Friedman s test

The results of such multiple paired comparison tests are usually analyzed with Friedman s rank sum test [4] or with more sophisticated methods, e.g. the one using the Bradley-Terry model [5]. A good introduction to the theory and applications of paired comparison tests is David [6]. Since Friedman s rank sum test is based on less restrictive, ordering assumptions it is a robust alternative to two-way analysis of variance which rests upon the normality assumption. For each panellist (and presentation) the three products are scored, i.e. a product gets a score 1,2 or 3, when it is preferred twice, once or not at all, respectively. The rank scores are summed for each product i. One then tests the hypothesis that this result could be obtained under the null hypothesis that there is no difference between the three products and that the ranks were assigned randomly. Friedman s test statistic for this reads... 

Separate analyses were performed for the test series conducted at 34 and 36 weeks PCA. For each behavioural measure the results were compared across the 4 odour stimuli with Friedman s tests. A similar series of within-subject comparisons was performed for the changes in baseline cardiac rates following odour presentations. 

Test for significance among the different treatments, using Friedman s test for related samples. The days are blocks for this test. If significant overall, examine differences between pairs of treatments by the Wilcoxon signed ranks test. Remember, the main question is whether predator odor reduces feeding. 

Chi-.square. binomial test, runs test, one-sample Kolmogorov Smirnov test. Mann-Whitney U test. Moses test. Wald-Wolfowitz test. Kruskal Wallis te.st, Wilcoxon signed rank test. Friedman s test. Kendall s W test, Cochran s Q test... 

We have already seen (Sections 3.4 and 6.3) that when paired results are compared, special statistical tests can be used. These tests use the principle that, when two experimental methods that do not differ significantly are applied to the same chemical samples, the differences between the matched pairs of results should be close to zero. This principle can be extended to three or more matched sets of results by using a non-parametric test devised in 1937 by Friedman. In analytical chemistry, the main application of Friedman s test is in the comparison of three (or more) experimental methods applied to the same chemical samples. The test again uses the statistic, in this case to assess the differences that occur between the total rank values for the different methods. The following example illustrates the simplicity of the approach. 

Friedman s test is evidently much simpler to perform in practice than the ANOVA method (Sections 3.8-3.10), though it does not have the latter s ability to study interaction effects (see Chapter 7). 

Comparison of >2 matched data sets 17 Friedman s test 6.7 Non-parametric... 

Do simple statistical tests. Average food consumption for the 20-min periods on each day. Use Friedman s two-way analysis of variance for randomized blocks (the days are the blocks, constituting one factor, the treatments are the second factor) followed by pairwise comparisons. Compare two treatments of particular interest, such as lowest MA concentration vs. EtOH only. 

All statistical analyses were done using SAS. Cochran s Q was used to analyze differences in choice between the three treatments. Friedman s signed-rank test was used to analyze differences between treatments in all other quantifiable measures. 

Friedman s repeated measures ANOVA. Differences in vaginal marking across estrous cycle days (D2 vs. PE) were analyzed within each odor condition and on combined scores with Wilcoxon tests. Mann-Whitney tests were used to compare the marking scores of LOT and sham females within each odor condition and cycle day as well as on scores collapsed across estrous days and odor conditions. Flank marking scores were only analyzed (Mann-Whitney test) between groups as LOT females almost never marked in any of the conditions. 

Young, D.S. Thomas, D.W. Friedman, R.B..and Pestaner, L.C. "Effects of Drugs on Clinical Laboratory Tests". Clin. 

Young, D.S. Friedman, R.B. and Pestaner, L.C. "Automatic Monitoring of Drug-Laboratory Test Interactions" Drug Interactions, pp. 393-401, Morselll, P.L., Garattlnl, S., and Cohen, S.N., Editors, Raven Press, New York, 1974. 

Friedman et al. (2000) tested this approach on a data set for yeast cell cycle expression patterns provided by Spellman and co-workers (1998), writing that This data set contains 76 gene expression measurements of the mRNA levels of 6177 S. cerevisiae ORFs. These experiments measure six... 

Fig. 17.3 Proportion of spotted hyena pastings that were overmarks by age and sex. Males increased their overmarking activity with age (Wilcoxon signed-rank test, S = 32.5, P = 0.04), however, females did not (cub vs. subadult S = — 15.5, P = 0.24 across subadult periods N = 6, Friedman ANOVA x2 = 3.5, P = 0.17). Although male and female cubs did not differ in their frequency of overmarking (Mann-Whitney U test, U = 75, P = 0.67), a sex difference was apparent among subadults (U = 37, P = 0.02)...

Lopez-Avila V, Beckert WF, Billets S. 1992. Supercritical fluid extraction and its application to environmental analysis. In Friedman D, ed. Waste testing and quality assurance third volume. ASTM Special Technical Publication 1075. Philadelphia, PA American Society for Testing and Materials, 141-153. 

Peterson, S.A., Greene, J.C. and Miller, W.E. (1990) Toxicological evaluation of hazardous waste samples extracted with deionized water or sodium acetate (TCLP) leaching media, in D. Friedman (ed.), Waste Testing and Quality Assurance, ASTM STP 1062, Philadelphia, USA, 2, 107-129. 

D. S. Young and R. B. Friedman, Ejfect of Diseases on Clinical Laboratory Tests, 4th ed. Washington, DC American Association of Clinical Chemistry, 2001. 

Results of the Friedman test, where jt> s 0.10 jt> s 0.05. The values used in the Friedman test are means of the field and laboratory replicates. metal concentrations follow the gradient site 1 > site 2 > site 3. " metal concentrations either follow the gradient site 3 > site 2 > site 1, or do not show an apparent gradient. 

Fig. 20.5 Using bioassay-guided fractionation to identify the molecular size of female sex pheromone. The dependent measure is the number of male blue crabs out of 72 tested that performed courtship stationary paddling. Stimuli were male or female urine fractionated into the indicated molecular sizes (S small <500 Da, M medium 500-1,000 Da, L large >1,000 Da, a mixture of S+M+L Mix) and positive control (unprocessed pubertal female urine = Urine) and a negative control (.SW sea water). Friedman ANOVA shows an overall difference in the responsiveness to these stimuli (P < 0.0001, n = 10). An asterisk marks stimuli that elicit significantly more males to respond compared to the sea water control (Wilcoxon post hoc tests, P < 0.05)...

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