Inferential statistics: Differences

Chapter 12 of Performing Music Research considers statistical tests designed for use in experimental, survey, and observational research to compare differences between groups. It describes three kinds of test and their variations: t-tests, which are used to identify differences between two groups on one dependent variable; analyses of variance (ANOVAs), which are used to test effects by identifying differences between two or more groups on one dependent variable; and multivariate analyses of variance (MANOVAs), which are used to test effects by identifying differences between two or more groups on two or more dependent variables. For each test, the chapter sets out an example of the situations in which it can be used, provides guidance on conducting it using standard statistical software, and advises on how best to interpret and report its results.

Research spotlight

Box 12.3
A wellbeing profile of classical musicians

Research investigating the degree to which professional musicians are mentally well through experiencing positive emotions, engagement, relationships, meaning, and accomplishment in their lives.

Credits

Ascenso S, Perkins R, & Williamon A (2018), Resounding meaning: a PERMA wellbeing profile of classical musicians, Frontiers in Psychology, 9 (1895), 1-14 [DOI].

Film produced by: Tantrwm Digital Media

Datasets

12.1 Practice dataset for a one-sample t-test (.xlsx)
12.2 Practice dataset for an independent-samples t-test (.xlsx)
12.3 Practice dataset for a paired-samples t-test (.xlsx)
12.4 Practice dataset for a one-way ANOVA (.xlsx)
12.5 Practice dataset for a repeated-measures ANOVA (.xlsx)
12.6 Practice dataset for a 2 × 2 factorial ANOVA (.xlsx)
12.7 Practice dataset for a one-way MANOVA (.xlsx)

Practice questions

These questions test your knowledge of the content of Chapter 12.

A(n) __________ t-test would be used to examine a difference between the mean performance scores of flautists and trumpeters.

How many distinct groups would a 6x2x2 factorial ANOVA compare?

The Wilcoxon signed-rank test is the nonparametric equivalent of the paired-samples t-test.

Which standard contrast would you use to compare the mean outcome for each individual group (except the first) with the mean of outcomes for all of the groups?

Box's test is used to test the assumption of sphericity when conducting an ANOVA.

Friedman's MANOVA is the nonparametric equivalent of a one-way MANOVA.

Both the Tukey and Scheffé tests should be run alongside any ANOVA with more than two groups.

Which test would be most appropriate to run to examine differences between the mean self-efficacy scores between five groups of guitarists while controlling for years of study (measured as a continuous variable)?