Under the null hypothesis, the chi-square distribution with k – 1 degrees of freedom approximates the distribution of H. The approximation is reasonably accurate when no group has fewer than five observations. A higher H value provides stronger evidence for the null hypothesis that the difference between some of the medians is statistically significant.
Some authors, such as Lehmann (1975)1, suggest adjusting H when the data have ties. Minitab displays H(adj) when the data have ties.
Under the null hypothesis, the chi-square distribution with k – 1 degrees of freedom approximates the distribution of H and H(adj).
P-value = 1 – CDF (χ2H, df)
P-value = 1 – CDF (χ2H(adj), df)
For small samples, Minitab recommends that you use exact tables. For more details, see Hollander and Wolfe (1973)2.
| nj|| number of observations in group j |
|N||total sample size|
|average of the ranks in group j|
|average of all of the ranks|
|ti||number of tied values in the ith set of ties|