| 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} + \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 <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))