Introduction: what is statistics? Part 1 Looking at data - distributions: displaying distributions - measurement, variation, stemplots, histograms, looking at data, time plots; describing distributions - measuring centre, resistant measures of spread, the standard deviation, changing the unit of measurement; the normal distributions - density curves, normal distributions, normal distribution calculations, assessing normality. Part 2 Looking at data - relationships: scatterplots - interpreting scatterplots, smoothing scatterplots, categorical explanatory variables; least squares regression - fitting a line to data, least-squares regression, residuals, outliers and influential observations; an application - exponential growth - the nature of exponential growth, the logarithm transformation, residuals again; correlation - computing the correlation, correlation in the regression setting, interpreting correlation and regression; relations in categorical data - analyzing two-way tables, Simpson's paradox; the question of causation - smoking and lung cancer, establishing causation, Part 3 Producing data: first steps - the need for design, sampling, experiments - exercises; design of experiments - comparative experiments, randomization, how to randomize, cautions about experimentation, other experimental designs; sampling design - simple random samples, other sampling designs, cautions about sample surveys; toward statistical inference - sampling distributions, bias, variability, what about experiments?, conclusion. Part 4 Probability - the study of randomness: the idea of probability, the uses of probability; probability models - sample spaces, assigning probabilities, addition and multiplication rules; random variables - discrete random variables, continuous random variables; means and variances of random variables - the mean of a random variable, the law of large numbers, rules for means, the variance of a random variable, rules for variances; probability laws - general addition rules, conditional probabilities and general multiplication rules. Part 5 From probability to inference: counts and proportions - the binomial distributions, binomial probabilities, binomial mean and variance, sample proportions, normal approximations for proportions and counts; sample means - the distribution of a sample mean, the central limit theorem; control charts - control charts, out-of-control signals. (Part contents)
