Anderson-Darling test for normality
Performs the Anderson-Darling test for the composite hypothesis of normality, see e.g. Thode (2002, Sec. 5.1.4).
ad.test(x)
x |
a numeric vector of data values, the number of which must be greater than 7. Missing values are allowed. |
The Anderson-Darling test is an EDF omnibus test for the composite hypothesis of normality. The test statistic is
A = -n -\frac{1}{n} ∑_{i=1}^{n} [2i-1] [\ln(p_{(i)}) + \ln(1 - p_{(n-i+1)})],
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).
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. |
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.
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.
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.
ad.test(rnorm(100, mean = 5, sd = 3)) ad.test(runif(100, min = 2, max = 4))
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