Elementary Statistical Concepts Research Articles

Frequentist and Bayesian approaches to data analysis: Evaluation and estimation

Statistical thinking is essential to understanding the nature of scientific results as a consumer. Statistical thinking also facilitates thinking like a scientist. Instead of emphasizing a “correct” procedure for data analysis and its outcome, statistical thinking focuses on the process of data analysis. This article reviews frequentist and Bayesian approaches such that teachers can promote less well-known statistical perspectives to encourage statistical thinking. Within the frequentist and Bayesian approaches, we highlight important distinctions between statistical evaluation versus estimation using an example on the facial feedback hypothesis. We first introduce some elementary statistical concepts, which are then illustrated with simulated data. Finally, we demonstrate how these approaches are applied to empirical data obtained from a Registered Replication Report. Data and R code for the example are provided as supplementary teaching material. We conclude with a discussion of key learning outcomes centred on promoting statistical thinking.

Errors and difficulties in understanding elementary statistical concepts

This paper presents a survey of the reported research about students’ errors, difficulties and conceptions concerning elementary statistical concepts. Information related to the learning processes is essential to curricular design in this branch of mathematics. In particular, the identification of errors and difficulties which students display is needed in order to organize statistical training programmes and to prepare didactical situations which allow the students to overcome their cognitive obstacles. This paper does not attempt to report on probability concepts, an area which has received much attention, but concentrates on other statistical concepts, which have received little attention hitherto.

An integrated, software-based approach to teaching introductory computer programming

We have developed a course in scientific and statistical programming consisting of an introduction to computer programming and data analysis concepts using a variety of software packages. This approach addresses the problems inherent in introducing programming to non-computer science majors, particularly those in engineering, the sciences, and the social sciences where computing and statistical data analysis techniques are essential professional tools, as well as to computer science majors with minimal or nonexistent programming backgrounds. Key programming concepts are introduced, including variables and identifiers, absolute versus relative addresses, assignment statements, IF/THEN/ELSE statements, nested and compound IF statements, truth tables, precedence of operations, use of built-in and user-defined functions, dummy variables, passing by value and reference, the importance of order in specifying input to functions, modular program design, subprograms, debugging and testing techniques, properties of good programs, and iterative loops. Elementary statistical concepts and data analyses are covered within a computing environment context that emphasizes data analysis and interpretation of results. Assignments and examples are developed in collaboration with the students' major departments to insure relevance and interest to the students.

Elementary Statistical Concepts.

Elementary Statistical Concepts.

Book Reviews

Abstract Lies, Damn Lies, and Statistics: The Manipulation of Public Opinion in America. Michael Wheeler. New York: Liveright Publishing Co., 1976. xviii + 300 pp. $9.95. Reviewed by Gerard E. Dallal The Logical Foundations of Statistical Inference. Henry E. Kyburg, Jr. Boston, Mass.: D. Reidel Publishing Co., 1974. ix + 427 pp. $14.75 (paperback). Reviewed by George F. Rhodes, Jr. Decisions with Multiple Objectives: Preferences and Value Tradeoffs. Ralph L. Keeney and Howard Raiffa. New York: John Wiley & Sons, Inc., 1976. xxviii + 569 pp. $19.95. Reviewed by Peter C. Fishburn Elementary Statistical Concepts. Ronald E. Walpole. New York: Macmillan Publishing Co., Inc., 1976. viii + 231 pp. $10.95. Reviewed by Richard S. Kleber Understanding Statistics, 2nd Edition. William Mendenhall and Lyman Ott. North Scituate, Mass.: Duxbury Press, 1976. xi + 387 pp. $12.95. Reviewed by Richard S. Kleber Elementary Statistics, 2nd Edition. Robert R. Johnson. North Scituate, Mass.: Duxbury Press, 1976. xviii + 638 pp. $13.95. Reviewed by Richard S. Kleber Statistics. Norma Gilbert. Philadelphia: W.B. Saunders Company, 1976. ix + 364 pp. $12.95. Reviewed by Richard S. Kleber Basic Statistics: Tales of Distributions. Chris Spatz and James O. Johnston. Monterey, California: Brooks/Cole Publishing Company, 1976. xii + 380 pp. $12.95. Reviewed by Richard S. Kleber Advanced Geostatistics in the Mining Industry. Massimo Guarascio, M. David, and C. Huijbregts (eds.). Boston, Mass.: D. Reidel Publishing Co. Inc., 1976. xvi + 461 pp. $39.50. Reviewed by Geoffrey S. Watson Social Information Processing and Statistical Systems—Change and Reform. Edgar S. Dunn, Jr. New York: John Wiley & Sons, Inc., 1974. × + 246 pp. $17.95. Reviewed by Richard C. Taeuber Multivariate Statistical Methods in Behavioral Research. R. Darrell Bock. New York: McGraw-Hill Book Co., 1975. xiii + 623 pp. $21.00. Reviewed by P.A. Lachenbruch Statistics: A Guide to Business and Economics. J.M. Tanur, F. Mosteller, Wm. Kruskal, R.F. Link, R.S. Pieters, G.R. Rising, and E.L. Lehmann (eds.). San Francisco, Calif.: Holden-Day, Inc., 1976. xii + 132 pp. $3.50 (paperback). Reviewed by Stephen E. Fienberg Selected Tables in Mathematical Statistics, Volume III. H.L. Harter and D.B. Owen. Providence, R.I.: American Mathematical Society, 1975. viii + 419 pp. $21.50. Reviewed by Joseph McKean Normal Approximations and Asymptotic Expansions. R.N. Bhattacharya and R.R. Rao. New York: John Wiley & Sons, Inc., 1976. xiv + 274 pp. $21.95. Reviewed by P.K. Sen Markov Chains, Theory and Applications. Dean L. Isaacson and Richard W. Madsen. New York: John Wiley & Sons, Inc., 1976. × + 256 pp. $18.95. Reviewed by Chris Paige Operations Research: Principles and Practice. Don T. Phillips, A. Ravindran, and James Solberg. New York: John Wiley & Sons, Inc., 1976. xvii + 585 pp. $16.95. Reviewed by Ronald A. Thisted

