Statistical analysis

Given the two-alternative nature of the task, the outcome of each trial could either be ‘correct’ or ‘incorrect’, and the success rate at chance level was 0.50. A success rate significantly higher than chance in a 20-trial experiment was therefore calculated to be 0.70 (binomial cumulative distribution function). In cases where the number of valid trials was lower than 20, this threshold was adjusted accordingly, such that it significantly exceeded chance at a significance level of p<0.05. Similarly, the median group performance was compared to chance (0.50) using a two-sided sign-test. A comparison of group performance across conditions was carried out using an analysis of variance (ANOVA). To reduce the effect of outliers on the result of this study, we focused our analysis on the group medians. However, the results remained the same even when we used the group mean (i.e., performed a one-sample two-sided t-test).

In addition to standard testing of the data against a null hypothesis, we also subjected the data in each analysis to Bayesian one-sample t-tests with success rate as the dependent variable, compared to chance performance (0.50) with a Cauchy prior of 0.707 (Good, 1962) The added insight gained from this approach stems from its ability to quantify the evidence in favor of two different models. Bayesian statistics are advantageous in assessing the relative probability of the null hypothesis over the experimental hypothesis. This advantage becomes a necessity when one does not reject H₀ (i.e., ‘non-significant results’) and needs to quantify the evidence to support this claim (Leech and Morgan, 2002). We therefore detailed our Bayesian statistics alongside each regular sign-test. The output Bayesian statistic used was the BF₁₀, which depicts an odds ratio; namely, the probability, or simply how likely the data are under both hypotheses. In our interpretation, we used the standard recommendation that a BF₁₀ between 1 and 3 implies anecdotal evidence, 3–10 substantial, and 10–30 strong evidence, where BF₁₀ quantifies evidence for the alternative hypothesis relative to the null hypothesis. All the Bayesian statistical analyses were conducted in JASP (2019) version 0.9.2. Statistical analyses concerning the values of the respiratory phase were carried out using functions implemented in CircStat MATLAB, a toolbox for circular statistics that are analogous to the regular t-test or ANOVA (Berens, 2009).