NUMBAT OER - Open Educational Resources

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 (Tcritical) using a Critical Value Table such as the one below (e.g. if α = 0.05 and df = 9, then Tcritical = 5).

Second, compare Tcritical 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 ≥ Tcritical (significant result).

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

For example, if T = 7.6 and Tcritical = 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 4th edition. Prentice-Hall, New Jersey.