First, use the Critical Significance Level (α) chosen in Step 2 and degrees of freedom (df) calculated in Step 3 (df = number of pairs of data which have different values (i.e. the difference is none-zero)) to find the Critical Value of T (T_{critical}) using a Critical Value Table such as the one below (e.g. if α = 0.05 and df = 9, then T_{critical} = 5).

Second, compare T_{critical} with the value for the T statistic calculated in Step 3.

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

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

For example, if T = 7.6 and T_{critical} = 5 then reject the Null Hypothesis.

Table of Critical Values for Critical Significance Levels (α) of 0.1, 0.05 and 0.01 for the *T* statistic where degrees of freedom (df) is othe number of pairs of data points that have a none-zero difference for a Wilcoxon Signed-Rank test.

df | α = 0.1 | α = 0.05 | α = 0.01 |

1 | |||

2 | |||

3 | |||

4 | |||

5 | 0 | ||

6 | 2 | 0 | |

7 | 3 | 2 | |

8 | 5 | 3 | 0 |

9 | 8 | 5 | 1 |

10 | 10 | 8 | 3 |

11 | 13 | 10 | 5 |

12 | 17 | 13 | 7 |

13 | 21 | 17 | 9 |

14 | 25 | 21 | 12 |

15 | 30 | 25 | 15 |

16 | 35 | 29 | 19 |

17 | 41 | 34 | 23 |

18 | 47 | 40 | 27 |

19 | 53 | 46 | 32 |

20 | 60 | 52 | 37 |

21 | 67 | 58 | 42 |

22 | 75 | 65 | 48 |

23 | 83 | 73 | 54 |

24 | 91 | 81 | 61 |

25 | 100 | 89 | 68 |

26 | 110 | 98 | 75 |

27 | 119 | 107 | 83 |

28 | 130 | 116 | 91 |

29 | 140 | 126 | 100 |

30 | 151 | 137 | 109 |

31 | 163 | 147 | 118 |

32 | 175 | 159 | 128 |

33 | 187 | 170 | 138 |

34 | 200 | 182 | 148 |

35 | 213 | 195 | 159 |

36 | 227 | 208 | 171 |

37 | 241 | 221 | 182 |

38 | 256 | 235 | 194 |

39 | 271 | 249 | 207 |

40 | 286 | 264 | 220 |

Critical values of the (two-tailed) Wilcoxon *T* distribution based on Zar (1999) and sources therein.

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