Yang et al. 2008 — Randomization in Laboratory Procedure Is Key to Obtaining Reproducible Microarray Results

1. Citation

Yang H, Harrington CA, Vartanian K, Coldren CD, Hall R, Churchill GA. “Randomization in Laboratory Procedure Is Key to Obtaining Reproducible Microarray Results.” PLoS ONE 2008 Nov 14;3(11):e3724. DOI 10.1371/journal.pone.0003724. PMCID PMC2579585; PMID 19009020. Received 2008-09-16; Accepted 2008-10-26. Editor: Thomas Preiss. Page count 11.

Author list VERIFIED against the published article — the invocation’s list is correct. As printed: Hyuna Yang¹, Christina A. Harrington², Kristina Vartanian², Christopher D. Coldren³, Rob Hall⁴, Gary A. Churchill¹ (corresponding, gary.churchill@jax.org). Affiliations: ¹The Jackson Laboratory, Bar Harbor, ME; ²Gene Microarray Shared Resource, OHSU Cancer Institute, Oregon Health and Science University, Portland, OR; ³Pulmonary Sciences and Critical Care Medicine, University of Colorado Health Sciences Center, Denver, CO; ⁴Center for Array Technologies, Department of Microbiology, University of Washington, Seattle, WA. Contributions as printed: “Conceived and designed the experiments: GAC. Performed the experiments: CH KV CDC RH. Analyzed the data: HY CH KV. Wrote the paper: HY GAC.” Competing interest as printed: Dr. Harrington has a significant equity interest in Affymetrix, Inc.

Open access: https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0003724 ; https://pmc.ncbi.nlm.nih.gov/articles/PMC2579585/ . Access date 2026-07-13.

2. Access note

Full text read in full (PLOS JATS XML + PDF + PMC HTML), including Tables 1–3, all figure captions, Materials and Methods, footnotes. Not read: the two supplementary files — Table S1 (“Deatil sample processing information”, 0.03 MB XLS), which is where the per-center protocol/batch detail actually lives, and Figure S1 (1.69 MB TIF). Figures 1–6 are images and were not machine-readable; they are described from their captions and from the Results prose, not transcribed. Everything below is from the main text unless marked.

License — exact wording as printed. The PDF and the PLOS/PMC full text carry only this, with no version number and no license URL anywhere in the article:

“Copyright: © 2008 Yang et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.” (verbatim, PDF p. 1 / JATS <permissions><license>; the PMC rendering says “properly credited” — a one-word variant of the same statement.)

So the guidance’s expectation of a printed “CC-BY-2.5” could not be confirmed: the article prints an unversioned CC-BY. The only versioned evidence available is PLOS’s own CrossRef license deposit for this DOI, which gives http://creativecommons.org/licenses/by/4.0/ (start 2008-11-14, content-version: unspecified) — hence CC-BY-4.0 / LICENSES/CC-BY-4.0.LICENSE in frontmatter, flagged rather than assumed. Both candidates are verbatim-ok, so the license-aware posture (§7 short verbatim load-bearing quotes, marked) is safe either way.

GEO accession: not present. The article names no GEO/ArrayExpress accession and contains no data-availability statement; data are described only as “Data from each center were provided in the form of CEL files.”

3. Thesis

The same RNA samples processed at different laboratories give dramatically different differential-expression results, and a primary cause is batch effects in array processing; when processing batches are confounded with the biological factors of interest, the effects cannot be separated and DE-gene lists fill with artifacts — hence samples must be assigned to processing batches by randomization.

4. Problem & context

Microarray data accumulate in public repositories and are routinely combined across studies. Prior multi-lab/multi-platform comparisons ([2]–[5]) generally concluded there is substantial concordance, but the authors note this positive message rested on comparisons of the best-performing laboratories [2] or on small sets of top-ranked genes [3]. The authors chose to isolate one variable: the effect of processing the same samples at different laboratory sites, on a common platform, with a common sample set carrying moderate expression differences.

5. Method / approach

Samples (n=16). Kidney tissue from two male and two female mice from each of four mouse strains: C57BL/6J plus three chromosome substitution strains (CSSs) C57BL/6J-Chr1^A/J, C57BL/6J-Chr6^A/J, C57BL/6J-Chr15^A/J — denoted B, A1, A6, A15. In each CSS one chromosome from A/J is crossed onto the C57BL/6J background [6]. RNA prepared as in [18]. Samples were prepared centrally and distributed to each of four centers.

