Non parametric substitutes for t tests
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NON-PARAMETRIC SUBSTITUTES FOR t-TESTS. ParametricNon-Parametric Independent t Wilcoxon Rank-Sum or Mann-Whitney Dependent t Wilcoxon T. WILCOXON RANK-SUM TEST. Purpose: Compare the medians of two groups. Design: between subjects Assumptions: independent observations

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NON-PARAMETRIC SUBSTITUTES FOR t-TESTS

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NON-PARAMETRIC SUBSTITUTES FOR t-TESTS

ParametricNon-Parametric

Independent tWilcoxon Rank-Sum or

Mann-Whitney

Dependent tWilcoxon T


WILCOXON RANK-SUM TEST

  • Purpose: Compare the medians of two groups.

  • Design: between subjects

  • Assumptions:

    • independent observations

    • at least ordinal level data


Example

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


APA Format Sentence

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.


WILCOXON T

  • 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


Wilcoxon T Calculation

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!


APA Format Sentence

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

p > .05 .


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