adk.test {adk} | R Documentation |
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).
adk.test(...)
... |
Either several sample vectors of respective sizes
n.1, ... , n.k, with n.i > 4 recommended, or a list of such sample vectors |
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.
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 . |
Fritz Scholz
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.
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
## 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