Lecture 8 – Comparing more than two means (Between-Groups)

One-Way Between-Subjects ANOVA

Used to compare the means of more than two independent groups to determine if there are statistically significant differences in group means.

Independent Variable (IV)

A categorical variable with 3 or more levels.

Dependent Variable (DV)

A continuous variable measured on an interval or ratio scale.

Sum of Squares (SS)

A measure of variance; includes Group SS (variance between group means and overall mean) and Residuals SS (variance within each group).

Degrees of Freedom (df) between-groups

Calculated as k - 1, where k is the number of groups.

Degrees of Freedom (df) within-groups

Calculated as N - k, where N is the total number of observations.

Assumptions of ANOVA: Normality

Residuals should be normally distributed.

Assumptions of ANOVA: Homogeneity of Variance

Variances among the groups should be approximately equal, tested using Levene's test.

Assumptions of ANOVA: Independence

Observations must be independent of one another.

Post-Hoc Test

Conducted to determine which specific groups differ after finding a significant ANOVA result.

Post-Hoc Comparison

Controls for Type 1 error when making multiple comparisons, e.g., Tukey, Bonferroni.

Practical Applications of ANOVA

Understanding the impact of substances (like caffeine) on cognitive functions and designing experiments to compare multiple groups.