Metrics and mappings: A framework for understanding real-world quantitative estimation.

Abstract

Estimation is influenced by a variety of processes: application of heuristics, domain-specific reasoning, and intuitive statistical induction, among them. In this article, we propose the metrics and mapping framework to account for how these processes are integrated to generate estimates. This framework identifies 2 types of information as critical: knowledge of distributional properties (metric knowledge) and knowledge of relative status of individual entities within the distribution (mapping knowledge). Heuristics and domain-specific knowledge are both viewed as cues that contribute to mapping knowledge; intuitive statistical induction is viewed as providing cues to metric properties. Results of 4 experiments illustrate the framework's usefulness for integrating these types of information and for predicting when people emphasize heuristics and when they emphasize domain-specific knowledge.

Real-world estimation: Estimation modes and seeding effects

“…Several years ago, Siegler and I proposed that people depend on two types of knowledge when they generate real-world estimates: metric knowledge and mapping knowledge (Brown & Siegler, 1993). Metric knowledge was defined as knowledge of or beliefs about pertinent statistical properties of the target dimension.…”

“…For example, the evidence that seeding often improves estimation accuracy suggests that educators should be able to counter domain-specific innumeracy by exposing their students to a few key facts. However, there is also evidence that the effectiveness of the seeding procedure depends on what people already know about the target domain and on the specific identities of the seeds and the transfer items (Brown & Siegler, 1993;Friedman & Brown, 2000a,b;Kerkman, Friedman, Brown, Stea, & McCormick, 2001;Murray & Brown, 2001). Thus, the selection of an optimal set of seed facts may well require a thorough understanding of the relevant domain knowledge and of those cognitive mechanisms that produce positive seeding effects.…”

“…On the one hand, quantitative estimates are affected by and often reflect the content and structure of the information used to generate them. As a result, quantitative estimates can reveal much about a given domain of knowledge (Brown, 1990;Brown & Siegler, 1993;Friedman & Brown, 2000a,b;Friedman, Brown, & McGaffey, in press-a;Murray & Brown, 2001). On the other hand, because real-world knowledge is complex, and relevant between-domain differences are large, estimation strategies vary from task to task, and different strategies often compete within the same task.…”

“…To date, experiments that have used the standard 3-phase seeding procedure have demonstrated robust and positive seeding effects on estimates of national populations (Brown & Siegler, 1993, 1996LaVoie et al, in press). Seeding has also been shown to increase estimation accuracy when people estimate latitudes and longitudes (Friedman & Brown, 2000a,b;Friedman et al, in press-b), cityto-city distances (Brown & Siegler, 2001;, automobile prices (Murray & Brown, 2001), fatality rates (Bostrom & Brown, 2001), university tuitions (Lawson & Bhagat, in press), and the nutritional value of fast food (Walbaum, 1997); In addition, recent studies that employed a simplified procedure (one seed fact and one transfer item) have shown that seeding also improves accuracy when people estimate corporate sales figures, CD sales, national land area, populations of endangered species, and the heights of mountains (Beck & Carlson, 1998;Brown, 2001;Friel & Carlson, 2000).…”

“…On the other hand, because real-world knowledge is complex, and relevant between-domain differences are large, estimation strategies vary from task to task, and different strategies often compete within the same task. It follows that the study of real-world estimation should produce information about the range of estimation strategies people use, the factors that influence strategy selection, and the ways that people coordinate competing sources of information (Brown, 1995(Brown, , 1997Brown & Siegler, 1993;Conrad, Brown, & Cashman, 1998). In brief, because performance on many real-world estimation tasks reflects the systematic interplay of process and content, it is possible to employ these tasks to investigate both.…”