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).
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.