One-Way ANOVA, Two-Way ANOVA, Test Selection, Post-Hoc, Assumptions

What is the purpose of a one-way ANOVA?

To compare the means of three or more groups with one independent variable (factor).

What does the “one” in one-way ANOVA mean?

One factor (independent variable).

What does a significant ANOVA tell you?

That at least one group mean differs from the others.

Does a significant ANOVA tell you which groups differ?

No — you need a post-hoc test to find out which ones.A significant ANOVA indicates that there is a difference among group means, but does not specify which groups are different.

Why not use multiple t-tests instead of ANOVA?

It increases Type I error (false positives).

What are “levels” in ANOVA terminology?

The groups or conditions within a factor.

What is the F-ratio formula?

F = MS Between / MS Within.

What does large between-group variance suggest?

The independent variable likely has an effect.

What does within-group variance represent?

Random error or individual differences.

What is the grand mean?

The overall mean of all participants across all groups.

When do you perform a post-hoc test?

Only when the ANOVA is significant.

What is Tukey HSD used for?

To determine which groups differ significantly.

When is a pair significantly different in Tukey HSD?

When the absolute difference in means is greater than the HSD value.

How many factors does a two-way ANOVA have?

Two independent variables.

What three effects does a two-way ANOVA test?

Main effect of A, main effect of B, and the interaction (A × B).

What is a main effect?

The effect of one factor, ignoring the other.

What is an interaction?

When the effect of one factor depends on the level of the other.

Which is usually more interesting in research: main effects or interactions?

Interactions.

How do you interpret a significant main effect?

Identify which levels have higher or lower means.

How do you interpret an interaction?

Describe how the pattern of means differs across factors (often using a graph).

What does an asterisk (*) mean in an ANOVA table?

The effect is significant at α = .05.

What does eta-squared (η²) measure?

The proportion of variance explained by a factor or interaction.

How do you find which factor is most influential?

Choose the largest η² value.

What are the assumptions of ANOVA?

• Independent samples

• Normally distributed populations

• Homogeneity of variance

• Balanced groups preferred

What does homogeneity of variance mean?

Population variances are equal.

You compare a sample mean to a population mean. What test?

One-sample t-test.

You compare two independent groups. What test?

Independent samples t-test.

You compare two matched/paired groups or two time points. What test?

Paired samples t-test.

You compare three or more groups with one factor. What test?

One-way ANOVA.

You compare groups involving two factors. What test?

Two-way ANOVA.

What instantly tells you the test is a two-way ANOVA?

There are two independent variables in the scenario.

What is experiment-wise error?

The total Type I error accumulated across multiple inferential tests.

In a one-way ANOVA, what determines the number of rows in the ANOVA table?

The number of groups minus one.

When are balanced sample sizes ideal?

Always — they improve statistical accuracy.

What does a non-significant main effect mean?

There is no significant main effect of Factor X.

What must you do on the exam even if the ANOVA is already known to be significant?

Show all work for the F-statistic.