Elementary Statistical Concepts

Elementary Statistical Concepts

Elementary Statistical Concepts

Elementary Statistical Concepts

Elementary statistical concepts, by Ronald E. Walpole. Pp viii, 231. £7·25. 1976 SBN 0 02 424090 7 (Collier-Macmillan)

Elementary statistical concepts, by Ronald E. Walpole. Pp viii, 231. £7·25. 1976 SBN 0 02 424090 7 (Collier-Macmillan)

Elementary Statistical Concepts.

Elementary Statistical Concepts.

Elementary Statistical Concepts

Elementary Statistical Concepts

Elementary Statistical Concepts 1st Ed

Elementary Statistical Concepts 1st Ed

Alternate versions of overhead transparency projectuals designed to teach elementary statistical concepts

This study does not lend support to the assumption that sequencing of information for concept learning is superior to presenting the information as one complete whole. Transparency Versions 1 and 2 presented the concepts visually in controlled sequential order while Transparency Version 3 presented the concepts visually as a complete unit. The differences between the three transparency styles (F = 21049) were the smallest of the three main effects of the study. An equivalent set of 2 × 2 slides might have accomplished the same results as Transparency Versions 2 and 3.

A Graphic Matching Test for Properties of Frequency Distributions

Two of the often repeated criticisms against the new or ob jective examinations are that (1) they often measure only small and detached details of information rather than general principles and real understanding of the subject matter, and that (2) they are a test of the student's ability to memorize rather than his ability to organize remem bered facts and use them in solving problems related to the field covered by the examination. Because of these criticisms the objective questions are often found to be most satisfactory when used in combination with questions of the old style or essay type even though this latter type of question involves the expenditure of a disproportionately large amount of time in the reading of the papers, and is further objectionable because it is difficult to keep the standard of judgment constant throughout the reading. Instructors in the Elementary Psychology Laboratory course in the University of Minnesota have been particularly interested in simplifying examination methods because of the large number of students who work in the laboratory. Approximately two hundred-fifty students register for this course every academic year, and it is important, therefore, to supple ment the commonly used objective questions, not with the essay type dis cussion questions but with some objective questions designed especially to test the student's understanding of the subject matter and his ability to organize and interpret the facts he remembers. Several varieties of such questions have been tried out during the last few years, and the series described below has proved to be one of the most successful. Since the technique here described is concerned with elementary statistical concepts, it might prove useful in connection with courses in Experimental Psy chology, Mental Testing, Individual Differences, or courses in any field where the rudiments of statistical methods are taught and an under standing of the simplest measures of central tendency and variability are necessary for the correct interpretation of experimental results. The questions are not based on any particular statistical textbook. They require a half hour of the student's time and each paper can be scored in fifteen seconds, with an objective key. They occupy four, 365