Lecture 9: Analysis of Variance (ANOVA)

These flashcards cover key terms and concepts from the lecture notes on the Analysis of Variance (ANOVA) and related statistical methods.

Analysis of Variance (ANOVA)

A statistical method used to compare the means of three or more independent groups.

One-Way ANOVA

• A type of ANOVA that involves one independent variable and one scale dependent variable

• to compare means of three or more independent groups/levels of IV

• ANOVA produces F-statistic by dividing different between independent groups by variance w/in groups

assumptions of oneway anova

• groups are unrelated

• dependent variable is normally distributed  w/in groups of IV

• variances in groups are equal

• if variances are significant, you have to do a post-hoc test because the one-way anova will not tell you where the difference in variance is 

F-statistic

A value calculated in ANOVA that represents the ratio of variance between groups to variance within groups.

Homogeneity of variance

An assumption that the variances among different groups are equal in ANOVA.

Levene’s Test

A statistical test used to assess the equality of variances for a variable calculated for two or more groups.

Post-hoc tests

Tests conducted after ANOVA to determine which specific group means are different. These compare all possible pairs of groups. 

Kruskal-Wallis H test

• A non-parametric test that compares three or more groups based on ranks and is used for ordinal data.

• when dependent variable is ordinal and the independent variable has 3+, or when dependent is scale but skewed

chi-square

• used when DV is nominal or dichotomous

GLM repeated-measures ANOVA test

• general linear model - for within group design - three or more related groups

• dependent variable is scale

• within group, this is like your time 1 time 2 type study

Friedman Test

• A non-parametric test for comparing related samples to detect differences in treatments across multiple test attempts.

• when dependent variable is ordinal and it’s a within group design

• can also be used when data for scale is badly skewed

Cochran's Q test

• A non-parametric test used for binary responses to compare three or more related groups.

• when DV is nominal or dichotomous and it’s a within group design for 3+ attempts or timing periods

• assumes that sample is randomly selected from population and responses are categorical or dichotomous

Degrees of Freedom (df)

The number of independent values in a statistical calculation.

Tukey’s HSD

• A post-hoc test used after ANOVA to find means that are significantly different from each other.

• this is used when Levene’s test is not statistically significant, aka, variances between groups are equal

Games-Howell Test

• A post-hoc test used when the assumption of equal variances is violated, to compare group means.

• done when p-value of Levene’s test is statistically significant