CramerVonMisesTest.RdPerforms the Cramer-von Mises test for the composite hypothesis of normality, see e.g. Thode (2002, Sec. 5.1.3).
CramerVonMisesTest(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 $$ W = \frac{1}{12 n} + \sum_{i=1}^{n} \left (p_{(i)} - \frac{2i-1}{2n} \right), $$ 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).
A list of class htest, containing the following components:
the value of the Cramer-von Mises statistic.
the p-value for the test.
the character string “Cramer-von Mises normality test”.
a character string giving the name(s) of the data.
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.
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.
CramerVonMisesTest(rnorm(100, mean = 5, sd = 3))
#>
#> Cramer-von Mises normality test
#>
#> data: rnorm(100, mean = 5, sd = 3)
#> W = 0.045832, p-value = 0.5716
#>
CramerVonMisesTest(runif(100, min = 2, max = 4))
#>
#> Cramer-von Mises normality test
#>
#> data: runif(100, min = 2, max = 4)
#> W = 0.28912, p-value = 0.0004285
#>