ABSTRACT
The chapter begins with a discussion of statistics as estimators of population parameters, the notion of a sampling distribution and definitions of bias and mean squared error. The distinction between accuracy and precision is made. The construction of confidence intervals for a population mean, in the case of known population standard deviation and in the case of unknown population standard deviation using the t-distribution, is covered. The discussion of the assumptions leads to bootstrap methods. The correspondence between confidence intervals and hypothesis testing is explained, The importance of choosing an appropriate sample size is discussed and a principle for calculating a sample size via a specification of width of a confidence interval is given. Having established general principles, comparisons of means and proportions using independent and matched samples are covered. The chi-square distribution is introduced for inferences about variances in normal populations. The F-test for comparing variances from independent random samples is covered. Prediction intervals and statistical tolerance intervals are introduced. The chapter ends with formal tests of goodness of fit: the chi-square test, and empirical distribution function tests. Calculations using the derived formulae are compared with results obtained using inbuilt MATLAB and R functions. The associated experiment in Appendix E is a paired comparison of reaction times, using a reaction ruler with reaction times related to driving a car. The chapter ends with: a summary of: notation used; the main results, MATLAB and R syntax; and exercises.
