Re: st: ksmirnov

[Nick Cox <njcoxstata@gmail.com>]

Sorry, but you have to think about this yourself based on your data
and your problem. One is a fit based on mean and SD and the other is
more robust being, less sensitive to outliers in the data. A perfect
fit would mean that the data follow the line exactly. There aren't
agreed guidelines for imperfect fit.

You can get reference plots by simulating from t(8). As said earlier,
you may have difficulties as a side-effect of any dependence structure
in your data.

Nick

On Tue, Aug 21, 2012 at 10:40 AM, Guessab Houda
<houda.guessab@gre.generali.com> wrote:
> Nick
>
> From scatter mpg expected ///
> || function t_8 = `mean' + x * `sd' / sqrt(4/3), ra(exp) ///
> || function t_8_2 = `median' + x * `iqr' / (2 * invttail(8, 0.25)), ra(exp)
>
> I get two lines, which one I use and how can I interpret it then? I mean how can I say that the distribution is more or less similar to student with 8 degrees?
>
>
>
> Houda GUESSAB
>
>
>
> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Nick Cox
> Sent: mardi 21 août 2012 11:27
> To: statalist@hsphsun2.harvard.edu
> Subject: Re: st: ksmirnov
>
> When you say the qnormal function, I presume you mean the -qnorm- command.
>
> There is no one way to do it. With the normal distribution, most
> people regard matching means and SDs to be the way to do it, but there
> is a good case for fitting a more robust line. In the case of t with 8
> d.f. (henceforth t(8))  the case is even stronger. By my calculation
> t(8) has SD = sqrt(8/6) = sqrt(4/3), but you could use the IQR or any
> other pair of quantiles. Similarly, although t(8) has mean, median and
> any other measure of level all 0, it is open for discussion how the
> data should be summarized. It may even be that 0 is a natural
> reference for whatever your data are.
>
> The straight lines come from manipulating
>
> (observed y - level for y) / (expected x - level for x) = (spread for
> y) / (spread for x)
>
> where in practice level for x is always 0.
>
> Example code:
>
>  sysuse auto, clear
>  egen rank = rank(mpg), unique
>  su rank, meanonly
>  gen expected = -invttail(8, (rank - 0.5) / `r(max)')
>  su mpg, detail
>  local mean = r(mean)
>  local sd = r(sd)
>  local median = r(p50)
>  local iqr = r(p75) - r(p25)
>
>
>  scatter mpg expected ///
> || function t_8 = `mean' + x * `sd' / sqrt(4/3), ra(exp) ///
> || function t_8_2 = `median' + x * `iqr' / (2 * invttail(8, 0.25)), ra(exp)
>
>
> On Tue, Aug 21, 2012 at 9:41 AM, Guessab Houda
> <houda.guessab@gre.generali.com> wrote:
>> OK you are right. Then I will use the program you sent me.
>>
>> sysuse auto, clear
>>>> egen rank = rank(mpg), unique
>>>> su mpg, meanonly
>>>> local N = r(N)
>>>> gen tquantile = -invttail(8, (rank - 0.5) / `N')
>>>> scatter mpg tquantile
>>
>> I just need to draw 45 degree reference line like the qnormal function does; can you help me with that?
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