Content, Philosophy, and Goals, Overview, Prerequisites, Design criteria and implementation, Advantages of Java over proprietary Statistics Packages, Suggestions for evaluating the materials, About the Author, Acknowledgments.

How to use these online materials

Rules of reasoning, arguments, validity and soundness, some valid rules of reasoning, formal fallacies, common formal fallacies, informal fallacies, fallacies of relevance and fallacies of evidence, fallacies of relevance, common fallacies of relevance, fallacies of evidence, common fallacies of evidence, summary, key terms.

Introduction. Data: types of variables, sample data sets, frequency tables, histograms, skewness and modes, percentiles and quartiles, estimating percentiles from histograms, summary, key terms.

Measures of location (mean, median and mode), spread and variability, importance of variability, measures of spread: range, IQR and SD, affine transformations, Markov's inequality and Chebychev's inequality for lists, summary, key terms.

Multivariate data, scatterplots, describing scatterplots: linearity and nonlinearity, homoscedasticity and heteroscedasticity, outliers, summary, key terms.

Association, post hoc ergo propter hoc, summary, key terms.

The correlation coefficient, the effect of nonlinear association, homoscedasticity and heteroscedasticity and outliers on the correlation coefficient, summary, key terms.

Computing the correlation coefficient, standard units, computing r, ecological correlation, summary, key terms.

SD line, graph of averages, regression line, estimating using the regression line, the equation of the regression line, summary, key terms.

Residuals and residual plots, reading residual plots, summary, key terms.

The RMS error of regression, the distribution in a vertical slice through a scatterplot, the regression effect, the regression fallacy, summary, key terms.

Counting can be hard, The Fundamental Rule of Counting, permutations, combinations, card hands, summary, key terms.

Theories of Probability, Random events, Equally Likely Outcomes, Frequency Theory, Subjective Theory, shortcomings of the theories, summary, key terms.

Naive set theory, connecting probability to set theory, summary, key terms.

Sets and categories, existential and universal quantifiers, categorical syllogisms, testing syllogisms, summary, key terms.

Logical operations, evaluating compound propositions, logical arguments as compound propositions, valid arguments versus sound arguments, logic and sets, summary, key terms.

The axioms of probability, conditioning, the multiplication rule, Bayes' rule, independence, summary, key terms.

Background, assumptions and arguments, assumptions and rules of the game, argument 1 (don't switch—naive), argument 2 (don't switch—conditional probability), argument 3 (switch—heuristic), argument 4 (switch—conditional probability), summary, key terms.

Introduction, a box model for the Let's Make a Deal problem, the binomial probability distribution, dependence of the binomial on n and p, when the binomial does not apply, using the binomial distribution, continuation of the Let's Make a Deal problem, summary, key terms.

Random variables, sampling from 0-1 boxes, geometric distribution, the negative binomial distribution, sampling without replacement, the hypergeometric distribution, calculating binomial, geometric, hypergeometric, and negative binomial probabilities, discrete distributions, case study: trade secret litigation, summary, key terms.

The Law of Large Numbers, implications of the law of large numbers, expected value of a random variable, expected value of the sample sum, expected value of binomial hypergeometric distributions, properties of the expected value, expected value of the sample mean and sample percentage, gambling and fair bets, expected values of some common distributions, summary, key terms.

Expected value of a transformation of a random variable, standard error of random variables, the standard error transformations of a random variable, independent random variables, standard errors of some common random variables, the SE of a single draw from a box of numbered tickets, SE of the sample sum of n random draws with replacement from a Box of Tickets, the SE of the sample mean of n random draws from a box of numbered tickets, the square-root law, the law of averages, the standard error of the binomial, geometric and negative binomial distributions, SE of the sample sum and mean of a simple random sample, the SE of the hypergeometric distribution, the finite population correction, summary, key terms.

The normal approximation, standard units for random variables, the normal curve, the normal approximation to probability histograms, the continuity correction, the normal approximation to the hypergeometric distribution, Markov's and Chebychev's inequalities for random variables, summary, key terms.

Parameters and statistics, why sample?, sample surveys, The Hite Report, bias in surveys, Sampling designs: cluster sampling, stratified sampling, multistage sampling, hybrid designs, ways of drawing samples, convenience samples, quota samples, systematic samples, probability samples, simple random samples, systematic random samples, Sampling from hypothetical populations, summary, key terms.

Quantifying the error of estimators: bias, standard error, and mean squared error, estimating means and percentages, a conservative estimate of the SE of the sample percentage, the Bootstrap estimate of the SD of a list of zeros and ones, the sample standard deviation and the sample variance, caveats, summary, key terms.

Confidence intervals, conservative confidence intervals for percentages, conservative confidence intervals for the mean of bounded populations, approximate confidence intervals for percentages, approximate confidence intervals for the population mean, exact confidence intervals for percentages, confidence intervals for the median and percentiles, summary.

Hypothesis testing, Examples of hypothesis testing problems, significance level and power, test statistics and P-values, hypotheses about parameters; one-sided and two-sided alternatives, case study: employment discrimination, caveats, the meaning of rejection, statistical significance and practical importance, interpreting P-values, multiplicity and data mining, garbage in, garbage out, summary.

The Method of Comparison, confounding, historical controls, longitudinal and cross-sectional comparisons, Simpson's Paradox, experiments and observational studies, assessing online instructions, the Placebo Effect, John Snow's study of the mode of communication of cholera, The Kassel Dowsing Experiment, summary.

Fisher's Exact Test for an effect--dependent samples, the normal approximation to Fisher's Exact Test, testing equality of two percentages using independent samples, Fisher's Exact Test using independent samples, the Z test for the equality of two percentages using independent Samples, the normal approximation to Fisher's exact test and the z Test, summary, key terms.

z Tests, P values for z tests, examples of z tests, z test for a population percentage, the z test for a population mean, z-test for a difference of population means (paired samples, independent samples), t tests, nearly normally distributed populations, Student's t-curve, t test for the mean of a nearly normal population, hypothesis tests and confidence intervals, confidence intervals using Student's t curve, summary, key terms

The multinomial distribution, the chi-square statistic, the sampling distribution of the chi-square statistic and the chi-square curve, the chi-square test of goodness of fit, summary, key terms.