# Friedman Twoway Analysis of Variance (ANOVA) by Ranks

• Thomas W. MacFarland
• Jan M. Yates
Chapter

## Abstract

The Friedman Twoway Analysis of Variance (ANOVA) by Ranks Test is often viewed as the nonparametric equivalent of the parametric Twoway Analysis of Variance (ANOVA). Both the nonparametric Friedman Test and parametric Twoway ANOVA are used to determine if there are statistically significant differences for comparisons of multiple groups, with different factors for each group. However, it may be too convenient to view these tests as being mere complements of each other. The Friedman Test, as a nonparametric test, is used with ranked data, particularly for when: (1) the data do not meet the rigor of interval data, (2) there are serious concerns about extreme deviation from normal distribution, and (3) there is considerable difference in the number of subjects for each breakout group. The use of a block-type research design, a factorial design typically associated with ANOVA, is introduced in this lesson. This lesson also reinforces the many quality assurance measures that should be attempted before actual implementation of this type of inferential analysis.

## Keywords

Anderson-Darling test Bar plot (stacked, side-by-side) Block Block-type research design Box plot Breakout groups Code book Comma-separated values (.csv) Continuous scale Density plot Descriptive statistics Distribution-free Dot plot Factor Factorial research design Frequency distribution Friedman twoway analysis of variance (ANOVA) by ranks Hinge (lower and upper) Histogram Interaction plot Interval Mean Median Mode Multiple comparisons (Bonferroni, Hochberg, Holm, Least significant difference (LSD), Scheffé, and Tukey) Nominal Nonparametric Normal distribution Null hypothesis Ordinal Outlier Parametric Percentile Probability (p-value) Quantile-Quantile (QQ, Q-Q) Ranking Sample (quota, convenience) Statistical significance Treatment Twoway analysis of variance (ANOVA) Violin plot Whisker (lower and upper)

## Supplementary material

385146_1_En_7_MOESM1_ESM.csv (1 kb)
AlfalfaWeevil (CSV 1 kb)

© Springer International Publishing Switzerland 2016

## Authors and Affiliations

• Thomas W. MacFarland
• 1
• Jan M. Yates
• 2
1. 1.Office of Institutional EffectivenessNova Southeastern UniversityFort LauderdaleUSA
2. 2.Abraham S. Fischler College of EducationNova Southeastern UniversityFort LauderdaleUSA