# cvm.test

##### Cramer-von Mises test for normality

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

- Keywords
- htest

##### Usage

`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 $$W = \frac{1}{12 n} + \sum_{i=1}^{n} (p_{(i)} - \frac{2i-1}{2n}),$$ where $p_{(i)} = \Phi([x_{(i)} - \overline{x}]/s)$. Here, $\Phi$ 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.

##### 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

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

*Documentation reproduced from package nortest, version 1.0-1, License: GPL (>= 2)*