Centers (5 datasets from 4 labs). “Sample[s] were distributed to each of four centers, and one center processed two sets of the 16 samples at different times using different labeling protocols. For simplicity we refer to these as five centers (C1–C5).” → 5 × 16 = 80 arrays. Samples were “delivered to each of the sites with the suggestion that they be processed according to standard protocols in a manner typical for that laboratory.” Data returned as CEL files. Design expectation (not a truth standard): DE genes between B and each CSS should be enriched on the substituted chromosome; the paper states explicitly “there are no truth standards so our results reflect the precision but not necessarily the accuracy of the platform.”

Platform. Affymetrix GeneChip Mouse 430v2. All centers used the Affymetrix-recommended one-cycle cDNA synthesis / in vitro-transcription (IVT) method. Centers 1, 3, 4, 5 used the Affymetrix IVT reagent kit; center 2 used the ENZO IVT kit. Center 2 used the original Affymetrix labeling protocol incorporating two labeled NTPs (biotin UTP and biotin CTP); all others used a newer protocol incorporating one NTP (biotin UTP). Named protocol differences across centers: (1) amount of hybridization solution applied to each array; (2) rotation per minute (rpm) of hybridization oven; (3) batch design for labeling, hybridization and post-hybridization processing. Per-center protocol detail is in Supplementary Table S1 (not read).

Analysis. RMA [11] normalization per center, separately (all reported results). Per-gene general linear model with main effects for sex and strain, no interaction (so strain tests are adjusted for sex and vice versa). Test statistics: Fs [20] via the MAANOVA package, and moderated F [21] via LIMMA; the two agreed and only Fs is reported. P-values by nested permutation of sample labels. Multiple-testing adjustment by FDR/q-value [12][13]. GO-term enrichment by hypergeometric test in the GOstats R package [15] at p<0.01. PCA per center. Classification via NMF metagene projection (Tamayo et al. [9]): weight matrix W from one training center, H* = W⁻¹V* projected onto the other centers, then clustered. Hierarchical clustering of raw data used Euclidean distance and complete linkage [23]. The authors also normalized all 80 arrays together as an aside only.

6. Key claims / findings

The batch-confounding retrospective (the core evidence — Results, “Batch effects”)

The authors state the four processing steps as: “Affymetrix GeneChip arrays are processed in four steps: labeling, hybridization, wash and staining, and scanning.” They then did a retrospective analysis of which samples were processed together at each step at each center. Stated cause of batching: “Due to personnel and equipment constraints, all samples may not be processed at one time. For instance, one fluidics station used for the wash and staining step, is able to process only up to four samples. The numbers of array that can be hybridized together is constrained along with several other steps in sample processing.”

Per center — what they did with processing, and the consequence:

The authors’ summary of the pattern: “In all cases where processed batches correspond to a biologically interesting feature of the data, we see an increase in the number of apparently differentially expressed genes.” And in the Discussion: “In centers 2 and 3, female and male samples were processed separately at the washing step, and in centers 4 and 5, samples were hybridized together in groups defined by strain. In all cases, the gene lists corresponding to the confounded factors were substantially longer than gene lists obtained from the other centers where the same confounding was not present.”

