# Inferential statistics: Relationships

Chapter 13 of Performing Music Research outlines a range of statistical approaches designed to identify associations (or “relationships”) between variables. it starts with correlation and regression, which allow the nature and strength of the relationships between two or more variables to be quantified. Next, it considers approaches with specific applications: analyzing relationships between categorical variables; testing the reliability of questionnaires and raters; reducing a large number of variables to a smaller number of underlying factors; and understanding complex interactions within networks of variables. The chapter sets out examples of the situations in which each test can be used, provides guidance on conducting it using standard statistical software, and advises on how best to interpret and report its results.

# Datasets

13.1 Practice dataset for a Pearson correlation and a multiple regression (.xlsx)
13.2 Practice dataset for a chi-square test (.xlsx)

# Practice questions

These questions test your knowledge of the content of Chapter 13.

A Pearson correlation coefficient can only meaningfully describe linear relationships between variables.

When one variable tends to show higher values that correspond to lower values in a second variable, this is known as a __________.

__________ tau is a nonparametric alternative to the Pearson correlation coefficient that is particularly useful when many scores have tied ranks.

In a regression analysis, predictor variables can be nominal so long as they have more than two groups.

Unstandardized beta measures the extent to which a regression model predicts that the outcome variable will change if the predictor variable increases by one standard deviation.

Where the chi-square test can examine relationships between two categorical variables, __________ analysis can examine relationships between more than two variables.

Cronbach's alpha is a test of ________.

EFA stands for __________ Factor Analysis.

Which test determines the degree to which a third variable accounts for the relationship between two other variables?

There is always one single correct quantitative analytical approach to any given research question and dataset.