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
Famous quotes containing the words related, error and/or rates:
“One does not realize the historical sensation as a re-experiencing, but as an understanding that is closely related to the understanding of music, or rather of the world by means of music.”
—Johan Huizinga (1872–1945)
“We shall yet acknowledge His wisdom and our own error therein.”
—Abraham Lincoln (1809–1865)
“In the U.S. for instance, the value of a homemaker’s productive work has been imputed mostly when she was maimed or killed and insurance companies and/or the courts had to calculate the amount to pay her family in damages. Even at that, the rates were mostly pink collar and the big number was attributed to the husband’s pain and suffering.”
—Gloria Steinem (20th century)