# [Rd] Shapiro Test P Value Incorrect? (PR#9768)

Petr Savicky savicky at cs.cas.cz
Fri Jul 6 12:31:51 CEST 2007

```This is not a bug. The algorithm uses different approximation of the
p-value for n=3 (exact value), 4<=n<=11 and n>=12 as seen in
src/library/stats/src/swilk.c
below the line 202
/*  Calculate significance level for W */

The W statistic monotonically decreases in the presented example.

Petr.

> Full_Name: Jason Polak
> Version: R version 2.5.0 (2007-04-23)
> OS: Xubuntu 7.04
> Submission from: (NULL) (137.122.144.35)
>
>
> Dear R group,
>
> I have noticed a strange anomaly with the shapiro.test() function. Unfortunately
> I do not know how to calculate the shapiro test P values manually so I don't
> know if this is an actual bug.
>
> So, to produce the results, run the following code:
>
> pvalues = 0;
> for (i in 1:17)
> {
> 	j = 1:(i+3);
> 	pvalues[i]=shapiro.test(j)\$p;
> }
>
> plot(pvalues);
> print(pvalues);
>
> Now I just made the graph to illustrate that the p-values are strictly
> decreasing. To me this makes intuitive sense: we are using the Shapiro test to
> test normality of (1,2,3,4),(1,2,3,4,5), and so on. So the p-value should
> decrease.
>
> These are the p-values:
>  [1] 0.9718776 0.9671740 0.9605557 0.9492892 0.9331653 0.9135602 0.8923668
>  [8] 0.8698419 0.8757315 0.8371814 0.7964400 0.7545289 0.7123167 0.6704457
> [15] 0.6294307 0.5896464 0.5513749
>
> However, there is an increase in p-value when you go from (1,..,11) to
> (1,..,12). Is this just a quirk of the Shapiro test, or is there an error in the
> calculation algorithm?
>
> ______________________________________________
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>

```