Table 5.

Common statistical tests

Test	Description	Assumptions
Descriptive statistics	Measures of center [mean (arithmetic average) and median (value in the middle)] and variability (standard deviation, mean, or median absolute deviation and IQR)	May need to be normalized; standard deviation for single measurements, IQR for data not normally distributed
One-sample comparisons	Used to evaluate a single-group one-sample t-test (parametric) and one-sample χ2-test for variances	Variables continuous, data independent, randomly selected; and normally distributed; no outliers
Two-group comparisons t-test	Used to evaluate two groups:	All; no outliers
	•Paired t-test (Wilcoxon signed-rank test is the nonparametric version)•Unpaired t-test (Mann-Whitney U-test is the non-parametric version)	•Parametric; dependent variable is continuous; subjects paired or dependent; data normally distributed or sample size large enough that central limit theorem is satisfied; homogeneity of variance; if unequal variation, log transform or use Wilcoxon signed-rank test
		•Parametric; dependent variable is continuous; independent variable is categorical; dependent variable normally distributed (or sample size large enough that central limit theorem is satisfied) and randomly selected; observations are independent
Chi-square test	•Association: determines whether the observed distribution differs from chance	Nonparametric; variables are independent; relatively large sample size (minimum expected n >5 for each group; if n < 50 for 2 × 2 table, use Fisher’s exact test)
	•Goodness of fit: determines whether an observed distribution differs from known distribution.
Kaplan-Meier	Time to an event (e.g., survival) analysis; can accommodate censored data; nonparametric log-rank test used to compare distributions	Data independent; time intervals uniform and clearly defined; censoring similar between groups
Regression	Predicts the value of one variable from a predictor (univariate) or ≥2 predictors (multivariate)	Variables are multivariate; little or no multicollinearity; limited autocorrelation; homogeneity of variance
	•Linear regression: correlation coefficients
	•Deming regression: line of best fit for a two-dimensional data set
	•Logistic regression: odds ratio (with 95% confidence intervals)
Bland-Altman plot	Analyzes agreement between two different assays	Data independent, randomly selected; and normally distributed
≥3-group comparison analysis of variance	Test for differences of means among groups	Continuous dependent variable; categorical independent variable; independent observations; data randomly sampled; dependent variables are normally distributed or sample size large enough that the Central Limit Theorem is satisfied (use log or arcsin transformation for data not normally distributed); homogeneity of variance; no outliers
	•One-way: 1 variable examined
	Multiway; ≥2 variables examined
	•Repeated measures: over time, dose range
	•Nonparametric: Kruskal-Wallis and Friedman
	Post tests evaluate which groups are different. The following are examples.
	•Parametric: Bonferroni, Duncan, Dunnett, False discovery rate, Student-Newman-Keuls, Fisher least significant difference, Sidak, Holm-Sidak, and Tukey
	•Nonparametric: Dunns

IQR, interquartile range.