Real Statistics Support for Cochran’s Q Test

Worksheet Functions

Real Statistics Functions: The Real Statistics Resource Pack provides the following functions:

COCHRAN(R1, raw, cont) = Cochran’s Q statistic

QTEST(R1, raw, cont) = p-value for Cochran’s Q test

QRATIO(R1, raw) – an array function that returns a row range with the percentages of each independent variable for Cochran’s Q test

Two data input formats are supported: raw data (raw = TRUE) and summarized data (raw = FALSE, default), i.e. data in the form of a multi-variable frequency table.

If cont = TRUE (default), then a continuity correction of 1 is employed when there are only two variables. This makes Cochran’s Q test equivalent to McNemar’s test when there are two variables.

For Example 1 of Cochran’s Q Test, the formulas

• COCHRAN(B4:D23,TRUE) = 6.705882
• QTEST(B4:D23,TRUE) = 0.034981
• QRATIO(B4:D23,TRUE) produces the output in range L4:N4 of Figure 3 of Cochran’s Q Test.

For Example 1 of Cochran’s Q Test using Summary Data, COCHRAN(A4:E19) = 7.366972, QTEST(A4:E19) = 0.061077, and = QRATIO(A4:E19) produces the output in range M4:P4 of Figure 3 of Cochran’s Q Test using Summary Data.

These functions can also be used with completely blank columns. We can, therefore, calculate Cochran’s Q for the data in Figure 4 of Cochran’s Q Test. In this case, COCHRAN(B51:D70,TRUE,FALSE) = 5.333333 and QTEST(B51:D70,TRUE,FALSE) = 0.020921. These are the results without using a continuity correction. The results using a continuity correction (i.e. for McNemar’s test) are COCHRAN(B51:D70,TRUE) = 4.6785 and QTEST(B51:D70,TRUE) = 0.030383.

Data Analysis Tool

Real Statistics Data Analysis Tool: The Real Statistics Resource Pack provides support for Cochran’s Q Test as part of the Non-parametric Tests data analysis tool.

For example, to produce the output for Example 1 of Cochran’s Q Test using Summary Data, press Ctrl-m and double-click on the Non-parametric Tests option (after first selecting the Misc tab if using the multipage interface). Fill in the dialog box that appears as described in Figure 1.

Figure 1 – Non-parametric Tests dialog box

When you click on the OK button, the output shown in Figure 2 is displayed.

Figure 2 – Cochran’s Q Test output

When there are only two variables, the data analysis tool will apply a continuity correction of 0.5, so the results will be equivalent to those of McNemar’s test.

Links

↑ Cochran’s Q test

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