[R] question about shapiro.test()

[Greg Snow]

Why are you doing the test for normality?

The 2 most common reasons are:

1. want to test if data comes from an exact normal distribution.
2. want to know if tests based on normal assumptions are reasonable to use with this data.

Technically, the Shapiro-Wilk test does not do either of the above, but further suggestions depend on what you are trying to accomplish, or what question you want answered.

--
Gregory (Greg) L. Snow Ph.D.
Statistical Data Center
Intermountain Healthcare
greg.snow at imail.org
801.408.8111


> -----Original Message-----
> From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-
> project.org] On Behalf Of Eugene A. Semenko
> Sent: Friday, November 21, 2008 8:19 AM
> To: r-help at stat.math.ethz.ch
> Subject: [R] question about shapiro.test()
>
> Hi all!
> I tried to perform Shapiro-Wilk test for my sample of 243 values.
> > Us
>   [1] -10.4 -13.1 -12.2  38.1 -18.8 -13.3 -11.7  29.3  49.7   6.8  12.7
> 16.3
>  [13]   5.8  -0.7 -29.4   4.1  38.8  -1.4   8.8  15.6  32.9  -5.3  19.1
> 35.8
>  [25]   4.0  -1.5   0.6  -4.2 -10.0  -4.0   1.1  48.9 -21.0  -5.3   5.8
> -10.8
>  [37]  21.9   8.2  -3.2  -3.9  -2.3  12.6  -4.7  -8.0  11.8  27.4  -9.5
> -20.8
>  [49]  -8.1  -5.4   0.7 -13.2  -6.1  -5.7  -9.6   0.3  -2.1 -15.2   1.7
> -15.2
>  [61]   7.4 -16.0  13.1   8.7  -8.9 -21.2  29.8 -22.6  10.5   7.5   9.9
> -13.0
>  [73]  -8.3 -22.9  -9.7  -3.7   8.2  -9.0 -21.8  28.5 -10.2   8.8 -10.1
> 15.3
>  [85]   5.5 -35.0 -14.5 -61.2  -8.3 -17.5 -16.3  -8.5   2.0 -17.5 -12.2
> -10.8
>  [97] -16.7   6.8 -12.4  -1.9 -13.3  -8.2 -22.6  20.7 -12.5 -21.9  -6.0
> 9.2
> [109]  -1.1 -17.5 -13.5   6.1 -18.5  18.1   6.3 -13.1 -16.2 -30.5 -23.4
> 4.3
> [121] -11.2 -18.5 -17.7  26.7   2.2  -9.4   1.8  -7.7  -5.1   6.3   7.1
> 7.4
> [133]  -9.2  24.8  53.5  23.9   0.0 -25.7 -33.3   6.9  -9.7 -22.6  -1.5
> 18.0
> [145] -20.5 -12.9 -14.3   3.9   5.5  -6.3   2.1 -11.2  -4.9   6.1   3.3
> 7.0
> [157]   4.1   0.3  -0.7  -6.4  -5.1 -17.6  -3.3   6.7   1.5  -8.8  31.2
> -30.5
> [169] -16.3 -23.4 -30.7  -3.2   8.3  18.1 -17.0  12.1   0.6  -1.6  -1.4
> 6.3
> [181]   3.6   5.3   1.6   1.8  23.7 -14.1   1.1  12.4  18.9 -11.5  -1.8
> -21.1
> [193]   2.4  23.4 -11.4  -5.9  -5.2  16.9 -19.8  19.5  -4.4   0.5  -1.4
> -8.1
> [205]   5.4  -2.7  -2.3  -2.9   4.4   8.0  -7.8  32.0   5.4   2.7   3.6
> 14.9
> [217]  -7.0   3.6 -12.1   3.8  47.8  -5.8   3.0  12.6  -1.1   2.0   1.5
> -0.1
> [229]  11.2  -1.4  -3.1  22.0 -14.4 -10.5  -4.1 -37.5 -17.6  -3.3   3.0
> -0.6
> [241]  33.8   1.6  -3.9
> Output is:
> > shapiro.test(Us)
>         Shapiro-Wilk normality test
> data:  Us
> W = 0.9686, p-value = 3.417e-05
>
> So, if I understand correctly, output inform me that H0 hypotesis of
> normality
> of my sample shoud be rejected because p-value << 0.05 (at 5% level).
> Is'n
> it? But actually my data distributed very close to the normal
> distribution.
>         Thanks in advance.
>                 Eugene
> --
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