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Choosing between t-tests
Haemoglobin is measured in the same 40 women before and again after three months of iron supplementation. Which test compares the two sets of readings, and why?
- A. Unpaired t-test, because there are two sets of readings
- B. Chi-square test, because the outcome is anaemia
- C. Analysis of variance, because there are two time points
- correctD. Paired t-test, because each woman provides both readings
Explanation
Key fact
Ask whether each observation in one group is tied to a specific observation in the other. If it is, the test must be paired.
Paired t-test. Each woman is her own control, so the analysis works on the difference within each pair.
Why
The two readings come from the same 40 women, not from two groups of women.
Each woman's own baseline removes between-person variation.
The test therefore analyses 40 differences, not 80 independent values.
That gives more power for the same sample size.
Treating them as unpaired throws away the pairing and understates the effect.
Paired or unpaired: one question decides it
Why not the others
- A. Unpaired t-test, because there are two sets of readings — would be right if the two sets came from different women. Here they do not.
- B. Chi-square test, because the outcome is anaemia — applies to proportions. The outcome measured here is haemoglobin, a continuous variable.
- C. Analysis of variance, because there are two time points — is for comparing three or more means. With two it reduces to the t-test anyway.
Remember
Same people twice: paired. Different people once: unpaired.
Go deeper
If the data are skewed or the sample small, the non-parametric equivalents are the Wilcoxon signed-rank test for paired data and the Mann-Whitney test for unpaired.
The chi-square, sign, Fisher exact and Mann-Whitney tests are all non-parametric; the Student t-test is not, which is a favourite examination distinction.
Fisher exact test replaces chi-square when any expected cell count falls below five.
Park K. Park's Textbook of Preventive and Social Medicine, 28th ed. (Bhanot, 2025).