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First, use the Critical Significance Level (α: alpha) glossary item: Critical Significance Level chosen in Step 2 and degrees of freedom (df) glossary item: degrees of freedom calculated in Step 3 (df = one less than the number of categories) to find the Critical Value glossary item: Critical Value of Χ22critical) using a Critical Value Table such as the one below e.g., if α = 0.05 and df = 3, then Χ2critical = 7.8.

 

Second, compare Χ2critical with the value for the Χ2 statistic calculated in Step 3.

Reject your Null Hypothesis glossary item: Null Hypothesis if your calculated value is greater than or equal to the Critical value; Χ2 ≥ Χ2critical (significant result).

Accept your Null Hypothesis glossary item: Null Hypothesis if your calculated value is less than the Critical value; Χ2 < Χ2critical (non-significant result).

E.g., if Χ2 = 8.1 and Χ2critical = 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 categories for one-way chi-squared.
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