The following steps describe the essential elements of Bayesian inference: 1.
It is easy to think that these stories are simply another round in the familiar game of rebutting utilitarianism by counter-examples, and hence that Williams' integrity objection boils down to the straightforward inference (1) utilitarianism tells Jim to do X and George to do Y, (2) but X and Y are wrong (perhaps because they violate integrity?), so (3) utilitarianism is false.
In this study, we focused on two broad issues in TRN inference: (1) development of an analysis method that utilizes multiple types of data and (2) network analysis at the network motif level.
Therefore, we took as psychological factor the contrast between HR and LR hits, irrespective of trial type (direct, inference 1 and inference 2 trials).
Direct trials were used during the learning, test, and retest sessions, while inference 1 and 2 trials were only used during the test and retest sessions.
Both groups performed above chance level for HR and LR trials and direct, inference 1 and inference 2 trials (one-way T-tests p<0.05).
This can be best achieved by contrasting more distant pairs (inference 2 trials) to less distant pairs (inference 1 trials) in inference trials; inference 2 trials involving higher integrative demands than inference 1 trials, while both types of trials have a very similar learning status (unlike direct trials which were first presented (and tested) during the learning session).
To test specifically for the integration of associative memories (and not the consolidation of previously seen associations, as in direct trials), we considered associations between non-consecutive images with distinct relational distances by comparing inference 2 to inference 1 trials (inference 2 > inference 1).
We performed ANOVAs on mean and median RT values with Reward (high, low) and Relational Distance (direct, inference 1, inference 2) as within-subject factors, and Group (Sleep, Wake) as between-subject factor.
Concerning the correlation mentioned above by the reviewers, we realize that we did not explicitly justify the use of the contrast "inference 2 > inference 1" for the correlation with sleep spindles.
Therefore, the reported test in the fourth paragraph of the Results section (comparing inference 2 > inference 1) was performed on purpose and does not correspond to one among multiple possible options.
