# adAllPairsTest: Anderson-Darling All-Pairs Comparison Test In PMCMRplus: Calculate Pairwise Multiple Comparisons of Mean Rank Sums Extended

## Description

Performs Anderson-Darling all-pairs comparison test.

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14``` ```adAllPairsTest(x, ...) ## Default S3 method: adAllPairsTest(x, g, p.adjust.method = p.adjust.methods, ...) ## S3 method for class 'formula' adAllPairsTest( formula, data, subset, na.action, p.adjust.method = p.adjust.methods, ... ) ```

## Arguments

 `x` a numeric vector of data values, or a list of numeric data vectors. `...` further arguments to be passed to or from methods. `g` a vector or factor object giving the group for the corresponding elements of `"x"`. Ignored with a warning if `"x"` is a list. `p.adjust.method` method for adjusting p values (see `p.adjust`). `formula` a formula of the form `response ~ group` where `response` gives the data values and `group` a vector or factor of the corresponding groups. `data` an optional matrix or data frame (or similar: see `model.frame`) containing the variables in the formula `formula`. By default the variables are taken from `environment(formula)`. `subset` an optional vector specifying a subset of observations to be used. `na.action` a function which indicates what should happen when the data contain `NA`s. Defaults to `getOption("na.action")`.

## Details

For all-pairs comparisons in an one-factorial layout with non-normally distributed residuals Anderson-Darling's all-pairs comparison test can be used. A total of m = k(k-1)/2 hypotheses can be tested. The null hypothesis H_{ij}: F_i(x) = F_j(x) is tested in the two-tailed test against the alternative A_{ij}: F_i(x) \ne F_j(x), ~~ i \ne j.

This function is a wrapper function that sequentially calls `adKSampleTest` for each pair. The calculated p-values for `Pr(>|T2N|)` can be adjusted to account for Type I error multiplicity using any method as implemented in `p.adjust`.

## Value

A list with class `"PMCMR"` containing the following components:

method

a character string indicating what type of test was performed.

data.name

a character string giving the name(s) of the data.

statistic

lower-triangle matrix of the estimated quantiles of the pairwise test statistics.

p.value

lower-triangle matrix of the p-values for the pairwise tests.

alternative

a character string describing the alternative hypothesis.

a character string describing the method for p-value adjustment.

model

a data frame of the input data.

dist

a string that denotes the test distribution.

## References

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

`adKSampleTest`, `adManyOneTest`, `ad.pval`.
 ```1 2 3 4 5``` ```adKSampleTest(count ~ spray, InsectSprays) out <- adAllPairsTest(count ~ spray, InsectSprays, p.adjust="holm") summary(out) summaryGroup(out) ```