Suggested Components of the Introductory Statistics Course
1. Recognizing that statistics surround us in everyday living. Reported statistics are sometimes incorrect or misused; thus it is important for each of us to be a critical consumer of statistics given by the media. We must ask questions about the quality of the data and the reliability of the analysis.
2. Understanding variability: bias, sampling error, systematic error, measurement error, and the regression effect. In particular, understanding: Actual observation = Fitted + Residual, and in statistics we try to detect the pattern (fitted) and describe the variation (residual) from that pattern.
3. Collection and summarization of data, including basic exploratory data analysis. Outliers and how statistical measures change with various changes in the data (that is, aspects of robustness).
4. Graphs, including plotting data taken sequentially (that is, basic time-series concepts) and categorical data using contingency tables.
5. Sampling and surveys, including the importance of getting quality data.
6. Elementary designs of experiments, with some discussion about the ethics of experimentation and the distinction between observational and experimental investigating.
7. Formulation of problems and understanding the importance of operational definitions and the process of inquiry. That is, understanding the iterative nature of the scientific method, including the Plan-Do-Check [Study]-Act cycle. We want the capability to make and understand predictions. That is, statistics represents a process concerned with gaining knowledge and solving problems and is not a collection of isolated tools.
8. Basic distributions (such as the normal and binomial) as approximations to variability in data sets; that is, study modeling.
9. Correlation and regression and other measures of association.
10. Elementary probability, including trees, conditional probability and contingency tables.
11. Central limit theorem.
12. Elementary inference from samples, recognizing there are not unique answers in statistics. This includes inference on means, proportions and counts. Statistical significance vs. practical significance.
13. Ability to use at least one statistical software package.
14. Simulation. Use of simulation is highly beneficial in probability, sampling, CLT and inference.
First Courses in Statistical Science: The Status of Educational Reform Efforts
Joan Garfield, Bob Hogg, Candace Schau, Dex Whittinghill
Journal of Statistics Education Volume 10, Number 2 (2002)