Which analysis of variance should be applied when an experiment has more than one independent variable.
What are the assumptions and limitations of the analysis of variance in comparison with the t test including a discussion of post hoc tests.
When there are two independent variables, a two-way ANOVA can be applied.
Assumptions from scores in their respective populations are that they are normally distributed and have homogeneous variances. Samples are independently and randomly selected. In comparing the ANOVA with the t-test, the ANOVA can be applied when an independent variable has more than two levels.
One of the most common post hoc tests include Tukey's HSD test. There are others you can find as well.
I hope this will help.
When an experiment has more than one independent variable, the appropriate analysis of variance (ANOVA) to be applied is called a factorial ANOVA. It allows researchers to examine the main effects of each independent variable, as well as any interaction effects between them.
In terms of assumptions, ANOVA assumes that the dependent variable follows a normal distribution and that the variances of the dependent variable are equal across the different levels of the independent variables. Additionally, ANOVA assumes that the observations are independent.
One of the primary limitations of ANOVA, compared to the t-test, is that it can only determine if there are overall differences between the groups, but it does not specify which specific groups differ from each other. This is where post hoc tests come into play. Post hoc tests are additional statistical tests that can be conducted after an ANOVA to determine which specific groups differ significantly from each other.
The choice of post hoc test depends on the specific research question and the design of the experiment. Commonly used post hoc tests include Tukey's Honestly Significant Difference test (HSD), Bonferroni correction, Scheffe's test, and Newman-Keuls test. These tests control for the familywise error rate, which is the probability of making at least one Type I error across all pairwise comparisons.
In conclusion, when an experiment has more than one independent variable, the appropriate analysis of variance is a factorial ANOVA. Assumptions of ANOVA include normal distribution of the dependent variable, equal variances across the groups, and independent observations. The limitations of ANOVA include the inability to determine specific group differences, which can be addressed through post hoc tests that control for Type I errors. The choice of post hoc test depends on the research question and the experiment's design.