On 25/05/2013 18:36, David Jones wrote:> Probably, that site knows what a "two-sided test" means whereas, judging> by your description of simulation for the skewness, you do not.

I know what a "two-sided test" means (I wrote some 2-sided tests to testRNG's), but I could be a bit confused in writing a simulation for a2-sided test. Anyway, I don't think that it is very important. Here I'mjust trying to understand how they get those critical values because Ineed to be sure that my simulation works fine.

> The simplest change to your procedure would be to use the absolutevalue of> the calculated skewness, since that is the test statistic for a> two-sided test in this case. On the webpage, "alpha" is the total area> of the two tails, not just one tail.

I know that (I saw the 2 red tails).

If I use the absolute value of the skewness calculated (many times) for7 numbers in N(0,1) and I see that the 90th percentile is .8163, I wouldargue that 90% of the times the |skewness| <= .8163. Am I wrong?If I'm right, .8163 should be the critical values for their alpha= 0.1.Even if I don't know anything about 2-sided tests, could someone tellme, please, how in the earth they get 1.307?

Cristiano

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Have you tried finding an alternative source of critical values? Judging by values in "Biometrika Tables" (which need to be adjusted for differences in definition, and which give values only for n=25 upwards, and which may be subject to some approximation error), the values for skewness on that webpage seem right. You could check "Biometrika Tables" for details of how they got their values (Pearson ES, Hartley HO (1969) Biometrika Tables for Statisticians, Vol 1, 3rd Edition, Cambridge University Press), but it is unlikely that the webpage used those methods.

Thus there is at least some evidence that the webpage is correct at least for n>=25, and there that your programming is wrong somewhere. You could try testing against published values for the variance of the skewness, which would potentially avoid doubts about those webpage tables.