# Cramer-von Mises test for normality

### Description

Performs the Cramer-von Mises test for the composite hypothesis of normality, see e.g. Thode (2002, Sec. 5.1.3).

### Usage

1 | ```
cvm.test(x)
``` |

### Arguments

`x` |
a numeric vector of data values, the number of which must be greater than 7. Missing values are allowed. |

### Details

The Cramer-von Mises test is an EDF omnibus test for the composite hypothesis of normality. The test statistic is

*W = 1/(12n) + ∑_{i=1}^n (p_(i) - (2i-1)/(2n))^2,*

where *p_{(i)} = Φ([x_{(i)} - \overline{x}]/s)*. Here,
*Φ* is the cumulative distribution function
of the standard normal distribution, and *\overline{x}* and *s*
are mean and standard deviation of the data values.
The p-value is computed from the modified statistic
*Z=W (1.0 + 0.5/n)* according to Table 4.9 in
Stephens (1986).

### Value

A list with class “htest” containing the following components:

`statistic` |
the value of the Cramer-von Mises statistic. |

`p.value ` |
the p-value for the test. |

`method` |
the character string “Cramer-von Mises normality test”. |

`data.name` |
a character string giving the name(s) of the data. |

### Author(s)

Juergen Gross

### References

Stephens, M.A. (1986): Tests based on EDF statistics. In: D'Agostino, R.B. and Stephens, M.A., eds.: Goodness-of-Fit Techniques. Marcel Dekker, New York.

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`

, `lillie.test`

,
`pearson.test`

, `sf.test`

for performing further tests for normality.
`qqnorm`

for producing a normal quantile-quantile plot.

### Examples

1 2 |

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