Experiments without biological replicates do not allow for estimation of the dispersion of counts around the expected value for each group, which is critical for differential expression analysis. If an experimental design is supplied which does not contain the necessary degrees of freedom for differential analysis, DESeq will provide a warning to the user and follow the strategy outlined in Anders and Huber (2010) under the section 'Working without replicates', wherein all the samples are considered as replicates of a single group for the estimation of dispersion. As noted in the reference above: "Some overestimation of the variance may be expected, which will make that approach conservative." Furthermore, "while one may not want to draw strong conclusions from such an analysis, it may still be useful for exploration and hypothesis generation." We provide this approach for data exploration only, but for accurately identifying differential expression, biological replicates are required.
A technical replicate is when you test the same sample multiple times - it's used to test the variability in the testing protocol itself. A biological replicate is where you perform the same test on multiple samples of the same material / type of cells / tissue.
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