the study, this could include both people and organizations.

Once you've defined the population and chosen your sampling method, it's time to collect data. You can obtain this data by conducting experiments, surveys, or interviews. Make sure to collect feedback from every person or entity on the population list to generate an exhaustive population sample.

4. Analyze the data

After collecting the data, it's important to analyze it to draw meaningful conclusions about the population. This analysis should include calculating the sample mean and sample standard deviation for the data set, as well as comparing these values to the population mean and population standard deviation.

5. Draw conclusions

Once you've analyzed the data, use the results to draw conclusions about the population. Make sure to be as accurate and objective as possible when making claims about the population.

Choosing high-quality samples

High-quality samples are essential when it comes to research. A high-quality sample will produce accurate and reliable study results. A poor-quality sample can result in incorrect or inexact data. These results can be costly and time-consuming to fix.

A good-quality sample is representative of the population. That means the sample has similar characteristics as the population in terms of age, gender, race, and other factors. The sample should also be randomly selected so as not to bias the results. In addition, the sample should be of a large enough size to be statistically significant.

How to select a high-quality sample

Choose a probability sampling method

Random selection is the most important part of choosing a high-quality sample. You want to ensure that the sample truly represents the population and that no bias has been introduced. You can do this through methods such as random sampling, stratified sampling, cluster sampling, and systematic sampling.

Monitor selection process

You should monitor the selection process to ensure that no bias has been introduced during the selection process. You should also make sure that the sample size is large enough to be statistically significant.

Test for accuracy

You should test the accuracy of your sample by comparing it to the population data. Compare the sample mean vs. population mean, sample vs. population standard deviation, and other factors. If there are any discrepancies between the two, then the sample may not be representative of the population and should be re-evaluated.

By following these steps, you can ensure that your sample is quality and that it correctly reflects the population and produces precise and accurate results.

Using sample and population data can be beneficial in many ways. For example, using sample data allows researchers to make more efficient use of resources while still being able to conclude the population. Additionally, sample data is useful in making statistical inferences about a population, such as the mean or standard deviation.

On the other hand, population data provides an accurate representation of the whole population, which can be beneficial when researchers need detailed information.

To ensure accurate and representative data, researchers must understand the differences between populations and weigh the advantages and risks of each sampling technique. By understanding the difference between population and sample data, researchers can gain valuable insights about their target group and use these insights to make informed decisions.

# data[].attributes.attachment_link.title
Population vs. Sample - A Comprehensive Guide

# data[].attributes.attachment_link.description
When it comes to research, understanding population vs. sample data is key. This guide breaks down the differences and explains when you should use each type of data.

# data[].attributes.body
Sample data is analytic subset of a larger population, often used in statistics and research

https://www.investopedia.com/terms/s/sample.asp#:~:text=A%20sample%20is%20used%20in,be%20expensive%20and%20time%2Dconsuming.

# data[].attributes.attachment_link.readable_text
What Is a Sample?

The term sample refers to a smaller, manageable version of a larger group. It is a subset containing the characteristics of a larger population. Samples are used in statistical testing when population sizes are too large to include all possible members or observations. A sample should represent the population as a whole and not reflect any bias toward a specific attribute.

There are several sampling techniques used by researchers and statisticians, each with benefits and drawbacks. The issue of sampling has taken mainstream attention with the advent of artificial intelligence and the data it is trained on. Now, the debate is intense around whether the sampling made in the data chosed to train AI is not biased towards some segments of the population, some actors, some information, some ideas, some regions, and so on.

Understanding Samples

A population is the total number of observations (i.e., individuals, animals, items, data, etc.) contained in a given group or context. A sample is a portion, part, or fraction of the whole group, and acts as a subset of that population. Samples are used in a variety of settings where research is conducted. Scientists, marketers, government agencies, economists, and research groups are among those who use samples for their studies and measurements.

Using whole populations for research comes with challenges. Researchers may have problems gaining access to entire populations. And, because of the nature of some studies, researchers may have difficulties getting the results they need in a timely fashion. This is why samples are used. Using a smaller group to represent the entire population can still produce valid results while reducing time and resources.

