Median Test

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A Median Test is a non-parametric hypothesis test for comparing medians of two or more samples.



References

2017

  • [math] H_0:[/math] All k populations have the same median.
  • [math] H_a:[/math] All least two of the populations have different medians
Test Statistic: [math]\frac{N^2}{ab}\sum^k_{i=1}\frac{(O_{1i}−n_ia/N)^2}{n_i}[/math]
where
  • [math]a[/math] the number of observations greater than the median for all samples
  • [math]b[/math] the number of observations less than or equal to the median for all samples
  • [math]N[/math] the total number of observations
  • [math]O_{1i}[/math] the number of observations greater than the median for sample i
Significance Level: [math]\alpha[/math]
Critical Region: [math]T\gt \chi^2_{1−\alpha;k−1}[/math]
where [math]\chi^2[/math] is the percent point function of the chi-square distribution and k-1 is the degrees of freedom
Conclusion: Reject the independence hypothesis if the value of the test statistic is greater than the chi-square value.

2016