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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 = 0.1 p = 0.05 p = 0.02
1 1.64 2.71 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 and 0.02.

df p = 0.1 p = 0.05 p = 0.02
1 2.71 3.84 5.41
2 4.6 5.99 7.82
3 6.25 7.82 9.84
4 7.78 9.49 11.67
5 9.24 11.07 13.39
6 10.64 12.59 15.03
7 12.02 14.07 16.62
8 13.36 15.51 18.17
9 14.68 16.92 19.68
10 15.99 18.31 21.16
11 17.28 19.68 22.62
12 18.55 21.03 24.05
13 19.81 22.36 25.47
14 21.06 23.68 26.87
15 22.31 25 28.26
16 23.54 26.3 29.63
17 24.77 27.59 31
18 25.99 28.87 32.35
19 27.2 30.14 33.69
20 28.41 31.41 35.02

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

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