Judgment of Association between Potential Factors and Associated Risk in 2x2 Tables: A Study with Psychology Students

Abstract

(ProQuest: ... denotes formulae omitted.)IntroductionIn the past decades we have observed an increasing interest towards risk perception and management in many organizations, such as private companies, banks, hospitals, or schools. Slovic (2000) described a risk as an uncertain event or condition that when happening has a positive or negative effect on a person or a group of people. Gigerenzer (2003) suggested that such an event should be associated w7ith a probability or a frequency with is based on empirical data about its past or potential occurrence. In this definition the author includes different interpretations of probability; such as subjective probability (degree of belief of the person assigning the probability), propensity (physical property of an object; for example, regularity in a dice) or frequentist estimation (infonnation from a large number of observations of the event). Consequently, an event could be perceived or not as a risk, depending on the person's conception of probability.Today an increasing number of events are described in terms of risk using mathematical formats, such as probabilities, proportions or percentages. The underlying concepts have to be learned in school and for this reason, mathematics educators are becoming interested in students' perception and understanding of risk (Martignon, 2014). In the same way, the assessment of students' potential biases, wrong strategies and misconceptions when interpreting risks is a relevant area of research in mathematics education (Nunes, & Bryant, 2011).In health or clinical contexts, including psychological evaluation or diagnosis, risk is synonymous of hazards and dangers; for example an illness or the undesirable effect of a treatment (Power, 2007). Risks in these contexts are often associated to decision making in such a way that it is impossible to make a 'risk-free' decision, unless we leave some potential risk factors unmanaged. A sound understanding of risk and of the associated numerical information is essential for these professionals, in order to make adequate decisions. However, numerous examples that this understanding is not complete are described in the literature related with risk perception and management. For example, Gigerenzer et al. (2007) termed collective statistical illiteracy the fact that many professionals have difficulties in interpreting health statistics and draw wrong conclusions in the clinical practice without noticing. Gigerenzer and Edwards (2003) suggest that misperception of risk factors occur by confusing single event probabilities, conditional probabilities, and relative risks. They also suggest that the situation can be improved by education and by representing the information regarding risks in ways that are transparent for the human mind, such as natural frequencies, tree diagrams or two-way tables.In fact, two-way tables are a main representational tool for bivariate data, and are often used in professional journals to report the influence of risk factors on different pathologies. Its understanding is related to risk perception (Nunes, & Bryant, 2011). Adi, Karp lus, Lawson, and Pulos (1978) suggested that providing subjects with information already organised in tables improves their performance in tasks in which they are asked to assess whether there is an association between two events.These tables; in particular 2x2 tables (two-way tables with only two columns and two rows) are also an important tool in diagnosis and psychological evaluation, where psychologists are confronted with different potential risk factors that may be associated or not with a disorder (risk) (Diaz, & Gallego, 2006). The estimation of association in these tables is the first step to determine which factors are associated to specific risks. However, even when association judgment is a priority learning issue in statistics courses (Zieffler, 2006), little attention is paid to its teaching, in assuming that the interpretation of 2x2 tables is easy. …