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.

University of Michigan - Ann Arbor

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.

Sampling Bias

Pearl, J., & Mackenzie, D. (2018). $\mathit{The \ Book \ of \ Why: \ The \ New \ Science \ of \ Cause \ and \ Effect.}$ Basic Books.

The Book of Why


**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

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?

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