Magnitude of the distortion

• “For overall strain effects, the numbers of differentially expressed genes from centers 4 and 5 can be as much as five times that of other centers.”
• Table 1, strain overall, p-value thresholds (C1|C2|C3|C4|C5): p<0.001 → 377 | 462 | 517 | 1390 | 1290; p<0.01 → 939 | 1160 | 1200 | 4907 | 4522; p<0.05 → 2732 | 3296 | 3119 | 10943 | 10618.
• Table 1, strain overall, q-value → 116 | 134 | 170 | 0 | 184 (tightest threshold); 188 | 219 | 265 | 571 | 819; 285 | 376 | 423 | 6362 | 5361. ⚠️ Published-table label anomaly, reported not corrected: Table 1’s three strain q-value rows are labeled 0.001, 0.05, 0.01 in that order. The row labeled “0.01” (285/376/423/6362/5361) carries exactly the numbers Table 3 reports for q<0.05, and Table 3 is captioned “q-value<0.05”. So the last two q-value row labels appear transposed in the published Table 1; the q<0.05 strain counts are 285 | 376 | 423 | 6362 | 5361. The C4 value of 0 at the tightest q threshold is real and is explained by the Figure 2 caption: “Center 4 has smaller number of genes than other centers until p-value<2e-04 (panel c), then the number of gets increased, and that causes sudden increase in q-value (panel e).”
• Table 1, sex effect: p<0.001 → 3250 | 5099 | 5842 | 4003 | 3663; q<0.05 → 6360 | 18910 | 17475 | 8872 | 8071.
• Table 1, fold-change criteria (log2-based; strain): FC>1 → 135|103|118|216|532; FC>1.5 → 56|44|52|69|124; FC>2 → 29|23|35|34|57; FC>3 → 7|6|8|8|10. Sex: FC>1 → 313|277|320|347|368; FC>1.5 → 139|126|139|167|145; FC>2 → 86|70|89|110|88; FC>3 → 35|31|36|54|40. The between-center spread is largest under q-value and smallest under fold-change: “In all cases, these differences are the most pronounced when using the q-value criteria and least when fold-change criteria are used.”
• Table 1 pairwise strain, p<0.001 (C1|C2|C3|C4|C5): B vs A1 → 223|252|270|458|295; B vs A6 → 119|190|198|1206|417; B vs A15 → 150|133|123|821|616; A1 vs A6 → 323|367|463|820|605; A1 vs A15 → 284|301|372|1180|1005; A6 vs A15 → 209|287|254|313|1053. ⚠️ Published-table label anomaly: Table 1 prints the label “A1 vs.A15” twice; the second block is the A6-vs-A15 contrast (the Results text discusses “the comparison of A6 versus A15 in center 4”), so it is labeled A6 vs A15 here.
• Table 2 — estimated proportion of non-DE genes (π₀): strain → C1 0.96, C2 0.95, C3 0.99, C4 0.42, C5 0.43. Sex → C1 0.70, C2 0.36, C3 0.39, C4 0.53, C5 0.62. The centers whose batches were confounded with strain estimate that ~58% of all genes are differentially expressed by strain. Consequence: “When π₀ is lower, the q-value corresponding to a fixed p-value is lower. Thus the q-value criteria will tend to exaggerate differences in the list lengths as we have observed.” (q-value at a fixed p<0.05 for strain: 0.80 | 0.65 | 0.72 | 0.09 | 0.09.)

Downstream consequences

• Overlap (Table 3, q<0.05). C4 and C5 have more DE genes and share more in absolute terms (C4&C5 = 1672) but “the proportion of shared genes is only about 17%”; C1/C2/C3 have fewer DE genes and fewer in common but the proportion is higher, “about 50%”. Only 182 strain DE genes are common to all five centers. Sex effect: proportion in common ~50%, C2&C3 ~54%, 4044 genes common to all five — “indicating greater consistency across centers for sex effect than for strain effect.”
• GO enrichment (Table 3, hypergeometric p<0.01). GO terms from strain lists: C1 14, C2 11, C3 16, C4 50, C5 47. Overlap among all five: a single GO term (GO:0048276, gastrulation). Sex: ~50 GO terms each, two GO terms common to all five (GO:0019752 carboxylic acid metabolic process; GO:0006631 fatty acid metabolic process).
• Rank-based agreement is much better than list-length agreement (CAT plots [2]). Strain: correspondence peaks at a list length of about 70 genes with 60%–80% pairwise correspondence, about 50% common across all centers. Sex: peak at list length 500, correspondence 50%–70%, persisting for very long lists. The authors’ reading: “Strong concordance based on rank order indicates that many of the centers are picking the same genes and suggests that calibration of p-values and q-values is contributing to the difference in list lengths. It does not guarantee that the lists are biological in origin.”
• Intensity/MAD. Centers 4 and 5 have the highest internal variation (MAD) across the 16 arrays; center 2 the lowest. Center 2 has the highest median intensity (explained by the two-NTP labeling protocol); centers 4 and 5 are notably low.
• Normalization does not fix it. Normalizing all 80 arrays together “reduced the overall intensity differences but created an even greater difference in MAD distributions between centers 4 and 5 compared to the other centers.”
• Clustering. Hierarchical clustering of all centers’ raw data together “is first clustered perfectly by center”; within center, perfectly by sex, then reasonable pairing by strain.
• Classification/projection. With center 3 as NMF training set, projection recovers a reasonable strain/sex structure; with center 4 as training set, “there is no consistent pattern in the clusters.” Other centers fall between the two extremes (Figure S1).
• PCA. In every center, PC1 corresponds to the sex effect (separates male/female). PC2 differs per center and separates strains inconsistently.

