CramerVonMisesTest: Cramer-von Mises Test for Normality

In DescTools: Tools for Descriptive Statistics

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

CramerVonMisesTest(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} \left (p_{(i)} - \frac{2i-1}{2n} \right),

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 of 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 <[e-mail]>

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. AndersonDarlingTest, LillieTest, PearsonTest, ShapiroFranciaTest for performing further tests for normality. qqnorm for producing a normal quantile-quantile plot.

Examples

CramerVonMisesTest(rnorm(100, mean = 5, sd = 3))
CramerVonMisesTest(runif(100, min = 2, max = 4))

DescTools documentation built on Sept. 26, 2024, 1:07 a.m.