Describes the use of simulation to introduce the bootstrapping technique of creating confidence intervals for the mean, median, and variance. These bootstrap confidence intervals are compared to the traditional confidence intervals for the purpose of analyzing accuracy of the technique. A Minitab program to produce confidence intervals is included. (MDH)
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)
An approach to teaching probability. First the history of probability concepts are outlined, then the concept of probability is introduced. Two other chapters deal with using combinatorics to solve probability problems and factors affecting probabilistic judgements in children and students. Finally curricula in probability and statistics for grades 5 to 12 are discussed. At the end there is an extended bibliography of English, French and German literature.
Describes a student project which illustrates interrelationships among the topics of random sampling, relative frequency concept of probability, design of experiments, and computer generation of data and which involves determining the configurations of numbers and letters on license plates through a microcomputer program. The computer program is included. (MBR)
Students in an introductory statistics course are often preoccupied with learning the computational routines of specific summary statistics and thereby fail to develop an understanding of the meaning of those statistics or their conceptual basis. To help students develop a better understanding of the meaning of three frequently used statistics, this document presents HyperCard programs and a Lotus 1-2-3 spreadsheet for use by teachers in classroom simulation demonstrations of Pearson's correlation coefficients, t-test of two independent population means, and one-way analysis of variance. The instructional contents and typical computer screen outputs for each demonstration are discussed in association with their respective HyperCard programs, which are included in the appendix. (JJK)
This manual designed for grade 5 is part of a series for a program to integrate the teaching and learning of mathematical and computer concepts and skills in the elementary school. The manual contains 27 lessons. Each lesson includes information on the topic, suggested grade level, mathematics concepts and skills, objective, prerequisite skills needed, and activities. Topics contained in the lessons include: (1) problem solving; (2) geometry; (3) numbers; (4) number concepts; (5) statistics; (6) measurement; and (7) probability, statistics, and graphing. Software programs used for the activities are specified for each lesson. (KR)
Discussed is the design, development, and evaluation of a self-paced college program in statistics which used computer assisted instruction. The program permitted a great deal of individual attention to weak students and freed the strong student to whip through the acquisition of the tools necessary to plan and conduct research. (RM)
The Pearson product moment (P.M.) correlation ("r") and four of its most widely used variations--the phi, the rho, the biserial, and the point-biserial coefficients--are reviewed. Using small data sets between one and nine, the conditions under which the various forms are restricted in power and robustness are explored. Seven sample data sets were constructed to illustrate the effects of the following conditions: (1) perfect correlation; (2) restriction of range; (3) measurement error (one variable); (4) measurement error (two variables); (5) extreme scores (one outlier); (6) extreme scores (two outliers); and (7) heterogeneity of sample distribution (one variable). Conceptual and algebraic linkages among the coefficients, and teaching practices that will facilitate the assimilation of these concepts and that will allow a student to predict the practical effects of the conditions are discussed. Two data tables are included. Appendix A contains definitions, formulas, and examples of the coefficients, which are presented as reproductions of a Macintosh computer hypercard stack designed for instructional purposes. Appendix B contains sample spreadsheet calculations for the seven conditions studied. (SLD)
Experiences in collecting and handling data are described. Activities dealing with measures of central tendency (including a computer program), measures of dispersion, an introduction to correlation, and use of graphs to display data are illustrated. (MNS)
Maple, a computer algebra system, is employed in introductory statistics courses to promote conceptual learning by students of statistical principles without direct use of mathematics. Maple's symbolic computation, graphic display, and animation capabilities support an integrated set of procedures for active study of sampling distributions and concepts related to samples, populations, statistical decision making, error, and power. Students select parameter values for 1-line commands and examine the effects of alternatives on computer-generated graphical representations of distributions. The 20 procedures written to support active student exploration of basic statistical concepts are described, and examples of exercises to support their use are provided. (PsycLIT Database Copyright 1996 American Psychological Assn, all rights reserved)