adk.pval {adk} | R Documentation |
This function "adk.pval" evaluates the p-value of the
observed value tx of T_m, the standardized Anderson-Darling
statistic. It is used by adk.test
and
adk.combined.test
.
adk.pval(tx,m)
tx |
threshold for which the right tail probability of the standardized Anderson-Darling statistics T_m is to be calculated |
m |
index of the standardized T_m statistic (see reference) |
This function first interpolates the upper T_m quantiles as given in Table 1 (see reference below) to the given value of m by fitting a quadratic in 1/sqrt(m) to the quantiles as tabulated for the upper quantile levels .25, .10, .05, .025, .01.
Next a quadratic in the interpolated quantiles (for m) is fitted to the log-odds of the upper probability levels defining these quantiles and the fitted log-odds value at tx is converted back to the calculated upper probability value, i.e., the p-value. p-values outside the tabulated range [.01,.25] are obtained by linear extrapolation of the fitted quadratic.
A list with components
p0 |
p-value of tx, i.e., p0=P(T_m>= tx) |
extrap |
a logical indicator, |
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.
adk.test
and
adk.combined.test
## compute p-value when tx = 3 and m = 6 adk.pval(3,6)