public class AndersonDarlingPValue extends Object
We use a twostep procedure to interpolate the data in Table 1. In the first step, the dependent variables are 1/\sqrt(m) and 1/m, where m = 1, ... 10, 1000000. The independent variable is statistics corresponding to upper percentiles 0.25, 0.1, 0.05, 0.025, 0.01. The prediction values corresponding to actual number of samples minus 1 are stored. Therefore there are 5 OLS regressions in this step and 5 prediction values.
In the second step, the dependent variables are 5 predictions and their squares, and the independent variables are the pvalues {0.25,0.1,0.05,0.025,0.01}. The pvalue corresponding to the actual statistics t_{m} is predicted by the linear regression model t_{m}(\alpha) = b_{0}+b_{1}/\sqrt(m)+b_{2}/m.
The details of this step is not mentioned in the paper. The process of calculating pvalue when the statistics is not in the table is documented by only one sentence in right column paragraph 3, p. 920: "Similarly, one could interpolate and even extrapolate pvalue for the observed AndersonDarling statistic; see Section 7 for an example." The author suggests using linear extrapolation. We use the second order extrapolation for two reasons: 1) By regressing the pvalues against the statistics in Table 1. We found that the coefficient of the second order term is significant in most cases and the R square value is higher than the regression which only include the first order term. This indicates by including the second order term, the extrapolation is more accurate. Take m=1 as an example: the pvalue of the second order coefficient is 0.03352. The corresponding R square 0.9994. On the other hand the R square of regression which only includes the first order term is 0.9939. 2) The R program includes also the second order term.
Constructor and Description 

AndersonDarlingPValue(int m)
Construct the AndersonDarling distribution for a particular number of samples.

Modifier and Type  Method and Description 

double 
alpha(double tm)
Gets the pvalue for a test statistic.

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