PSYU2248 Lecture 5: Pt. 1 One-way ANOVA

One-way ANOVA

A statistical method used for comparing means across three or more independent groups.

Type I error

Incorrect rejection of a true null hypothesis (false positive).

Omnibus test

• Tests overall significance among multiple group means before detailed comparisons.

Variance partitioning

Separating total variance into between-group and within-group variance.

Between-group variance

Variability due to differences among group means.

Within-group variance

Variability due to individual differences within each group

Effect size (Eta-squared, η²)

Indicates the proportion of variance explained by the independent variable.

Independent variable (IV)

Categorical variable with multiple levels/groups.

Dependent variable (DV)

Continuous (numerical) variable influenced by the IV.

Degrees of Freedom (df)

Number of independent values available to vary in calculating a statistic.

Mean Square (MS)

Variance estimate obtained by dividing Sum of Squares (SS) by degrees of freedom (df).

F-ratio

Statistic used in ANOVA to compare variance between groups against variance within groups (MS_between/MS_within).

ANOVA Assumptions

• Numerical DV (interval/ratio scale)

• Independence of observations

• Normal distribution within each group

• Homogeneity of variance

Follow-up Analyses of ANOVA

• Simple (pairwise): Compare two group means.

• Complex: Compare combined groups versus another group.

• Planned comparisons: Hypothesis-driven; defined before data collection.

• Post hoc comparisons: Exploratory; follow a significant omnibus F-test.

Descriptive statistics (numeric summaries) command

tabstat DV, by(IV) stat(n mean sd)

Normality (histogram) command

histogram DV, by(IV)

Normality (Shapiro-Wilk test)

by IV, sort: swilk DV

Homogeneity of variance (Levene’s test)

robvar DV, by(IV)

Omnibus ANOVA test

anova DV IV

Alternative basic ANOVA command (Bartlett’s test)

oneway DV IV, tabulate

Omnibus F-test interpretation

Significant F value suggests at least one group mean significantly differs from others.

Effect size interpretation (Eta-squared, η²)

• Small: 0.01

• Medium: 0.06

• Large: >0.14