Related Error Rates
The discovery of the FDR was preceded and followed by many other types of error rates. These include:
- (per-comparison error rate) is defined as: . Testing individually each hypothesis at level guarantees that (this is testing without any correction for multiplicity)
- (the family wise error rate, in the weak sense) is defined as: . There are numerous procedures that control the FWER.
- (the family wise error rate, in the strong sense) is defined as: . There are numerous procedures that control the FWER.
- (The tail probability of the False Discovery Proportion), suggested by Lehmann and Romano, van der Laan at al, is defined as: .
- (Suggested by Sarker) is defined as: .
- is the proportion of false discoveries amound the discoveries", suggested by Soric in 1989, and is defined as: . This is a mixture of expectations and realizations, and has the problem of control for .
- (or Fdr) was used by Benjamini and Hochberg, and later called "Fdr" by Efron (2008) and earlier. It is defined as: . Controlling this error rate does not provide a weak control of the FWER.
- (or pFDR) was used by Benjamini and Hochberg, and later called "pFDR" by Storey (2002). It is defined as: . Controlling this error rate does not provide a weak control of the FWER.
- is defined as:
- The local fdr is defined as:
- False exceedance rate (the tail probability of FDP), defined as:
- (Weighted FDR). Associated with each hypothesis i is a weight, the weights capture importance/price. The W-FDR is defined as: .
- (False Discovery Cost Rate). Stemming from statistical process control: associated with each hypothesis i is a cost and with the intersection hypothesis a cost . The motivation is that stopping a production process may incur a fixed cost. It is defined as:
- (per-family error rate), at level, is defined as: .
- (False Non-Discovery Rates) by Sarkar; Genovese and Wasserman is define as:
Read more about this topic: False Discovery Rate
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