When normalization induces correlation: shared and unstable references can create hidden dependencies.

Correlation analyses are widely used to infer biological relationships, yet preprocessing can introduce structural dependencies that inflate correlation estimates. Here, we examine an under-recognized mechanism: shared-reference transformations, in which multiple variables are centered or scaled using the same reference before correlation-based inference. We derive analytically that, even when two variables are independent, subtracting a shared reference induces nonzero covariance and yields an expected correlation that increases with the variance of the reference. Simulations show that this artifact is systematic, strengthens as the reference becomes more variable, and does not disappear with increasing sample size. We further show that sequential shared transformations of the form (X-Z)/W can become unstable when denominators fluctuate or approach zero, producing highly dispersed correlations consistent with heavy-tailed ratio effects. As an illustrative count-based example,we introduce a simulation with sample-level scaling showing that downstream shared-reference steps can reintroduce dependence after an initial correction step. Finally, real-data analysis across multiple preprocessing pipelines confirms that shared-reference transformations can inflate correlation estimates in practice. These results highlight shared-reference preprocessing as a potential source of artificial dependence that should be explicitly considered when interpreting correlation-based findings.