Chi squared test

A significant difference from your null hypothesis (i.e. difference from your expectation) is indicated when your calculated X2 value is greater than the c2 value shown in the 0.05 column of this table (i.e. there is only a 5% probability that your calculated X2value would occur by chance). You can be even more confident if your calculated value exceeds the c2 values in the 0.01 or 0.001 probability columns.

If your calculated X2 value is equal to, or less than, the tabulated c2 value for 0.95 then your results give you no reason to reject the null hypothesis.

In a few special circumstances (though not generally) a calculated X2 value lower than the c2value in the 0.95 or 0.99 columns provides evidence that your results agree well with a null hypothesis.

 

Degrees of Freedom Probability, p
  0.99 0.95 0.05 0.01 0.001
1 0.000 0.004 3.84 6.64 10.83
2 0.020 0.103 5.99 9.21 13.82
3 0.115 0.352 7.82 11.35 16.27
4 0.297 0.711 9.49 13.28 18.47
5 0.554 1.145 11.07 15.09 20.52
6 0.872 1.635 12.59 16.81 22.46
7 1.239 2.167 14.07 18.48 24.32
8 1.646 2.733 15.51 20.09 26.13
9 2.088 3.325 16.92 21.67 27.88
10 2.558 3.940 18.31 23.21 29.59
11 3.05 4.58 19.68 24.73 31.26
12 3.57 5.23 21.03 26.22 32.91
13 4.11 5.89 22.36 27.69 34.53
14 4.66 6.57 23.69 29.14 36.12
15 5.23 7.26 25.00 30.58 37.70
16 5.81 7.96 26.30 32.00 39.25
17 6.41 8.67 27.59 33.41 40.79
18 7.02 9.39 28.87 34.81 42.31
19 7.63 10.12 30.14 36.19 43.82
20 8.26 10.85 31.41 37.57 45.32
21 8.90 11.59 32.67 38.93 46.80
22 9.54 12.34 33.92 40.29 48.27
23 10.20 13.09 35.17 41.64 49.73
24 10.86 13.85 36.42 42.98 51.18
25 11.52 14.61 37.65 44.31 52.62
26 12.20 15.38 38.89 45.64 54.05
27 12.88 16.15 40.11 46.96 55.48
28 13.57 16.93 41.34 48.28 56.89
29 14.26 17.71 42.56 49.59 58.30
30 14.95 18.49 43.77 50.89 59.70

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