nortest (version 1.0-4)

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

cvm.test(x)

Arguments

x

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

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.

Details

The Cramer-von Mises test is an EDF omnibus test for the composite hypothesis of normality. The test statistic is $$ W = \frac{1}{12 n} + \sum_{i=1}^{n} \left(p_{(i)} - \frac{2i-1}{2n}\right)^2, $$ 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).

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))