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                    I am comparing the results of DESeq2 'background' normalization with library size normalization with two different spike-ins (specified using the SpikeIn column in the samplesheet). I am getting the exact same Pvalues for all three methods. I did check that the DBA$norm$DESeq2$norm.facs values are different in each case. The MA plot using normalized counts also does not seem to be consistent with the DB sites called; lots of up-regulated sites called even though the distribution is globally shifted to <0 fold change.
dba.plotMA(diffbind, contrast=1, th = fdr_cutoff)
# make DBA object
diffbind <- dba(sampleSheet = samples %>% dplyr::select(-out_pref))
# set num cores and how many reads to store in memory
diffbind$config$cores <- db_config$cores-1
diffbind$config$yieldSize <- 20000000
# get counts
diffbind$config$scanbamparam <- ScanBamParam(flag = scanBamFlag(isDuplicate=FALSE, isSecondaryAlignment=FALSE, isSupplementaryAlignment=FALSE, isPaired=TRUE, isProperPair=TRUE, isNotPassingQualityControls=FALSE, isUnmappedQuery=FALSE, hasUnmappedMate=FALSE, isMinusStrand=NA, isMateMinusStrand=NA))
# get counts
diffbind <- dba.count(diffbind, summits=DB_summits, bUseSummarizeOverlaps = TRUE, bParallel = TRUE)
print(diffbind)
# normalization
if ("Spikein" %in% colnames(samples)){
    diffbind <- dba.normalize(diffbind, normalize=DBA_NORM_LIB, spikein=TRUE)
} else{
    diffbind <- dba.normalize(diffbind, normalize = DBA_NORM_NATIVE, background = TRUE)
}
# print the normalization methods
dba.normalize(diffbind, bRetrieve=TRUE)
comps <- list(
  list("GroupA", "GroupB")
)
for (comp in comps){
  diffbind <- dba.contrast(diffbind, 
                           group1=diffbind$masks[[ comp[[1]] ]], 
                           group2=diffbind$masks[[ comp[[2]] ]],
                           name1=comp[[1]], 
                           name2=comp[[2]])
}
dba.show(diffbind, bContrasts=TRUE)
diffbind <- dba.analyze(diffbind, bBlacklist=FALSE, bGreylist=FALSE)
dba.show(diffbind, bContrasts = TRUE)
## R version 4.2.1 (2022-06-23)
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## [161] ape_5.7-1

To help make it easier to reproduce this issue, I was able to reproduce similar behavior using the included tamoxifen dataset. I also realized that while the PValues are identical, the 'Conc' columns are distinct.
Packages loaded
Library size norm
Background counts RLE
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SessionInfo