kruskal-wallis vs. F test ANOVAs

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Millo Marin 2013-4-18

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https://ww2.mathworks.cn/matlabcentral/answers/72514-kruskal-wallis-vs-f-test-anovas

Hi, I have a 3x156 matrix of some fishery data, and I'm triying to find the possible significant diferences between each column (each column being a different location for the same fishery).. since the data doesn't approach to a normal distribution (Kolmogorov-Smirnov test for normality was rejected in each of the three columns) nor the variances between the three is statistically similar (the Bartlett test was rejected), I used the kruskalwallis function to apply a non parametric one-way ANOVA. I get that the p-value is really close to the significance level that I chose for all the analysis (0.05 is the chosen value, and I get a p-value of 0.0505 for the test). Just as a curiosity I ran a one way ANOVA F test (using the anova1 function), and I get a p value way lower (5.1444e-006) than the kruskalwallis test. The problem is that if I stick to the central limit theorem (and present the results obtained in the F test) I get that there's statistically significant differences amongst areas, but if I stick to the Kruskal-Wallis test, the result is the oposite. I remember reading somewhere that the Kruskal-Wallis test often fails to find significant differences when this differences are not very noticeable, but I don't remember where. Any suggestions on which result should I keep? ANOVA tables are below.

Kruskal-Wallis: Source SS df MS Chi-sq Prob>Chi-sq ---------------------------------------------------------- Columns 108646.8 2 54323.4 5.98 0.0502 Error 8372422.7 465 18005.2 Total 8481069.5 467

F test: Source SS df MS F Prob>F ------------------------------------------------------- Columns 0.09797 2 0.04898 12.5 5.14436e-006 Error 1.8219 465 0.00392 Total 1.91986 467

Thanks a lot for your answers (and your time). Greetings.