## Stata 15 help for sfrancia

```
[R] swilk -- Shapiro-Wilk and Shapiro-Francia tests for normality

Syntax

Shapiro-Wilk normality test

swilk varlist [if] [in] [, swilk_options]

Shapiro-Francia normality test

sfrancia varlist [if] [in] [, sfrancia_options]

swilk_options         Description
-------------------------------------------------------------------------
Main
generate(newvar)    create newvar containing W test coefficients
lnnormal            test for three-parameter lognormality
noties              do not use average ranks for tied values
-------------------------------------------------------------------------

sfrancia_options      Description
-------------------------------------------------------------------------
Main
boxcox              use the Box-Cox transformation for W'; the default
is to use the log transformation
noties              do not use average ranks for tied values
-------------------------------------------------------------------------

by is allowed with swilk and sfrancia; see [D] by.

swilk

Statistics > Summaries, tables, and tests > Distributional plots and
tests > Shapiro-Wilk normality test

sfrancia

Statistics > Summaries, tables, and tests > Distributional plots and
tests > Shapiro-Francia normality test

Description

swilk performs the Shapiro-Wilk W test for normality for each variable in
the specified varlist.  Likewise, sfrancia performs the Shapiro-Francia
W' test for normality.  See [MV] mvtest normality for multivariate tests
of normality.

Options for swilk

+------+
----+ Main +-------------------------------------------------------------

generate(newvar) creates new variable newvar containing the W test
coefficients.

lnnormal specifies that the test be for three-parameter lognormality,
meaning that ln(X-k) is tested for normality, where k is calculated
from the data as the value that makes the skewness coefficient zero.
When simply testing ln(X) for normality, do not specify this option.
See [R] lnskew0 for estimation of k.

noties suppresses use of averaged ranks for tied values when calculating
the W test coefficients.

Options for sfrancia

+------+
----+ Main +-------------------------------------------------------------

boxcox specifies that the Box-Cox transformation of Royston (1983) for
calculating W' test coefficients be used instead of the default log
transformation (Royston 1993).  Under the Box-Cox transformation, the
normal approximation to the sampling distribution of W', used by
sfrancia, is valid for 5<=n<=1000.  Under the log transformation, it
is valid for 10<=n<=5000.

noties suppresses use of averaged ranks for tied values when calculating
the W' test coefficients.

Remarks

swilk can be used with 4<=n<=2000 observations. sfrancia can be used with
10<=n<=5000 observations; however, if the boxcox option is specified, it
can be used with 5<=n<=1000 observations.

Examples

---------------------------------------------------------------------------
Setup
. sysuse auto

Test whether mpg and trunk are normally distributed
. swilk mpg trunk

---------------------------------------------------------------------------
Setup
. sysuse cancer
. generate lnstudytime = ln(studytime)

Test that studytime is distributed lognormally
. swilk lnstudytime

Test that ln(studytime - k) is normally distributed, where k is chosen so
that the resulting skewness is zero
. lnskew0 lnstudytimek = studytime, level(95)
. swilk lnstudytimek, lnnormal

---------------------------------------------------------------------------
Setup
. webuse lbw, clear

Perform Shapiro-Francia normality test using default log transformation
. sfrancia bwt

Perform Shapiro-Francia normality test using Box-Cox transformation
. sfrancia bwt, boxcox

---------------------------------------------------------------------------

Stored results

swilk and sfrancia store the following in r():

Scalars
r(N)           number of observations
r(p)           p-value
r(z)           z statistic
r(W)           W or W'
r(V)           V or V'

References

Royston, P. 1983.  A simple method for evaluating the Shapiro-Francia W'
test for non-normality.  Statistician 32: 297-300.

------. 1993.  A pocket-calculator algorithm for the Shapiro-Francia test
for non-normality: An application to medicine.  Statistics in
Medicine 12: 181-184.

```