Examine the results of a chi-square test of association to determine whether the
association between the variables is statistically significant. Use the p-values, observed
and expected cell counts, and the contribution to the chi-square statistic to evaluate
variable association.

To determine whether the variables are independent, compare the p-value to the significance level. Usually, a significance level (denoted as α or alpha) of 0.05 works well. A significance level of 0.05 indicates a 5% risk of concluding that an association between the variables exists when there is no actual association.

- P-value ≤ α: The variables have a statistically significant association (Reject H
_{0}) - If the p-value is less than or equal to the significance level, you reject the null hypothesis and conclude that there is a statistically significant association between the variables.
- P-value > α: Cannot conclude that the variables are associated (Fail to reject H
_{0}) - If the p-value is larger than the significance level, you fail to reject the null hypothesis because there is not enough evidence to conclude that the variables are associated.

Chi-Square | DF | P-Value | |
---|---|---|---|

Pearson | 11.788 | 4 | 0.019 |

Likelihood Ratio | 11.816 | 4 | 0.019 |

In these results, the Pearson chi-square statistic is 11.788 and the p-value = 0.019. The likelihood chi-square statistic is 11.816 and the p-value = 0.019. Therefore, at a significance level of 0.05, you can conclude that the association between the variables is statistically significant.

To determine which variable levels have the most impact, compare the observed and expected counts or examine the contribution to the chi-square statistic.

By looking at the differences between the observed cell counts and the expected cell counts, you can see which variables have the largest differences, which may indicate dependence. You can also compare the contributions to the chi-square statistic to see which variables have the largest values that may indicate dependence.

1st shift | 2nd shift | 3rd shift | All | |
---|---|---|---|---|

1 | 48 | 47 | 48 | 143 |

56.08 | 46.97 | 39.96 | ||

1.1637 | 0.0000 | 1.6195 | ||

2 | 76 | 47 | 32 | 155 |

60.78 | 50.91 | 43.31 | ||

3.8088 | 0.2998 | 2.9530 | ||

3 | 36 | 40 | 34 | 110 |

43.14 | 36.13 | 30.74 | ||

1.1809 | 0.4151 | 0.3468 | ||

All | 160 | 134 | 114 | 408 |

In this table, the cell count is the first number in each cell, the expected count is the second number in each cell, and the contribution to the chi-square statistic is the third number in each cell. In these results, the expected count and the observed count are the largest for the 1st shift with Machine 2, and the contribution to the chi-square statistic is also the largest. Investigate your process during the 1st shift with Machine 2 to see if there is a special cause that can explain this difference.