Samples must resemble the broader population to make accurate inferences or predictions. All the participants in the sample should share the same characteristics and qualities. So, if the study is about male college freshmen, the sample should be a small percentage of males that fit this description. Similarly, if a research group conducts a study on the sleep patterns of single women over 50, the sample should only include women within this demographic.

Special Considerations

Consider a team of academic researchers who want to know how many students studied for less than 40 hours for the CFA exam and still passed. Since more than 200,000 people take the exam globally each year, reaching out to every exam participant would burn time and resources.

In fact, by the time the data from the population is collected and analyzed, a couple of years would have passed, making the analysis worthless since a new population would have emerged. What the researchers can do instead is take a representative population and get data from this sample.

To achieve an unbiased sample, the selection has to be random so everyone from the population has an equal and likely chance of being added to the sample group. This is similar to a lottery draw and is the basis for simple random sampling.

Sampling Methods

Sampling methods refer to the way samples are chosen from the general population. Researchers can use one of two sampling methods to conduct their studies:

Probability Sampling: There is no deliberate choice in probability sampling. That's why it's also referred to as random sampling. Because there is no bias involved, probability sampling can be time-consuming and, at times, costly.

Non-Probability Sampling: Researchers who use this sampling method deliberately choose their samples. This makes it a non-random sampling method. Since it isn't random, only a certain portion of the population has a chance to participate in the study. Samples are chosen based on certain factors, including location or convenience.

Types of Sampling

Now that you know the methods of sampling, it's important to understand the different types of sampling that statisticians and researchers can use. We've highlighted just a few kinds of sampling below.

Simple Random Sampling

Simple random sampling is ideal if every entity in the population is identical. If the researchers don't care whether their sample subjects are all male or all female or a combination of both sexes in some form, simple random sampling may be a good selection technique.

Let's say 200,000 test-takers sat for the CFA exam in 2021, out of which 40% were women and 60% were men. The random sample drawn from the population should, therefore, have 400 women and 600 men for a total of 1,000 test-takers.

Systematic Sampling

Systematic sampling is a form of probability sampling. Similar to simple random sampling, it involves choosing random samples within a fixed periodic interval. Researchers calculate the interval by dividing the total population by the required sample size.

Unlike simple random sampling, systematic sampling is more efficient when it comes to time and cost. There is also a lower risk of data being manipulated.

This type of sampling is best used when:

There is some order in the population

When the population is large and known, especially when time and resources are limited

When the sample is evenly spread across the population

Stratified Random Sampling

But what about cases where knowing the ratio of men to women who passed a test after studying for less than 40 hours is important? Here, a stratified random sample would be preferable to a simple random sample.

This type of sampling, also referred to as proportional random sampling or quota random sampling, divides the overall population into smaller groups. These are known as strata. People within the strata share similar characteristics.

What if age was an important factor that researchers wanted to include in their data? Using the stratified random sampling technique, they could create layers or strata for each age group. The selection would have to be random so everyone in the bracket has a likely chance of being included.

For example, two participants, Alex and David, are 22 and 24 years old, respectively. The sample selection cannot pick one over the other based on some preferential mechanism. They both should have an equal chance of being selected from their age group. The strata could look something like this:

From the table, the population has been divided into age groups. For example, 30,000 people within the age range of 20 to 24 years old took the CFA exam in 2021. Using this same proportion, the sample group will have (30,000 ÷ 200,000) × 1,000 = 150 test-takers that fall within this group. Alex or David-or both or neither-may be included among the 150 random exam participants of the sample.

There are many more strata that could be compiled when deciding on a sample size. Some researchers might populate the job functions, countries, marital status, etc., of the test-takers when deciding how to create the sample.

Cluster Sampling

Cluster sampling is a form of random sampling. Clusters are defined as different subsets of the larger population. Individual samples within the cluster have similar characteristics. Cluster sampling is commonly used when there are large populations that are spread out, making it expensive and time-consuming to study each subject.

There are a few steps to cluster sampling:

1. Understand and identify the population that is being studied.

2. Create the cluster. This means dividing the entire population into groups and choosing random samples from those groups to study.

3. Select the sample from the clusters.

4. Researchers conduct their study by interviewing the samples. Once this is done, data is collected and analyzed.

As noted above, cluster sampling can save time and money. But, there are certain disadvantages to using this type of sampling. For instance, researchers may be biased when they choose their clusters and samples. As such, the samples may not accurately represent the population at large.

