A new statistical method to test equivalence: an application in male and female eastern bluebird song

Understanding complex natural systems requires approaches with minimal statistical limitations and biases. Previously, however, the fields of behaviour, ecology and evolution generally have been restricted to evaluating differences between statistical distributions. This framework can be very powerful. Unfortunately, it has also created a bias in these, and many other, fields towards publications focusing only on phenomena for which there are statistically significant differences. However, there is a wide range of questions that would benefit from reversing the existing paradigm and testing, instead, for equivalence. We have adapted the two one-sided test (TOST), also known as equivalence testing, from pharmaceutical science to be applicable to behavioural and ecological studies. We created a repeated measures analysis that allows researchers to statistically examine similarities between distributions. We compared song structure in male and female eastern bluebirds, Sialia sialis, as a case study for this method. We failed to find significant differences between male and female songs via a more traditional test, repeated measures ANOVA. Therefore, no definitive conclusion could be drawn about the similarities or differences in song structure. However, our repeated measures equivalence test showed that, based on five standard measures of song variation, male and female eastern bluebirds sing statistically equivalent songs. Our study highlights the presence of complex female song in a temperate songbird species. Additionally, we provide a new statistical test useful for expanding the statistical toolbox to assess new behavioural and ecological questions, and to help counteract publication bias in our fields.