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First, use the Critical Significance Level (α: alpha) chosen in Step 2 and degrees of freedom (df) calculated in Step 3 (where df = one less than the number of rows multiplied by one less than the number of columns in the contiguency table) to find the Critical Value of Χ² (Χ²_critical) using a Critical Value Table such as the one below e.g., if α = 0.05 and df = 3, then Χ²_critical = 7.8.

 

Second, compare Χ²_critical with the value for the Χ² statistic calculated in Step 3.

Reject your Null Hypothesis if your calculated value is greater than or equal to the critical value; Χ² ≥ Χ²_critical (significant result).

Accept your Null Hypothesis if your calculated value is less than the critical value; Χ² < Χ²_critical (non-significant result).

E.g., if Χ² = 9.62 and Χ²_critical = 7.8 then reject the Null Hypothesis.

 

Table of Critical Values for Critical Significance Levels (α: alpha) of 0.9, 0.5, 0.1, 0.05 and 0.01 for the Chi-squared statistic where degrees of freedom (df) is one less than the number of rows multiplied by one less than the number of columns in the contingency table for two-way chi-squared test.

degrees of freedom	α = 0.9	α = 0.5	α = 0.1	α = 0.05	α = 0.01
1	0.016	0.455	2.706	3.841	6.635
2	0.211	1.386	4.605	5.991	9.210
3	0.584	2.366	6.251	7.815	11.345
4	1.064	3.357	7.779	9.488	13.277
5	1.610	4.351	9.263	11.070	15.086
6	2.204	5.348	10.645	12.592	16.812
7	2.833	6.346	12.017	14.067	18.475
8	3.490	7.344	13.362	15.507	20.090