FIGURE 5.

Overview of the structure of songbird data and statistical methods used to analyze it. a) A graphical representation of the hierarchical structure of songbird data. As shown, there are typically multiple experimental groups consisting of several birds each. Each bird in turn sings several syllables and each syllable may be sung several hundreds of times (called iterations). b) In “Traditional” statistics, each syllable iteration is treated as independent and therefore all syllable iterations across syllables and birds are pooled in order to get the population statistics which is then used to perform statistical tests. c) In “Summarized” statistics, the mean for each syllable is calculated from the syllable iterations and the resulting means are pooled across birds in the experimental group. This population of means is then used to perform statistical tests. As detailed in the results, neither of these approaches is valid since even in the “Summarized” case, we are not ensuring independence between data points since syllables within birds are still more similar than syllables between birds.