Results

S.S. Bayesian Independent Samples T-Test

In the Summary Statistics module, we can obtain a Bayesian result, based only on the observed test statistic and sample size. Here, the t-statistic is 2.02 and the sample sizes are 92 and91, for the flag and control group, respectively. Below we see the results of the two-sided analysis, including a prior/posterior plot.

(1) The two-sided Bayes factor is 1.059, which means that the two hypotheses under consideration predicted the data equally well. This means that the data are inconclusive: based on these data, we cannot make a meaningful decision about which of the two hypotheses predicted the data best.

(2) The corresponding p-value is 0.045, which illustrates that using an alpha of 0.05 is not a very strict alpha level: a frequentist analysis of these data would have resulted in rejecting the null hypothesis, whereas a Bayesian analysis indicates that there is not really grounds to do so.

S.S. Bayesian Independent Samples T-Test - One-Sided

In order to test the authors' hypothesis, we can conduct a one-sided hypothesis test, where the alternative hypothesis postulates that the flag group (n=92) scores greater than the control group (n=91).

(3) The corresponding Bayes factor (BF₊₀) is 2.062, which means that the data are about 2 times more likely under the alternative hypothesis than under the null hypothesis. This is slightly in favor of the alternative, but a Bayes factor of 2 is not very convincing evidence (using the table from the lecture, this would be considered "weak" or "anecdotal" evidence).

(4) The Robustness check below shows how the Bayes factor looks for various values for the prior width. The maximum Bayes factor would be 3.238 for a width of 0.1959. The line is mostly situated in the "anecdotal" region, which means that for many of the prior settings, we would not get any convincing evidence for the alternative hypothesis.

(5) Meow!