7. Load-bearing statements — VERBATIM (license-aware mode: CC-BY → verbatim-ok)

Mode: license-aware. Short verbatim quotes below, each with location. (Rationale in §2 — article prints unversioned CC-BY; both candidate versions are verbatim-ok.)

1. The recommendation, including the recommendation AGAINST common practice (Discussion):

   “It is a common practice to organize samples having similar characteristics in groups that are processed together. We strongly recommend against this practice. It is important to identify all potential batch effects in a sample processing pipeline and to assign samples to batches using a randomization mechanism.”

2. The prescribed design for this experiment (Discussion, next sentences):

   “With the benefit of hindsight, we might have recommended that in this experiment the samples be processed in each laboratory as follows. The samples should be hybridized in two batches of eight. Each batch should consist of a randomly chosen sample from each of the eight sex-strain pairs. Within each batch the wash and staining should be done on randomly selected sets of four samples, or with random selections balanced across sexes. In addition to avoiding confounding, this strategy has the added benefit that batch can be included as a random effect term in the per-gene ANOVA model to reduce error variation and thus increase power of the design.”

3. Design-it-out beats correct-it-after, when confounded (Discussion):

   “Methods to correct for batch effects have been proposed [16], [17] and their benefits have been demonstrated. However when a batch effect is confounded with an experimental factor, correcting for the batch will also effectively remove the biological signal.”

4. Irreversibility, and the single-center blind spot (Results, “Batch effects”):

   “For any one center it is not possible to distinguish the effect of batch processing from the biological effect. The magnitude of the batch effect can be significant or negligible, but it cannot be removed from the data without compromising the biological signal.”

5. What the statistics are actually doing (Discussion):

   “The statistical criterion is correctly identifying genes that differ between groups, but the perturbations that causes these differences represent a mixture of biological and technical effects. In a randomized experiment, technical variation will be balanced across treatment groups, and differentially expressed gene lists will more accurately reflect the biological differences between samples.”

(Also load-bearing, Results: “there are differences in the distribution of intensity across centers that cannot be removed by normalization procedures.”)

8. Stated scope, assumptions, limitations (the source’s own caveats)

• No truth standard. “[T]here are no truth standards so our results reflect the precision but not necessarily the accuracy of the platform.” No spike-ins, no knockout mixtures.
• Retrospective, not designed. The batch structure was not assigned by the study; it was reconstructed after the fact (“A retrospective analysis of the laboratory steps used to process the samples revealed…”). Centers were told to process “in a manner typical for that laboratory.”
• n=5 datasets from 4 labs, 16 samples, one platform (Affymetrix Mouse 430v2), one tissue (kidney), one species (mouse), moderate biological signal.
• The model fitted has no strain×sex interaction; “Other models and comparisons could be considered but we found these to be sufficient for illustrating the differences among centers.”
• Not a claim that microarrays are unreliable: “We do not intend to convey a message that the microarray data are not reliable.”
• Effect localized to list length: “The effects we observed here primarily impact the length of differentially expressed gene lists, and these are exacerbated by the application of FDR correction [13].”
• Feasibility caveat on the recommendation itself: “This can be a challenging problem that requires careful coordination of samples to achieve efficient throughput without compromising data integrity.”
• Annotation limits: “[T]his kind of detailed information about sample processing is not typically available in publicly archived microarray data.”

