Interpret the key results for Chi-Square Test for Association

Complete the following steps to interpret a chi-square test of association. Key output includes p-values, cell counts, and each cell's contribution to the chi-square statistic.

In This Topic

Step 1: Determine whether the association between the variables is statistically significant
Step 2: Examine the differences between expected counts and observed counts to determine which variable levels may have the most impact on association

Step 1: Determine whether the association between the variables is statistically significant

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 H₀): 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 H₀): 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 Test

	Chi-Square	DF	P-Value
Pearson	11.788	4	0.019
Likelihood Ratio	11.816	4	0.019

Key Results: P-Value for Pearson Chi-Square, P-Value for Likelihood Ratio Chi-Square

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.

Step 2: Examine the differences between expected counts and observed counts to determine which variable levels may have the most impact on association

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

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.

Rows: Machine ID Columns: Worksheet columns

	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

Key Results: Count, Expected count, Contribution to Chi-square

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.