R: Cramer-von Mises Test for Normality

CramerVonMisesTest {DescTools} | R Documentation

## 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} + ∑_{i=1}^{n} ≤ft (p_{(i)} - \frac{2i-1}{2n} \right),

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 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 <gross@statistik.uni-dortmund.de>

### 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))

[Package DescTools version 0.99.38 Index]