20.4.18  Wilcoxon or Mann-Whitney distribution

The Wilcoxon test polynomial.

The wilcoxonp command computes the polynomial for the Wilcoxon or Mann-Whitney test.

• wilcoxonp takes one mandatory argument and one optional argument:
  • n, an integer.
  • Optionally, k an integer.
• wilcoxonp(n ⟨,k⟩) returns the polynomial for the Wilcoxon test.

Examples

The Wilcoxon/Mann-Whitney statistic.

The wilcoxons command computes the Wilcoxon or Mann-Whitney statistic.

• wilcoxons takes two arguments:
  • L, a list.
  • M, either a list or a real number (a median).
• wilcoxons(L,M) returns the Wilcoxon statistic.

Examples

The Wilcoxon or Mann-Whitney test.

The wilcoxont command will perform the Wilcoxon or Mann-Whitney test.

• wilcoxont takes two mandatory arguments and two optional arguments:
  • L, a sample (list).
  • M, either another sample or a number (a median).
  • Optionally, f, a function.
  • Optionally, x, a real number.
• wilcoxont(L,M  ⟨,f,x⟩) returns the results of the Wilcoxon test.

Examples

Mann-Whitney 2-sample test, H0 same Median, H1 <>
ranksum 93.0, shifted ranksum 27.0
u1=83, u2=27, u=min(u1,u2)=27
Limit value to reject H0 26
P-value 9055/176358 (0.0513444244094), alpha=0.05 H0 not rejected

Mann-Whitney 2-sample test, H0 same Median, H1 <>
ranksum 81.5, shifted ranksum 26.5
u1=73.5, u2=26.5, u=min(u1,u2)=26.5
Limit value to reject H0 35
P-value 316/4199 (0.0752560133365), alpha=0.3 H0 rejected

Wilcoxon 1-sample test, H0 Median=10, H1 M<>10
Wilcoxon statistic: 18, p-value: 0.375, confidence level: 0.05