Assessment, Statistics, and Research

In statistics, an effect size ( ES ) indicates the strength of the relationship between two variables. In psychological experiments, researchers are interested in the strength of the effect of the Independent Variable on the Dependent Variable. In psychotherapy studies, researchers may be interested in the effects of treatment on a measure of the dependent variable. A research questions may be framed: How effective is a set of 6 CBT sessions on the reduction of depression? Psychologists have often described effect sizes as small, medium, or large. Cohen's d Cohen's d is a measure of effect size between two groups. The mean of one group is subtracted from a second group and divided by the pooled standard deviation of the two groups. ES = (M1 - M2) / SD Effect Size  Label 0.2     Small 0.5     Medium 0.8     Large Pearson Correlation Coefficient ( r ) 0.1 to 0.3  Small 0.3 to 0.5  Medium 0.5 to 1.0   Large Converting Cohen's d to the correlation coefficient r =   d / √ d 2

There are several types of ANOVA procedures. The term ANOVA refers to Analysis of Variance . Variance is a statistical term we will review later. Variance refers to differences, so the ANOVA procedures examine differences in scores among groups of people who complete a survey, a test, or produce a scorable response. For example, an ANOVA can be used to assess the effects of three temperatures on math. The Independent Variable is temperature varies three ways (75, 85, 95 degrees F). The dependent variable is math. The dependent measure of math is a math test. When there is only one independent variable (IV), the ANOVA is called a one-way ANOVA. If there are two IVs the ANOVA is a two-way ANOVA, and so forth. It is rare to go beyond a four-way because the interpretation of interactions is complicated. The ANOVA procedure is usually reported with an F value. The larger the F value, the more likely it is that the differences the researchers found are not due to chance. There may be s