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THE CHI-SQUARE TEST ISN'T ALWAYS THE BEST CHOICE.
Six Sigma practitioners occasionally conduct studies to assess differences between items such as operators or machines. When the experimental data are measured on a continuous scale (measuring nozzle diameter in microns, for example), a procedure such as "Student's" two-sample t-test may be appropriate.1 When the response variable is recorded using counts, however, Karl Pearson's test may be employed.2
But when the number of observations obtained for analysis is small, the test may produce misleading results. A more appropriate form of analysis (when presented with a 2 * 2 contingency table) is to use R.A. Fisher's exact test.
Example
On the Late Show With David Letterman, the host (David) and the show's musical director (Paul Shaffer) frequently assess whether particular items will or will not float when placed in a tank of water. Let's assume Letterman guessed correctly for eight of nine items, and Shaffer guessed correctly for only four items. Let's also assume all the items have the same probability of being guessed.
You would typically use the [chi]^sup 2^ test when presented with the contingency table results in Figure 1. In this case, the [chi]^sup 2^ test assesses what the expected frequencies would be if the null hypothesis (equal proportions)...