Examples of Samples

In 2022, the population of the world was nearly 7.95 billion, out of which 49.7% were female and 50% were male. The total number of people in any given country can also be a population size. The total number of students in a city can be taken as a population, and the total number of dogs in a city is also a population size. Samples can be taken from these populations for research purposes.

Following our CFA exam example, the researchers could take a sample of 1,000 CFA participants from the total 200,000 test-takers-the population-and run the required data on this number. The mean of this sample would be taken to estimate the average of CFA exam takers who passed even though they only studied for less than 40 hours.

The sample group taken should not be biased. This means that if the sample mean of the 1,000 CFA exam participants is 50, the population mean of the 200,000 test takers should also be approximately 50.

Why Do Analysts Use Samples Instead of Measuring the Population?

Often, a population is too large or extensive in order to measure every member and measuring each member would be expensive and time-consuming. A sample allows for inferences to be made about the population using statistical methods.

What Is a Simple Random Sample?

This sampling method uses respondents or data points that are randomly selected from the larger population. With a large enough sample size, a random sample removes bias.

Why Do Random Samples Allow for Inference?

How Large of a Sample Do You Need?

This will depend on the size of the population and the type of analysis you'd like to do (e.g., what confidence intervals you are using). Power analysis is a technique for mathematically evaluating the smallest sample size needed based on your needs. Another rule of thumb is that your sample should be large enough, but no more than 10% as large as the population.

The Bottom Line

Sampling can help us understand the nuances of large populations. It is a cost-effective way for researchers to study them while saving time. Because it can be difficult to study large groups, marketers, scientists, governments, and other researchers use smaller subsets-known as samples-to analyze and make important decisions.

# data[].attributes.attachment_link.title
Sample: What It Means in Statistics, Types, and Examples

# data[].attributes.attachment_link.description
A sample is a smaller, manageable version of a larger group. Samples are used in statistical testing when population sizes are too large.

# data[].attributes.body
Categorical data classifies information into distinct groups or categories, lacking a specific numerical value. It refers to a form of information that can be stored and identified based on their names or labels. Categorical Data is a type of qualitative data that is easily measured numerically.

# data[].attributes.body
Sample data refers to a subset of individuals or observations selected from a larger population, which is used to make inferences or draw conclusions about that population. This data is crucial for statistical analysis as it allows researchers to estimate population parameters, like proportions or means, without having to survey every individual in the population. Properly collected and analyzed sample data can support claims about the larger group, including insights into relationships between variables.

# data[].attributes.body
A group of entities

# data[].attributes.attachment_link.readable_text
Populations

In statistics the term "population" has a slightly different meaning from the one given to it in ordinary speech. It need not refer only to people or to animate creatures - the population of Britain, for instance or the dog population of London. Statisticians also speak of a population of objects, or events, or procedures, or observations, including such things as the quantity of lead in urine, visits to the doctor, or surgical operations. A population is thus an aggregate of creatures, things, cases and so on.

Although a statistician should clearly define the population he or she is dealing with, they may not be able to enumerate it exactly. For instance, in ordinary usage the population of England denotes the number of people within England's boundaries, perhaps as enumerated at a census. But a physician might embark on a study to try to answer the question "What is the average systolic blood pressure of Englishmen aged 40-59?" But who are the "Englishmen" referred to here? Not all Englishmen live in England, and the social and genetic background of those that do may vary. A surgeon may study the effects of two alternative operations for gastric ulcer. But how old are the patients? What sex are they? How severe is their disease? Where do they live? And so on. The reader needs precise information on such matters to draw valid inferences from the sample that was studied to the population being considered. Statistics such as averages and standard deviations, when taken from populations are referred to as population parameters. They are often denoted by Greek letters: the population mean is denoted by μ(mu) and the standard deviation denoted by ς (low case sigma)

Samples

A population commonly contains too many individuals to study conveniently, so an investigation is often restricted to one or more samples drawn from it. A well chosen sample will contain most of the information about a particular population parameter but the relation between the sample and the population must be such as to allow true inferences to be made about a population from that sample.

