On 22 Oct 2003 05:38:30 -0700, [EMAIL PROTECTED] (Luca Meyer) wrote: > Hello, > > I m a running parallel chi-squared tests on the same sample, and I have > sort of noticed that if I select a somehow smaller set of observations I > tend to get smaller, less significative Chi-Squared values. > > Is this the case? I mean, chi-squared values are sort of dependent upon > sample sizes?
For a 2x2 table, one measure of the "effect size" is the Pearson product-moment correlation -- in particular for 2x2, it is called phi. Since 'phi' describes the *effect*, you have to translate it in one way or another in order to get a *test*. You can look it up in a table with N, if you want. Or, the product of phi-squared times N is equal to chi-squared; and chi-squared is a *test* statistic. The value of 3.84, for 1 d.f., is always the 5% 'test'. For any stated value of phi (other than 0) you can always describe an N where the table would be apparently non-random. Thus, chisquared is not a decent measure of 'effect' -- except, perhaps, when tables are based on the same N. That is one reason that "same N" is always easier to work with and report, that is, because the Effects and Tests are strictly parallel. > If so, what woudl be a correction/alternative test that > avoids this dependency? I hope I've answered that -- You can't do both at once. You can't report 'effect' and 'test' without a dependency. Some effects, like phi (or r-squared) have a simple link to the N. However, some links more complex. For instance, the Odds Ratio is wonderfully lovely, at times, for being a consistent and robust descriptor of effect sizes; however, it is *relatively* tougher to form its *test* since it depends on (a) the smallest cell and (b) the smallest marginal total, in addition to depending on (c) the total N. - Chi-squared has absorbed the N; doubling the cells doubles he test-value. - Phi or phi-squared is immune to the N; but, phi giving a simple transformation to chi-squared, you can test directly from the phi-squared and N. - OR is immune to the N; plus, you need the margins to make the test: two tables with same ORs can have different tests. -- Rich Ulrich, [EMAIL PROTECTED] http://www.pitt.edu/~wpilib/index.html "Taxes are the price we pay for civilization." . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
