Class Notes, 08/24

Core concepts of statistical thinking

Probability

Commonsense understanding of probability: What is the relative frequency of various outcomes?

Expectation

Knowing what's true overall (in the "population"), what do we expect (in the sample)?

Estimation

Given the data (our sample), what is our best guess (estimation) about what is true overall (in the "population")?

Hypothesis Testing

Given the data (sample) and hypotheses about what is true overall (population), which hypothesis is most likely to be correct?

Given the data (sample) and a hypothesis about what is true overall (population), is the hypothesis likely to be true?

Predictor Variables

How can we design an experiment to get good data and make good decisions relative to our question?

Two important estimators

The sample mean is an estimator of the population mean.

The sample variance is an estimator of the population variance.

Physical analogues

The mean of a set of data is analogous to its center of gravity.

The variance is analogous to the moment of inertia about the mean.

Statistics theory is based on probability theory and decision theory

In the 1980s, statistical methods were used in manufacturing to greatly increase the quality of manufactured goods.