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).

NA values are removed and the user is alerted with the total NA count. It is up to the user to judge whether the removal of NA's is appropriate.

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 calculation 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 1.0-2 Index]