Retrospective Study — Definition, Formula & Examples
A retrospective study is an observational study that looks backward in time: researchers start with outcomes that have already happened and dig through past records or memories to see which earlier factors went along with them.
A retrospective study is an observational study in which data on the explanatory variable(s) are collected from events that occurred before the study began, typically through existing records or subject recall. Researchers impose no treatments, and subjects are often selected based on their value of the response variable. A study that instead follows subjects forward to record future outcomes is called prospective.
Worked Example
Problem: Researchers review hospital records for 400 adults. Of these, 100 have lung disease and 300 do not. The records show that 60 of the patients with lung disease smoked, and 90 of the patients without lung disease smoked. Explain why this is a retrospective study, compare the smoking rates, and state what you can conclude.
Step 1: Identify the design. The researchers chose subjects by their outcome (lung disease or not) and then looked back at past smoking behavior in existing records. No treatment was assigned. That makes it a retrospective observational study.
Step 2: Find the proportion of smokers among patients with lung disease.
Step 3: Find the proportion of smokers among patients without lung disease.
Answer: Smoking was twice as common among patients with lung disease (0.60 vs. 0.30). This shows an association between smoking and lung disease. Because the study is observational, with no random assignment, it cannot by itself prove that smoking causes lung disease. Confounding variables, such as workplace exposure, could explain part of the difference.
Why It Matters
AP Statistics free-response questions often ask you to name a study's type and explain why it does or does not support a cause-and-effect conclusion. In epidemiology, retrospective case-control studies are the standard first tool for rare diseases. Waiting for enough new cases to appear in a forward-looking study could take decades.
Common Mistakes
Mistake: Concluding that the explanatory variable causes the outcome because the difference between groups is large.
Correction: A retrospective study is observational, so it shows association only. Past records can also be incomplete, and people may not remember past events accurately. Only a randomized experiment can justify a causal claim.