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#### 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...

#### 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...

#### 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...

#### 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...

#### More Post-Hoc Testing with Kruskal-Wallis

The Kruskal-Wallis test extends the Mann-Whitney-Wilcoxon Rank Sum test for more than two groups. The test is nonparametric similar to the Mann-Whitney test and as such does not assume the...

#### 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...

#### 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...

#### Estimating Professor Salaries with Confidence Intervals

Introduction Estimating with confidence intervals is another form of hypothesis testing that is often preferred over standard hypothesis testing such as what was explored in the previous post. A primary reason...

#### Two-Sample Hypothesis Testing with University Professor Salaries

Introduction to Hypothesis Testing Classical hypothesis testing is concerned with testing two statements, the null, and alternative hypothesis. The null hypothesis is believed to be true while the alternative hypothesis is...