R: Shapiro-Francia test for normality

sf.test {nortest} | R Documentation

## Shapiro-Francia test for normality

### Description

Performs the Shapiro-Francia test for the composite hypothesis of normality, see e.g. Thode (2002, Sec. 2.3.2).

### 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.

### Author(s)

Juergen Gross

### 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.

### See Also

`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.

### Examples

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

[Package nortest version 1.0-4 Index]