Consequently, the first important attribute of a sample is that every individual in the population from which it is drawn must have a known non-zero chance of being included in it; a natural suggestion is that these chances should be equal. We would like the choices to be made independently; in other words, the choice of one subject will not affect the chance of other subjects being chosen. To ensure this we make the choice by means of a process in which chance alone operates, such as spinning a coin or, more usually, the use of a table of random numbers. A limited table is given in the Table F (Appendix), and more extensive ones have been published.(1-4) A sample so chosen is called a random sample.The word "random" does not describe the sample as such but the way in which it is selected.

To draw a satisfactory sample sometimes presents greater problems than to analyse statistically the observations made on it. A full discussion of the topic is beyond the scope of this book, but guidance is readily available(1)(2). In this book only an introduction is offered.

Before drawing a sample the investigator should define the population from which it is to come. Sometimes he or she can completely enumerate its members before beginning analysis - for example, all the livers studied at necropsy over the previous year, all the patients aged 20-44 admitted to hospital with perforated peptic ulcer in the previous 20 months. In retrospective studies of this kind numbers can be allotted serially from any point in the table to each patient or specimen. Suppose we have a population of size 150, and we wish to take a sample of size five. contains a set of computer generated random digits arranged in groups of five. Choose any row and column, say the last column of five digits. Read only the first three digits, and go down the column starting with the first row. Thus we have 265, 881, 722, etc. If a number appears between 001 and 150 then we include it in our sample. Thus, in order, in the sample will be subjects numbered 24, 59, 107, 73, and 65. If necessary we can carry on down the next column to the left until the full sample is chosen.

The use of random numbers in this way is generally preferable to taking every alternate patient or every fifth specimen, or acting on some other such regular plan. The regularity of the plan can occasionally coincide by chance with some unforeseen regularity in the presentation of the material for study - for example, by hospital appointments being made from patients from certain practices on certain days of the week, or specimens being prepared in batches in accordance with some schedule.

As susceptibility to disease generally varies in relation to age, sex, occupation, family history, exposure to risk, inoculation state, country lived in or visited, and many other genetic or environmental factors, it is advisable to examine samples when drawn to see whether they are, on average, comparable in these respects. The random process of selection is intended to make them so, but sometimes it can by chance lead to disparities. To guard against this possibility the sampling may be stratified.This means that a framework is laid down initially, and the patients or objects of the study in a random sample are then allotted to the compartments of the framework. For instance, the framework might have a primary division into males and females and then a secondary division of each of those categories into five age groups, the result being a framework with ten compartments. It is then important to bear in mind that the distributions of the categories on two samples made up on such a framework may be truly comparable, but they will not reflect the distribution of these categories in the population from which the sample is drawn unless the compartments in the framework have been designed with that in mind. For instance, equal numbers might be admitted to the male and female categories, but males and females are not equally numerous in the general population, and their relative proportions vary with age. This is known as stratified random sampling.For taking a sample from a long list a compromise between strict theory and practicalities is known as a systematic random sample.In this case we choose subjects a fixed interval apart on the list, say every tenth subject, but we choose the starting point within the first interval at random.

Unbiasedness and precision

The terms unbiased and precision have acquired special meanings in statistics. When we say that a measurement is unbiased we mean that the average of a large set of unbiased measurements will be close to the true value. When we say it is precise we mean that it is repeatable. Repeated measurements will be close to one another, but not necessarily close to the true value. We would like a measurement that is both accurate and precise. Some authors equate unbiasedness with accuracy,but this is not universal and others use the term accuracy to mean a measurement that is both unbiased and precise. Strike (5) gives a good discussion of the problem.

An estimate of a parameter taken from a random sample is known to be unbiased. As the sample size increases, it gets more precise.

Randomisation

Another use of random number tables is to randomise the allocation of treatments to patients in a clinical trial. This ensures that there is no bias in treatment allocation and, in the long run, the subjects in each treatment group are comparable in both known and unknown prognostic factors. A common method is to use blocked randomisation. This is to ensure that at regular intervals there are equal numbers in the two groups. Usual sizes for blocks are two, four, six, eight, and ten. Suppose we chose a block size of ten. A simple method using Table F (Appendix) is to choose the first five unique digits in any row. If we chose the first row, the first five unique digits are 3, 5, 6, 8, and 4. Thus we would allocate the third, fourth, fifth, sixth, and eighth subjects to one treatment and the first, second, seventh, ninth, and tenth to the other. If the block size was less than ten we would ignore digits bigger than the block size. To allocate further subjects to treatment, we carry on along the same row, choosing the next five unique digits for the first treatment. In randomised controlled trials it is advisable to change the block size from time to time to make it more difficult to guess what the next treatment is going to be.

