1. BIOSTATISTICS Statistical tests part IV: nonparametric tests

2. 1.Mann-Whitney test 2.Wilcoxon test 3.Kruskal-Wallis test Applicability Definition Example Copyright ©2012, Joanna Szyda INTRODUCTION

3. SAMPLE STRUCTUREHYPOTHESES TEST Copyright ©2011, Joanna Szyda INTRODUCTION

4. MANN-WHITNEY TEST

5. 1.Comparison of means 2.Quantitative or ordered data (ranks) 3.No normal distribution required 4.Two independent samples Copyright ©2012, Joanna Szyda

6. DATA SET 1.Shrimp length in different water salinities 3.Shrimp length [mm] at 4 weeks of age MEDIUMHIGH 5.56.0 7.0 5.07.5 7.06.0 5.57.5 6.08.0 7.011.0 6.09.0 8.0 7.011.0 6.08.0 7.08.0 6.07.0 8.07.0 6.07.0 9.0 MANN-WHITNEY TEST

7. 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 = 0.05 3.Choose the statistical test and calculate test value Excel: example MANN-WHITNEY TEST

8. Copyright ©2011, Joanna Szyda 3.Choose the statistical test and calculate test value MANN-WHITNEY TEST

9. 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

10. Copyright ©2011, Joanna Szyda 4.Determine distribution of the test 5.Determine  t : Excel: example or compare with a critical value: MANN-WHITNEY TEST

11. Copyright ©2012, Joanna Szyda 6.Decision  t <  max U t < UH 0 H 1 shrimp length depends on water salinity ATTENTION !!! MANN-WHITNEY TEST

12. WILCOXON TEST

13. 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

14. Copyright ©2011, Joanna Szyda 1.Feeding behaviour of sheep 2.Data collected in1994-1996 in Canada, Rocky Mountains region 3.Differences in time of feeding with / without lamb 4.% time spent on feeding DATA SET IIDNO LAMBLAMB 172.0055.50 262.3543.80 355.7766.80 459.9868.00 551.6057.88 661.4861.90 752.5745.40 852.5056.67 956.4373.30 1060.1377.50 1148.6063.53 1242.9054.50 1353.5055.58 1470.4391.10 1547.1064.05 1650.0871.40 WILCOXON TEST

15. Copyright ©2011, Joanna Szyda DATA SET IIDNO LAMBLAMB 172.0055.50 262.3543.80 355.7766.80 459.9868.00 551.6057.88 661.4861.90 752.5745.40 852.5056.67 956.4373.30 1060.1377.50 1148.6063.53 1242.9054.50 1353.5055.58 1470.4391.10 1547.1064.05 1650.0871.40 WILCOXON TEST

16. 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 = 0.05 3.Choose the statistical test and calculate test value Excel: example WILCOXON TEST

17. Copyright ©2011, Joanna Szyda 3.Choose the statistical test and calculate test value WILCOXON TEST

18. 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

19. 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

20. KRUSKAL-WALLIS TEST

21. 1.Comparing variability 2.Quantitative or ordered data (ranks) 3.No normal distribution required 4.Analysis of variance Copyright ©2012, Joanna Szyda

22. Copyright ©2011, Joanna Szyda DATA SET KRUSKAL-WALLIS TEST 1.Height of adult women in the USA 2.Three age groups 20-29 30-3940-49 161.925164.465173.990 173.355171.450175.260 158.115173.355167.640 170.815175.260166.370 179.705164.465168.910

23. 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 = 0.05 3.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

24. 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

25. Copyright ©2012 Joanna Szyda NONPARAMETRIC TESTS