TwoWay Between Groups ANOVA Chapter 14 TwoWay ANOVAs

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

The basic 2 Way. ANOVA situation 2 or more Nominal Independent Variable with two or more levels 1 Scale Dependent Variable Effects of Drug and Age on recovery time Effects of Exercise and Diet on number of friends Effects of Toy Color and Gender on toy popularity

One Way ANOVA is Limited Avg Weekly Hours Workout 7 Sex Differences in Workout Hours/Week 6 5 4 3 Total 2 1 0 Female Male Sex • Previous data, hour of exercise by relationship status. If I want to look at sex differences for hours of exercise, I have to do a second one-way ANOVA, and it will not tell me if there is a connection between sex and relationship status on hours of exercise.

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

Understanding Graphs • Main Effects: distance between lines • Quantitative

Understanding Graphs • Interactions: slopes of lines • Qualitative

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

Determining the Cutoff Point

Effect Size for Two-Way ANOVA

Variations on ANOVA