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RATHER SEE ONCE THAN READ NUMEROUS TIMES? ANIMATED VISUAL AIDS IN PROBABILISTIC REASONING

Lenka Kostovičová

Faculty of Mathematics, Physics and Informatics, Comenius University in Bratislava

[1] S. A. Sloman, D. Over, L. Slovak, and J. M. Stibel, “Frequency illusions and other fallacies,“ Organizational Behavior and Human Decision Processes, vol. 91, no. 2, pp. 296-309, 2003.

[2] P. Sedlmeier, Improving statistical reasoning: Theoretical models and practical implications. Mahwah, NJ: Erlbaum, 1999.

[3] G. L. Brase, “Pictorial representations in statistical reasoning,” Applied Cognitive Psychology, vol. 23, no. 3, pp. 369-381, 2009.

[4] M. Sirota, L. Kostovičová and M. Juanchich, “The effect of visual displays on statistical reasoning: Evidence in favor of the null hypothesis,” Psychonomic Bulletin & Review, Advance online publication, 2013.

[5] L. Cosmides and J. Tooby, “Are humans good intuitive statisticians after all? Rethinking some conclusions from the literature on judgment under uncertainty,” Cognition, vol. 58, no. 1, pp. 1-73, 1996.

References

Bayes´ formula ... ... is not necessary for arriving at an accurate

solution.

Model situation

Results showed a better understanding of the task instances (Fig.3), t(22) = -2.08, p = .05, d = 0.85 and a higher proportion of correct Bayesian inferences (Fig.4), χ2(1) = 3.56, p = .08; φ = 0.39 in the experimental condition (EC) with the visual aid compared to the control group (CG). Moreover, the level of a problem comprehension score differed according to the particular solving strategies (Fig.5), t(22) = -8.54, p < .01, d = 3.60. Fig. 3. Problem compre - Fig.4. Bayesian reasoning hension score performance

A – strategies 3,4,6 B – strategies 1,2,5

Fig.5. Problem comprehension & strategies

Background

In our research, we aimed to design animated visual aids, examine whether their presence improves Bayesian reasoning and identify the key components responsible for potential facilitation of performance. Here we report a pilot phase of our investigation.

Research objectives

We found support for the hypothesis of performance enhancement through directly experienced animation of a nested-sets structure of information from the conditional probability task, without transformation of the format. Thus, these findings corroborate the nested-sets rather than the ecological rationality account of statistical reasoning.

Discussion

Implications

Results

Unfortunately, your test is positive. However, we know the following. The risk that a randomly chosen person suffers from Disease X is 6 out of 100. If the person is infected, the chance that he gets a positive result is 4 out of 6. Nevertheless, the risk that he gets a positive result if he does not suffer from Disease X is 16 out of 94.

Oh, that´s definitely my end.

1972

Man is not Bayesian at all.

HEURISTICS AND BIASES PROGRAM Amos Tversky & Daniel Kahneman

ECOLOGICAL RATIONALITY ACCOUNT e.g., Gerd Gigerenzer

1990s

People are good intuitive statisticians - under ecologically valid conditions.

P H D = P H ∗ P(D|H)

P H ∗ P D H + P ¬H ∗ P(D|¬H)

→ .06∗ .667

.06∗.667+ .94∗ .17≐ .20 = 20%

NESTED SETS ACCOUNT e.g., Steven Sloman

There is no evolutionary conditioned, cognitively privileged format of

Bayesian tasks or their visualization.

Recent findings

Recent evidence on the effects of static pictorial displays in solving probabilistic tasks is ambiguous. The visual aids (e.g. Venn diagrams, decision trees) accompanying problems with normalized structures benefited participants [1,2]. However, they were found to either improve [3,4] or did not affect [1,5] the performance in tasks with nested-sets structures (i.e., sets and subsets).

Twenty-four Slovak high school students (12♀ + 12♂, M = 18.3 years, SD = 0.7) participated in our experiment.

The only difference between the control (n = 12) and the experimental group (n = 12) was the presence of an animated visual aid.

The interactive animation (Fig. 1), was written in JavaScript, using GreenSock Animation Platform library. It was playable within a web browser.

Fig. 1. An overview of a final stage of the animation

Research material consisted of the Disease X problem in a chance / risk format [4], a problem-comprehension scale (Fig.2), a socio-demographic questionnaire and a space for comments and suggestions for improvement of the current version of the visual display which will be considered and implemented into the final design.

Fig. 2. The problem-comprehension scale

We categorized solutions as follows:

1. Bayesian strategy: 4 out of 20

2. pre-Bayesian strategy: 6 out of 20

3. conservatism: 6 out of 100

4. representative thinking: 4 out of 6

5. only evidence: 20 out of 100

6. other unclassifiable strategies

Data analysis was performed using SPSS 17.0.

Methods

8.3%

41.7%

0

10

20

30

40

50

CG EC

3.75

4.83

0

1

2

3

4

5

6

CG EC

2.78

5.20

0

1

2

3

4

5

6

A B

additional qualitative analysis of suggestions provided by our participants

testing various versions of animated visual aids (e.g., decision trees) and comparing their effectiveness and key components responsible for the facilitation

• using thinking aloud protocols

• better representation of sampling process

Follow-up studies

statistical literacy „debiasing“ efforts