NonparametricTest - Data Analysis in Psychology - Lecture Slides, Slides of Advanced Data Analysis

Download NonparametricTest - Data Analysis in Psychology - Lecture Slides and more Slides Advanced Data Analysis in PDF only on Docsity!

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, Rank order all scores with group ID 6C,8C,9E,10C,11E,13C,15E Count # of Es that precede each C: U = 0 + 0 +1 + 2 = 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.

K-W (H)

H N N Rni N

i

2

( ) (^ )

K = # of groups n = number of cases in a group N = total number of cases R = sum of ranks in a group

H = 14 14^12 + 1 225 + 375 + 464 − 3 14 + 1

2 2 2

( ) [^ (^ )

This is tested against Chi-Squared (k-1) df. Go to Chi-Squared Table , with 2 df and alpha.

Friedman’s Test for k related samples

One-way repeated measures

Example Patients Psy(rank) drug(rank) psy/drug(rank) 1 6(2) 8(3) 5(1) 2 4(1) 8(3) 6(2) 3 9(3) 7(2) 4(1) 4 5(2) 4(1) 6(3) 5 2(1) 7(3) 3(2) 6 6(1) 8(3) 7(2) 7 7(2) 9(3) 5(1) 8 4(1) 8(3) 5(2) 9 6(3) 5(2) 4(1) 10 72) 8(3) 6(1) Totals 18 26 16

Χ 2 F^ = Nk N (^12 + 1 ) ∑ R j^2 − 3 N k ( + 1 )

N = # of patients

= 10 3( )( )^12 4 ( 18 2 + 26 2 + 16 2 ) −3 10( )( ) 4

This is test against Chi-Squared (k-1) df. Fail to reject at alpha .05.