Discuss analysis of variance including main effects, interaction effects, and post hoc tests.
What will be an ideal response?
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Analysis of variance (ANOVA) is used to test an effect when more than two groups or conditions are being considered. The average variance is used in the calculation of mean differences and sampling error, which is why the test is called analysis of variance. An F statistic is calculated for each effect tested based on the ratio of average variance between the condition means and the average variance within the conditions. The calculated F statistic is compared with the distribution of F values when the null hypothesis is true to determine the corresponding p value based on the critical region of the distribution set by the alpha level.
The comparison of means for each level of an independent (or quasi-independent) variable is called the main effect. Thus, an ANOVA will test main effects for each independent variable separately in the analysis. If a main effect is significant in an ANOVA, it indicates that there is a mean difference somewhere among the means tested. But the main effect does not tell you which means are different from one another. You must conduct additional tests, called post hoc tests, to determine which means are different.
An interaction effect is also tested in an ANOVA for all combinations of independent variables. The interaction effect tests the effect of one independent variable at each level of the other variable. In other words, does the independent variable effect depend on the levels of another independent variable? The interaction effect is tested by comparing the difference in condition means across levels of one independent variable for each level of the other independent variable(s).
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