Final answer:
To break down an interaction for significant effects, simple main effects analysis is used for within-factor comparisons, contrast analysis for testing specific hypotheses about differences between means, factorial ANOVA for interactions between multiple factors, and MANOVA for multiple dependent variables.
Step-by-step explanation:
To break down an interaction to see where the significant effects are happening, you would typically use a simple main effects analysis. This method allows you to examine the mean differences within each factor of your experiment under certain conditions. If, for instance, you're dealing with a two-way ANOVA, you might explore simple main effects within each level of one factor while holding the other factor at a specific level. On the other hand, contrast analysis can be used to test specific hypotheses about the differences between means by comparing them in a pairwise or more complex manner. If you are looking at the interaction between multiple factors, then factorial ANOVA would be appropriate. For multivariate responses where there are several dependent variables, MANOVA (Multivariate Analysis of Variance) is the proper technique.
Regarding the one-way ANOVA hypothesis test, it is specifically used to determine if several population means are equal. It looks at one independent variable and one dependent variable under the condition of the assumptions that populations are normally distributed, they have equal standard deviations, and the samples are randomly and independently selected from each population.