9. Failure modes / invalidity patterns (referee-relevant)

• Grouping like samples into a processing batch = confounding. Whenever a processing batch corresponds to a biologically interesting feature, apparent DE inflates. Observed at two distinct steps: hybridization day ↔ strain (C4, C5) and wash/stain set ↔ sex (C2, C3).
• Batch correction cannot rescue a confounded design. Correcting for a batch that is confounded with the experimental factor removes the biological signal too (§7 quote 3).
• Normalization cannot rescue it either — joint RMA over all 80 arrays widened the MAD gap.
• The distortion is invisible from inside a single center. “If we had data from only one center, it would be difficult to detect these problems or to determine how many genes are truly differentially expressed.” No detector is offered that works within one confounded dataset.
• FDR/q-value amplifies the artifact. A confounded center’s π₀ collapses (0.42/0.43 vs 0.95–0.99), which lowers the q-value at a fixed p-value, which exaggerates list-length differences. Named symptom: an implausibly low π₀ / implausibly high estimated DE proportion (C4/C5 imply ~58% of genes DE by strain).
• Named diagnostics/symptoms in the paper (each is a symptom, not a proof):
  • intensity distribution and MAD across arrays within a center (Figure 1) — centers 4/5 stand out;
  • hierarchical clustering that clusters perfectly by center/batch before biology (Figure 6a);
  • rank-order (CAT) concordance much better than list-length concordance — signals that the p/q calibration, not the gene ranking, is what differs;
  • a short within-batch contrast beside a long across-batch contrast for the same factor (C4: B-vs-A1 458 and A6-vs-A15 313, both within-day, vs B-vs-A6 1206 across-day; C5: B-vs-A1 295 within-day vs A6-vs-A15 1053 across-day). This is the paper’s sharpest internal fingerprint of batch confounding.
  • GO enrichment inflating in step with the gene lists (C4 50 / C5 47 terms vs 11–16 elsewhere) — functional analysis does not filter the artifact.
  • Projection/classification instability: training NMF on a confounded center (C4) yields “no consistent pattern in the clusters”; the authors warn “in practice it may be difficult to know when the projection method is effective.”
• Randomization does not guarantee balance in small designs. C1 randomized and still got partial batch↔sex confounding (3 males in the 4-sample batch) purely by chance — the paper reports this without prescribing a fix (its own recipe for the redo uses restricted randomization instead; see §12).

10. What the source does NOT address (confident silences — verified by full-text search)

• INSTRUMENT RUN ORDER / INJECTION ORDER / POSITION WITHIN A RUN: NOT ADDRESSED. This is a hard silence, not a soft one. The word “order” appears in the paper only as “rank order” of genes by test statistic (the CAT analysis) — never as processing, run, hybridization, wash, or scan order. The words “drift”, “carryover”/“carry”, “sequence”, “position”, “slot”, “run order” do not appear at all in the body. The paper’s unit of concern is the discrete processing batch (which samples are processed together in a group), never the sequence within a group or a run. Its recommendation is randomized assignment to batches (“assign samples to batches using a randomization mechanism”; “a randomly chosen sample from each of the eight sex-strain pairs”; “randomly selected sets of four samples”) — i.e. randomized membership, not randomized order. Even the multi-day cases (C4 two days; C5 three days) are treated as discrete day-batches, not as a temporal trend or drift; no continuous time/run-index covariate is fitted or discussed anywhere. This source cannot be cited for “randomize the injection/run order” or for continuous temporal drift. It supports randomized assignment to discrete processing batches, and nothing more.
• The word “blocking” never appears (0 occurrences of “block”). The paper never contrasts randomization with blocking by name.
• No variance decomposition. Nowhere does the paper quantify what fraction of variance is attributable to batch/processing vs biology — no variance components, no % variance explained, no ICC. The evidence is entirely DE-count, π₀, MAD, clustering, and PCA-structure based. (The only quantitative “how much” statements are the DE-count ratios: “as much as five times”.)
• No batch-effect correction method is applied or benchmarked. ComBat-style correction is cited in passing ([16] SVA, [17]) but never run on these data.
• RNA extraction / tissue collection as a batch-generating step is not analyzed — samples were prepared centrally at one site and shipped, so extraction is not a center-level batch here.
• Scanning is named as one of the four processing steps but no scanner or scan-date batch effect is reported for any center; likewise no labeling-batch confounding is reported (labeling protocol differences between centers are, but not labeling-batch↔factor confounding). The recommended recipe (§7 quote 2) covers hybridization batches and wash/stain sets only — it prescribes nothing for labeling or scanning order/grouping.
• No sample-size / power calculation, no randomization algorithm or software is given — the paper says “using a randomization mechanism” without specifying one (no tool, no objective function, no stratification procedure beyond the one worked example).
• No GEO/ArrayExpress accession, no data-availability statement.
• No RNA-seq, no mass spectrometry, no non-microarray platform. Single platform (Affymetrix Mouse 430v2), single vendor.
• Randomization vs statistical adjustment: it does address this (§7 quote 3, and batch as a random effect in §7 quote 2) — see §12 — but it never treats adjustment for a non-confounded, unrandomized batch, and gives no guidance on residual/partial confounding like C1’s.

