       Re: Normality test

• To: mathgroup at smc.vnet.net
• Subject: [mg107204] Re: Normality test
• From: Ray Koopman <koopman at sfu.ca>
• Date: Fri, 5 Feb 2010 03:24:08 -0500 (EST)
• References: <hk8nns\$8jv\$1@smc.vnet.net> <hk93dv\$f7b\$1@smc.vnet.net>

```Here, prompted by off-line conversations, is an improved version of
qqnorm:

qqnorm2[data_] := Block[{n, y,y1,y2,y3, x,x1,x2,x3, b,a},
n = Length@data; y = Sort@data; {y1,y2,y3} = Quartiles@y;
x = InverseErf[Range[1-n,n-1,2]/(n+.33(n-1.25)^-.1)]*Sqrt[2.];
{x1,x2,x3} = Quartiles@x; b = (y3-y1)/(x3-x1); a = y1 - b*x1;
ListPlot[Transpose@{x,y}, PlotRange->All, Frame->True, Axes->None,
AspectRatio->((Last@y-First@y)/(y3-y1))/((Last@x-First@x)/(x3-x1)),
Prolog->Line[{#,#*b+a}&/@{First@x,Last@x}],
FrameLabel->{"Standard Normal","Observed Data"}]]

The most notable changes are that the reference line is now drawn so
that it passes through the joint first and third quartile points, and
the aspect ratio now varies so that the visual slope of the reference
line is always approximately 1. Also, the normal scores are now a
better approximation of the expected order statstics.

On Feb 2, 3:48 am, Ray Koopman <koop... at sfu.ca> wrote:
> On Feb 2, 12:28 am, michael partensky <parten... at gmail.com> wrote:
>> Hi.
>> I wonder if anybody knows a function similar to qqnorm(data) from
>> *R*, producing a normal scores plot, or some related tools in M.
>> for testing normality of data?
>>
>> Thanks
>> Michael Partenskii
>
> qqnorm[y_] := Block[
>  {n = Length@y, m = Mean@y, s = StandardDeviation@y, x},
>  x = InverseErf[Range[1-n,n-1,2]/n]*Sqrt[2.];
>  ListPlot[Transpose@{x,Sort@y},
>  PlotRange->All, Frame->True, Axes->None, AspectRatio->1,
>  Prolog->Line[{{x[],x[]*s+m},{x[[-1]],x[[-1]]*s+m}}],
>  FrameLabel->{"Theoretical Standard Normal Quantiles",
>               "Observed Quantiles"}]]

```

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