ShapiroFranciaTest {DescTools} R Documentation

## Shapiro-Francia Test for Normality

### Description

Performs the Shapiro-Francia test for the composite hypothesis of normality.

### Usage

ShapiroFranciaTest(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 of 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.

### Author(s)

Juergen Gross <gross@statistik.uni-dortmund.de>

### 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. (2002, Sec. 2.3.2)

shapiro.test for performing the Shapiro-Wilk test for normality. AndersonDarlingTest, CramerVonMisesTest, LillieTest, PearsonTest for performing further tests for normality. qqnorm for producing a normal quantile-quantile plot.
ShapiroFranciaTest(rnorm(100, mean = 5, sd = 3))