It is important to realise that patients in a randomised trial are not a random sample from the population of people with the disease in question but rather a highly selected set of eligible and willing patients. However, randomisation ensures that in the long run any differences in outcome in the two treatment groups are due solely to differences in treatment.

Variation between samples

Even if we ensure that every member of a population has a known, and usually an equal, chance of being included in a sample, it does not follow that a series of samples drawn from one population and fulfilling this criterion will be identical. They will show chance variations from one to another, and the variation may be slight or considerable. For example, a series of samples of the body temperature of healthy people would show very little variation from one to another, but the variation between samples of the systolic blood pressure would be considerable. Thus the variation between samples depends partly on the amount of variation in the population from which they are drawn.

Furthermore, it is a matter of common observation that a small sample is a much less certain guide to the population from which it was drawn than a large sample. In other words, the more members of a population that are included in a sample the more chance will that sample have of accurately representing the population, provided a random process is used to construct the sample. A consequence of this is that, if two or more samples are drawn from a population, the larger they are the more likely they are to resemble each other - again provided that the random technique is followed. Thus the variation between samples depends partly also on the size of the sample. Usually, however, we are not in a position to take a random sample; our sample is simply those subjects available for study. This is a "convenience" sample. For valid generalisations to be made we would like to assert that our sample is in some way representative of the population as a whole and for this reason the first stage in a report is to describe the sample, say by age, sex, and disease status, so that other readers can decide if it is representative of the type of patients they encounter.

Standard error of the mean

If we draw a series of samples and calculate the mean of the observations in each, we have a series of means. These means generally conform to a Normal distribution, and they often do so even if the observations from which they were obtained do not (see Exercise 3.3). This can be proven mathematically and is known as the "Central Limit Theorem". The series of means, like the series of observations in each sample, has a standard deviation. The standard error of the mean of one sample is an estimate of the standard deviation that would be obtained from the means of a large number of samples drawn from that population.

A general practitioner in Yorkshire has a practice which includes part of a town with a large printing works and some of the adjacent sheep farming country. With her patients' informed consent she has been investigating whether the diastolic blood pressure of men aged 20-44 differs between the printers and the farm workers. For this purpose she has obtained a random sample of 72 printers and 48 farm workers and calculated the mean and standard deviations, as shown in Table 3.1.

To calculate the standard errors of the two mean blood pressures the standard deviation of each sample is divided by the square root of the number of the observations in the sample.

These standard errors may be used to study the significance of the difference between the two means, as described in successive chapters

Standard error of a proportion or a percentage

Just as we can calculate a standard error associated with a mean so we can also calculate a standard error associated with a percentage or a proportion. Here the size of the sample will affect the size of the standard error but the amount of variation is determined by the value of the percentage or proportion in the population itself, and so we do not need an estimate of the standard deviation. For example, a senior surgical registrar in a large hospital is investigating acute appendicitis in people aged 65 and over. As a preliminary study he examines the hospital case notes over the previous 10 years and finds that of 120 patients in this age group with a diagnosis confirmed at operation 73 (60.8%) were women and 47 (39.2%) were men.

If p represents one percentage, 100 p represents the other. Then the standard error of each of these percentages is obtained by (1) multiplying them together, (2) dividing the product by the number in the sample, and (3) taking the square root:

which for the appendicitis data given above is as follows:

Problems with non-random samples

In general we do not have the luxury of a random sample; we have to make do with what is available, a " convenience sample ". In order to be able to make generalisations we should investigate whether biases could have crept in, which mean that the patients available are not typical. Common biases are:

hospital patients are not the same as ones seen in the community;

volunteers are not typical of non-volunteers;

patients who return questionnaires are different from those who do not.

In order to persuade the reader that the patients included are typical it is important to give as much detail as possible at the beginning of a report of the selection process and some demographic data such as age, sex, social class and response rate.

