Nonparametric Statistic and the Runs Test for Stationarity - Signal Processing of Random Physiological Signals - page 69

TABLE 8.4: Example of Wilcoxon-Matched Pairs Signed-Ranked Test

RANK OF RANK WITH LESS

INTERVAL DIFFERENCE DIFFERENCE FREQUENT SIGN

1 2 3

2 − 1 − 1.5 1.5

3 3 4

4 0

5 − l − 1.5 1.5

6 5 5

7 6 6

N = 6 T = 3 . 0

1. Take signed difference for each matched pair.

2. Rank differences without respect to sign; if there is a tie, assign the average of

the tied ranks.

3. Affix “ + ”or“ − ” to rank according to the difference.

4. Determine T , where T is the smaller of the sums of like ranked signs.

5. Determine N , where N is the number of differences having signs (zeroes do not

count).

6. If N 25, then the critical value is obtained from the “Table of Critical Values

of T in the Wilcoxon-Matched Pairs Signed-Ranks Test.” If the observed T is
less than or equal to the table value, then the null hypothesis, H 0 , is not accepted
(rejected).

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7. If N 25, then the Z value must be calculated from (8.10) and the table of

Critical Values of T used.

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