Being able to interpret ‘null effects’ is important for cumulative knowledge generation in science. To draw informative conclusions from null-effects, researchers need to move beyond the incorrect interpretation of a non-significant result in a null-hypothesis significance test as evidence of the absence of an effect. We explain how to statistically evaluate null-results using equivalence tests, Bayesian estimation, and Bayes factors. A worked example demonstrates how to apply these statistical tools and interpret the results. Finally, we explain how no statistical approach can actually prove that the null-hypothesis is true, and briefly discuss the philosophical differences between statistical approaches to examine null-effects. The increasing availability of easy-to-use software and online tools to perform equivalence tests, Bayesian estimation, and calculate Bayes factors make it timely and feasible to complement or move beyond traditional null-hypothesis tests, and allow researchers to draw more informative conclusions about null-effects.
Relevance for Patients: Conclusions based on clinical trial data often focus on demonstrating differences due to treatments, despite demonstrating the absence of differences is an equally important statistical question. Researchers commonly conclude the absence of an effect based on the incorrect use of traditional statistical methods. By providing an accessible overview of different approaches to exploring null-results, we hope researchers improve their statistical inferences. This should lead to a more accurate interpretation of studies, and facilitate knowledge generation about proposed treatments.
1 Department of Psychology, University of Bonn, Germany
2 Human Technology Interaction Group, Eindhoven University of Technology, Eindhoven, the Netherlands
Christopher Harms, Kaiser-Karl-Ring 9, 53111 Bonn, Germany.
Department of Experimental Surgery, Academic Medical Center, University of Amsterdam, Amsterdam, the Netherlands