Variance estimation in systematic sampling by splitting the sample into equal halves can lead to very serious bias. The expression for this bias relative to the true variance is given in terms of intraclass correlation coefficients. The danger of serious bias is still present when successive pairs of units are treated as "independent" replicates; an expression for this relative bias is also given.
J. C. Koop. "On Splitting a Systematic Sample for Variance Estimation." Ann. Math. Statist. 42 (3) 1084 - 1087, June, 1971. https://doi.org/10.1214/aoms/1177693336