The adjusted residuals are the raw residuals (or the difference between the observed counts and expected counts) divided by an estimate of the standard error. Use adjusted residuals to account for the variation due to the sample size.
Minitab estimates the standard deviation of the observed counts using the formula found in Adjusted residuals.
You can compare the adjusted residuals in the output table to see which categories have the largest difference between the expected counts and the actual counts relative to sample size. For example, you can see which machine or shift has the largest difference between the expected number of defectives and the actual number of defectives.
 
 

The Pearson chisquare statistic (χ^{2}) involves the squared difference between the observed and the expected frequencies.
The likelihoodratio chisquare statistic (G^{2}) is based on the ratio of the observed to the expected frequencies.
Use the chisquare statistics to test whether the variables are associated.
 

Minitab displays each cell's contribution to the chisquare statistic, which quantifies how much of the total chisquare statistic is attributable to each cell's divergence.
Minitab calculates each cell's contribution to the chisquare statistic as the square of the difference between the observed and expected values for a cell, divided by the expected value for that cell. The chisquare statistic is the sum of these values for all cells.
Use the individual cell contributions to quantify how much of the total chisquare statistic is attributable to each cell's divergence.
 
 

The degrees of freedom (DF) is the number of independent pieces of information on a statistic. The degrees of freedom for a cross tabulation is the number of rows  1, multiplied by the number of columns  1.
Minitab uses the degrees of freedom to determine the pvalue associated with the test statistic.
 

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.
You can compare the observed values and the expected values in the output table.
 
 

The pvalue is a probability that measures the evidence against the null hypothesis. Lower probabilities provide stronger evidence against the null hypothesis.
Use the pvalue to determine whether to reject or fail to reject the null hypothesis, which states that the variables are independent.
Minitab uses the chisquare statistic to determine the pvalue.
Minitab does not display the pvalue when any expected count is less than 1 because the results can be invalid.
 

You can compare the observed values and the expected values in the output table.
 
 

The standardized residuals are the raw residuals (or the difference between the observed counts and expected counts), divided by the square root of the expected counts.
You can compare the standardized residuals in the output table to see which category of variables have the largest difference between the expected counts and the actual counts relative to size, and seem to be dependent. For example, you can assess the standardized residuals in the output table to see the association between machine and shift for producing defects.
 
 

Use the table percentages to understand how the counts are distributed between the categories.
In these results, the cell count is the first number in each cell. Then the row percentages, column percentages, and total percentages are in order as the next numbers in the cell. You can select one or more of these percentages to display.
 
 
