False Positive Rate or False Discovery Rate?

For the researcher interpreting the results of a biomarker discovery experiment (or any similar experiment involving a large number of measurements), the false discovery rate is usually more useful than the false positive rate.

• The false positive rate (often called the p-value) gives the error rate of a single measurement. But if you have done 1000 measurements, it's not so straightforward to figure out how to effectively interpret the false positive rate.
• The false discovery rate gives the error rate in the subset of putative biomarkers identified on the basis of meeting or exceeding a threshold. For example, if you have done 1000 measurements and have found 50 of the measurements to be "interesting" (meets or exceeds threshold), the false discovery rate gives the error rate in the subset of 50 "interesting" measurements.

The following applet lets you explore the false positive rate and the false discovery rate under various conditions. For simplicity, the distributions of incorrect answers and correct answers are modeled as normal distributions.

Some things to notice:

• A false positive rate of 1% can correspond to a false discovery rate much higher than 1%.
• The false positive rate is dependent on the distribution of incorrect answers only, while the false discovery rate is dependent on the distribution of both incorrect answers and correct answers.

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