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:
“Perhaps it is nothingness which is real and our dream which is non-existent, but then we feel think that these musical phrases, and the notions related to the dream, are nothing too. We will die, but our hostages are the divine captives who will follow our chance. And death with them is somewhat less bitter, less inglorious, perhaps less probable.”
—Marcel Proust (1871–1922)
“It is error alone which needs the support of government. Truth can stand by itself.”
—Thomas Jefferson (1743–1826)
“Good government cannot be found on the bargain-counter. We have seen samples of bargain-counter government in the past when low tax rates were secured by increasing the bonded debt for current expenses or refusing to keep our institutions up to the standard in repairs, extensions, equipment, and accommodations. I refuse, and the Republican Party refuses, to endorse that method of sham and shoddy economy.”
—Calvin Coolidge (1872–1933)