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)

Pluralisms of various sorts are popular in philosophy of science, including those that imply some scientific concept x should be eliminated from science in favour of a plurality of concepts x1, x2, … xn. This article focuses on influential and representative arguments for such eliminative pluralism about the concept species. The main conclusions are that these arguments fail, that all other extant arguments also fail, and that this reveals a quite general dilemma, one that poses a defeasible presumption against many (...) eliminative pluralisms about various scientific concepts. The article ends by outlining a novel integrative alternative in defence of species. 1) Introduction 2) The species Concept, the Category ‘Species’, and the ‘Species’ Category Problem 3) What Are Eliminative Pluralism about species, and the Arguments for It? 4) Evaluation of Arguments 4.1 Splitting? 4.2 Lumping? 4.3 The eliminative pluralist’s dilemma 5) More General Lessons6Species Cohesion: An Integrative Alternative7Conclusion. (shrink)