I thought this was interesting: perhaps the first use I've read of odds in a psychology paper. From Sprenger et al 2013:

8.1. A Bayesian analysis of WM training effectiveness

To our knowledge, our study is the first to include a Bayesian analysis of working memory training, which we view as particularly well suited for evaluating its effectiveness. For example, we suspect that at least some of the existing studies reporting positive transfer of WM training will fail the Bayesian “sniff test.” Indeed, even for studies that have faithfully observed statistically significant effects of training it is instructive to evaluate these findings in light of one's subjective prior probabilities. For illustrative purposes, suppose a pessimist adopts prior odds of 10:1 against the effectiveness of WM training, citing the plethora of historical evidence that cognitive abilities are stable. In contrast, suppose an optimist adopts a prior odds of 1:10 in favor of the effectiveness of WM training. How might these two individuals change their beliefs in light of the available evidence?

Chein and Morrison (2010, Table 2) report significant one-tailed t-tests on the gain scores for both Stroop (t(40) = 1.80) and reading comprehension (t(38) = 1.80). The corresponding BFs = 1.06 and BF = 1.067, respectively, using the JZS prior. These BFs are interpreted as providing equivalent support for the null and the alternative—that is, the BF indicates that the data are equally supportive of both the alternative and null hypotheses. The t-tests for fluid IQ (t(40) = 0.24) and reasoning (t(40) = 1.39) were both non-significant, and have corresponding BFs of 4.37 and 1.92 in favor of the null hypothesis. The average BF across all four tasks is 2.10 in favor of the null. Turning to the experiments reported above, across all measures of fluid abilities in Experiment 1, the average BF at post-test is 2.59 in favor of the null, and this includes operation span and symmetry span which arguably reflects stimulus specific training effects. Similarly, the average BF of the untrained assessment tasks in Experiment 2 across all three training groups is 4.18, again in favor of the null. Multiplying these BFs with the priors gives us the posterior odds ratios. For the pessimist, the posterior odds against the effectiveness of WM is over 227:1 (10 ∗ 2.10 ∗ 2.59 ∗ 4.18). This corresponds to a posterior probability p(null is true|data) = 227 / 228 = 0.996. But, even for the optimist, the posterior odds favors the null at a ratio of 2.27:1 (0.1 ∗ 2.10 ∗ 2.59 ∗ 4.18 = 2.27), with a posterior probability p(null is true|data) = 2.27 / 3.27 = 0.694. In other words, based on the result of Chein and Morrison (2010) and the experiments reported herein, even the optimist should express some skepticism in the hypothesis that WM-training is effective.3