Shapiro test returning negative p-value

My issue is about logical error while running shapiro test

Reproducing code example:

>>> from scipy import stats
>>> trans_val, maxlog = stats.boxcox([122500,474400,110400])
>>> stats.shapiro(trans_val)
ShapiroResult(statistic=0.08333337306976318, pvalue=-1.4407120943069458)

Error message:

The correct range of p-value should be [0,1]. The sample shown above is giving negative p-value which is incorrect.

Scipy/Numpy/Python version information:

>>> import sys, scipy, numpy; print(scipy.__version__, numpy.__version__, sys.version_info)
1.7.0 1.19.1 sys.version_info(major=3, minor=7, micro=6, releaselevel='final', serial=0)

[josef-pkt]

given that y is already sorted before going to the fortran code, it might be better to subtract the median (or next value close to it)

median would be robust to outliers compared to mean

[josef-pkt]

Nonzero mean is no problem if the variation is large enough compare to it. But if mean is huge compared to variation, then some computation get imprecise.

I only have examples in other contexts and don’t know or remember the details for shapiro-wilk, so I don’t know which computation cause the numerical problem.

Would you recommend subtracting the mean before passing the data to swilk?

I think that would be good. Fixes or improves precision for these kind of issues. It’s possible to make it conditional on a small relative range as in your example, but just unconditionally removing the mean is simpler.