• Glossary.
• Preface.
• • 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.
• Introduction.
• • How to use these online materials
• Chapter 1. Tables, percentiles, and histograms.
• • Introduction. Data: types of variables, sample data sets, frequency tables, histograms, skewness and modes, percentiles and quartiles, estimating percentiles from histograms, summary, key terms.
• Chapter 2. Measures of location and spread.
• • 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.
• Chapter 3. Multivariate data.
• • Multivariate data, scatterplots, describing scatterplots: linearity and nonlinearity, homoscedasticity and heteroscedasticity, outliers, association, post hoc ergo propter hoc, summary, key terms.
• Chapter 4. Association and correlation.
• • The correlation coefficient, the effect of nonlinear association, homoscedasticity and heteroscedasticity and outliers on the correlation coefficient, computing the correlation coefficient, standard units, computing r, ecological correlation. summary, key terms.
• Chapter 5. Regression.
• • SD line, graph of averages, regression line, estimating using the regression line, the equation of the regression line, summary, key terms.
• Chapter 6. Errors in regression.
• • Residuals and residual plots, reading residual plots, the RMS error of regression, the distribution in a vertical slice through a scatterplot, the regression effect, the regression fallacy. summary, key terms.
• Chapter 7. Counting.
• • Counting can be hard, The Fundamental Rule of Counting, permutations, combinations. card hands, summary, key terms.
• Chapter 8. Probability: philosophy and mathematical background.
• • Theories of Probability, Equally Likely Outcomes, Frequency Theory, Subjective Theory, shortcomings of the theories, random experiments, the language of probability theory, rudiments of set theory, elementary logic, evaluating compound propositions, logic and sets. summary, key terms.
• Chapter 9. Probability: axioms and fundaments.
• • The axioms of probability, conditional probability, the multiplication rule, Bayes' rule, independence. summary, key terms.
• Chapter 10. The "Let's Make a Deal" (Monty Hall) problem: subtleties of conditional probability.
• • 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.
• Chapter 11. Probability meets data.
• • 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.
• Chapter 12. Random variables and discrete distributions.
• • 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.
• Chapter 13. The long run and the expected value.
• • 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.
• Chapter 14. Standard error.
• • 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.
• Chapter 15. The Normal curve, the Central Limit Theorem, and Markov's and Chebychev's inequalities for random variables.
• • 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.
• Chapter 16. Sample surveys and sampling designs.
• • 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.
• Chapter 17. Estimating parameters from simple random samples.
• • 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.
• Chapter 18. Confidence intervals.
• • Confidence intervals, conservative confidence intervals for percentages, approximate confidence intervals for percentages, approximate confidence intervals for the population mean, confidence intervals for the median and percentiles, summary.
• Chapter 19. Hypothesis testing: does chance explain the results?
• • 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.
• Chapter 20. Does treatment have an effect?
• • 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.
• Chapter 21. Testing whether two percentages are equal.
• • 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.
• Chapter 22. Approximate hypothesis tests: the z test and the t test
• • z Tests, P values for z tests, examples of z tests, P-values for 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
• Chapter 23. Multinomial models for categorical data and the chi-square test for goodness of fit.
• • 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.
• Chapter 24. A case study in natural resource legislation.
• Bibliography.

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