BiostatisticsTier 1Medical Sciences concept

Statistical test selection (chi-squared, Fisher's exact, t-test, Mann-Whitney)

Core concept

Test choice depends on two questions: (1) what type is the outcome variable (categorical vs continuous), (2) is continuous data normally distributed (parametric) or not (non-parametric), and (3) are groups paired or independent
Categorical outcome, independent groups -> chi-squared test (expected cell counts adequate) or Fisher's exact test (small samples/expected cell count <5)
Continuous outcome, independent groups, normal distribution -> t-test (2 groups) or ANOVA (>2 groups); not normally distributed -> Mann-Whitney U (2 groups) or Kruskal-Wallis (>2 groups)

Data type	Parametric (normal)	Non-parametric
2 independent groups, continuous	t-test	Mann-Whitney U
>2 independent groups, continuous	ANOVA	Kruskal-Wallis
Paired/matched, continuous	Paired t-test	Wilcoxon signed-rank
Categorical, independent	Chi-squared	Fisher's exact (small n/low expected counts)
Correlation, continuous	Pearson's	Spearman's rank
Time-to-event	-	Log-rank test / Cox regression

Fisher's exact, not chi-squared, when any expected cell count <5 -- chi-squared becomes unreliable with sparse data; this substitution is a common exam trap
Trap: applying a t-test to obviously skewed data (e.g. length of stay, biomarker levels with outliers) -- check/assume non-normality and use the non-parametric equivalent
Paired vs independent matters as much as data type: the same patients measured before/after needs a paired test (paired t-test/Wilcoxon), not the independent-groups version

Non-parametric tests are also the fallback for ordinal data (e.g. pain scores, Likert scales) even when the underlying distribution isn't strictly assessed
Choice of test determines what summary statistic is reported: mean/SD for parametric, median/IQR for non-parametric -- a table reporting median and IQR is a clue the authors used non-parametric methods
Log-rank test compares whole survival curves, and pairs directly with the Kaplan-Meier note

3 more sections, plus exam facts

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