Cochran’s Q Test using Summary Data

On this webpage, we explain how to conduct Cochran’s Q Test for data in frequency table format. See Cochran’s Q Test for the case where data is in raw format.

Example

Example 1: One hundred people are asked to rate four different drug formulations as effective or not for hay fever. Based on the data in Figure 1 (where 1 means effective in treating hay fever and 0 means ineffective in treating hay fever) determine whether there is a significant difference between the four drug formulations.

This time the data is displayed in the form of a frequency table.

Figure 1 – Data for Cochran’s Q Test

Test Statistic

We use the following version of the Q statistic.

where m = the number of rows, x_ij = the value in the ith row and jth column, f_i = the frequency for the ith row (thus the total sample size n = ), x_i = ,  x_j =  and N = .

Results

The calculations are shown in Figure 2.

Figure 2 – Cochran’s Q Test

This time p-value = 0.061, and so we cannot reject the null hypothesis that the drugs are equally effective. We display the percentage of effectiveness for each drug in Figure 3 (as shown in row 20 of Figure 2).

Figure 3 – Percentage of effectiveness

Examples Workbook

Click here to download the Excel workbook with the examples described on this webpage.

References

Wikipedia (2014) Cochran’s Q
https://en.wikipedia.org/wiki/Cochran%27s_Q_test

NCSS (2014) Cochran’s Q test
https://www.ncss.com/wp-content/themes/ncss/pdf/Procedures/NCSS/Cochrans_Q_Test.pdf