Common questions

Given measurements on a sample, what is the difference between a standard deviation and a standard error?

A standard deviation is a sample estimate of the population parameter; that is, it is an estimate of the variability of the observations. Since the population is unique, it has a unique standard deviation, which may be large or small depending on how variable the observations are. We would not expect the sample standard deviation to get smaller because the sample gets larger. However, a large sample would provide a more precise estimate of the population standard deviation than a small sample.

A standard error, on the other hand, is a measure of precision of an estimate of a population parameter. A standard error is always attached to a parameter, and one can have standard errors of any estimate, such as mean, median, fifth centile, even the standard error of the standard deviation. Since one would expect the precision of the estimate to increase with the sample size, the standard error of an estimate will decrease as the sample size increases.

When should I use a standard deviation to describe data and when should I use a standard error?

It is a common mistake to try and use the standard error to describe data. Usually it is done because the standard error is smaller, and so the study appears more precise. If the purpose is to describe the data (for example so that one can see if the patients are typical) and if the data are plausibly Normal, then one should use the standard deviation (mnemonic D for Description and D for Deviation). If the purpose is to describe the outcome of a study, for example to estimate the prevalence of a disease, or the mean height of a group, then one should use a standard error (or, better, a confidence interval; see Chapter 4) (mnemonic E for Estimate and E for Error).

References

1. Altman DG. Practical Statistics for Medical Research.London: Chapman & Hall, 1991

2. Armitage P, Berry G. Statistical Methods in Medical Research.Oxford: Blackwell Scientific Publications, 1994.

3. Campbell MJ, Machin D. Medical Statistics: A Commonsense Approach.2nd ed. Chichester: John Wiley, 1993.

4. Fisher RA, Yates F. Statistical Tables for Biological, Agricultural and Medical Research,6th ed. London: Longman, 1974.

5. Strike PW. Measurement and control. Statistical Methods in Laboratory Medicine.Oxford: Butterworth-Heinemann, 1991:255.

Exercises

Exercise 3.1

The mean urinary lead concentration in 140 children was 2.18 mol/24 h, with standard deviation 0.87. What is the standard error of the mean?

Exercise 3.2

In Table F (Appendix), what is the distribution of the digits, and what are the mean and standard deviation?

Exercise 3.3

For the first column of five digits in Table F take the mean value of the five digits and do this for all rows of five digits in the column.

What would you expect a histogram of the means to look like?

What would you expect the mean and standard deviation to be?

# data[].attributes.attachment_link.description
Populations In statistics the term "population" has a slightly different meaning from the one given to it in ordinary speech. It need not refer only to people or to animate creatures - the population of Britain, for instance or the dog population of London. Statisticians also speak of a population

# data[].attributes.body
Population data means information about how many people live in a place in their characteristics

https://www.questionpro.com/blog/population-data/#:~:text=Population%20data%20is%20defined%20as,this%20as%20the%20natural%20population.

# data[].attributes.attachment_link.readable_text
A population is a fundamental aspect of our existence. Population data is defined as a set of individuals who share a characteristic or set of these. A population is mainly determined by geographies, such as all people in California, or all people in the United States. Demographers (people who study human populations) categorize this as the natural population. A collection of any living beings is considered a population, but we will focus only on human populations in this blog.
Select your respondents
Geography is one of the many ways in which the population is defined and analyzed. The era, political inclinations, religious beliefs, or physical characteristics are ways of dividing people into different communities. The study of populations is achieved by examining these diverse populations and observing where they coincide. For example, suppose you know the population of Americans who are Republicans and see the population that lives in Texas. In that case, you can study where those populations are intertwined and learn something about Republicans and Texans.

Why is accurate population data necessary?

Critical decisions for a nation, organization, or family are made based on population data. Population data contains various influential details such as birth, death, demographic information such as age, sex, annual income, occupation, language, etc. The overall socio-economic, economic, political, cultural progress of a country is dependent on population data to a large extent.

Answers to questions such as "How many of us are there in the country?", "On what basis are we divided?" "Do we possess enough food, land, and other such resources?" are obtained by evaluating population data.

