First, use the Critical Significance Level (α) chosen in Step 2 and degrees of freedom (df) calculated in Step 3 (df = one less than the number of rows, multiplied by one less than the number of columns in the contingency table) to find the Critical Value of Χ^{2} (Χ^{2}_{critical}) using a Critical Value Table such as the one below (e.g. if α = 0.05 and df = 3, then Χ^{2}_{critical} = 7.8).

Second, compare Χ^{2}_{critical} with the value for the Χ^{2} statistic calculated in Step 3.

Reject your Null Hypothesis if your calculated value is greater than or equal to the Critical value; X^{2} ≥ X^{2}_{critical} (significant result).

Accept your Null Hypothesis if your calculated value is less than the Critical value; X^{2} < X^{2}_{critical} (non-significant result).

For example, if Χ^{2} = 9.62 and Χ^{2}_{critical} = 7.8 then reject the Null Hypothesis.

Table of Critical Values for Critical Significance Levels (α) 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 |

Critical values of the chi-square distribution generated using the CHINV() function in Microsoft Excel, which returns the inverse of the one-tailed probability of the chi-squared distribution. Table generated by Toby Carter.