Calculates the Shapiro-Wilk test for Normality (R.W. Payne).

### Option

`PRINT` = string tokens |
What to print (`test` ); default `test` |
---|

### Parameters

`DATA` = variates |
Samples of data to be tested for Normality |
---|---|

`W` = scalars |
Saves the Shapiro-Wilk W statistic for each sample |

`PROBABILITY` = scalars |
Saves the probability for W under the assumption that the data are Normal |

### Description

`WSTATISTIC`

uses the Shapiro-Wilk test to assess whether a sample of data comes from a Normal distribution. The data values must be supplied, in a variate, using the `DATA`

parameter. By default `WSTATISTIC`

prints the statistic, W, with its probability value under the assumption that the data are Normal. (So a low probability indicates that the data are unlikely to be from a Normal distribution.) The printed output can be supressed by setting option `PRINT=*`

. The test statistic can be saved, in a scalar, using the `W`

parameter, and its probability can similarly be saved using the `PROBABILITY`

parameter.

Option: `PRINT`

.

Parameters: `DATA`

, `W`

, `PROBABILITY`

.

### Method

`WSTATISTIC`

calculates the statistic and its probability using the methods of Royston (1993, 1995).

### Action with `RESTRICT`

The `DATA`

variate can be restricted to assess a subset of the data.

### References

Royston, P. (1993). A toolkit for testing for non-normality in complete and censored samples. *The Statistician*, 42, 37-43.

Royston, P. (1995). A remark on Algorithm AS 181: the W-test for Normality. *Applied Statistics*, 44, 547-551.

### See also

Directive: `DISTRIBUTION`

.

Procedures: `EDFTEST`

, `NORMTEST`

.

Commands for: Basic and nonparametric statistics.

### Example

CAPTION 'WSTATISTIC example','Data from Royston (1995)'; STYLE=meta,plain VARIATE [VALUES=4.2,4.9,5.2,5.3,6.7,6.7,7.2,7.5,8.1,8.6,8.8,9.3,\ 9.5,10.3,10.8,11.1,12.2,12.5,13.3,15.1,15.3,16.1,19.0,19.5] Glucose WSTATISTIC Glucose