Characteristics of population data

The amount of people in the population is not all that can be known about these. There are also data such as:

Age: The age of a population can tell us a lot about what that population is doing and what it is going to do in the future.

Location: Finding out where people live is one of the main reasons why various countries conduct their census. Many government programs also base their funds on demographic patterns . The location data also inform us about the movement of people.

Socio-economic Data: They help us know the type of concentrations of people in some urban regions or the high concentrations of people with cancer near certain industrial zones.

Race: The demographic study of the breed is very controversial. Scientifically, there are no different "races" of human beings. The difference between Asians and blacks is the same as the difference between people with brown eyes and blue eyes. However, the idea of race continues to play an essential role in our societies. Many of us identify ourselves as part of a certain race for cultural reasons.

Human population data classification and estimation

There are two primary classifications of population data:

Primary population data collection sources: Data collected directly by a researcher or statistician or a government body via sources such as census, sample survey, etc. are called primary population data collection.

Secondary Population Data Collection Sources: Data obtained from existing sources such as journals, newspapers, magazines, annual research reports, etc. and not directly by a government or a research organization is called secondary population data collection.

The below-mentioned resources are the most used for human population data classification.

Census: The simplest, yet not the most accurate or useful way to evaluate population is counting everyone. This is known as a census and is usually done by governments. In the past, religious organizations carried out censuses, but generally at a local or regional level. The Roman Empire carried out censuses to estimate the group of men of military age and for tax purposes, but these were limited since the Romans had to report with the government officials in their hometown to be counted. Poor people or those who could not travel were rarely counted.

A census is sometimes referred to as a complete enumeration. Each person is counted by personal interviews, surveys, or any other type of interview. There are no estimates.

Even a complete census has limits. In countries with very remote areas, it may be impossible for census takers to count everyone.

There are two ways of conducting census:

De facto method: When the census is conducted at an individual's current residence, it is known as the de facto method. Generally, this census is carried out at night, and thus, it is also known as 'one- night enumeration.' It is conducted in urban regions in a country with high income.

De jure method: When the census is conducted at a person's permanent residence, it is known as the de jure method. Compared to de facto, it is more practical and scientific and is also called 'period enumeration.' Nepal is one of the very few countries which follow this method.

Census has a list of the following attributes:

Geographic segmentation attributes include current residence, permanent residence, place of birth, workplace information, etc.

Personal and demographic analysis details such as age, sex, marital status, literacy, language spoken at home, the number of people residing at home, etc.

Information on an individual's economic background, such as occupation, the current status of employment, primary source of income, etc.

Sample surveys: An alternative to a full enumeration census is a sampling. You might be familiar with this as the method that market research companies and political analysts use to conduct their research. Statisticians use a mathematical formula to know the minimum number of people needed to constitute a population's representative sample. For example, if the total population is 1,000 people, researchers could directly survey 150 of them. Then, they can take the data from the sample and extrapolate it to the entire population. If 10% of the sample people are left-handed, it can be assumed that 100 of a population of 1,000 are left-handed.

Sampling can yield more accurate results than full enumeration, but there are some caveats. All samples have a margin of error because of the possibility that samples differ from the total population.

This is expressed in terms of variation of error percentage, such as +/- 4%. The larger the sample size, the smaller the margin of error. Besides, samples must be chosen in the most unexpected way possible. This can be more difficult than it sounds.

Let's say you want to survey a sample of all people in Chicago. A method used in the past was to select random names from the phone book. However, this eliminates the possibility of certain classes of people being selected for the sample: low-income people who do not have a telephone.

Administrative records: The collection of population data from places that do not carry out censuses or historical periods where censuses were not common is achieved by gathering all available demographic information in administrative records. There could be partial censuses, data from the local population, or information collected by religious or civic groups. Examining birth and death records provides other clues.

LEARN MORE: Population vs Sample

Importance of population data

Collecting and analyzing population data is integral as there is constant change in each passing day, month, and year. Here are three main reasons why population data is essential:

Collect data on population growth and decline:

The human population has increased practically non-stop throughout history. In 1,000 BC, there were between 1 and 10 million human beings. That number rose to 50 million in 1,000 BC. In 600 AD, the world population had reached 200 million, and at the beginning of the 20th century, 1,500 million human beings lived on the planet.

