Reasoning: Analysis of the effects of context on the rate of conjunctive responses in the probabilistic truth table task
By: Christos Theodoropoulos
Tags: Reasoning, Cognitive Psychology, Cognitive Science, Cognition, Decision Making

Experiment and Results

The experiment consisted of 4 different conditions based on the context of the task and the way the different truth table cases are displayed. The different logical cases were presented as corresponding to the six sides of a die or as cards taken from a deck. Regarding the way of presentation, the logical cases were presented in four easily distinguishable sets or completely at random [1]. The following table shows the 4 different conditions:

Experimental conditions (Image by Author)

The participants of the experiment were 96 first-year psychology students. They were split randomly into 4 groups of 24 subjects, one for each experiment condition [1]. The number of participants seems big enough in order to effectively check the hypothesis of the study. However, maybe it would be better to perform all possibleexperiment conditions with all participants without the initial split. The final results were biased on the initial split of the participants, even if the split was random. Another idea is to reproduce the experiment with a new set of participantswith similar characteristics. This approach tends to make the final results more robust.

The experiment process consisted of two stages. The first stage contained 4 training trials, which were the same for the 4 different experiment conditions. This step is important in order to make the participants familiar with the procedure and minimize the possibility of giving false answers due to misunderstanding of the experiment environment. The second stage consisted of 20 experimental trial. Two successive trialswere not identical andpresentedalways a differentconditional sentence [1]. The bucket of 20 trials was the same for each of the four experimental conditions but the order of presentation was random for every participant. This is essential, especially if the 20 chosen trials were highly representative of each condition. Moreover, the final analysis of the results should be based on the same trials in order to extract more robust outcomes. In each trial a set of white squares with a colored shape on them was presented. The participants knew if the set of squares represented the sides of a die or cards chosen from a deck. In case of die representation, the squares were always 6, equal with the number of sides of a die. Otherwise, the number was varying from 6 to 9. This detail is important in order to test if participants wrongly used possible previous experience of probability problems with dice. After clarification of the representation type (die or deck of cards), a conditional sentence of the form “If there is A, then it is C”, where variable A was referred to shape and C to color. The following table shows the different shapes and colors.

Shapes-Colors combination (Image by Author)

The way of choosing the different combination of colored shapes was quite strict. “In each trial, the items showed four combination of two different shapes and two different colors corresponding to the four logical cases (A C, ¬A C, A ¬C, ¬A ¬C) defined bythe corresponding conditional, with 1–3 exemplars of each” [1]. Using of four combinations may have simplified the problem for the participants, as they may found patterns in the sequence of the trials which lead them to produce similar type of answers (conditional or conjunctive). Maybe, the parameter of the number of combinations should be open (always greater or equal with 4). The phenomenon of anchoring may appear. The experiment process is a sequence of trials (20) under the same condition (for example, context: die with mixed representation). “People making difficult or long sequences of judgements often the previous item as a point of reference. The precise effects of anchors and reference points depend on how people approach the comparison process” [11]. So, if we see the experiment process as a whole, then anchoring effects may come up using the previous trials as anchors. By differentiating, under the requirements, as much as possible, each trial of the sequence, the risk of anchoring is reduced.

The results of the task were interesting in terms of the effects of context and the way of presentation. Overall, the conditional responses were 61%, the conjunctive 33% and the rest percentage was out of interest (unclassified). Using ANOVA for performing analysis of variance on the number of conjunctive and conditional responses was a good choice. This technique has a robust design and increases statistical power. “The analysis revealed that the distribution different responses strongly varied as a function of the experimental condition” [1]. More precisely the context (dice or deck of cards) had the main effect in the responses. The way of representation (grouped or mixed) and the interaction between the two factors didnot reveal significant effects. Reasoning about dice produced significantly more conjunctive responses (almost half of them).

One important aspect in the results was about the consistency of the participants on their responses. Only 9 participants out of 87 were not consistent (less than 14 similar answers). There were 58 conditional responders (19.09 average conditional responses) and 29 conjunctive responders (18.97 average conjunctive responses) [1]. It is critical to point out that the average values were very high, showing that the participants tend to be highly consistent on their responses. This type of analysis revealed a strong correlation between conditional responders in the cards context (34 out of 42).

Although, the analysis showed that the participants were highly consistent in general, the shift rate between the two interpretations (conditional and conjunctive) was worth mentioning. This shift often happened at the beginning of the task or during the training process ([1]). These findings were aligned with the generally noticed consistency because after the early shift, most of the participants were consistent .The total number of shifts that were detected was 34. It is worth mentioning that 27 of these were shifts toward the conditional response. Using binary logistic regression revealed that the main factor of shift towards conditional interpretation was positioning of different cases (mixed or grouped). The context and the interaction of context and positioning were not significant factors for shifting [1]. “According to the model, participants presented with grouped positioning were 2.28 times more likely to shift toward the conditional interpretation than those presented with mixed positioning” [1]. Grouped positioning seemed to help the participants to realize that conjunctive interpretation was not correct and this realization makes them shift towards the conditional interpretation.