MANOVA Test Statistics with R

Multiple tests of significance can be employed when performing MANOVA. The most well known and widely used MANOVA test statistics are Wilk’s [latex]\Lambda[/latex], Pillai, Lawley-Hotelling, and Roy’s test. Unlike ANOVA in which only one dependent variable is examined, several tests are often utilized in MANOVA due to its multidimensional nature....

Multiple Analysis of Variance (MANOVA)

MANOVA, or Multiple Analysis of Variance, is an extension of Analysis of Variance (ANOVA) to several dependent variables. The approach to MANOVA is similar to ANOVA in many regards and requires the same assumptions (normally distributed dependent variables with equal covariance matrices). This post will explore how MANOVA is performed...

Games-Howell Test for Post-Hoc Analysis

The Games-Howell post-hoc test is another nonparametric approach to compare combinations of groups or treatments. Although rather similar to Tukey’s test in its formulation, the Games-Howell test does not assume equal variances and sample sizes. The test was designed based on Welch’s degrees of freedom correction and uses Tukey’s studentized...

Post-Hoc Analysis with Tukey’s Test

In a previous example, ANOVA (Analysis of Variance) was performed to test a hypothesis concerning more than two groups. Although ANOVA is a powerful and useful parametric approach to analyzing approximately normally distributed data with more than two groups (referred to as ‘treatments’), it does not provide any deeper insights...

ANOVA for Comparing More than Two Groups

ANOVA, or Analysis of Variance, is a commonly used approach to testing a hypothesis when dealing with two or more groups. One-way ANOVA, which is what will be explored in this post, can be considered an extension of the t-test when more than two groups are being tested. The factor,...

Measuring Cabbages with Mann-Whitney

In previous examples, hypothesis testing with two independent samples drawn from normally distributed populations was explored. Often, however, data is not normally distributed, which causes the t-test to output incorrect results. In the case of non-normally distributed data, nonparametric methods can be used. Nonparametric methods are so named since they...