Errors in centering of array data can induce biases in correlation estimates

For a general class of microarray data sets, the sample specific centering errors can constitute correlated measurement errors. These errors are perfectly correlated within samples in the sense that all spot assays within a given sample are centered with the same error. Under certain biological conditions, the centering errors can also be correlated to a specific subset of spot assays. In contrast to the within-sample correlated errors, the correlation of centering errors to select spot assays can be thought of as an across-sample correlation (e.g., for the cases presented in this manuscript, the spot assay by centering error correlation only exists if the skew of the distribution varies across samples with the variation dependent on a subset of spot assays). We demonstrate that the perfect within sample correlation of the centering errors induces a positive bias in spot assay by spot assay correlation estimates while negative across-sample correlations can induce a negative bias in said estimates. We provide analyses of a real and simulated data set and demonstrate that, under realistic conditions, the centering errors can induce biases in spot assay by spot assay correlation estimates while not significantly affecting permutation-based thresholds for significance; a combination which can lead to a breakdown in error control.