Controlling the False Discovery Rate: A Practical and Powerful Approach to Multiple Testing

• p. 13 References, Hochberg (1988) entry

  75, 800-803.

• p. 13 References, Rom

  Rom, D. M. (1990) A sequentially rejective test procedure based on a modified Bonferroni inequality. Biometrika, 71, 663-665.

• p. 13 References, Hochberg (1988)

  Biometrika, 75, 800-803.

• p. 13

  Rom, D. M. (1990) A sequentially rejective test procedure based on a modified Bonferroni i

Only the authors can say what is right here.

Judge's note: Rests on outside knowledge: that Hochberg (1988) occupies Biometrika 75, pages 800-802. The page image of PDF page 13 does print "75, 800-803.", so the quote is accurate, but the true page range cannot be checked from the files. The cluster also contains a second claim, that the Rom (1990) entry gives volume 71. That claim is an OCR mistake in the extracted text: the page image clearly prints the bold volume number as 77 ("Biometrika, 77, 663-665."), which is consistent with 1990 and with the Crossref record cited by the reviewer. Only the Hochberg last-page point survives, and it is a minor matter that does not hinder finding the article.

Second check: another model agreed, code check

• p. 2 Summary

  rate is equivalent to the FWER when all hypotheses are true but is smaller otherwise

• p. 4 Section 2.1, property (b)

  When m0 < m, the FDR is smaller than or equal to the FWER

Judge's note: Both sentences read on the page images (pp. 2 and 4). The summary states a strict inequality; the property shown is the weak one, P(V>=1) >= Qe. Loose abstract wording, not a mathematical error.

Second check: another model agreed

• p. 6 Section 3.1, text after inequality (2)

  distribution of P″1, . . ., P″m1 which corresponds to these false hypotheses

• p. 6 Lemma, inequality (2)

  E(Q | Pm0+1 = p1, . . ., Pm = pm1)

• p. 12 Appendix A, after inequality (4)

  denote the right-hand side of inequality (4) at j0 by p″

Judge's note: Enlarged render of PDF page 6 shows double primes on P_1 and P_{m1} in the sentence after (2); the lemma just above uses P_{m0+1},...,P_m. PDF page 12 defines p″ as the right-hand side of (4) and uses single primes for true-null p-values. Meaning is recoverable from context; notational inconsistency only.

Second check: another model agreed

• p. 7 Section 3.1, paragraph after Hochberg's procedure

  controlling procedure are step-down procedures, which start by comparing p(m)

• p. 7 Section 3.1

  are step-down procedures, which start by comparing p(m) with α

• p. 7 Section 3.1, paragraph after Hochberg's procedure

  are step-down procedures, which start by comparing p(m)

Only the authors can say what is right here.

Judge's note: Rests on outside knowledge: the convention (as in Hochberg and Tamhane 1987) that procedures starting from the least significant p-value are 'step-up' and Holm-type procedures starting from the smallest are 'step-down'. The sentence is on PDF page 7 as quoted and the description that follows it is of starting at p(m) and proceeding to smaller p-values. The paper does not define the term, so this is a terminology point for the authors.

Second check: another model agreed

• p. 9 Section 4.1

  L was chosen at two levels—5 and 10—thereby varying the signal-to-noise ratio

• p. 10 Fig. 1 caption

  (a) decreasing; (b) equally spread; (c) increasing

• p. 11 Section 4.2, observation (f)

  equally spread in four clusters from 1.25 to 5

Judge's note: Read pages 9-11. Fig. 1 has 12 panels (three configurations by four null proportions) and its caption does not mention L; searching the text finds L only in Section 4.1. No result for L = 10 is reported and no statement says it was omitted. An omission in reporting, not an error in a number.

Second check: another model agreed

• p. 11 Section 4.2, observation (f)

  testing as few as four hypotheses, half of which are true, the values are 0.62 and 0.70 respectively

• p. 10 Fig. 1, row "50% Null", panels (a) and (b), at m = 4

  50% Null

Only the authors can say what is right here.

