Perform the Anderson-Darling normality test.
Arguments
- x
numeric()vector of data values. Missing values are allowed, but the number of non-missing values must be greater than 7.
Value
A list inheriting from classes "htest" containing the following components:
statistic: the value of the statistic.
p.value: the p-value of the test.
method: the character string
"Anderson-Darling normality test".data.name: a 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 $$ A^2 = -n -\frac{1}{n} \sum_{i=1}^{n} (2i - 1) [\ln(z_{i}) + \ln(1 - z_{n + 1 - i})] $$ where \(z_{i} = \Phi(\frac{x_{i} - \bar{x}}{s})\). Here, \(\Phi\) is the cumulative distribution function of the standard normal distribution, and \(\bar{x}\) and \(s\) are mean and standard deviation of the data values. The p-value is computed from the modified statistic \(A^2_*=A^2 (1.0 + 0.75/n + 2.25/n^{2})\) according to Table 4.9 in Stephens (1986).
References
Stephens, A. M (1986). “Goodness-of-Fit-Techniques.” In D'Agostino, B. R (eds.), chapter Tests based on EDF statistics. CRC Press.
Thode, C. H (2002). Testing for normality, 1 edition. CRC Press. doi:10.1201/9780203910894 .
See also
stats::shapiro.test() for performing the Shapiro-Wilk test for normality.
nortest::cvm.test(), nortest::lillie.test(), nortest::pearson.test(),
nortest::sf.test() for performing further tests for normality.
stats::qqnorm() for producing a normal quantile-quantile plot.
Examples
set.seed(123)
ad.test(rnorm(100, mean = 5, sd = 3))
#>
#> Anderson-Darling normality test
#>
#> data: rnorm(100, mean = 5, sd = 3)
#> A = 0.182, p-value = 0.9104
#>
ad.test(runif(100, min = 2, max = 4))
#>
#> Anderson-Darling normality test
#>
#> data: runif(100, min = 2, max = 4)
#> A = 1.3941, p-value = 0.001244
#>