Estimating the number of true null hypotheses from a histogram of p values

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Abstract

In an earlier article, an intuitively appealing method for estimating the number of true null hypotheses in a multiple test situation was proposed. That article presented an iterative algorithm that relies on a histogram of observed p values to obtain the estimator. We characterize the limit of that iterative algorithm and show that the estimator can be computed directly without iteration. We compare the performance of the histogram-based estimator with other procedures for estimating the number of true null hypotheses from a collection of observed p values and find that the histogram-based estimator performs well in settings similar to those encountered in microarray data analysis. We demonstrate the approach using p values from a large microarray experiment aimed at uncovering molecular mechanisms of barley resistance to a fungal pathogen.