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NON-PARAMETRIC SUBSTITUTES FOR t-TESTS

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ParametricNon-Parametric

Independent tWilcoxon Rank-Sum or

Mann-Whitney

Dependent tWilcoxon T

- Purpose: Compare the medians of two groups.
- Design: between subjects
- Assumptions:
- independent observations
- at least ordinal level data

Four students with ADD were assigned to receive counseling, and four others with ADD were assigned to receive Ritalin. The number of minutes out of their seats per day was recorded.

COUNSELINGRITALIN

3141

6025

7231

1954

STEP 1: Rank all scores from lowest to highest.

COUNSELINGRITALIN

31 Rank =3.541 Rank = 5

60 Rank = 725 Rank = 2

72 Rank = 831 Rank = 3.5

19 Rank = 154 Rank = 6

COUNSELINGRITALIN

31 Rank = 3.541 Rank = 5

60 Rank = 725 Rank = 2

72 Rank = 831 Rank = 3.5

19 Rank = 154 Rank = 6

SR = 19.5SR = 16.5

STEP 2: Sum the ranks for each group.

STEP 3: W is the smaller SR.

W = 16.5

STEP 4: Compare to critical value of W. Observed W must be EQUAL OR LESS THAN W-critical to be significant.

For N1 = 4, N2 = 4, a = .05 two-tailed

W-crit = 10

W = 16.5, not significant

A Wilcoxon Rank-Sum test showed that the Ritalin and Counseling groups were not significantly different, W (n1 = 4, n2 = 4) = 16.50, p > .05.

- Purpose: Test whether two distributions are different
- Design: within subjects or matched
- Assumptions:
- at least ordinal level data
- populations are identical except for means
- minimum N of 6

Example: Eight patients are exposed to a placebo and an experimental treatment (at different times). They are measured on severity of symptoms. Was there a significant difference between conditions? (scores on next page)

PatientPE

1108

21410

31213

41515

564

6811

796

81412

PatientPEDiff

1108+2

21410+4

31213-1

415150

564+2

6811-3

796+3

81412+2

STEP 1: Determine difference scores

PatientPEDiffRank

1108+23

21410+47

31213-11

415150

564+23

6811-35.5

796+35.5

81412+23

STEP 2: Rank the difference scores from smallest to largest, ignoring differences of zero.

STEP 3: Compute the sum of the positive ranks and the sum of the negative ranks.

SR positive = 3 + 7 + 3+ 5.5 + 3 = 21.5

SR negative = 1 + 5.5 = 6.5

STEP 4: The Wilcoxon T is the smaller SR.

T = 6.5

STEP 5: Compare to critical value.

N = number of NONZERO differences

N = 7

Tcrit = 2

Your T must be LESS THAN or equal to Tcrit to be significant!

A Wilcoxon T showed no significant difference between the placebo and experimental treatments, T (N = 7) = 6.5,

p > .05 .