  Statistical insignificance does not suggest the absence of effect, yet
scientists must often use null results as evidence of negligible (near-zero)
effect size to falsify scientific hypotheses. Doing so must assess a result's
null strength, defined as the evidence for a negligible effect size. Such an
assessment would differentiate strong null results that suggest a negligible
effect size from weak null results that suggest a broad range of potential
effect sizes. We propose the most difference in means ($\delta_M$) as a
two-sample statistic that can both quantify null strength and perform a
hypothesis test for negligible effect size. To facilitate consensus when
interpreting results, our statistic allows scientists to conclude that a result
has negligible effect size using different thresholds with no recalculation
required. To assist with selecting a threshold, $\delta_M$ can also compare
null strength between related results. Both $\delta_M$ and the relative form of
$\delta_M$ outperform other candidate statistics in comparing null strength. We
compile broadly related results and use the relative $\delta_M$ to compare null
strength across different treatments, measurement methods, and experiment
models. Reporting the relative $\delta_M$ may provide a technical solution to
the file drawer problem by encouraging the publication of null and near-zero
results.
