Mann-Whitney U test Non-parametric test Tests the central tendency between two populations, does NOT test the means. Use sample sizes instead of degrees of freedom to look up critical values. Also known as the Wilcox rank test, or the Kendall’s S test INTRODUCTION

Mann-Whitney U test EXAMPLE 21 plants Treatment A n A = 11 Treatment A n A = 11 Treatment B n B = 10 Treatment B n B = 10 Ho: no difference between treatments A and B

Mann-Whitney U test Group AGroup B mean EXAMPLE

Mann-Whitney U test EXAMPLE

Mann-Whitney U test EXAMPLE the two samples are randomly and independently drawn independence within samples and mutual independence between samples the measurement scale is at least ordinal Assumptions for test

Mann-Whitney U test EXAMPLE Raw measure rank From sample AAAAABBBABAABBAABABBB Assemble measures into a single set Rank-order from lowest to highest

Mann-Whitney U test EXAMPLE Ranked measures Group AGroup B A & B tog. Sum of ranks Avg or ranks Rank values substitute for raw measures in table. Used to calculate critical value (test statistic)

Mann-Whitney U test EXAMPLE n i is the sample size in group i R i is the sum of ranks in group i UiUi = n 1 n 2 + ni(ni+1)ni(ni+1)- R i 2

Mann-Whitney U test EXAMPLE U = n 1 n 2 + n1(n1+1)n1(n1+1)- R 1 2 U'U' = n 1 n 2 + n2(n2+1)n2(n2+1)- R 2 2 U A = – 96.5 = 79.5 U B = – = 30.5 See ZAR Table B.10

Mann-Whitney U test EXAMPLE Degrees of freedom n 1 = 10 and n 2 = 11 alpha = 0.05 Two-tailed - 84 One-tailed - 79