Judge's note: Enlarged render of Fig. 1 (PDF page 10), 50% null row at m=4: panel (a) Bonferroni about 0.64-0.65, FDR about 0.70; panel (b) about 0.80 and 0.85. The first example in the sentence is explicitly 'equally spread'; the second names no configuration. Values are read from a scanned plot (about ±0.02), so the 0.62 against about 0.65 in panel (a) is within reading error; the unstated configuration is the point for the authors.

Second check: another model agreed

• p. 12 Appendix A, first displayed equation

  E(Q | P1 = p1, . . ., Pm = pm) = 0 ≤ m0/(m + 1) q*

• p. 12 Appendix A, equation (5)

  Pm = pm1

• p. 13 Appendix A, equations (8) and (9)

  Pm = pm1

Only the authors can say what is right here.

Judge's note: I checked the page images for p.12 (m0 = 0 display and eq. (5)) and p.13 (eqs. (8) and (9)). They print P_m as the last conditioned p-value, the same as the lemma statement on p.6, where m1 = m − m0. The induction step, though, treats m+1 hypotheses: the text says "showing it to hold for m + 1", and the bounds use m+1. So the m0 = 0 case leaves out P_{m+1}. In (5), (8) and (9), the range m0+1..m has m − m0 entries, one short of the m+1−m0 false nulls. I reworked the step with P_{m+1} in place of P_m. Eq. (6): m0/(m0+j0)·p''^{m0} = m0/(m+1) q* p''^{m0−1}, using p'' = (m0+j0)/(m+1) q*. Eq. (9): ∫_{p''}^1 (m0−1)/((m+1)p) q* m0 p^{m0−1} dp = m0/(m+1) q*(1 − p''^{m0−1}). Adding them gives m0/(m+1) q*, so the lemma and Theorem 1 still hold. The fault is an indexing slip in the proof's notation, not in the stated result.

Second check: another model agreed

• p. 2 Footnote, address for correspondence

  benja@math.tav.ac.il

• p. 2 Address for correspondence footnote

  E-mail: benja@math.tav.ac.il

Only the authors can say what is right here.

Judge's note: Rests on outside knowledge: Tel Aviv University's internet domain is tau.ac.il (the copy under review was fetched from www.math.tau.ac.il). Enlarged render of PDF page 2 shows 'tav' with a clear v, so it is not an OCR artefact. Whether a 'tav' host existed in 1995 cannot be settled from the files.

Second check: none (judge only)

• p. 7 Section 3.2, family (d)

  after the start of thrombolitic treatment

• p. 7 Section 3.2, family (d)

  cardiac and other events after the start of thrombolitic treatment

Judge's note: PDF page 7 image shows 'thrombolitic' in item (d); the same section opens with 'Thrombolysis'. Not an OCR artefact.

Second check: none (judge only)

• p. 13 References, Neuhaus entry

  thrombolysis in acute myocardial infarction front-loaded administration of Alteplase

Only the authors can say what is right here.

Judge's note: Rests on outside knowledge: that the published title reads "...acute myocardial infarction with front-loaded administration of alteplase...". Checked on the page image of PDF page 13: the line reads "thrombolysis in acute myocardial infarction front-loaded administration of Alteplase" with no "with" on that line or at the end of the previous line, so it is not an extraction loss. The title as printed does not parse, which supports a dropped word independently of the outside fact; the exact missing word is for the authors to confirm.

Second check: none (judge only)

• p. 13 References, last entry

  On the optimality of some multiple comparison procedure.

• p. 13 References, Spjøtvoll entry

  On the optimality of some multiple comparison procedure

Only the authors can say what is right here.

Judge's note: Rests on outside knowledge: that the published title is "On the optimality of some multiple comparison procedures". Checked on the page image of PDF page 13: the word is printed as "procedure." with no final s, so it is not an OCR loss. The singular is also ungrammatical after "some multiple comparison", which supports the reading as a dropped letter. Cosmetic.

Second check: none (judge only)