Genome::Model::Tools::Music::PathScan::CombinePvals(3pm) User Contributed Perl Documentation Genome::Model::Tools::Music::PathScan::CombinePvals(3pm)

# NAME¶

CombinePvals - combining probabilities from independent tests of significance into a single aggregate figure

# SYNOPSIS¶

```        use CombinePvals;
my \$obj = CombinePvals->new (\$reference_to_list_of_pvals);
my \$pval = \$obj->method_name;
my \$pval = \$obj->method_name (@arguments);
```

# DESCRIPTION¶

There are a variety of circumstances under which one might have a number of different kinds of tests and/or separate instances of the same kind of test for one particular null hypothesis, where each of these tests returns a p-value. The problem is how to properly condense this list of probabilities into a single value so as to be able to make a statistical inference, e.g. whether to reject the null hypothesis. This problem was examined heavily starting about the 1930s, during which time numerous mathematical contintencies were treated, e.g. dependence vs. independence of tests, optimality, inter-test weighting, computational efficiency, continuous vs. discrete tests and combinations thereof, etc. There is quite a large mathematical literature on this topic (see "REFERENCES" below) and any one particular situation might incur some of the above subtleties. This package concentrates on some of the more straightforward scenarios, furnishing various methods for combining p-vals. The main consideration will usually be the trade-off between the exactness of the p-value (according to strict frequentist modeling) and the computational efficiency, or even its actual feasibility. Tests should be chosen with this factor in mind.

Note also that this scenario of combining p-values (many tests of a single hypothesis) is fundamentally different from that where a given hypothesis is tested multiple times. The latter instance usually calls for some method of multiple testing correction.

Here is an abbreviated list of the substantive works on the topic of combining probabilities.

• Birnbaum, A. (1954) Combining Independent Tests of Significance, Journal of the American Statistical Association 49(267), 559-574.
• David, F. N. and Johnson, N. L. (1950) The Probability Integral Transformation When the Variable is Discontinuous, Biometrika 37(1/2), 42-49.
• Fisher, R. A. (1958) Statistical Methods for Research Workers, 13-th Ed. Revised, Hafner Publishing Co., New York.
• Lancaster, H. O. (1949) The Combination of Probabilities Arising from Data in Discrete Distributions, Biometrika 36(3/4), 370-382.
• Littell, R. C. and Folks, J. L. (1971) Asymptotic Optimality of Fisher's Method of Combining Independent Tests, Journal of the American Statistical Association 66(336), 802-806.
• Pearson, E. S. (1938) The Probability Integral Transformation for Testing Goodness of Fit and Combining Independent Tests of Significance, Biometrika 30(12), 134-148.
• Pearson, E. S. (1950) On Questions Raised by the Combination of Tests Based on Discontonuous Distributions, Biometrika 37(3/4), 383-398.
• Pearson, K. (1933) On a Method of Determining Whether a Sample Of Size N Supposed to Have Been Drawn From a Parent Population Having a Known Probability Integral Has Probably Been Drawn at Random Biometrika 25(3/4), 379-410.
• Van Valen, L. (1964) Combining the Probabilities from Significance Tests, Nature 201(4919), 642.
• Wallis, W. A. (1942) Compounding Probabilities from Independent Significance Tests, Econometrica 10(3/4), 229-248.
• Zelen, M. and Joel, L. S. (1959) The Weighted Compounding of Two Independent Significance Tests, Annals of Mathematical Statistics 30(4), 885-895.
 2020-11-06 perl v5.30.3