Literature Index

This document consists of three modules concerned with aspects of statistics. The first provides knowledge of the effect of imperfect correlation and random error on differences between means, and the reasons for the necessity of random allocation of objects to experimental and control conditions in scientific experimentation. The second unit shows how to: 1) Use frequency distributions and histograms to summarize data; 2) Calculate means, medians, and modes as measures of central location; 3) Decide which measures of central location may be most appropriate in a given instance; and 4) Calculate and interpret percentiles. The third module is designed to enable the student to: 1) discuss how approximation is pervasive in statistics; 2) compare "structural" and "mathematical" approximations to probability models; 3) describe and recognize a hypergeometric probability distribution and an experiment in which it holds; 4) recognize when hypergeometric probabilities can be approximated adequately by binomial, normal, or Poisson probabilities; 5) recognize when binomial probabilities can be approximated adequately by normal or Poisson probabilities; 6) recognize when the normal approximation to binomial probabilities requires the continuity correction to be adequate; and 7) calculate with a calculator or computer hypergeometric or binomial probabilities exactly or approximately. Exercises and tests, with answers, are provided in all three units. (MP)

Ways of knowing statistical concepts are reviewed. A general three-category structure for knowing is proposed: (a) calculations, (b) propositions, and (c) conceptual understanding. Test items were developed that correspond to the first category and to a partitioning of the two latter categories into words and symbols. Thirty-one items covering the five types were administered to 57 graduate students. Correlation of student scores on the 10-item calculations subtest and the 10-item propositions subtest was . 61, whereas the other two intercategory correlations were .40 (Calculations vs. Conceptual Understanding) and .37 (Propositions vs. Conceptual Understandings). The result suggest that students should be tested in more than one domain, and that instructors should expect students to develop conceptual understanding in addition to skills in computation.

A controversy has arisen concerning the relative merits of conceptually-oriented teaching versus calculation-centered teaching. Marks (1989) maintains that concepts are far more important than computations, and that they can be successfully taught without the related computations. In contrast, Khamis (1989) claims that students cannot truly understand statistical information until they have had experience doing calculations by hand. Both authors present persuasive arguments, but no empirical evidence to support their conclusions. The present paper outlines a study which aimed to fill this gap. First, however, we try to place the controversy into the context of wider cognitive issues.

A 34 item scale entitled Statistics Attitude Survey (SAS) was developed and administered to three samples of students taking a beginning statistics course. Analyses showed that the scale was highly homogenous and that total scale scores had moderate correlations with statistics grades.