Pass or fail? Binomialrelated hypothesis testing and confidence intervals using paired samples - Improving the User Experience through Practical Data Analytics - page 134

5.5 SUMMARY
In this chapter we studied hypothesis testing for “nominal/categorical” data, more
speciically, “pass/fail” data. But, in contrast to the situation in Chapter 4, where we
had independent samples, this chapter had paired data or a within-subjects design.
This meant that the chi-square test of independence was no longer appropriate.
Thus, we introduced the Cochran Q test. We emphasized how knowing the paired
responses, and not only the overall pass/fail rates, is critical to performing the analy-
sis. The reasoning behind this is similar to the discussion in Chapter 3 when we intro-
duced the paired t-test and contrasted it with the t-test with independent samples. We
considered the Cochran Q test in both Excel (with formulas, since the technique is
not part of Excel) and in SPSS, where the Cochran test is available.
5.6 EXERCISE
1. Consider tasks 6, 7, and 8 of Table 5.1 . Test the hypothesis that there is no dif-
ference in the true pass/fail rates for the three tasks. The design is a repeated
measures design. The input in Excel is in a ile named Chapter 5.Exercise 1. In
SPSS, the input is in a ile Chapter 5..Exercise 1.input and the output is in a ile
named Chapter 5..Exercise 1.output.
A Word ile (ile name: Chapter 5.Exercise 1.discussion) is also provided, which
discusses the results.
REFERENCES
Cochran, W.G., 1950. The comparison of percentages in matched samples. Biometrika 37,
256-266.
McNemar, Q., 1947. Note on the sampling error of the difference between correlated
proportions or percentages. Psychometrika 12, 153-157.