StatisticsdrillBenjamini-Hochberg: how many discoveries
A statistics problem from Statisticsdrill. Solve it with one answer box, with a fresh sample on every attempt and the worked steps and spreadsheet function in the answer, and it is checked the moment you submit.
The task
A growth team tested 6 ad creatives against the control and got these p-values: 0.0204, 0.0302, 0.0007, 0.0056, 0.1585, 0.0468. They control the false discovery rate at q = 0.05 with the Benjamini-Hochberg procedure. How many of the 6 tests are declared significant? Give a whole number.
What this problem teaches
The step-up rule matters: once the largest passing rank is found, every smaller rank is rejected too, even one whose own p-value exceeded its threshold. Bonferroni uses one threshold, q / m, and finds fewer.
A hint if you get stuck
Sort the p-values from smallest to largest. Compare the k-th smallest with k × q / m. Find the largest k that passes; that k and every smaller rank are significant, even if some of them individually failed.
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