Question

Using StatCrunch, construct a labeled contingency table (with row, column, and total %s), as well as the contribution to the chi-square statistic, for the following set of data for 300 people:

                                                Group A          Group B          Group C          Total

            Had flu shot                     20                   30                    38                   88

            Didn’t have flu shot         80                   70                    62                 212

            Total                               100                 100                  100               300

        Is the value of the chi-square statistically significant?

Answer 1

For each of the 9 cells, the expected frequency is computed here as:

E_i = (Row_i Total) ( Column_i Total) / 300 ,
Also the chi square test statistic for each cell is computed as:

This is computed for each of the 9 cells as:

The values in the circular bracket are expected frequencies and in square bracket are the chi square contributions.

The chi square test statistic thus is computed here as:

Df = (num of rows - 1)(num of columns - 1) = 2

Therefore the p-value here is computed as:

Note that the value is clearly greater than 0.01, but less than 0.05. Therefore it is significant at 5% level of significance but not at 1% level of significance.