adk.test {adk}R Documentation

Anderson-Darling K-Sample Test

Description

The Anderson-Darling k-sample test may be used to test the hypothesis that k samples of various sizes ( > 4 ) come from one common continuous distribution. It is a rank test and it is consistent against all alternatives, a property not shared by the Kruskal-Wallis k-sample rank test. Also provided is a version that adjusts for a moderate number of ties (due to rounding).

Usage

adk.test(...)

Arguments

... Either several sample vectors of respective sizes n.1, ... , n.k, with n.i > 4 recommended,

or a list of such sample vectors

Details

See the given reference for details on the Anderson-Darling k-sample criterion AD and its modification in case of ties. The standardized value of AD, i.e., T = (AD - mu)/sig, is used as test statistic. Here mu = k-1 and sig are the mean and standard deviation of AD. The P-value = P( T > t.obs ) corresponding to an observed t.obs of T is computed by quadratic interpolation w.r.t. 1/sqrt(mu) and by quadratic interpolation w.r.t. log(p/(1-p)), where p is the tail probability corresponding to the quantiles given in Table 1 of the cited reference. Both interpolations are reasonably accurate. For p beyond the range [.01,.25] of Table 1 linear exptrapolation is used w.r.t. the log(p/(1-p)) fit. Such extrapolation affects the accuracy of the P-value caluculation to some extent but this should not strongly affect any decisions regarding the tested hypothesis.

Value

A list of class adk with components

k number of samples being compared
ns vector of the k sample sizes c(n.1, ...,n.k)
n total sample size = n.1 + ... + n.k
n.ties number of ties in the combined set of all n observations
sig standard deviation of the AD statistic
adk 2 x 3 matrix containing t.obs, P-value, extrapolation, not adjusting for ties and adjusting for ties. extrapolation = 1 when the P-value was extrapolated.
warning logical variable, warning = TRUE if n.i < 5 for at least one of the samples, otherwise warning = FALSE .

Author(s)

Fritz Scholz

References

Scholz F.W. and Stephens M.A. (1987), K-sample Anderson-Darling Tests, Journal of the American Statistical Association, Vol 82, No. 399, 918–924.

See Also

kruskal.test as a nonparametric alternative to adk.test and adk.combined.test for combining several such tests for different and independent groups of samples

Examples

## Create input list of 3 sample vectors.
x <- list(c(1,3,2,5,7),c(2,8,1,6,9,4),c(12,5,7,9,11))
out <- adk.test(x) # or out <- adk.test(c(1,3,2,5,7),c(2,8,1,6,9,4),c(12,5,7,9,11))
## Examine the component names of out
names(out)

## Examine the matrix adk of out.
out$adk

## Fully print formatted object out of class adk.
out

[Package adk version 1.0 Index]