Complete the following steps to interpret a cross tabulation analysis. Key output includes counts and expected counts, chi-square statistics, and p-values.
Step 1: Determine whether the association between the variables is statistically significant
Use the p-value to determine whether to reject or fail to reject the null hypothesis, which states that the variables are independent.
To determine whether 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 statistical 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: The variables have no association (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 Test
Chi-Square
DF
P-Value
Pearson
11.79
4
0.0190
Likelihood Ratio
11.82
4
0.0188
Key Result: P-Value
In these results, the p-values are 0.0190 and 0.0188. Because the p-values are less than the significance level of 0.05, you must reject the null hypothesis. You can conclude that the variables are associated.
Step 1: Examine the differences between expected counts and observed counts to determine which variable levels may have the most impact on association
The observed counts are the actual number of observations in a sample that belong to a category.
The expected counts value is the projected frequency that would be expected in a cell, if the variables are independent. Minitab calculates the expected counts as the product of the row and column totals, divided by the sample size.
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 standardized residuals to see which variables have the largest difference between the expected counts and the actual counts relative to sample size.
Rows: Machine ID Columns: Worksheet columns
1st shift
2nd shift
3rd shift
All
1
48
47
48
143
56.08
46.97
39.96
-1.08
0.01
1.27
2
76
47
32
155
60.78
50.91
43.31
1.95
-0.55
-1.72
3
36
40
34
110
43.14
36.13
30.74
-1.09
0.64
0.59
All
160
134
114
408
Cell Contents:
Count
Expected count
Standardized residual
Key Results: Counts and Expected Counts
In this cross tabulation table, the cell count is the first number in each cell, the expected count is the second number in each cell, and the standardized residual 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 standardized residual is also the largest.
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