Objectives: A "null field" is a scientific field where there is nothing to discover and where observed associations are thus expected to simply reflect the magnitude of bias. We aimed to characterize a null field using a known example, homeopathy (a pseudoscientific medical approach based on using highly diluted substances), as a prototype.
Study design and setting: We identified 50 randomized placebo-controlled trials of homeopathy interventions from highly cited meta-analyses. The primary outcome variable was the observed effect size in the studies. Variables related to study quality or impact were also extracted.
Results: The mean effect size for homeopathy was 0.36 standard deviations (Hedges' g; 95% confidence interval: 0.21, 0.51) better than placebo, which corresponds to an odds ratio of 1.94 (95% CI: 1.69, 2.23) in favor of homeopathy. 80% of studies had positive effect sizes (favoring homeopathy). Effect size was significantly correlated with citation counts from journals in the directory of open-access journals and CiteWatch. We identified common statistical errors in 25 studies.
Conclusion: A null field like homeopathy can exhibit large effect sizes, high rates of favorable results, and high citation impact in the published scientific literature. Null fields may represent a useful negative control for the scientific process.
Keywords: Bias; Homeopathy; Meta-Research; Null field; Replication crisis; Research integrity; Treatment effects.
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