where and are the respective population proportions from group 1 and 2.
The categorical data are summarized in the count of the specific type (Observed) and the total sample size (Size) in the first row (Group 1) and the second row (Group 2) as follows.
The test statistic is calculated as
where and are the point estimates of and as they appear in the column Probability in the above table.
is called a pooled estimate of the common population proportion. Having constructed the hypothesis testing problems `` '', `` '', or `` '', we can make our decision via p-value = . Also, we may want to see the confidence interval for the difference . The confidence interval for can be calculated by
= ( , )