# cvm.test: 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.

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.

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

Search within the nortest package
Search all R packages, documentation and source code

Questions? Problems? Suggestions? or email at ian@mutexlabs.com.

Please suggest features or report bugs with the GitHub issue tracker.

All documentation is copyright its authors; we didn't write any of that.