cvm.test {rotRPackage} | R Documentation |
Performs the Cramer-von Mises test for the composite hypothesis of normality, see e.g. Thode (2002, Sec. 5.1.3).
cvm.test(x)
x |
a numeric vector of data values, the number of which must be greater than 7. Missing values are allowed. |
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).
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. |
Juergen Gross
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.
cvm.test(rnorm(100, 5, 3)) cvm.test(rnorm(100, 2, 4))