Analysis of Variance (ANOVA)

Abstract

In the previous chapter, you learned to compare the means of a numeric variable between two groups. But what if you want to compare a ratio or interval variable between more than two groups? If you are interested in comparing across more than two groups, you cannot run multiple t-tests because it increases the risk of a type I error (mistakenly concluding an intervention is effective or efficacious). In these instances, you will want to conduct a one-way analysis of variance (ANOVA). In this chapter, you will walk through how to conduct ANOVA and the appropriate post hoc tests by comparing frequencies of stop and searches conducted by the police between neighborhoods across different local authorities in London.

Key Terms

Bonferroni Correction

A post-hoc pairwise comparison of means that controls the type I error rate by dividing the selected α-level by the number of pairwise comparisons made.

Data transformation

An adjustment of data to a different unit or scale (normally to deal with normality issues).

Eta squared

The proportion of the total sum of squares that is accounted for by the between sum of squares. Eta squared is sometimes referred to as the percent of variance explained.

F -distribution

A continuous probability distribution used as the null distribution in ANOVA.

Kruskal-Wallis test

A nonparametric test of statistical significance for multiple groups, requiring at least an ordinal scale of measurement.

Levene's test

A test of the equality of variances.

Multiple comparisons problem

The problem associated with heightened chance of obtaining a false-positive (type I error) increase as the number of comparisons increase.

One-way analysis of variance (ANOVA)

A parametric test of statistical significance that assesses whether differences in the means of several samples (groups) can lead the researcher to reject the null hypothesis that the means of the populations from which the samples are drawn are the same.

Q-Q plot

Used to check for normality of data, plots the correlation between the sample and a normal distribution.

Scheffé’s test

A multiple comparisons test that accounts for family-wise error rate by weighting the test statistic by the mean squared error, between-samples degrees of freedom, and group sizes.

Tukey’s Honest Significant Difference (HSD)

A parametric test of statistical significance, adjusted for making pairwise comparisons. The HSD test defines the difference between the pairwise comparisons required to reject the null hypothesis.

Welch’s ANOVA

ANOVA test for when the equality of variances assumption (homoscedasticity) is not met.