Should false discovery be controlled at the data acquisition level, or should this be at the data interpretation level?
I have an experiment in which microarrays were used to quantify the expression of about 30,000 genes (variables) in two groups of biological tissues (group-sizes of 75 and 76). Raw array data was pre-processed to remove background signals and genes whose expression levels are undetectable, and to normalize values across arrays. The final data was then examined using the Mann-Whitney U test to compare gene expression between the two groups to identify differentially expressed genes, with false discovery rate (FDR) controlled with the Benjamini-Hochberg procedure. At FDR <5%, no gene is identified as differentially expressed, and I formally conclude that 'there is no differential expression of genes between the two tissues.'
Now, suppose someone is interested in the expression of only one specific gene. Using my pre-processed gene expression data-set and the U test, they compare the two groups for the expression of only this gene and notice a P value <0.05, the commonly used significance threshold in my field of study. As this does not involve multiple testing, there is no false discovery control. Can this observer formally conclude that 'the gene is differentially expressed between the two tissues,' contradicting my conclusion?'
Or should the observer have applied false discovery control because such a control has to be applied at the data acquisition level (as per which, data on multiple variables were collected) and not at the data interpretation level (as per which, data for only one variable was analyzed)?