Contra-Analysis for Determining Negligible Effect Size in Scientific Research

Scientific experiments study interventions that show evidence of an effect size that is meaningfully large, negligibly small, or inconclusively broad. Previously, we proposed contra-analysis as a decision-making process to help determine which interventions have a meaningfully large effect by using contra plots to compare effect size across broadly related experiments. Here, we extend the use of contra plots to determine which results have evidence of negligible (near-zero) effect size. Determining if an effect size is negligible is important for eliminating alternative scientific explanations and identifying approximate independence between an intervention and the variable measured. We illustrate that contra plots can score negligible effect size across studies, inform the selection of a threshold for negligible effect based on broadly related results, and determine which results have evidence of negligible effect with a hypothesis test. No other data visualization can carry out all three of these tasks for analyzing negligible effect size. We demonstrate this analysis technique on real data from biomedical research. This new application of contra plots can differentiate statistically insignificant results with high strength (narrow and near-zero interval estimate of effect size) from those with low strength (broad interval estimate of effect size). Such a designation could help resolve the File Drawer problem in science, where statistically insignificant results are underreported because their interpretation is ambiguous and nonstandard. With our proposed procedure, results designated with negligible effect will be considered strong and publishable evidence of near-zero effect size.