Shapiro-Francia test for normality
Performs the Shapiro-Francia test for the composite hypothesis of normality, see e.g. Thode (2002, Sec. 2.3.2).
- a numeric vector of data values, the number of which must be between 5 and 5000. Missing values are allowed.
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).
A list with class htest containing the following components:
- the value of the Shapiro-Francia statistic.
- the p-value for the test.
- the character string Shapiro-Francia normality test.
- a character string giving the name(s) of the data.
The Shapiro-Francia 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 quantile-quantile plot by
qqnorm for sample sizes greater than 10.
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.
shapiro.test for performing the Shapiro-Wilk test for normality.
pearson.test for performing further tests for normality.
qqnorm for producing a normal quantile-quantile plot.
sf.test(rnorm(100, mean = 5, sd = 3)) sf.test(runif(100, min = 2, max = 4))