sf.test
ShapiroFrancia test for normality
Performs the ShapiroFrancia test for the composite hypothesis of normality, see e.g. Thode (2002, Sec. 2.3.2).
 Keywords
 htest
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.
Details
The test statistic of the ShapiroFrancia test is simply the squared correlation between the ordered sample values and the (approximated) expected ordered quantiles from the standard normal distribution. The pvalue is computed from the formula given by Royston (1993).
Value

A list with class “htest” containing the following components:
 statistic
 the value of the ShapiroFrancia statistic.
 p.value
 the pvalue for the test.
 method
 the character string “ShapiroFrancia normality test”.
 data.name
 a character string giving the name(s) of the data.
Note
The ShapiroFrancia test is known to perform well,
see also the comments by Royston (1993). The expected ordered quantiles
from the standard normal distribution are approximated by
qnorm(ppoints(x, a = 3/8))
, being slightly different from the approximation
qnorm(ppoints(x, a = 1/2))
used for the normal quantilequantile plot by
qqnorm
for sample sizes greater than 10.
References
Royston, P. (1993): A pocketcalculator algorithm for the ShapiroFrancia test for nonnormality: an application to medicine. Statistics in Medicine, 12, 181184.
Thode Jr., H.C. (2002): Testing for Normality. Marcel Dekker, New York.
See Also
shapiro.test
for performing the ShapiroWilk test for normality.
ad.test
, cvm.test
,
lillie.test
, pearson.test
for performing further tests for normality.
qqnorm
for producing a normal quantilequantile plot.
Examples
sf.test(rnorm(100, mean = 5, sd = 3))
sf.test(runif(100, min = 2, max = 4))