
**Context**: Let's say we have a neurologist from Hospital X who wants to investigate the relationship between cancer and stroke risk in the general population with a case-control study. The cases are all the neurologist's patients with a history of strokes. The control group consists of all her patients without a stroke history. Both groups were assessed for cancer. 

**How it Relates to Selection Bias**: Patients in the hospital may be more predisposed to those conditions or may have been brought to the hospital for those conditions. Therefore, they may be overrepresented in the study compared to the general population.

Example: Selection Bias in Case-Control Studies

Take Tobacco case as an example, the number of cancer patients admitted to hospital is by no means representative of the entire population, or even of smokers.

Another example of selection bias in Case-control Studies


- The COVID-19 testings tend to focus on already hospitalized people, not accounting for the people with mild symptoms and the asymptomatics leading to selection bias.  
- The differences in death rates across countries may not be attributed to clinical, demographic, and environmental factors.  
- Together with random sampling/testing, the Bayesian Network model allows causal explanations from data for better predictions.  


Summary of "COVID-19 infection and death rates: the need to incorporate causal explanations for the data and avoid bias in testing"

Non-response bias is a specific form of sampling bias that occurs when individuals who choose not to participate in a survey differ systematically from those who do complete it. Even when a study employs careful random sampling, this bias can skew results and lead to inaccurate conclusions because the final respondents no longer accurately represent the original intended sample.

Non-response Bias

The 1936 Literary Digest straw poll was a survey conducted to predict the outcome of the presidential election between Alf Landon and Franklin Roosevelt. The magazine attempted to forecast the results by sending ballots, which were also subscription requests, to millions of Americans. Based on this method, the editors incorrectly predicted that Landon would win in a landslide.

1936 Literary Digest Straw Poll

What type of systematic error occurs when the method used to select participants results in a sample that fails to accurately represent the broader target population?

Sampling bias is a systematic error that occurs when the method used to select participants results in a sample that fails to accurately represent the broader target population. Because the selected individuals differ in important ways from the overall group, any statistical findings derived from this unrepresentative sample will likely be inaccurate and cannot be safely generalized.

University of Michigan - Ann Arbor

Google

- Recall bias
- Selection bias
- Collider bias
- Omitted variable bias

Types of Bias

Depending on the study and hypothesis, a cohort study is not the best design that can be used. However, the biases included in this list can be avoided with good experimental design.

 - Expensive to conduct 
 - Prospective cohort study is often time-consuming
 - Inefficient for rare outcomes 
 - Selection bias 
 - Recall bias

Weaknesses of Cohort Studies

In research, the sample is studied with the goal of generalizing the results to the broader population from which the sample was drawn. This process allows researchers to make inferences about a large group based on data collected from a smaller, representative subset. The relationship is visually comparable to extracting a small representative group from a vast crowd.

Relationship Between Sample and Population

A sample is a smaller subset of individuals selected from a larger population of interest. Because it is usually impossible to study every member of a population, researchers measure variables within a sample with the intention of generalizing their findings back to the broader group, ideally using a representative sample that closely resembles the population.

Sample

Catalogue of Bias Collaboration, Nunan D, Bankhead C, Aronson JK. Selection bias. Catalogue Of Bias 2017: [www.catalogofbias.org/biases/selection-bias/](https://www.catalogofbias.org/biases/selection-bias/) 

Catalog of Bias

https://kpu.pressbooks.pub/psychmethods4e/

KPU Research Methods in Psychology - 4th American Edition

Recall bias is a error that occurs when participants do not remember previous events or experiences accurately or omit details: the accuracy and volume of memories may be influenced by subsequent events and experiences.

Recall Bias

When a single node is caused by two other nodes we encounter something called "collider-bias" where one condition explains-away another. 

Since A and C both effect the outcome of B, by conditioning on B, A and C become **dependent**.

$A \rightarrow B \leftarrow C$: The Collider

This type of bias is also known as "Confounded." It happens when good controls or confounders are not included in the regression model.

Omitted variable bias

Sampling Bias

Time consumption is an issue in prospective cohort studies as the investigator must reach out to the participants over a time frame whereas in retrospective studies, the information is already recorded. If the follow-up period is extremely long for a study, this could result in a series of issues. 
 - The study participants may outlive the investigator.
 - Non-response bias - Participants may begin to leave the study or may not be contactable; Participants who left the study may have different outcomes than those who stayed, resulting in a loss of data

Weakness of Time Frame in Prospective Cohort Studies

Rare outcomes would require an incredibly large study population. They can also have a long latency period, which could result in having a  follow-up period, which introduces its own problems. 