11. Open questions / ambiguities left unresolved

• What to do when randomization happens to produce partial confounding (C1’s 3-of-4 males) — the paper reports it, notes C1 still had the shortest lists, and offers no correction or re-draw rule.
• How to detect batch confounding from a single dataset — the paper says it is difficult and stops there.
• Which of the four steps carries the largest batch effect: “The effect is less than that for the strain comparisons between centers 4 and 5, which may indicate that the batch effects of wash and staining are less dramatic or may it reflect the strength of signal in the sex effect, or both.” — explicitly unresolved.
• Whether centers 4/5’s inflated lists are purely artifact: rank-order concordance is high, so “many of the centers are picking the same genes,” yet “[i]t does not guarantee that the lists are biological in origin.” The paper does not quantify the artifact fraction.
• Two internal numeric inconsistencies the paper does not resolve: Table 1 gives 423 strain DE genes at q<0.05 for C3 while Table 3 gives 426; Table 1 gives 8071 sex DE genes at q<0.05 for C5 while Table 3 gives 8971 (and Table 3’s C5 strain row reads 5361, matching Table 1). Plus the two Table 1 label anomalies flagged in §6.

12. Guidance answers

Q. Explicit recommendation about assignment to processing batches, and about order within a batch? Quote every such sentence, including any recommending AGAINST a common practice. Yes for assignment; NO sentence anywhere about order within a batch. The complete set of recommendation sentences is §7 quotes 1–2 (reproduced there verbatim), plus, from the Discussion: “we wish to highlight the importance of randomization in all laboratory procedures” and “The laboratories involved in this study have updated their practices to incorporate randomized assignment of samples to processing batches.” The against-common-practice sentence is: “It is a common practice to organize samples having similar characteristics in groups that are processed together. We strongly recommend against this practice.” Every recommendation is about which samples go in which batch, never about sequence/order within one.

Q. What exactly is randomized — batch membership, day, hybridization order, wash/stain order, scan order? Enumerate each level named. Levels the recommendation actually names: (1) hybridization batch membership — two batches of eight, each containing one randomly chosen sample from each of the eight sex-strain pairs; (2) wash/stain set membership — within each hyb batch, randomly selected sets of four (fluidics station capacity), or random selections balanced across sexes. That is all. Hybridization order, wash/stain order, and scan order are never mentioned. “Day” enters only as a description of what C4/C5 did wrong (hyb over 2 and 3 days), not as a randomization level in the recipe — the recipe’s two batches of eight are not assigned to days at all. The general rule adds: “identify all potential batch effects in a sample processing pipeline and … assign samples to batches using a randomization mechanism” — an instruction to enumerate steps, without enumerating them for you.

Q. The prescribed design as a concrete recipe (batch sizes, what is balanced, what is randomized within what). For the 16-sample, 4-strain × 2-sex experiment:

1. Hybridization: 2 batches × 8 samples. Each batch = one randomly chosen sample from each of the 8 sex-strain pairs → both batches are balanced (fully crossed) on sex and strain; the choice of which replicate goes to which batch is the randomized part. (Restricted/stratified randomization, though the paper never uses those words.)
2. Wash and staining: within each hyb batch, sets of 4 (the fluidics-station limit), either randomly selected or “with random selections balanced across sexes.”
3. Analysis: include batch as a random effect term in the per-gene ANOVA model — stated benefit: reduces error variation, increases power. Nothing is prescribed for labeling batches, scanning, or any within-batch ordering.

Q. The experiment: labs, samples, factors, platform, processing runs. 4 laboratories → 5 datasets (C1–C5), one lab having processed the 16 samples twice, at different times with different labeling protocols. 16 RNA samples (mouse kidney), factors strain (B, A1, A6, A15 — C57BL/6J plus three chromosome substitution strains for Chr1, Chr6, Chr15 from A/J) and sex (2 male + 2 female per strain). Platform Affymetrix GeneChip Mouse 430v2; 80 arrays total. Processing runs per center are the batch structures in §6’s table (C1: 2 hyb batches, same day; C4: 2 hyb days; C5: 3 hyb days; C2/C3: split wash/stain by sex).

