For the chi-squared test, the P-values and critical values can be calculated by finding the appropriate points on a chi-square distribution with k-1 degrees of freedom (where k is the number of bins). While this method is exactly correct when predefined distributions are used, it turns out to be only an approximation for distributions where BestFit estimated one or more distribution parameters. Conveniently, however, the approximation is always a conservative one. That is, the reported values for both your critical values and P-value will be slightly higher than the exact values. More information about this can be found in the Recommended Readings section of this manual.
Most critical values and P-values for the A-D and K-S fit statistics have been found by very detailed Monte-Carlo studies (see the Sources section for references). Unfortunately, not all distributions have been analyzed in enough detail for BestFit to be able to report them. Where possible BestFit will report the appropriate P-values and critical values. Often, where an exact P-value calculation is not possible, a range is returned for the P-value, indicating that the true P-value lies between the specified upper and lower limit.
