| Chi-square is a convenient measure of association | | | | have a brain. It is merely an algorithm of human |
| between two factors when the factors are not | | | | frequencies, a mechanical process based on numbers |
| quantitative. It indicates the degree to which the human | | | | regardless of what they represent. By itself, it never |
| frequencies in a cross-tab of the two factors deviate | | | | can take the place of a regression or correlation |
| from what they would be if there was no interrelation | | | | because it cannot describe the human frequencies, |
| at all between the factors. The computed chi-square | | | | only gauge their statistical significance, entirely |
| has a specific level of statistical significance looked up | | | | regardless of logic or sense. |
| in a standard table. | | | | Chi-square is non-parametric. To describe a human |
| Suppose we ask 300 testers to rate our pretzels (A) | | | | frequency in numerical terms, we need numerical |
| and another brand's (B) both in terms of overall | | | | values-that is, parameters. If we arbitrarily assign value |
| preference and preference regarding human | | | | +1 to preference for A and -1 to preference for B, we |
| frequencies. By a convenient coincidence, the "crunch" | | | | can compute a correlation coefficient-r= +.246 for the |
| preference divides exactly even, with 100 preferring A, | | | | original tabulation, and exactly half that for the |
| 100 preferring B, and 100 having no preference. | | | | corrected distribution. The parametric regression |
| Clearly, there is a strong association between the | | | | correlation, unlike chisquare, is affected by the way the |
| preference on "crunch" and overall human frequencies; | | | | rows and columns are labeled because each label has |
| chi-square is 18.4, indicating a significance level of 99%+ | | | | a specific value. |
| ... Wait a minute, there's the phone. What's that? I see... | | | | So chi-square is a very useful index when we cannot |
| a stub-labeling error, the last two lines got switched... | | | | assign values to human frequencies, but it is very easy |
| Okay, thanks. | | | | to misuse it; it doesn't have a brain, so the analyst has |
| So let's see, now we have: | | | | to use his or her own brain to interpret it correctly. |
| That still looks like a strong association for (A) but not | | | | Though one doesn't necessarily need fancy testing |
| for (B), so we should have a lower chi-square, right? | | | | equipment to know how they feel health-wise. Once |
| No. Chi-square is still 18.4. As long as the numbers stay | | | | the human body can absorb the right nutrition in the |
| the same, it doesn't matter how they are labeled. Like | | | | correct electrical patterns, health can't help but improve. |
| the Scarecrow in Wizard of Oz, chi-square doesn't | | | | |