# AndersonDarling: K-Sample Anderson Darling Test In MissMech: Testing Homoscedasticity, Multivariate Normality, and Missing Completely at Random

## Description

This is a non-parametric K-sample test that tests equality of distribution of a variable between k populations based on samples from each of the populations.

## Usage

 `1` ```AndersonDarling(data, number.cases) ```

## Arguments

 `data` A single vector consisting of concatenation of the k samples data being used for the test `number.cases` A vector consisting of the number of cases in samples 1, 2, ..., k, respectively

## Details

The data is a vector including all the k samples to be used for the test. The j-th element of number.cases is the number of cases in sample j (included in data), for j= 1,...,k.

## Value

 `pn ` The test's p-value. `adk.all ` The Anderson Darling test statistic corresponding to each group. `adl ` The sum of elements of adk.all. `var.sdk ` The variance of the finite sample distribution of the Anderson Darling test statistic under the null.

## Note

The test does not adjust for tie observations.

## Author(s)

Mortaza Jamshidian, Siavash Jalal, and Camden Jansen

## References

Scholz, F.W. and Stephens, M.A. (1987). ”K-Sample Anderson-Darling Tests,” Journal of the American Statistical Association, 82, 918-924.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19``` ```#---- Example 1 set.seed(50) n1 <- 30 n2 <- 45 n3 <- 60 v1 <- rnorm(n1) v2 <- runif(n2) v3 <- rnorm(n3, 2, 3) AndersonDarling(data = c(v1, v2, v3), number.cases=c(n1, n2, n3)) #---- Example 2 set.seed(50) n1 <- 30 n2 <- 45 n3 <- 60 v1 <- rt(n1,4) v2 <- rt(n2,4) v3 <- rt(n3,4) AndersonDarling(data=c(v1, v2, v3), number.cases=c(n1, n2, n3)) ```

```\$pn
 1.345932e-31

[,1]
[1,] 6.566425
[2,] 5.075349
[3,] 6.978307

 18.62008

\$var.sdk
 1.119502

\$pn
 0.3878912

[,1]
[1,] 0.6364330
[2,] 0.7773931
[3,] 0.5886475