For a real data set, if the values of the standard error of parameters of a distribution (say A) is higher than the other distribution (say B). But, if the distribution A has high P-Value and smaller Anderison Darling (AD), Cramer Von Mesis (CM) and Kalmogrove-Simrnov (KS) test statistics values than the distribution B.
(i) So, in such a case, which distribution is considered to be the best?
(ii) A distribution with smaller standard error is important or with smaller value of goodness of fit measures stated above?
(iii) Why such a problem occurs?
(iv) Is it neccessary that a distribution with smaller values of AD, CM KS will have smaller value of the standard error of the parameters?
(v) How can we interpret this result?
-Correct and careful interpretation of statistical tests demands examining the sizes of effect estimates and confidence limits, as well as precise P values (not just whether P values are above or below 0.05 or some other threshold.
-A large null P value simply flags the data as not being unusual if all the assumptions used to compute it (including the test hypothesis) were correct; but the same data will also not be unusual under many other models/tests and hypotheses besides the null. Again, one must look at the confidence interval to determine whether it includes effect sizes of importance.
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