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Comment by kgwgk | Hacker News Reader

You complained I didn't show anything, so there you have something. Do you have anything, even if it is a bald random Wikipedia assertion, supporting your position? (Rhetorical question, I couldn't care less.)

Here is a full derivation from a random blog, which I guess doesn't count either: https://shihho.wordpress.com/2012/11/27/pvalue_distribution/

Another one: https://joyeuserrance.wordpress.com/2011/04/22/proof-that-p-...

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You seem awfully invested in a discussion that you don't care about.

>https://shihho.wordpress.com/2012/11/27/pvalue_distribution/

This treatment commits the same error as the other poster (evanpw; I believe nonbel commits the same). The image at the bottom is only showing p-values for single observations. That is near useless (as the chart shows). An actual experiment requires repeated observation and analysis, not one-off observations.

    npval <- pnorm( rnorm(nSim, mean, std.dev), mean, std.dev )
    hist(npval, breaks=40, xlab=xlabel, main=title, col='gray')

R is probably the worst choice of language here, but my understanding of `pnorm` is that, when passed a list of numbers as the first argument (as `rnorm` returns), it will return a list of p-values (assuming normal distribution with given parameters), where the index in the list corresponds to the p-value, taking into account only that single observation (ie. it ignores all other observations in the list [ie. not how p-value hypothesis testing works {at least, in theory; real world practices may differ}]).

Your second link appears to be the same argument (at least, they appear to use the same equations).

The charts are a nice visualization of how you can get a uniform distribution from a normal one (or vice versa) though.

You might also want to take a look at the source of the function you are relying on:

    *  DESCRIPTION
     *
     *	The main computation evaluates near-minimax approximations derived
     *	from those in "Rational Chebyshev approximations for the error
     *	function" by W. J. Cody, Math. Comp., 1969, 631-637.  This
     *	transportable program uses rational functions that theoretically
     *	approximate the normal distribution function to at least 18
     *	significant decimal digits.  The accuracy achieved depends on the
     *	arithmetic system, the compiler, the intrinsic functions, and
     *	proper selection of the machine-dependent constants.
     *

So...yeah. I hope the constants the R authors picked work for your machine!

    const static double a[5] = {
	2.2352520354606839287,
	161.02823106855587881,
	1067.6894854603709582,
	18154.981253343561249,
	0.065682337918207449113
    };
    const static double b[4] = {
	47.20258190468824187,
	976.09855173777669322,
	10260.932208618978205,
	45507.789335026729956
    };
    const static double c[9] = {
	0.39894151208813466764,
	8.8831497943883759412,
	93.506656132177855979,
	597.27027639480026226,
	2494.5375852903726711,
	6848.1904505362823326,
	11602.651437647350124,
	9842.7148383839780218,
	1.0765576773720192317e-8
    };
    const static double d[8] = {
	22.266688044328115691,
	235.38790178262499861,
	1519.377599407554805,
	6485.558298266760755,
	18615.571640885098091,
	34900.952721145977266,
	38912.003286093271411,
	19685.429676859990727
    };
    const static double p[6] = {
	0.21589853405795699,
	0.1274011611602473639,
	0.022235277870649807,
	0.001421619193227893466,
	2.9112874951168792e-5,
	0.02307344176494017303
    };
    const static double q[5] = {
	1.28426009614491121,
	0.468238212480865118,
	0.0659881378689285515,
	0.00378239633202758244,
	7.29751555083966205e-5
    };

https://svn.r-project.org/R/trunk/src/nmath/pnorm.c

Edit: Ah, a drive-by downmodder. How nice.

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