<<<back to statistical tests

Chi squared can be used to test for:

And it can also be used to test for:

To find the correct critical value when calculating whether results are statistically significant using the chi squared test, you need to know:

  • Whether your experimental hypothesis is one-tailed or two-tailed (it’s probably going to be two-tailed if it’s chi squared)
  • The level of significance (p)
    • This will be given to you in the exam
  • The degrees of freedom (df)
    • This will be given to you in the exam, but is calculated as follows:
      • Multiply (number of rows in your data table – 1) x (number of columns in your data table – 1)

Your results are statistically significant if the observed value is equal to or greater than the critical value.

Note: Tables like the ones below will be provided in the exam – you don’t have to memorise all these critical values!

One-tailed chi squared test

One-tailed: The experimental hypothesis predicts a change in only one direction (also called a directional hypothesis).

df p = 0.10 p = 0.05 p = 0.025 p = 0.01
1 2.71 3.84 5.02 6.64

Your results are statistically significant if the observed value is equal to or greater than the critical value.

Two-tailed chi squared test

Two-tailed: The experimental hypothesis predicts a change in either direction (also called a non-directional hypothesis).

The following are critical values for two-tailed experiments where degrees of freedom (df) range between 1-20 and for p values of 0.1, 0.05, 0.025, and 0.01.

df p = 0.10 p = 0.05 p = 0.025 p = 0.01
1 2.71 3.84 5.02 6.64
2 4.61 5.99 7.38 9.21
3 6.25 7.82 9.35 11.35
4 7.78 9.49 11.14 13.28
5 9.24 11.07 12.83 15.09
6 10.65 12.59 14.45 16.81
7 12.02 14.07 16.01 18.48
8 13.36 15.51 17.54 20.09
9 14.68 16.92 19.02 21.67
10 15.99 18.31 20.48 23.21
11 17.28 19.68 21.92 24.73
12 18.55 21.03 23.34 26.22
13 19.81 22.36 24.74 27.69
14 21.06 23.69 26.12 29.14
15 22.31 25.00 27.49 30.58
16 23.54 26.30 28.85 32.00
17 24.77 27.59 30.19 33.41
18 25.99 28.87 31.53 34.81
19 27.20 30.14 32.85 36.19
20 28.41 31.41 34.17 37.57
21 29.62 32.67 35.48 38.93
22 30.81 33.92 36.78 40.29
23 32.01 35.17 38.08 41.64
24 33.20 36.42 39.36 42.98
25 34.38 37.65 40.65 44.31
26 35.56 38.89 41.92 45.64
27 36.74 40.11 43.20 46.96
28 37.92 41.34 44.46 48.28
29 39.09 42.56 45.72 49.59
30 40.26 43.77 46.98 50.89
40 51.81 55.76 59.34 63.69
50 63.17 67.51 71.42 76.15
60 74.40 79.08 83.30 88.38
70 85.53 90.53 95.02 100.43

Your results are statistically significant if the observed value is equal to or greater than the critical value.

<<<back to statistical tests