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. 2023 Nov 28;12:e79559. doi: 10.7554/eLife.79559

Appendix 3—table 1. Two types of circular analysis.

Circular analysis of noise Circular analysis of knowledge
Conceptual problem Explanation of the same aspect of the data twice: first as noise, and second as a new discovery non-independent of this noise. Explanation of the same aspect of the data twice: first as existing knowledge, and second as new discovery redundant with this knowledge.
Statistical problem Model overfitting that results in high variance (low precision) of estimated model parameters. Model overspecification that results in high bias (low trueness) of estimated model parameters.
Statistical solution Tests of independence against sampled data in which all benchmark (noise) features are maximally random and all other aspects of the data are preserved. Tests of non-redundancy against sampled data in which all benchmark (existing knowledge) features are preserved and all other aspects of the data are maximally random.