Saying 'no' with confidence: statistical approaches to test for the absence of an effect

Publishing non-significant findings is essential for the progress of science. However, many of us forget that 'absence of evidence is not evidence of absence' and believe that a statistically non-significant result is evidence of no effect. Regrettably, and despite the null hypothesis being simple, elegant and often underpinned by evidenced or reasoned convictions, conventional p-value analysis can only argue against the null hypothesis, never in favour of it. Here, I provide a quick-and-easy guide to simple yet powerful statistical options available to biologists for investigating the absence of a meaningful effect, namely equivalence tests, confidence intervals and credible intervals; or the absence of any effect, namely likelihood ratios and Bayes factors. These approaches, supported by accessible software, allow biologists to draw direct conclusions about the null hypothesis.