Statistical tests: Continuous data

This page contains general information for choosing commonly used statistical tests. The examples linked provide general guidance which should be used alongside the conventions of your subject area. Where possible, a brief explanation of the test is given with links to performing this test using Excel, SPSS and R. It is worth noting that the examples often contain information about interpreting the output and results so can act as a guide to interpreting statistical results too.

To navigate this table, consider the following questions:

• Is your outcome variable continuous?
• Does the data meet the requirements for a parametric test (e.g. normality)? Notice, that for each parametric test, where possible, a corresponding nonparametric test is presented.
• How many samples (or groups) do you have?
• Are the outcomes paired (or dependent)?

Parametric

 1 Sample One sample t testIf sigma is unknown, use a one sample t test to determine if the sample is likely to have come from a given population with a defined mean. Example Excel SPSS R 2 SamplesPaired(or dependent, repeated measures) Paired t testThe paired-samples t test is used when the data is from related, paired or longitudinal samples. Example Excel SPSS R 2 SamplesUnpaired(or independent) Unpaired t test.An unpaired t test is used to assess if the mean values of two independent samples are equal. Firstly, you need to assess equality of variances using an F-test, details of which are given within the examples below. Example Excel (σ1=σ2)Excel (σ1≠σ2) SPSS R 3+ SamplesRelated (or dependent) One-way repeated measures (within groups) ANOVAOne-way repeated measures analysis of variance (ANOVA) is a method for detecting differences between related mean values, it is an extension of the paired t test. A post-hoc test is needed to investigate where these differences might occur. Example Excel SPSS R 3+ SamplesUnrelated (or independent) One-way (between groups) ANOVAOne-way analysis of variance (ANOVA) is a method for testing whether three or more populations have the same mean value and is an extension of the unpaired t test. A post-hoc test is needed to investigate where these differences might occur. Example Excel SPSS R 3+ SamplesUnrelated (or independent) Two-way (between-groups) ANOVATwo-way (or three-way analysis of variance) is used to explore if two or more factors can influence the dependent variable. Example Excel SPSS R Relationship Pearson's CorrelationPearson’s Product-Moment Correlation (r) is used to measure the strength and direction of the association between two variables. The value of Pearson’s r is between +1 and –1: where r = +1 is a perfect positive correlation, r = -1 a perfect negative correlation and r=0 indicates no correlation between the variables. Example Excel SPSS R

Nonparametric

 1 Sample One sample sign (or median) testA one sample sign test is used to explore if the median of the sample data is equal to a given value. Example Excel SPSS R 2 SamplesPaired(or dependent) Wilcoxon signed rank testThe Wilcoxon signed ranks test is used to compare the medians of two related samples. Example Excel SPSS R 2 SamplesUnpaired(or independent) Mann-Whitney U testThe Mann-Whitney U test is used to compare the medians of two independent samples. Example Excel SPSS R 3+ SamplesRelated (or dependent) Friedman testThe Friedman test is designed to test whether three or more populations have the same median values, using data collected from related samples. It is the nonparametric equivalent of a simple repeated measures analysis of variance (ANOVA). Example Excel SPSS R 3+ SamplesUnrelated (or independent) Kruskal-Wallis test (independent observations)The Kruskal Wallis test tests whether three or more populations have the same median values. It is the nonparametric equivalent of a one-way analysis of variance (ANOVA). Example Excel SPSS R Relationship Spearman's Rank testSpearman’s correlation coefficient rho (ρ) is calculated from the ranked data and is used to measure the correlation between two variables The value of Spearman’s rho is between +1 and –1: and the sign and value of ρ are interpreted in the same way as the more conventional correlation coefficient, r. Example Excel SPSS R