Correcting p values for the bias due to using a statistical test when its assumptions are false

What is it about?

Statistical tests are regularly used to analyze data without knowing how well the assumptions behind the tests match reality. Mismatches lead to biases that can be estimated given the high numbers of p values that are available in many genomics studies. Once those biases are estimated, they can be corrected. This paper provides such a method of correcting the results of statistical tests for bad assumptions. The new method is applied to microarray data to illustrate its advantages.

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Why is it important?

This paper describes how fiducial probability may help solve a common problem in high-dimensional biology: the non-satisfaction of the assumptions behind statistical tests. The proposed method for multiple comparisons can take advantage of the estimated null distribution without any prior distribution. Simulations indicate that an exception is the t test in the presence of data from distributions with power-law tails.

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