AndersonDarlingTest: Anderson-Darling test for normality
Description
Performs the Anderson-Darling test for the composite hypothesis of normality,
see e.g. Thode (2002, Sec. 5.1.4).
Usage
AndersonDarlingTest(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 Anderson-Darling statistic.
p.valuethe p-value for the test.
methodthe character string Anderson-Darling normality test.
data.namea character string giving the name(s) of the data.
Details
The Anderson-Darling test is an EDF omnibus test for the composite hypothesis of normality.
The test statistic is
$$A = -n -\frac{1}{n} \sum_{i=1}^{n} [2i-1]
[\ln(p_{(i)}) + \ln(1 - p_{(n-i+1)})],$$
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
$Z=A (1.0 + 0.75/n +2.25/n^{2})$ 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.