Human Frequencies
By : Joe Bella | ID: 25495 | Views : 2400 | Words: 434 | Rating : Not Rated 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.
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.
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