Assessment, Statistics, and Research

  A post hoc test is a statistical test used to determine if a pair of values are significantly different from each other after the primary analysis has been completed. The term post hoc is a Latin phrase meaning after the event. A common use of post hoc tests is the comparison of group means after an F -test in an ANOVA has revealed significant differences among the groups. The reason to test for differences after an overall test like ANOVA is to reduce the risk of finding a significant difference by chance. That is, if researchers perform a large number of tests on a sample, they may find one or more tests significant by chance. There are many post hoc tests. Following are some examples of tests that compare the means of two groups. Bonferroni Test This is a popular test. By dividing the significance level by the number of comparisons, the risk of finding a significant difference by chance is reduced. This procedure is called the Bonferroni Correction. Tukey's Honest Significant ...

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...