## 2 Methodology
### Bayes Factors
The Bayes factor quantifies the degree to which the data justify a change in beliefs and thus represents the strength of the evidence that the data provide. Note that this measure of strength is symmetric: the evidence can support \(H_{0}\) as well as \(H_{1}\). A priori, none of the rival hypotheses enjoys any special status. For a scientist who wants to know whether or not a treatment had an effect, the share of posterior probabilities might seem the most obvious metric, as this reflects the plausibility of one hypothesis over another after considering the data. However, posterior probabilities depend on both the evidence provided by the data (i.e., the Bayes factor) and the prior probabilities. Prior probabilities capture beliefs before the experiment and introduce an often undesirable element of subjectivity: conclusions drawn from posterior beliefs could be biased. Scientists can disagree strongly about these a priori probabilities, even if they agree about the evidence, i.e., about the extent to which the data should change their beliefs. Since beliefs are considered less valuable for scientific information than evidence, the data-fueled Bayes factor is the least controversial, and therefore the preferred metric for making decisions. The Bayes factor has three qualitatively different logical states: (1) \(BF_{10}>x\), according to which there is convincing evidence of the effect of interest; (2) \(1/x<BF_{10}<x\), indicating the data do not carry enough weight to be able to make a diagnosis; and (3) \(BF_{10}<x\), where the data are sufficient proof of the absence of an effect. \(x\) represents the objective level of evidence defined by the researcher. [PERSON] proposed a logarithmic scale for interpreting the strength of evidence [30]. In it, the logarithmic values are equidistant such that \(10^{0.5}\approx 3\), \(10^{1}=10\), \(10^{1.5}\approx 30\), etc. He then compared these values with the critical values of the t-tests and \(\chi^{2}\) values, noting the equivalence between the \(p\)-value 0.05 and \(BF_{10}=3\), in addition to the \(p\)-value 0.01 and \(BF_{10}=10\). These reference values are still used: \(BF>3\) is considered moderate evidence for the numerator hypothesis, and \(BF>10\) is considered strong evidence. Because \(BF_{10}=1/BF_{01}\), this also defines the bounds for the hypothesis in the denominator such that \(BF_{10}<1/3\) is moderate evidence in favor of \(H_{0}\) and \(BF_{10}<1/10\) is strong evidence. Values of \(BF\) between 1/3 and 3 indicate that there is insufficient evidence to draw a conclusion for or against any hypothesis. For new findings, [PERSON] suggested that \(x=0\) is more appropriate than \(x=3\). These values are frequently used to categorize Bayes factors with slight differences in their interpretation [31]. However, each scientist in each field will have to decide whether to prefer test sensitivity for small samples or effects by using smaller \(x\) values, such as 3, or to avoid false conclusions by using higher \(x\) values, such as 10. In either case, readers can judge the strength of evidence directly from the numerical value of the \(BF\), since a \(BF\) twice as high provides evidence twice as strong. Crucially, the three-state system of the Bayes factor allows differentiating between evidence of absence and absence of evidence. This represents a fundamental conceptual advance in the way data are interpreted: instead of one knowledge-generating outcome (\(p<\alpha\)) of the frequentist approach, there are now two (\(BF>x\) and \(BF<x\)). Now that the Bayes factors have been explained, it is necessary to define the different elements of the present study (Figure 4). To begin with, the hypotheses to be compared (\(H_{0}\) and \(H_{1}\)) are defined. It should be recalled that the null hypothesis defines the absence of effect or difference between samples.