Friedman Twoway Analysis of Variance (ANOVA) by Ranks

Thomas W. MacFarland and Jan M. Yates
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Thomas W. MacFarland: Nova Southeastern University, Office of Institutional Effectiveness
Jan M. Yates: Nova Southeastern University, Abraham S. Fischler College of Education

Chapter Chapter 7 in Introduction to Nonparametric Statistics for the Biological Sciences Using R, 2016, pp 213-247 from Springer

Abstract: 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) (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/978-3-319-30634-6_7

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