BIOSTATISTICS Statistical tests part IV: nonparametric tests
1.Mann-Whitney test 2.Wilcoxon test 3.Kruskal-Wallis test Applicability Definition Example Copyright ©2012, Joanna Szyda INTRODUCTION
SAMPLE STRUCTUREHYPOTHESES TEST Copyright ©2011, Joanna Szyda INTRODUCTION
MANN-WHITNEY TEST
1.Comparison of means 2.Quantitative or ordered data (ranks) 3.No normal distribution required 4.Two independent samples Copyright ©2012, Joanna Szyda
DATA SET 1.Shrimp length in different water salinities 3.Shrimp length [mm] at 4 weeks of age MEDIUMHIGH MANN-WHITNEY TEST
Copyright ©20112 Joanna Szyda 1.Formulate hypotheses H 0 and H 1 H 0 : shrimp length does not depend on water salinity H 1 : shrimp length depends on water salinity H 0 : H = M H 1 : H ≠ M 2.Set the significance level MAX = Choose the statistical test and calculate test value Excel: example MANN-WHITNEY TEST
Copyright ©2011, Joanna Szyda 3.Choose the statistical test and calculate test value MANN-WHITNEY TEST
Copyright ©2011, Joanna Szyda 4.Determine distribution of the test Nonparametric test – no known distribution For n 1 n 2 > 20 – approximated by a normal distribution: no tables tables MANN-WHITNEY TEST
Copyright ©2011, Joanna Szyda 4.Determine distribution of the test 5.Determine t : Excel: example or compare with a critical value: MANN-WHITNEY TEST
Copyright ©2012, Joanna Szyda 6.Decision t < max U t < UH 0 H 1 shrimp length depends on water salinity ATTENTION !!! MANN-WHITNEY TEST
WILCOXON TEST
Copyright ©2011, Joanna Szyda WILCOXON TEST 1.Nonparamteric test 2.Quantitative or ordered data (ranks) 3.No normal distribution required 4.Comparison of two paired samples
Copyright ©2011, Joanna Szyda 1.Feeding behaviour of sheep 2.Data collected in in Canada, Rocky Mountains region 3.Differences in time of feeding with / without lamb 4.% time spent on feeding DATA SET IIDNO LAMBLAMB WILCOXON TEST
Copyright ©2011, Joanna Szyda DATA SET IIDNO LAMBLAMB WILCOXON TEST
Copyright ©2011, Joanna Szyda 1.Formulate hypotheses H 0 and H 1 H 0 : feeding time does not depend on a lamb H 1 : feeding time depends on a lamb H 0 : J = B H 1 : J ≠ B 2.Set the significance level MAX = Choose the statistical test and calculate test value Excel: example WILCOXON TEST
Copyright ©2011, Joanna Szyda 3.Choose the statistical test and calculate test value WILCOXON TEST
Copyright ©2011, Joanna Szyda 4.Determine distribution of the test Nonparametric test – no known distribution For N > 15 – approximated by a normal distribution: WILCOXON TEST
Copyright ©2011, Joanna Szyda 5.Determine t : or compare with a critical value : Excel: example 6.Decision t < max W t = WH 0 H 1 ? feeding time depends on a lamb ? WILCOXON TEST
KRUSKAL-WALLIS TEST
1.Comparing variability 2.Quantitative or ordered data (ranks) 3.No normal distribution required 4.Analysis of variance Copyright ©2012, Joanna Szyda
Copyright ©2011, Joanna Szyda DATA SET KRUSKAL-WALLIS TEST 1.Height of adult women in the USA 2.Three age groups
Copyright ©2011, Joanna Szyda 1.Formulate hypotheses H 0 and H 1 H 0 : women's height is the same in each age interval H 1 : women's height differs across age intervals H 0 : H 1 : 2.Set the significance level MAX = Choose the statistical test and calculate test value KRUSKAL-WALLIS TEST total no of observations number of groups mean ranking within group i mean overall ranking
Copyright ©2011, Joanna Szyda KRUSKAL-WALLIS TEST 3.Choose the statistical test and calculate test value 4.Determine distribution of the test: 5.Determine t : 6.Decision: t < max H 0 H 1 women's height differs across age intervals Excel: example
Copyright ©2012 Joanna Szyda NONPARAMETRIC TESTS