Statistics Toolbox

signrank

Wilcoxon signed rank test of equality of medians

Syntax

• p = signrank(x,y,alpha)
  [p,h] = signrank(x,y,alpha)
  [p,h,stats] = signrank(x,y,alpha)
  

Description

p = signrank(x,y,alpha) returns the significance probability that the medians of two matched samples, x and y, are equal. x and y must be vectors of equal length. y may also be a scalar; in this case, signrank computes the probability that the median of x is different from the constant y. alpha is the desired level of significance, and must be a scalar between zero and one.

[p,h] = signrank(x,y,alpha) also returns the result of the hypothesis test, h. h is zero if the difference in medians of x and y is not significantly different from zero. h is one if the two medians are significantly different.

p is the probability of observing a result equally or more extreme than the one using the data (x and y) if the null hypothesis is true. p is calculated using the rank values for the differences between corresponding elements in x and y. If p is near zero, this casts doubt on this hypothesis.

[p,h,stats] = signrank(x,y,alpha) also returns a structure stats containing the field stats.signedrank whose value is the signed rank statistic. For large samples, it also contains stats.zval, the value of the normal (Z) statistic used to compute p.

Example

This example tests the hypothesis of equality of means for two samples generated with normrnd. The samples have the same theoretical mean but different standard deviations.

• x = normrnd(0,1,20,1);
  y = normrnd(0,2,20,1);
  [p,h] = signrank(x,y,0.05)
  p =
      0.2959
  h =
       0
  

See Also
ranksum, signtest, ttest

schart

signtest