R: Shapiro-Francia Test for Normality

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)

### See Also

`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.

### Examples

    ShapiroFranciaTest(rnorm(100, mean = 5, sd = 3))
    ShapiroFranciaTest(runif(100, min = 2, max = 4))

[Package DescTools version 0.99.28 Index]