AdvancedNumeric answer
A hundred candidate signals · Part 3 of 3
A researcher tests 100 independent candidate signals, each at the 5% level. In truth 90 have no predictive value and 10 are real, and each real signal is detected with probability 0.8, the power of its test. Take the false-discovery share to be the expected number of false positives divided by the expected number of discoveries.
Keep the 5% level, the 100 signals and power 0.8, but suppose that k of the signals are real. What is the smallest k for which the false-discovery share is at most 0.20?
Answer with a number. Fractions, powers and expressions like 23/6 or C(52,5) are read correctly in practice.
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