Two-Way Between Groups ANOVA

Chapter 14

Two-Way ANOVAs

> Are used to evaluate effects of more than one IV on a DV

> Can determine individual and combined effects of the IVs

Testing for Interactions

> An interaction occurs when two IVs have an effect in combination that we do not see when looking at each IV individually

> Two-Way ANOVAs include to nominal IVs and a scale DV

> Factorial ANOVA uses one scale DV and at least two nominal IVs (factors)• Factor: IV in a study with more than one IV

Why Use Two-Way ANOVAs

> To evaluate effects of two IVs, it is more efficient to do a single study than two studies with one IV each.

> Can explore interactions between variables

More ANOVA Vocabulary

> Cell: box depicting a unique combination of levels of IVs in a factorial design

> Main effect: When one IV influences the DV

Two Types of Interactions in ANOVA

> Quantitative: interaction in which one IV exhibits strengthening or weakening of its effects at one or more levels of the other IV, but the direction of the effect does not change

> Qualitative: interaction of two or more IVs in which one IV reverses its effect depending on the level of the other IV

What if both IVs influence the DV?

> This is an interaction

Six Steps for Two-Way Between-Groups ANOVA

> Step 1. Identify the populations, distribution, and assumptions.

> Step 2. State the null and research hypotheses.

> Step 3. Determine the characteristics of the comparison distribution.

> Step 4. Determine critical values, or cutoffs.> Step 5. Calculate the test statistic.> Step 6. Make a decision.

df Formulae for ANOVAs

1 rowsrows Ndf

1 columnscolumns Ndf

))(( columnsrowsninteractio dfdfdf

1 totaltotal Ndf

3,1,3,1, OOYYwithin dfdfdfdfdf

Determining the Cutoff Point

Effect Size for Two-Way ANOVA

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SSR

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Variations on ANOVA