On 27/05/2013 1:07, Rich Ulrich wrote: > On Sat, 25 May 2013 12:43:38 +0200, Cristiano <cristiapi@NSgmail.com> > wrote: > >> On 25/05/2013 5:50, Rich Ulrich wrote: >>>> Yes, I do that, but to be more precise: >>>> 1) Draw 7; compute skewness; >>>> 2) if skewness < 0 discard the value, else save. >>> >>> Depending on what you mean by "discard," >> >> Uh? What I mean? Discard is discard; I mean discard. >> You can take a look here: >> http://www.thefreedictionary.com/discard >> "To throw away; reject." >> >>> this might introduce some unknown bias. Do you keep the count? >>> There will never be *exactly* 50% of the sample with >>> skewness less than 0. >> >> Sure, but where's the problem? > > Do you count it? "Throw away; reject" implies that > you will sample 100k values that are all positive, which > is clearly wrong. If you adapted by sampling 50k positive, > you will be wrong by the fraction off from 50%.
When I use only skewness >= 0, the only difference I see is the speed (there is no difference in the critical values, as expected for symmetrical distributions).
>>> As you say, the distribution *ought* to be exactly symmetrical. >>> >>> The lower limit provides a second value based on 100,000 >>> replications. (1) Why ignore it? (2) If there were some bias >>> in your RNG that these computations brought out, it would be >>> important to know it. >> >> The RNG I use doesn't have any bias. > > I expect that that is (nearly) true. But I expect that a professional > RNG creator/tester would never lay out that statement without > some qualification, such as, "that woud be detected in an experiment > like this one."
I use the dSFMT PRNG (which comes with a sound quality proof) and I checked its "randomness" using an improved version of RaBiGeTe.
>> I don't have any problem in using both tails, but does it make any sense? >> We already know that the critical values for the 5th and 95th percentile >> *must* be exactly the same. >> For example, using both tails I get: >> 0.05 -.82306 +/- 2.75e-4 >> 0.95 .82311 +/- 2.73e-4 >> (+/- indicates the confidence interval) >> The p-value have to come from a 2-sided test; there should be only one >> critical value. Where's the sense in using -.82306 and .82311? > > Here's a minor puzzle for me. Early, you were referring to the same > two-tailed limits (I think) as being about 1.2, not 0.82. Oh, well.
I calculated those values using a "complicated" algorithm to reduce the rounding errors, but I should have been wrong when I wrote the C++ code for that algorithm. Now I use the straightforward algorithm to calculate the skewness and I get very similar results to those presented in the site.