Location test

A ___location test^[1] is a statistical hypothesis test that compares the ___location parameter of a statistical population to a given constant, or that compares the ___location parameters of two statistical populations to each other. Most commonly, the ___location parameter (or parameters) of interest are expected values, but ___location tests based on medians or other measures of ___location are also used.

One-sample ___location test

The one-sample ___location test compares the ___location parameter of one sample to a given constant. An example of a one-sample ___location test would be a comparison of the ___location parameter for the blood pressure distribution of a population to a given reference value. In a one-sided test, it is stated before the analysis is carried out that it is only of interest if the ___location parameter is either larger than, or smaller than the given constant, whereas in a two-sided test, a difference in either direction is of interest.

Two-sample ___location test

The two-sample ___location test compares the ___location parameters of two samples to each other. A common situation is where the two populations correspond to research subjects who have been treated with two different treatments (one of them possibly being a control or placebo). In this case, the goal is to assess whether one of the treatments typically yields a better response than the other. In a one-sided test, it is stated before the analysis is carried out that it is only of interest if a particular treatment yields the better responses, whereas in a two-sided test, it is of interest whether either of the treatments is superior to the other.

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

Parametric and nonparametric ___location tests

The following table summarizes some common parametric and nonparametric tests for the ___location parameters of one or more samples.

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 rank-sum 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 or Barnard's test
		np ≥ 5	chi-squared test
	Paired		McNemar or Kappa
3 or more groups	Independent	np < 5	collapse categories for chi-squared test
		np ≥ 5	chi-squared test
	Dependent		Cochran's Q

References

1. "Location Test — sci_analysis 2.2.0 documentation". sci-analysis.readthedocs.io. Retrieved 14 April 2025.