CramerVonMisesTest: 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.
Value
A list with class htest containing the following components:
statisticthe value of the Cramer-von Mises statistic.
p.valuethe p-value for the test.
methodthe character string Cramer-von Mises normality test.
data.namea 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
$$W = \frac{1}{12 n} + \sum_{i=1}^{n} (p_{(i)} - \frac{2i-1}{2n}),$$
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).
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.