Our population seems to increase with more incredible speed as the centuries pass. The main reason for this is simple: every increase in population creates more people able to reproduce. The population grows exponentially.

According to the Malthus Growth Model, if a million individuals have enough children to double the population (considering mortality rates), then the next generation will be twice in number than what we are today. Doubling people gives rise to four million people.

Understand the problems that arise due to population increase:

As the population grows, it is put under pressure. This pressure may come from a lack of resources to feed, house, and provide services, an illness; a war; or lack of space. The pressure can be relieved with migration. Wars, diseases, and famine also relieve workplace stress as they kill part of the population.

Malthus's theory is known as" The Population Explosion" (The Population Bomb), and gained popularity with the environmental movement in the 70s fears of global overpopulation are based on several factors:

We will not be able to produce enough food to feed everyone.

There is not enough space for everyone to live in.

Humans harm the environment. Too many humans will practically destroy the ecosystem, further reducing our ability to produce food.

We can not provide the social infrastructure to care for all people.

Our vulnerability to these factors is based on population density; the number of people per unit area. Since the Industrial Revolution, urbanization has caused a massive increase in population density in cities.

The highest population density may have occurred in the walled city of Kowloon in Hong Kong. About 50,000 people lived in a mega block that averages about 150 by 200 meters. The practically anarchic district was evacuated and demolished to build a park. Nowadays, the areas of the most significant demographic density are found in the main urban areas. India and China have large areas of high population density.

As population density increases in a given area, it approaches what is known as carrying capacity. This is the maximum number of people an area can support in terms of available resources.

For animals, this is easy to calculate. For example, a goat might need 50 square yards of grass to survive. Therefore, an area of 200 yards can load four goats. Estimating the carrying capacity for humans is much more complicated. We can use technology to optimize our production of resources. We can transport resources from other areas. We can create sanitation systems and other infrastructures to support a higher density.

Control of the population

What happens when we reach the load capacity in an area? There are several options:

People move to another area.

People are less healthy, therefore, less able to reproduce.

The pressure of the population leads to war.

Unsanitary conditions and proximity cause outbreaks of disease.

We optimize the generation of resources and infrastructure, increasing the load capacity.

Humans are also able to control their populations voluntarily. This can occur on a large scale, such as a program or government law or individual level. People have had greater access to birth control since the 1960s.

Governments, for example, the Chinese government, controlled the increase in population by imposing penalties for having too many children. This way, having fewer children seems more convenient, which leads to more people sterilizing themselves. Unfortunately, some governments have adopted genocide, i.e., have tried to reduce or eliminate specific populations that they consider undesirable by killing them in masses.

# data[].attributes.attachment_link.title
Population Data: Definition, Classification, Estimation and Importance | QuestionPro

# data[].attributes.attachment_link.description
Population data refers to a set of individuals that share a characteristic or a set of these. Learn why accurate population data is essential in research.

# data[].attributes.body
A description of the empirical data used and the methods applied in revising past estimates of population and components of demographic change (fertility, child, adult and overall mortality, international migration) is available here for each country or area for the period 1950 to 2023. For the countries with less than 1,000 inhabitants in 2023, only the data sources for total population are made available.

# data[].attributes.attachment_link.readable_text
A description of the empirical data used and the methods applied in revising past estimates of population and components of demographic change (fertility, child, adult and overall mortality, international migration) is available here for each country or area for the period 1950 to 2023. For the countries with less than 1,000 inhabitants in 2023, only the data sources for total population are made available.

Select below a country or area to see the respective information, or download the whole set of metadata in PDF format for all countries or areas or a tabular version for each demographic component under Documentation.

# data[].attributes.attachment_link.description
A description of the empirical data used and the methods applied in revising past estimates of population and components of demographic change (fertility, child, adult and overall mortality, international migration) is available here for each country or area for the period 1950 to 2023. For the countries with less than 1,000 inhabitants in 2023, only the data sources for total population are made available.

# data[].attributes.body
A population is a fundamental aspect of our existence. Population data is defined as a set of individuals who share a characteristic or set of these. A population is mainly determined by geographies, such as all people in California, or all people in the United States. Demographers (people who study human populations) categorize this as the natural population. A collection of any living beings is considered a population, but we will focus only on human populations in this blog.