Nonparametric Test Distribution-Free Tests 1.No assumptions of normality 2.Focus on medians rather than means 3.Not affected by outliers 4.Des NOT really reduce power

Mann-Whitney U Test 1.Test for two independent groups 2.Assumptions for t-test cannot be made 3.Data is neither ratio nor interval 4.Data must be at least ordinal 5.Tests if two groups have the same distribution n1 = # of cases in the smaller of the groups n2 = # of cases in the larger of the groups E = experimental group membership C = control group membership e.g., E scores = 11,15,9 and C scores = 6,8,13,10 Rank order all scores with group ID 6C,8C,9E,10C,11E,13C,15E Count # of Es that precede each C: U = = 3 Go top table for P under Null Hypothesis associated with the data; n1 = 3, n2 = 4, U = 3 U equal or greater than 3 p =.20 Thus, fail to reject at alpha.05.

More than two groups: Kruskal-Wallis (H) (for ordinal data) One-Way ANOVA by ranks Null Hypothesis: k samples come from same population or identical populations with respect to central tendencies. Rank order all N scores from the smallest to the largest. e.g., Authoritarian Scores G1G2G Transformed

K-W (H) K = # of groups n = number of cases in a group N = total number of cases R = sum of ranks in a group = 6.4 This is tested against Chi-Squared (k-1) df. Go to Chi-Squared Table, with 2 df and alpha.05

Friedmans Test for k related samples One-way repeated measures Example PatientsPsy(rank)drug(rank)psy/drug(rank) 16(2)8(3)5(1) 24(1)8(3)6(2) 39(3)7(2)4(1) 45(2)4(1)6(3) 52(1)7(3)3(2) 66(1)8(3)7(2) 77(2)9(3)5(1) 84(1)8(3)5(2) 96(3)5(2)4(1) 1072)8(3)6(1) Totals N = # of patients = 5.6 This is test against Chi-Squared (k-1) df. Fail to reject at alpha.05.