Chi-square is a convenient measure of association between two factors when the factors are not quantitative. It indicates the degree to which the human frequencies in a cross-tab of the two factors deviate from what they would be if there was no interrelation at all between the factors. The computed chi-square has a specific level of statistical significance looked up in a standard table.



Suppose we ask 300 testers to rate our pretzels (A) and another brand's (B) both in terms of overall preference and preference regarding human frequencies. By a convenient coincidence, the "crunch" preference divides exactly even, with 100 preferring A, 100 preferring B, and 100 having no preference.

Clearly, there is a strong association between the preference on "crunch" and overall human frequencies; chi-square is 18.4, indicating a significance level of 99%+ ... Wait a minute, there's the phone. What's that? I see... a stub-labeling error, the last two lines got switched... Okay, thanks.

So let's see, now we have:

That still looks like a strong association for (A) but not for (B), so we should have a lower chi-square, right?

No. Chi-square is still 18.4. As long as the numbers stay the same, it doesn't matter how they are labeled. Like the Scarecrow in Wizard of Oz, chi-square doesn't have a brain. It is merely an algorithm of human frequencies, a mechanical process based on numbers regardless of what they represent. By itself, it never can take the place of a regression or correlation because it cannot describe the human frequencies, only gauge their statistical significance, entirely regardless of logic or sense.

Chi-square is non-parametric. To describe a human frequency in numerical terms, we need numerical values-that is, parameters. If we arbitrarily assign value +1 to preference for A and -1 to preference for B, we can compute a correlation coefficient-r= +.246 for the original tabulation, and exactly half that for the corrected distribution. The parametric regression/correlation, unlike chisquare, is affected by the way the rows and columns are labeled because each label has a specific value.

So chi-square is a very useful index when we cannot assign values to human frequencies, but it is very easy to misuse it; it doesn't have a brain, so the analyst has to use his or her own brain to interpret it correctly.

Though one doesn't necessarily need fancy testing equipment to know how they feel health-wise. Once the human body can absorb the right nutrition in the correct electrical patterns, health can't help but improve.