By Dani Ben-Zvi
Unique in that it collects, provides, and synthesizes innovative examine on various elements of statistical reasoning and applies this learn to the instructing of information to scholars in any respect academic degrees, this quantity will end up of significant worth to arithmetic and information schooling researchers, facts educators, statisticians, cognitive psychologists, arithmetic academics, arithmetic and information curriculum builders, and quantitative literacy specialists in schooling and government.
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Extra info for The Challenge of Developing Statistical Literacy, Reasoning and Thinking
A four-dimensional framework for statistical thinking in empirical enquiry. (From “Statistical Thinking in Empirical Enquiry,” by C. J. Wild and M. Pfannkuch, 1999, International Statistical Review, 67, p. 226. Copyright 1999 by International Statistical Institute. ) 20 MAXINE PFANNKUCH AND CHRIS WILD Reasoning with Statistical Models The predominant statistical models are those developed for the analysis of data. When we talk about “statistical models,” most people interpret the term as meaning, for example, regression models or time-series models.
This ground-breaking inference work of Bayes in 1764 was encouraged by two critical key ideas. The first key idea was not to think in terms of games of chance. UNDERSTANDING OF STATISTICAL THINKING 23 That is, instead of thinking of drawing balls from an urn, Bayes thought in terms of a square table upon which two balls were thrown. This new thinking tool allowed for continuous random quantities to be described as areas and for the problem to assume a symmetric character. The second key idea was from Simpson, who in 1755 had a conceptual breakthrough in an astronomical problem.
135) summarizes statistical thinking as: • • The omnipresence of variation in processes. Individuals are variable; repeated measurements on the same individual are variable. The domain of strict determinism in nature and in human affairs is quite circumscribed. The need for data about processes. Statistics is steadfastly empirical rather than speculative. Looking at the data has first priority. 38 MAXINE PFANNKUCH AND CHRIS WILD • • • The design of data production with variation in mind. Aware of sources of uncontrolled variation, we avoid self-selected samples and insist on comparison in experimental studies.