Math Forum Discussions

Cristiano

Posts: 60
Registered: 12/7/12

Re: Skewness and kurtosis p-values
Posted: May 27, 2013 7:59 AM

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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.

Cristiano