Q. Per center: what was done with processing order, and the DE-gene consequence, with numbers. Which centers confounded which biological factor with which procedural step? See the table in §6. In brief: C2, C3 → sex ↔ wash/stain batch (sex q<0.05 lists 18910 and 17475, vs 6360 at C1); C4, C5 → strain ↔ hybridization day (strain q<0.05 lists 6362 and 5361, vs 285/376/423 at C1/C2/C3; strain π₀ 0.42/0.43 vs 0.95–0.99); C1 → randomized, with incidental partial sex ↔ batch confounding from a 12/4 split that put 3 males in the batch of 4; C1 has the shortest lists in every comparison. Note precisely: no center is described as having done anything with processing order — the paper only records which samples each center processed together.

Q. Variance attributable to processing/batch vs biology — numbers. Not provided. The paper gives no variance decomposition or percentage. The closest quantitative statements are DE-count ratios (“as much as five times”), the π₀ estimates (Table 2), MAD comparisons (Figure 1b, qualitative in the text), and the fact that raw data cluster “perfectly by center” before biology.

Q. Which procedural steps are treated as batch-generating? List every one named. Exactly four, as printed: labeling, hybridization, wash and staining, and scanning. Equipment constraint named: the fluidics station for wash/stain handles up to four samples; hybridization capacity is “constrained” (number unspecified). RNA extraction and scan date/scanner are NOT analyzed (extraction was centralized; scanning is named in the four-step list but no scan batch effect is reported). “Day” is a batch label applied to hybridization only.

Q. Does it discuss instrument RUN ORDER / injection order within a run, or continuous temporal drift? Quote, or record the silence explicitly. IT DOES NOT. Recording the silence explicitly: there is no sentence in this paper about run order, injection order, within-run position, array position, scan sequence, or continuous temporal drift. Full-text search: “order” occurs only in “rank order”/“rank ordering” of genes; “drift”, “carryover”, “sequence”, “run order” occur zero times. The paper’s entire model of procedural nuisance is discrete batch membership — samples processed together in a group (a hyb day, a fluidics run of ≤4, a labeling set). Multi-day processing (C4: 2 days; C5: 3 days) is analyzed as discrete day-batches confounded with strain, not as a temporal trend. Do not stretch this source to mass-spec injection order or to run-order/drift claims of any kind — it does not reach there.

Q. Randomization vs blocking (deliberate balancing) — one, the other, or both? The word “blocking” never appears (0 occurrences), so the paper never frames the contrast. But its prescribed recipe is, in substance, both: each hyb batch is deliberately balanced — “Each batch should consist of a randomly chosen sample from each of the eight sex-strain pairs” (one per sex-strain cell = a complete block), with randomization operating within that constraint; and at wash/stain, “randomly selected sets of four samples, or with random selections balanced across sexes” — the explicit either/or between plain randomization and balance-constrained randomization. The stated headline rule, however, is randomization: “assign samples to batches using a randomization mechanism.”

Q. Statistically adjusting for batch after the fact vs designing it out? Addressed directly, twice, and it comes down on designing it out:

• §7 quote 3 — batch-correction methods exist and work, “However when a batch effect is confounded with an experimental factor, correcting for the batch will also effectively remove the biological signal.”
• §7 quote 4 — “The magnitude of the batch effect can be significant or negligible, but it cannot be removed from the data without compromising the biological signal.”
• But adjustment is endorsed when the design was randomized first: “batch can be included as a random effect term in the per-gene ANOVA model to reduce error variation and thus increase power of the design” (§7 quote 2). So: randomize/balance at design time; then model batch to recover power, not to rescue a confounded design.

Q. Pin: journal, article number, DOI, date, license wording/version, GEO accession, access date. PLoS ONE 3(11): e3724, published 2008-11-14; DOI 10.1371/journal.pone.0003724; PMCID PMC2579585 / PMID 19009020. License: unversioned “Creative Commons Attribution License” as printed (exact wording in §2) — no version number appears in the article; PLOS’s CrossRef deposit for the DOI says CC-BY 4.0. GEO accession: none given — the article names no accession and has no data-availability statement. Access date 2026-07-13.