Why People are Not Like Marbles in an Urn: An Effect of Context on Statistical Reasoning
✍ Scribed by DANIEL L. SCHWARTZ; SUSAN R. GOLDMAN
- Publisher
- John Wiley and Sons
- Year
- 1996
- Tongue
- English
- Weight
- 958 KB
- Volume
- 10
- Category
- Article
- ISSN
- 0888-4080
No coin nor oath required. For personal study only.
✦ Synopsis
A brief thought experiment, however, can demonstrate the power of context on statistical reasoning. In a study by Tversky and Kahneman (1983), subjects received the profile of 3 1 -year-old Linda who was described as single, outspoken, bright, philosophical, and deeply concerned about issues of social equity. The subjects had to decide which of two alternatives were more probable: (a) Linda is a bank teller; or (b) Linda is a bank teller and is active in the feminist movement. Most subjects incorrectly chose option (b). To see why this is the incorrect answer, consider another scenario that was not included in the Tversky and Kahneman study. There is an urn filled with poker chps and marbles of various colours. If one item is pulled from the urn, whch alternative is more probable: (a) the item would be a marble; or (b) the item would be a blue marble. Unlike the Linda problem, we suspect that most people would correctly choose option (a) in this scenario. They would not make the mistake of viewing a conjoint event (i.e., blue and marble) as more likely than one of the events alone (i.e., a marble). Yet, this is exactly the mistake that the subjects made by choosing the 'banker and feminist' option in the context of the Linda study.
Why would these two contexts have different effects on people's inclination to reason statistically? There are two answers to this question. The first is that people do not normally receive any instruction that helps them learn to apply statistical reasoning to everyday contexts like the Linda scenario. Probability instruction usually relies on explicit chance devices (e.g., the urn context). Students do not have an opportunity to consider probability in other, less obviously chance-based situations. Similarly, statistics instruction often emphasizes properties of numerical distributions (e.g., mean and mode), but takes for granted that students know how these distributions were generated. Students have little occasion to think about how events, behaviours, or opinions are randomly sampled from a context to create a distribution for statistical analysis. Therefore, one reason that people may not apply statistical reasoning when they should is that they have not learned how to turn an everyday situation into a statistical one (cf. .
The second answer to this question, the one that suggests that instruction may be necessary, is that people are predisposed to treat contexts involving people, such as the Linda example, differently than contexts involving marbles in an urn. This predisposition exists because of the intuitively-based understanding that certain properties of people 'cause' their actions, opinions and decisions. This leads to a tendency to think about sampling people in causal terms rather than in chance or random terms. No such 'causal' understanding exists for marbles in an urn so people reason about sampling marbles in chance terms. The following section explains this idea more fully.
CONFUSING THE ROLES OF CAUSE AND CHANCE IN PRODUCING DISTRIBUTIONS
To examine the effects of context on statistical reasoning, we begin by considering where contexts and statistical reasoning meet and why it might be difficult for people