Comparing means

The following tables provide guidance to the selection of the proper parametric or non-parametric statistical tests for a given data set.

Is there a difference ?

Ordinal and numerical measures

1 group		N ≥ 30		One-sample t-test
		N < 30	Normally distributed	One-sample t-test
			Not normal	Sign test
2 groups	Independent	N ≥ 30		t-test
		N < 30	Normally distributed	t-test
			Not normal	Mann–Whitney U or Wilcoxon signed-rank test
	Paired	N ≥ 30		paired t-test
		N < 30	Normally distributed	paired t-test
			Not normal	Wilcoxon signed-rank test
3 or more groups	Independent	Normally distributed	1 factor	One way anova
			≥ 2 factors	two or other anova
		Not normal		Kruskal–Wallis one-way analysis of variance by ranks
	Dependent	Normally distributed		Repeated measures anova
		Not normal		Friedman two-way analysis of variance by ranks

Nominal measures

1 group		np and n(1-p) ≥ 5	z-approximation
		np or n(1-p) < 5	binomial
2 groups	Independent	np < 5	fisher exact test
		np ≥ 5	chi-square test
	Paired		McNemar or Kappa
3 or more groups	Independent	np < 5	collapse categories for chi-square test
		np ≥ 5	chi-square test
	Dependent		Cochran´s Q

See also

• Statistical hypothesis testing
• Parametric statistics
• Non-parametric statistics

Sources

• Dawson-Saunders, Beth; Trapp, Robert G. (1994). Basic & Clinical Biostatistics. Lange Medical Books. ISBN 0-8385-0542-2. 

External links

• NIST statistics
• Statsoft basic statistics