Sample Size Calculation for Controlling False Discovery Proportion

Table 1

Outcomes and expected outcomes of testing 𝑚 hypotheses.

	Outcomes
	Reject 𝐻0	Accept 𝐻0	Total
𝐻0 is true	𝑉	𝑚0−𝑉	𝑚0
𝐻1 is true	𝑈	𝑚1−𝑈	𝑚1
Total	𝑅	𝑚−𝑅	𝑚
	Expected outcomes
	Reject 𝐻0	Accept 𝐻0	Total
𝐻0 is true	𝑚0𝛼	𝑚0(1−𝛼)	𝑚0
𝐻1 is true	𝑚1(1−𝛽)	𝑚1𝛽	𝑚1
Total	𝑚0𝛼+𝑚1(1−𝛽)	𝑚0(1−𝛼)+𝑚1𝛽	𝑚