Statistics for The Sciences
PREFACE. 1. INTRODUCTION. What is Statistics? Sampling and Estimation. Precision Versus Confidence. Hypothesis Testing. Preview. Review Exercises. 2. DESCRIPTION OF DATA. Introduction. Categorical Data. Ordinal Data. Ratio Data. Frequency Tables and Histograms. Grouped Data and Sturge?s Rule. Stem and Leaf Plot. Five-number Summary. Box Plot. The Mean. Variance and Standard Deviation. Ogives and Quantiles. Exploratory Data Analysis. Formulas for Histograms (optional). Review Exercises. 3. PROBABILITY THEORY. Overview. Definitions. Probabilities of Events. Rules of Probability. Three Diagrams. Bayes? Formula. Review Exercises. 4. DISCRETE RANDOM VARIABLES. Introduction. Basic Properties of Discrete Random Variables. Probability Histograms. Expected Value or Mean of a Random Variable. Functions of Random Variables. Variance and Standard Deviation of a Random Variable. Law of Large Numbers (optional). Review Exercises. 5. CONTINUOUS RANDOM VARIABLES. Continuous Random Variables. Basic Properties. Percentiles and Modes. Expected Value or Mean. Functions of Random Variables. Variance and Standard Deviation. Chebyshev?s Inequality. Review Exercises. 6. SPECIAL DISCRETE RANDOM VARIABLES. Discrete Uniform Random Variables. Bernoulli Random Variables. Binomial Random Variables. Hypergeometric Random Variables. Review Exercises. 7. HYPOTHESIS TESTING. Introduction. Two Types of Errors. The Sign Test. Binomial Exact Test. Fisher?s Exact Test. Trivial Effect Can be Significant. Review Exercises. 8. NORMAL RANDOM VARIABLES. Introduction. Normal Approximation of Binomial. Continuity Correction. Central Limit Theorem. Processes that Follow the Normal Curve. Review Exercises. 9. WAITING TIME RANDOM VARIABLES Geometric Random Variables. Exponential Random Variables. Poisson Random Variables. Poisson Approximation Binomial for Rare Events. Poisson Random Variable as Inverse Exponential. Review Exercises. 10. MULTIVARIATE RANDOM VARIABLES. Joint Densities. Independence of Random Variables. Expectation, Covariance, and Correlation. Linear Combinations of Random Variables. Review Exercises. 11. SAMPLING THEORY. Population and Parameters. Samples and Statistics. Law of Averages for the Sample Count. Law of Averages for Sample Proportion. Law of Averages for the Sample Sum. Law of Averages for the Sample Mean. The z Statistic. The t Statistic. Estimators of Parameters. Review Exercises. 12. THE z AND t TESTS OF HYPOTHESES. The z Test. Two-Sided z Test. Bootstrapping and the t Test. Which is the Null Hypothesis? Review Exercises. 13. INTERVAL ESTIMATION. Difference Between Confidence and Probability. Two-sided Confidence Intervals. One-sided Confidence Intervals. Bootstrapping and the t curves. Margin of Error. Interval Estimation of Proportion Pi. Small Sample Interval Estimates of Proportions. Review Exercises. 14. TWO SAMPLE INFERENCE. Matched Pair Samples. Independent Samples. Welch?s Formula. Independent Samples with Equal Variances. Resampling Methods. Review Exercises. 15. CORRELATION AND REGRESSION. Introduction. Scatter Plots. The Correlation Coefficient. Fitting a Scatter Plot by Eyes. The Regression Line. Estimation with Regression. The Regression Paradox. Testing for Correlation. Correlation is Not Causation. Review Exercises. 16. INFERENCE WITH CATEGORICAL DATA. Introduction / Comments on the Definition of x2. Testing Goodness-of-Fit. Contingency Table Tests. One-Sided Chi-Square Test for the 2 x 2 Contingency Table. Compound Hypotheses. Review Exercises. Statistical Tables. Answers to Selected Odd-numbered Exercises. Indices.