where p_{(i)} = Φ([x_{(i)} - overline{x}]/s). Here,
Φ 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).
Value
A list with class “htest” containing the following components:
statistic
the value of the Anderson-Darling statistic.
p.value
the p-value for the test.
method
the character string “Anderson-Darling normality test”.
data.name
a character string giving the name(s) of the data.
Note
The Anderson-Darling test is the recommended EDF test by Stephens (1986). Compared to the
Cramer-von Mises test (as second choice) it gives more weight to the tails of the distribution.
Author(s)
Juergen Gross
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.
cvm.test, lillie.test,
pearson.test, sf.test for performing further tests for normality.
qqnorm for producing a normal quantile-quantile plot.
Examples
ad.test(rnorm(100, mean = 5, sd = 3))
ad.test(runif(100, min = 2, max = 4))