What every high school graduate should know about statistics

This is my attempt to summarize the recommendations of the article by R. Scheaffer, A. Watkins and J. Landwehr (with the title above) that appears in Reflections on Statistics:Learning, Teaching and Assessment in Grades K-12 , Susanne P. Lajoie, editor, Lawrence Erlbaum Assoc., Mahwah New Jersey and London, 1998. The bold headings below are from the article. The items listed under each heading represent my own summary of the main recommendations.

JJM

Number Sense

• noticing the "world of quantity"
• variables: categorical/numerical, tabulating values of variables
• using and interpreting tables and graphs
• noticing associations

Planning a study and producing data

• study vs. experiment
• observational studies
  • identifying issues (measurability, testability)
  • defining target population; sample selection
  • measurement questions
  • managing and carrying out a study
  • drawing conclusions
• experiments
  • identifying issue to be investigated
  • variables: controlled, uncontrolled
  • experimental design, measurement
  • management
  • drawing conclusions

   

Data analysis

• univariate data
  • distributions
  • quantitative characteristics of data distributions
  • data display
• bivariate data
  • association
  • kinds of association (categorical, linear, exponential, etc.)
  • display of data
• time series

Probability. The following guidelines are quoted directly from the article. Remember, these are the authors' suggestions, not truths of nature:

1. Probability should be presented as the study of random events.
2. The unifying thread throughout the probability curriculum should be the idea of a distribution.
3. Probability distributions typically should be constructed by simulation.
4. Students' intuition about probabilistic events should be developed so that they can estimate probabilities of events and assess the reasonableness of research.
5. Every student should learn the language and basic formulas of probability.
6. Misconceptions about probability should be confronted head-on.
   

The authors also list the following topics. We have omitted the subheadings:

• Analyzing a probability distribution given in table form
• Constructing discrete probability distributions by simulation
• Constructing discrete probability distributions by theory
• Continuous probability distributions
• Detecting and simulating random behavior
• Law of large numbers
• Sampling distributions
• Common misconceptions about probability
• Applications

The article contains a sharp critique of the "Traditional Curriculum in Probability," which is faulted for overemphasis on combinatorics (e.g., what is the probability that a hand of five cards contains three face cards and a pair of aces?)

Statistical inference. The following outline of "key concepts" is given:

• Confidence intervals for proportions and means
  • Construction and verification by simulation
  • Sampling error, "margin of error"
• Tests of hypotheses
  • Addresses through confidence intervals
  • Addresses through simulation (informal notion of p-value)
• Modeling bivariate data
  • Least squares line
  • Heuristic inference for slope
  • Heuristic inference for correlation coefficient