Research Methods and Statistics

CHAPTER PREVIEW

In the previous chapters we introduced probability as the foundation for testing differences between two treatments. We then described how the independent t test allows us to determine if statistically significant differences are present between two groups receiving two different levels of an IV. Similarly, the repeated measures t test allows us to use a more sensitive analysis to examine differences in treatments using one group of subjects who experience both conditions. In this chapter we expand the probability model for testing statistical significance to include more than two levels of the IV. We explain how we can use an Analysis of Variance (ANOVA) to test for statistical significance when we have more than two groups or when participants experience more than two treatment conditions.

A between groups ANOVA is an inferential test of probability that we can use with one independent variable having more than two levels. In addition to determining whether groups differ as a function of the level of the independent variable, we must conduct additional statistical tests to determine where, exactly, the differences exist. We conduct post hoc analyses to isolate specific differences when we have more than two groups. We also derive an overall measure of effect size as an estimate of the strength of the treatment effect.

In most ways, a repeated measures ANOVA is much like the between groups ANOVA. The difference between these two inferential statistical tests is whether different groups receive the levels of the independent variable, or if one group of participants experiences all of the conditions, or levels, of the independent variable. The repeated measures ANOVA is more sensitive to detecting a statistically significant outcome because there is less error. So, when we find a statistically significant outcome, we also conduct post hoc analyses and calculate a measure of effect size.

Statistical Testing for Multiple Treatments

Thus far, our discussion of statistical analyses has been limited to comparing two levels of an independent variable. In the previous chapter, we used an example comparing two treatments for depression (i.e., treatment and control group), and we measured the effectiveness of the treatment using the Beck Depression Inventory (BDI-II). However, we frequently encounter research questions that include more than two levels of treatment.