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))
```

*DescTools*version 0.99.55 Index]