# naginterfaces.library.stat.test_​shapiro_​wilk¶

naginterfaces.library.stat.test_shapiro_wilk(x, a=None)[source]

test_shapiro_wilk calculates Shapiro and Wilk’s statistic and its significance level for testing Normality.

For full information please refer to the NAG Library document for g01dd

https://www.nag.com/numeric/nl/nagdoc_28.7/flhtml/g01/g01ddf.html

Parameters
xfloat, array-like, shape

The ordered sample values, , for .

aNone or float, array-like, shape , optional

If has been set to then before entry must contain the weights as calculated in a previous call to test_shapiro_wilk, otherwise need not be set.

Returns
afloat, ndarray, shape

The weights required to calculate .

wfloat

The value of the statistic, .

pwfloat

The significance level of .

Raises
NagValueError
(errno )

On entry, .

Constraint: .

(errno )

On entry, .

Constraint: .

(errno )

On entry, elements of not in order. , , .

(errno )

On entry, all elements of are equal.

Notes

test_shapiro_wilk calculates Shapiro and Wilk’s statistic and its significance level for any sample size between and . It is an adaptation of the Applied Statistics Algorithm AS R94, see Royston (1995). The full description of the theory behind this algorithm is given in Royston (1992).

Given a set of observations sorted into either ascending or descending order (sort.realvec_sort may be used to sort the data) this function calculates the value of Shapiro and Wilk’s statistic defined as:

where is the sample mean and , for , are a set of ‘weights’ whose values depend only on the sample size .

On exit, the values of , for , are only of interest should you wish to call the function again to calculate and its significance level for a different sample of the same size.

It is recommended that the function is used in conjunction with a Normal plot of the data. Functions normal_scores_exact() and normal_scores_approx() can be used to obtain the required Normal scores.

References

Royston, J P, 1982, Algorithm AS 181: the test for normality, Appl. Statist. (31), 176–180

Royston, J P, 1986, A remark on AS 181: the test for normality, Appl. Statist. (35), 232–234

Royston, J P, 1992, Approximating the Shapiro–Wilk’s test for non-normality, Statistics & Computing (2), 117–119

Royston, J P, 1995, A remark on AS R94: A remark on Algorithm AS 181: the test for normality, Appl. Statist. (44(4)), 547–551