test_normality SciMax Toolbox test_sign

SciMax Toolbox >> test_rank_sum

test_rank_sum

Maxima Function

Calling Sequence

test_rank_sum (x1, x2)
test_rank_sum(x1,x2,option_1)

Description

This is the Wilcoxon-Mann-Whitney test for comparing the medians of two continuous populations. The first two arguments x1 and x2 are lists or column matrices with the data of two independent samples. Performs normal approximation if any of the sample sizes is greater than 10, or if there are ties.

Option:

The output of function test_rank_sum is an inference_result Maxima object with the following results:

  1. 'method: inference procedure.

  2. 'hypotheses: null and alternative hypotheses to be tested.

  3. 'statistic: value of the sample statistic used for testing the null hypothesis.

  4. 'distribution: distribution of the sample statistic, together with its parameters.

  5. 'p_value: p-value of the test.

Examples:

Checks whether populations have similar medians. Samples sizes are small and an exact test is made.

(%i1) load("stats")$
(%i2) x:[12,15,17,38,42,10,23,35,28]$
(%i3) y:[21,18,25,14,52,65,40,43]$
(%i4) test_rank_sum(x,y);
              |                 RANK SUM TEST
              |
              |              method = Exact test
              |
              | hypotheses = H0: med1 = med2 , H1: med1 # med2
(%o4)         |
              |                 statistic = 22
              |
              |        distribution = [rank_sum, 9, 8]
              |
              |          p_value = .1995886466474702

Now, with greater samples and ties, the procedure makes normal approximation. The alternative hypothesis is H_1: median1 < median2.

(%i1) load("stats")$
(%i2) x: [39,42,35,13,10,23,15,20,17,27]$
(%i3) y: [20,52,66,19,41,32,44,25,14,39,43,35,19,56,27,15]$
(%i4) test_rank_sum(x,y,'alternative='less);
             |                  RANK SUM TEST
             |
             |          method = Asymptotic test. Ties
             |
             |  hypotheses = H0: med1 = med2 , H1: med1 < med2
(%o4)        |
             |                 statistic = 48.5
             |
             | distribution = [normal, 79.5, 18.95419580097078]
             |
             |           p_value = .05096985666598441
test_normality SciMax Toolbox test_sign