Performs the Shapiro-Francia test for the composite hypothesis of normality,
see e.g. Thode (2002, Sec. 2.3.2).

Usage

sf.test(x)

Arguments

x

a numeric vector of data values, the number of
which must be between 5 and 5000. Missing values are allowed.

Value

A list with class “htest” containing the following components:

statistic

the value of the Shapiro-Francia statistic.

p.value

the p-value for the test.

method

the character string “Shapiro-Francia normality test”.

data.name

a character string giving the name(s) of the data.

Details

The test statistic of the Shapiro-Francia test is simply the
squared correlation between the ordered sample values and the (approximated)
expected ordered quantiles from the standard normal
distribution. The p-value is computed from the formula given by Royston (1993).

References

Royston, P. (1993): A pocket-calculator algorithm for the
Shapiro-Francia test for non-normality: an application to medicine.
Statistics in Medicine, 12, 181--184.

Thode Jr., H.C. (2002): Testing for Normality. Marcel Dekker, New York.