# sf.test

0th

Percentile

##### 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).

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 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).

##### 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.

##### Note

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.

##### 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.

shapiro.test for performing the Shapiro-Wilk test for normality. ad.test, cvm.test, lillie.test, pearson.test for performing further tests for normality. qqnorm for producing a normal quantile-quantile plot.

• sf.test
##### Examples
sf.test(rnorm(100, mean = 5, sd = 3))
sf.test(runif(100, min = 2, max = 4))


Documentation reproduced from package nortest, version 1.0-4, License: GPL (>= 2)

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