First, use the Critical Significance Level (α) chosen in Step 2 and sample sizes (e.g. n_{1}, n_{2} and n_{3}) calculated in Step 3 to find the Critical Value of H (H_{critical}) using a Critical Value Table such as the one below

e.g. if α=0.05, n_{1} = 5, n_{2} = 5 and n_{3} = 5 then H_{critical} = 5.780.

Second, compare H_{critical} with the value of the H statistic calculated in Step 3.

Reject your Null Hypothesis if your calculated value is greater than or equal to the Critical value; H ≥ H_{critical} (significant result).

Accept your Null Hypothesis if your calculated value is less than the Critical value; H < H_{critical} (non-significant result).

For example, if H = 13.382 and H_{critical} = 5.780 then reject the Null Hypothesis.

Table of Critical Values for a Critical Significance Level (α) of 0.05 and three samples for the H statistic where n_{1} is the size of the first sample, n_{2} is the size of the second sample and n_{3} the size of the third sample.

n_{1} |
n_{2} |
n_{3} |
H |

2 | 2 | 2 | - |

3 | 2 | 1 | - |

3 | 2 | 2 | 4.714 |

3 | 3 | 1 | 5.143 |

3 | 3 | 2 | 5.361 |

3 | 3 | 3 | 5.600 |

4 | 2 | 1 | - |

4 | 2 | 2 | 5.333 |

4 | 3 | 1 | 5.208 |

4 | 3 | 2 | 5.444 |

4 | 3 | 3 | 5.791 |

4 | 4 | 1 | 4.967 |

4 | 4 | 2 | 5.455 |

4 | 4 | 3 | 5.598 |

4 | 4 | 4 | 5.692 |

5 | 2 | 1 | 5.000 |

5 | 2 | 2 | 5.160 |

5 | 3 | 1 | 4.960 |

5 | 3 | 2 | 5.251 |

5 | 3 | 3 | 5.648 |

5 | 4 | 1 | 4.985 |

5 | 4 | 2 | 5.273 |

5 | 4 | 3 | 5.656 |

5 | 4 | 4 | 5.657 |

5 | 5 | 1 | 5.127 |

5 | 5 | 2 | 5.338 |

5 | 5 | 3 | 5.705 |

5 | 5 | 4 | 5.666 |

5 | 5 | 5 | 5.780 |

Critical values of the Kruskal-Wallis *H* distribution based on Zar (1999) and sources therein.

Zar, JH (1999) **Biostatistical Analysis** 4^{th} edition. Prentice-Hall, New Jersey.