For more than 20 years, research has proven the beneficial effect of natural frequencies when it comes to solving Bayesian reasoning tasks (Gigerenzer & Hoffrage, 1995). In a recent meta-analysis, McDowell & Jacobs (2017) showed that presenting a task in natural frequency format increases performance rates to 24% compared to only 4% when the same task is presented in probability format. Nevertheless, on average three quarters of participants in their meta-analysis failed to obtain the correct solution for such a task (...) in frequency format. In this paper, we present an empirical study on what participants typically do wrong when confronted with natural frequencies. We found that many of them did not actually use natural frequencies for their calculations, but translated them back into complicated probabilities instead. This switch from the intuitive presentation format to a less intuitive calculation format will be discussed within the framework of psychological theories (e.g., the Einstellung effect). (shrink)

In teaching statistics in secondary schools and at university, two visualizations are primarily used when situations with two dichotomous characteristics are represented: 2×2 tables and tree diagrams. Both visualizations can be depicted either with probabilities or with frequencies. Visualizations with frequencies have been shown to help students significantly more in Bayesian reasoning problems than probability visualizations do. Because tree diagrams or double-trees (which are largely unknown in school) are node-branch-structures, these two visualizations (compared to the 2×2 table) can even simultaneously (...) display probabilities on branches and frequencies inside the nodes. This is a teaching advantage as it allows the frequency concept to be used to better understand probabilities. However, 2×2 tables and (double-) trees have a decisive disadvantage: While joint probabilities (e.g., P(AB)) are represented in 2×2 tables but no conditional probabilities (e.g., P(A|B)), it is exactly the other way around with (double-) trees. Therefore, a visualization that is equally suitable for the representation of joint probabilities and conditional probabilities is desirable. In this article, we present a new visualization—the frequency net—in which all absolute frequencies and all types of probabilities can be depicted. In addition to a detailed theoretical analysis of the frequency net, we report the results of a study with 249 university students that shows that “net diagrams” can improve reasoning without previous instruction to a similar extent as 2×2 tables and double-trees. Regarding questions about conditional probabilities, frequency visualizations (2×2 table, double-tree, or net diagram with natural frequencies) are consistently superior to probability visualizations. The frequency net performs as well as the frequency double-tree. Only the 2×2 table with frequencies—the only visualization that participants were already familiar with —led to higher performance rates. If, on the other hand, a question about a joint probability had to be answered, all implemented visualizations clearly supported participants’ performance, and no uniform format effect becomes visible. Participants reached the highest performance in the versions with probability 2×2 tables and probability net diagrams. Furthermore, after conducting a detailed error analysis, we report interesting error shifts between the two information formats and the different visualizations and give recommendations for teaching probability. (shrink)

The goals of the study were to examine whether fundamentalism and authoritarianism could be distinguished by the Big Five factors of personality in American, Romanian and German samples, and to determine whether fundamentalism and authoritarianism could be distinguished by factor analysis in any of the three cultures. The results in all three cultures indicate that fundamentalism and authoritarianism have virtually identical personality correlates. In all three cultures, the two constructs were indistinguishable via exploratory factor analysis and could only be distinguished (...) via confirmatory factor analysis, although direction-of-wording effects dwarfed the differences between fundamentalism and authoritarianism. The findings suggest that researchers should view fundamentalism as religious authoritarianism, and should therefore be cautious when making inferences about religiosity from research on fundamentalism. (shrink)

The goals of the study were to examine whether fundamentalism and authoritarianism could be distinguished by the Big Five factors of personality in American, Romanian and German samples, and to determine whether fundamentalism and authoritarianism could be distinguished by factor analysis in any of the three cultures. The results in all three cultures indicate that fundamentalism and authoritarianism have virtually identical personality correlates. In all three cultures, the two constructs were indistinguishable via exploratory factor analysis and could only be distinguished (...) via confirmatory factor analysis, although direction-of-wording effects dwarfed the differences between fundamentalism and authoritarianism. The findings suggest that researchers should view fundamentalism as religious authoritarianism, and should therefore be cautious when making inferences about religiosity from research on fundamentalism. (shrink)

(2000). Ecological rationality and its contents. Thinking & Reasoning: Vol. 6, No. 4, pp. 375-384.

In the present paper we empirically investigate the psychometric properties of some of the most famous statistical and logical cognitive illusions from the “heuristics and biases” research program by Daniel Kahneman and Amos Tversky, who nearly 50 years ago introduced fascinating brain teasers such as the famous Linda problem, the Wason card selection task, and so-called Bayesian reasoning problems (e.g., the mammography task). In the meantime, a great number of articles has been published that empirically examine single cognitive illusions, theoretically (...) explaining people’s faulty thinking, or proposing and experimentally implementing measures to foster insight and to make these problems accessible to the human mind. Yet these problems have thus far usually been empirically analyzed on an individual-item level only (e.g., by experimentally comparing participants’ performance on various versions of one of these problems). In this paper, by contrast, we examine these illusions as a group and look at the ability to solve them as a psychological construct. Based on an sample ofN= 2,643 Luxembourgian school students of age 16–18 we investigate the internal psychometric structure of these illusions (i.e., Are they substantially correlated? Do they form a reflexive or a formative construct?), their connection to related constructs (e.g., Are they distinguishable from intelligence or mathematical competence in a confirmatory factor analysis?), and the question of which of a person’s abilities can predict the correct solution of these brain teasers (by means of a regression analysis). (shrink)

This study examines factors associated with the decision of Malaysian youth to participate in a voluntary urban agriculture program. Urban agriculture has generated significant interest in developing countries to address concerns over food security, growing urbanization and employment. While an abundance of data shows attracting the participation of young people in traditional agriculture has become a challenge for many countries, few empirical studies have been conducted on youth motivation to participate in urban agriculture programs, particularly in non-Western settings. Drawing on (...) the theories of planned behavior and the functional approach to volunteer motivation, we surveyed 890 students from a public university in Malaysia about their intention to join a new urban agriculture program. Hierarchical regression findings indicated that the strongest predictor of participation was students’ attitude toward urban agriculture, followed by subjective norms, career motives and perceived barriers to participation. The findings from this study may provide useful information to the university program planners in Malaysia in identifying mechanisms for future students’ involvement in the program. (shrink)