Weakness of Cohort Studies with Rare Outcomes

Having a larger sample size boosts the generalizability of the study to the population.

Increasing Generalizability of the Sample

For a hypothetical experiment involving algebra students, the population of interest must first be defined. A broad population, such as 'all algebra students,' is often too large for a study. Therefore, it is narrowed to a more specific and manageable group, like 'all algebra students in a particular city.' To ensure the sample is representative, it should include students from diverse backgrounds, encompassing various income levels, family situations, races, ethnicities, religions, and geographic locations. From this more focused population, a random sample, for instance of 200 students, can be selected for the experiment.

Example of Defining a Population and Sample for Research

A team of researchers wants to determine the average screen time of all high school students in a large country. They conduct a detailed survey with 1,000 students from a single, affluent suburban high school known for its technology-rich classrooms. What is the most significant methodological challenge the researchers face when trying to draw a conclusion about the entire country's high school student population from their data?

A team of researchers wants to understand the typical sleep habits of all adults in a country of 50 million people. Since they cannot survey every individual, which of the following approaches would be the most practical and scientifically sound first step for their investigation?

A random sample is a subset of a larger population in which every member of the population has an equal chance of being selected. This method is often preferred for selecting experimental participants because, provided the sample is large enough, it provides reasonable assurance that the participating individuals are representative of the broader population.

Random Sample

To illustrate how a sample is used, a researcher might measure the talkativeness of a few hundred university students. This subset serves as the sample, which the researcher studies with the intention of drawing conclusions about the talkativeness of a much larger population, such as men and women in general.

Example of a Sample: Talkativeness Study

A representative sample is a study sample that is similar to the broader population in important respects. It is crucial for researchers to obtain a representative sample so they can appropriately generalize their findings from the small subset of participants to the entire population of interest.

Representative Sample

Inferential statistics are a set of mathematical techniques used by researchers to determine whether a statistical result or relationship observed in a study's sample reflects something that is genuinely true of the broader population.

Inferential Statistics

Probability sampling is a broad category of sampling methods where the researcher can mathematically specify the exact probability that each member of the defined population will be selected for the sample. Because it enables researchers to make highly accurate estimates about a population, it is the favored approach in survey research, though it requires a clear and precise specification of the target population before sampling begins.

Probability Sampling

Non-probability sampling encompasses methods where the researcher cannot mathematically specify the probability that any given member of the target population will be selected for the sample. Because it does not rely on structured random selection from a clearly defined population, it is the most common approach used in general psychological research, even though it limits the ability to make perfectly representative population estimates.

Non-probability Sampling

The optimal sample size for a survey generally depends on two primary factors: the researcher's desired level of statistical confidence and the practical constraints of the study's budget. While larger samples yield statistics that are closer to the true population value and provide greater confidence, they also require more time, effort, and money to collect. Researchers frequently use power analyses to balance these theoretical and practical considerations.

Determinants of Survey Sample Size

Convenience sampling is a common form of non-probability sampling where researchers study individuals who happen to be physically nearby and are readily willing to participate, such as college students in an introductory psychology course. While this approach is frequently used in psychological research due to its accessibility and efficiency, its main disadvantage is that the resulting sample may not accurately represent the broader population, severely limiting the ability to generalize the findings.

Convenience Sampling

A survey non-responder is an individual selected for a survey sample who fails to complete the questionnaire. This lack of participation can occur for various reasons, including moving away, being too busy, lacking interest in the topic, or refusing to participate on principle.

Survey Non-responder

Simple random sampling is a method for obtaining a study sample where every single member of the target population has an equal chance of being selected. While this approach is effective for ensuring a representative sample, it is often difficult or impossible to achieve in psychological research because populations are rarely defined clearly enough to give everyone an equal selection chance.

Simple Random Sampling

Measures of central tendency are descriptive statistics used to describe the typical, average, or center scores within a distribution. Common examples of these measures include the mean, median, and mode.

Measures of Central Tendency

To conduct a study, researchers typically select a smaller subset of individuals from a broader group of interest. This smaller subset is referred to as a ____.

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