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

Preliminary Content Outline, July 2000

Some Principles:

Format:

Roughly half activities, half exposition

Sequencing:

Change scenarios "one component at a time"

    1. Start with comparing two categorical variables, small samples, experimental setting
    2. Then change to observational studies, rest same
    3. Then change to one-sample
    4. Then move to large samples
    5. Then repeat these scenarios for estimation rather than testing
    6. Move from categorical to quantitative variables, repeat all of the above
    7. Then move to issues of bivariate analysis, association, prediction
      (The first course would probably end about here.)
    8. Then consider additional probability distributions, models, theory of estimation
    9. Then address theory of testing
    10. Conclude with linear prediction models

Chapter 1: Variation, Randomness, and Comparisons

Introduce idea of statistical significance in a setting of comparing experimental groups

(Scenario: categorical variables, two groups, small samples, experiment, comparison)

Chapter 2: Observation, Confounding, Causation

Compare/contrast conclusions to be drawn from controlled experiments vs. observational studies

(Scenario: categorical variables, two groups, small samples, observational study, comparison)

Chapter 3: Sampling

Introduce idea of random sampling and its associated concepts, binomial model

(Scenario: categorical variables, one group, small samples, comparison)

Chapter 4: Large-Sample Approximations

Study normal approximations to above analyses for large samples

(Scenario: categorical variables, large samples, comparison)

Chapter 5: Estimation

Introduce concept of confidence, interval estimation; apply to situations studied thus far

(Scenario: categorical variables, estimation)

Chapter 6: Quantitative Variables

Repeat all of the above analyses (graphical, numerical, inferential) with quantitative variables

(Scenario: quantitative variables)

Chapter 7: Bivariate Data, Association, Prediction

Investigate concepts related to association and prediction, emphasize model basics (data = fit + residual), apply in specific settings

Chapter 8: Probability Models, Distributions

Study "catalog" of common distributions as models, introduce estimation principles

Chapter 9: Theory of Testing, Decision

Investigate more theoretical aspects of testing and decision theory

Chapter 10: Linear Models

Study common structure, applicability of linear models