Class Notes, 08/24
Core concepts of statistical thinking
- Commonsense understanding of probability: What is the relative frequency
of various outcomes?
- Knowing what's true overall (in the "population"), what do we expect (in the sample)?
- Given the data (our sample), what is our best guess (estimation)
about what is true overall (in the "population")?
- 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?
- 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.
- 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
In the 1980s, statistical methods were used in manufacturing to
greatly increase the quality of manufactured goods.