# ad.test

##### 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).

- Keywords
- htest

##### Usage

`ad.test(x)`

##### Arguments

- x
- a numeric vector of data values, the number of which must be greater than 7. Missing values are allowed.

##### 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).

##### 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.

##### 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))
```

*Documentation reproduced from package nortest, version 1.0-1, License: GPL (>= 2)*