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Reference

Sampling Methods

Concept

Bias in a Sample

A bias in a sample is an error in sampling that results in misrepresentation of members of a population. It occurs when members of a population that are representing certain characteristics are more likely to be selected in a sample than others.

Definition
Unbiased Sample A sample that is representative of the population. Conclusions drawn on this sample can be generalized to the whole population.
Biased Sample A sample that overrepresents or underrepresents a certain part of the population. The inferences drawn based on this sample may be invalid.

The chosen sampling method may either introduce or minimize a bias in a sample. The following real-life scenarios present examples biased samples.

Biased Sample Explanation
A city council asks residents whether to have an off-leash area for dogs in a park. A hundred dog owners are surveyed at the park. The only people asked are dog owners. This means that respondents are more likely to have a strong opinion about the off-leash area for their dogs.
To asses experiences of customers who do the shopping online, a company e-mails purchasers with a link to a survey. Because this sample is self-selected, only those who are very satisfied or dissatisfied with the work of the company are likely to respond.
Every sixth boxer at a boxing camp is asked to name their favorite brand of boxing gloves. Not all boxers go to a boxing camp, as camps are usually sponsored by a brand and take place in a single city. Also, professional boxers organize their own private camps with hired sparring partners.

Concept

Simple Random Sample

In a simple random sample, each member of a population is equally likely to be selected as part of the sample. Consider the following example.
The researcher then puts all pieces of paper in a bag and draws four of them. Simple random samples can be generated as in the applet.
Generate a random sample
To generate a simple random sample, each member of a population can be assigned a unique ID, for example a whole number. Then, a random number generator can be used to generate IDs until the desired sample size is satisfied.

Extra

Biased or Unbiased Sampling

A simple random sample is an unbiased sample since it involves selecting members from a population randomly. This guarantees that each member of the population has an equal chance of being included in the sample. This type of sample is usually representative because it tends to have the same characteristics as the population.

Concept

Systematic Sample

In a systematic sample, the members of a population are ordered randomly or in a random-like way. The sample and its size are predetermined and selected among the members in a specified interval. The intervals are determined by dividing the population size by the sample size. Consider an example.
A sample of people is selected from a population of people using systematic sampling.
A systematic sample is often used when a complete list of the population is available. Different samples can be created by varying the starting point when using systematic sampling. This allows the ability to check if the conclusions hold across the samples.

Extra

Biased or Unbiased Sampling

Systematic samples can be either biased or unbiased.

  • If the initial order is biased, the sample will be biased. For example, if the population is arranged in a cyclical pattern that matches the sampling interval, it can lead to a group being preferred over other groups, which leads to bias in the sample.
  • On the other hand, if the members of the population are ordered randomly without a cyclic pattern, it is expected that the systematic sampling will be unbiased.

It is important to remember that unbiased samples are better suited to generate a representative sample.

Concept

Self-Selected Sample

In a self-selected sample, the members of the sample are the people who are willing to participate. Since people participate voluntarily in these samples, the samples are also called voluntary response samples. Consider an example.
The following applet shows a number of people volunteering to participate.
choose self-selected sample

Extra

Biased or Unbiased Sampling

A self-selected sample is a biased sample because people with strong opinions, either positive or negative, about the topic studied are more likely to volunteer. Also, people who are interested in the topic studied may be more likely to participate, while those who are not interested may refuse to participate.

As a result, such a sample is not representative of the population because it underrepresents people with neutral opinions about the topic or not interested in it.

Concept

Convenience Sample

In a convenience sample, members of a population are selected to be in a sample based on convenience or their availability to the researchers. Consider an example.
This is an example of convenience sampling because the researcher is selecting wolfs who are conveniently available and in close proximity.

This type of sampling is often used when the researchers have limited resources or are under certain time constraints.

Extra

Biased or Unbiased Sampling

Convenience sampling can lead to a biased sample since the researchers choose sample members that are easily available to them. Therefore, some groups of people in the population may not be represented in the sample because they are not easily accessible, causing the sample to not be representative of the population.

Concept

Stratified Sample

In a stratified sampling, members from a population are divided into subgroups. These subgroups can be formed depending on the factors like age, education, or health status. Then members of the sample are randomly selected from each subgroup. Consider an example.

  • A researcher wants to conduct a study about elementary students' achievement in a one of the school districts. The researcher could randomly select students from each grade to be in the sample.
Stratified sampling can be conducted as follows.
Different samples can be generated by randomly selecting people from each subgroups of the population.

Extra

Biased or Unbiased Sampling

The stratified sampling guarantees that each subgroup of a population is represented in the sample which means that the stratified sample is a representative sample. Therefore, the stratified sample might be considered as an unbiased sample.

Concept

Cluster Sample

For a cluster sample, a population is first divided into smaller groups, called clusters, with similar characteristics to the whole population and then one or more clusters are randomly selected. All members in the selected clusters form the sample. A member of the population cannot be included in more than one cluster. Consider an example.

  • A group of researchers conduct a study to examine the basic mathematical skills of all the eight-graders in a city. Considering the schools in the city as clusters, the researchers select one or more schools to collect data.
Cluster sampling can be conducted as follows.
Cluster sampling is particularly useful for widely geographically spread populations where simple random sampling is difficult to apply. Note that already existing groups such as cities and schools can be used as clusters.

Extra

Biased or Unbiased Sampling

This method is prone to a bias. When the clusters do not represent the characteristics of a population, the conclusions about the entire population would be biased as well.