Two-Way Analysis of Variance Flashcards
With a two-way analysis of variance (two-way ANOVA)…
each participant must have scores on three variables: two factors and a dependent variable.
Each factor divides cases into…
two or more levels, while the dependent variable describes cases on a quantitative dimension.
F tests are performed on the…
main effects for the two factors and the interaction between the two factors.
Follow-up tests may be conducted to assess…
specific hypotheses if main effect tests, interaction tests, or both are significant.
We can analyze data from different types of studies by using two-way ANOVA.
Experimental studies
Quasi-experimental studies
Field studies
First Main Effect:
Are the population means on the dependent variable the same among levels of the first factor averaging across levels of the second factor?
Second Main Effect:
Are the population means on the dependent variable the same among levels of the second factor averaging across levels of the first factor?
Interaction Effect:
Are the differences in the population means on the dependent variable among levels of the first factor the same across levels of the second factor?
If one or more of the overall effects are significant:
various follow-up tests can be conducted. The choice of which follow-up procedure to conduct depends on which effects are significant.
If the interaction effect is significant:
follow-up tests can be conducted to evaluate simple main effects, interaction comparisons, or both. The choice among tests depends on which best addresses the research questions.
If the interaction effect is not significant:
the focus switches to the main effects. If a main effect for a factor with more than two levels is significant, then follow-up tests can be conducted. These tests evaluate whether there are differences in the means among the levels of one factor averaged across levels of the other factor. These follow-up tests most often involve comparing means for pairs of levels of the factor associated with the significant main effect.
Assumption 1:
The Dependent Variable Is Normally Distributed for Each of the Populations
Assumption 2:
The Population Variances of the Dependent Variable Are the Same for All Cells
Assumption 3:
The Cases Represent Random Samples from the Populations, and the Scores on the Dependent Variable Are Independent of Each Other (The two-way ANOVA yields inaccurate p values if the independence assumption is violated.)
The General Linear Model procedure computes an effect size index, labeled:
partial eta squared. It may be computed for a main or interaction source with the use of the following equation:
