A Data-Oriented, Active Learning, Post-Calculus Introduction to Statistical Concepts, Applications, and Theory

Principal Investigators: Allan Rossman, Beth Chance
Department of Statistics, Cal Poly - San Luis Obispo
funded by NSF/DUE/CCLI #9950746, 0321973

  • Project Overview

  • This project aims to develop curricular materials for a course that introduces students at the post-calculus level to statistical concepts, applications, and theory. This course provides a more balanced introduction to the discipline of statistics than the standard sequence in probability and mathematical statistics. The materials incorporate many features of successful statistics education projects that target less mathematically prepared students.  The student audiences targeted by this project are particularly important because they have been overlooked by previous curricular reform projects. Most importantly, the proposed audience includes prospective teachers of statistics, introducing them to content and pedagogy that prepare them for implementing NCTM Standards with regard to statistics and probability and for teaching the Advanced Placement course in Statistics.

    Information and supplementary resources for forthcoming preliminary edition of Investigating Statistical Concepts, Applications, and Methods 
    Contact Duxbury Press for more information

    Course Principles
    Some of the principles that have guided the development of these materials are:

    • Motivate with real studies and genuine data.

    • Emphasize connections among study design, inference technique, and scope of conclusion.

    • Conduct simulations often.

    • Use variety of computation tools.

    • Investigate mathematical underpinnings.

    • Introduce probability “just in time.”

    • Foster active explorations.

    • Experience the entire statistical process over and over again.


    Content Outline
    oChapter 1: Comparisons and Conclusions – descriptive analyses of 2x2 tables (segmented bar graphs, conditional proportions, relative risk, odds ratio), types of variables, observational studies vs. controlled experiments, confounding variables, causation, randomization, Simpson’s paradox, statistical significance, hypergeometric distribution, Fisher's Exact Test 
    oChapter 2: Comparisons with Quantiative Variables - graphical and numerical descripitive analyses of quantitative variables (dotplots, boxplots, histograms, stemplots), measures of center and variability, empirical rule, z-score, resistance, simulating a randomization test, effect of sample size 

    oChapter 3: Sampling – parameter vs. statistic, sampling bias, precision, simple random sampling, probability samples, binomial distribution, binomial tests and confidence intervals, effect of sample size, type I and II error, power, sign test 

    oChapter 4: Models and Sampling Distributions - models, normal distribution, normal probability plots, normal approximation to binomial, large sample z procedures, exploration of confidence, Central Limit Theorem, t-procedures, paired t-tests, prediction intervals, bootstrapping 

    oChapter 5: Comparing Two Populations - comparing proportions (z-procedures, odds-ratios, randomized experiments), comparing means (t-procedures, randomization distribution), bootstrapping 

    oChapter 6: Comparing Several Populations, Exploring Relationships - Chi-square tests of homogeneity and association, Analysis of Variance, scatterplots, correlation coefficient, least-squares regression, inference for regression