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| Discrete Probability Distributions | |
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| Discrete Probability Distributions and Probability Mass Functions | |
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| Bernoulli Experiments and trials | |
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| Binomial Random Variables, Experiments, and Probability Functions | |
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| The Binomial Coefficient | |
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| The Binomial Probability Function | |
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| Mean, Variance, and Standard Deviation of the Binomial Probability Distribution | |
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| The Binomial Expansion and the Binomial Theorem | |
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| Pascal's Triangle and the Binomial Coefficient | |
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| The Family of Binomial Distributions | |
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| The Cumulative Binomial Probability Table | |
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| Lot-Acceptance Sampling | |
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| Consumer's Risk and Producer's Risk | |
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| Multivariate Probability Distributions and Joint Probability Distributions | |
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| The Multinomial Experiment | |
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| The Multinomial Coefficient | |
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| The Multinomial Probability Function | |
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| The Family of Multinomial Probability Distributions | |
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| The Means of the Multinomial Probability Distribution | |
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| The Multinomial Expansion and the Multinomial Theorem | |
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| The Hypergeometric Experiment | |
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| The Hypergeometric Probability Function | |
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| The Family of Hypergeometric Probability Distributions | |
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| The Mean, Variance, and Standard Deviation of the Hypergeometric Probability Distribution | |
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| The Generalization of the Hypergeometric Probability Distribution | |
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| The Binomial and Multinomial Approximations to the Hypergeometric Distribution | |
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| Poisson Processes, Random Variables, and Experiments | |
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| The Poisson Probability Function | |
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| The Family of Poisson Probability Distributions | |
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| The Mean, Variance, and Standard Deviation of the Poisson Probability Distribution | |
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| The Cumulative Poisson Probability Table | |
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| The Poisson Distribution as an Approximation to the Binomial Distribution | |
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| The Normal Distribution and Other Continuous Probability Distributions | |
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| Continuous Probability Distributions | |
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| The Normal Probability Distributions and the Normal Probability Density Function | |
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| The Family of Normal Probability Distributions | |
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| The Normal Distribution: Relationship between the Mean ([mu]), the Median ([mu]), and the Mode | |
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| Kurtosis | |
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| The Standard Normal Distribution | |
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| Relationship Between the Standard Normal Distribution and the Standard Normal Variable | |
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| Table of Areas in the Standard Normal Distribution | |
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| Finding Probabilities Within any Normal Distribution by Applying the Z Transformation | |
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| One-tailed Probabilities | |
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| Two-tailed Probabilities | |
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| The Normal Approximation to the Binomial Distribution | |
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| The Normal Approximation to the Poisson Distribution | |
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| The Discrete Uniform Probability Distribution | |
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| The Continuous Uniform Probability Distribution | |
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| The Exponential Probability Distribution | |
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| Relationship between the Exponential Distribution and the Poisson Distribution | |
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| Sampling Distributions | |
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| Simple Random Sampling Revisited | |
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| Independent Random Variables | |
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| Mathematical and Nonmathematical Definitions of Simple Random Sampling | |
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| Assumptions of the Sampling Technique | |
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| The Random Variable X | |
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| Theoretical and Empirical Sampling Distributions of the Mean | |
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| The Mean of the Sampling Distribution of the Mean | |
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| The Accuracy of an Estimator | |
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| The Variance of the Sampling Distribution of the Mean: Infinite Population or Sampling with Replacement | |
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| The Variance of the Sampling Distribution of the Mean: Finite Population Sampled without Replacement | |
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| The Standard Error of the Mean | |
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| The Precision of An Estimator | |
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| Determining Probabilities with a Discrete Sampling Distribution of the Mean | |
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| Determining Probabilities with a Normally Distributed Sampling Distribution of the Mean | |
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| The Central Limit Theorem: Sampling from a Finite Population with Replacement | |
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| The Central Limit Theorem: Sampling from an Infinite Population | |
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| The Central Limit Theorem: Sampling from a Finite Population without Replacement | |
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| How Large is "Sufficiently Large?" | |
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| The Sampling Distribution of the Sample Sum | |
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| Applying the Central Limit Theorem to the Sampling Distribution of the Sample Sum | |
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| Sampling from a Binomial Population | |
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| Sampling Distribution of the Number of Successes | |
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| Sampling Distribution of the Proportion | |
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| Applying the Central Limit Theorem to the Sampling Distribution of the Number of Successes | |
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| Applying the Central Limit Theorem to the Sampling Distribution of the Proportion | |
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| Determining Probabilities with a Normal Approximation to the Sampling Distribution of the Proportion | |
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| One-Sample Estimation of The Population Mean | |
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| Estimation | |
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| Criteria for Selecting the Optimal Estimator | |
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| The Estimated Standard Error of the Mean S[subscript x] | |
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| Point Estimates | |
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| Reporting and Evaluating the Point Estimate | |
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| Relationship between Point Estimates and Interval Estimates | |
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| Deriving P(x[subscript 1-alpha/2] [less than or equal] X [less than or equal] x[subscript alpha/2]) = P(-z[subscript alpha/2] [less than or equal] Z [less than or equal] z[subscript alpha/2]) = 1 - [alpha] | |
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| Deriving P(X - z[subscript alpha/2] [sigma subscript x] [less than or equal] [mu] [less than or equal] X + z[subscript alpha/2] [sigma subscript x]) = 1 - [alpha] | |
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| Confidence Interval for the Population Mean [mu]: Known Standard Deviation [sigma], Normally Distributed Population | |
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| Presenting Confidence Limits | |
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| Precision of the Confidence Interval | |
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| Determining Sample Size when the Standard Deviation is Known | |
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| Confidence Interval for the Population Mean [mu]: Known Standard Deviation [sigma], Large Sample (n [greater than or equal] 30) from any Population Distribution | |
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| Determining Confidence Intervals for the Population Mean [mu] when the Population Standard Deviation [sigma] is Unknown | |
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| The t Distribution | |
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| Relationship between the t Distribution and the Standard Normal Distribution | |
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| Degrees of Freedom | |
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| The Term "Student's t Distribution" | |
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| Critical Values of the t Distribution | |
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| Table A.6: Critical Values of the t Distribution | |
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| Confidence Interval for the Population Mean [mu]: Standard Deviation [sigma] not known, Small Sample (n [ 30) from a Normally Distributed Population | |
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| Determining Sample Size: Unknown Standard Deviation, Small Sample from a Normally Distributed Population | |
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| Confidence Interval for the Population Mean [mu]: Standard Deviation [sigma] not known, large sample (n [greater than or equal] 30) from a Normally Distributed Population | |
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| Confidence Interval for the Population Mean [mu]: Standard Deviation [sigma] not known, Large Sample (n [greater than or equal] 30) from a Population that is not Normally Distributed | |
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| Confidence Interval for the Population Mean [mu]: Small Sample (n [ 30) from a Population that is not Normally Distributed | |
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| One-Sample Estimation of the Population Variance, Standard Deviation, and Proportion | |
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| Optimal Estimators of Variance, Standard Deviation, and Proportion | |
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| The Chi-Square Statistic and the Chi-Square Distribution | |
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| Critical Values of the Chi-Square Distribution | |
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| Table A.7: Critical Values of the Chi-Square Distribution | |
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| Deriving the Confidence Interval for the Variance [sigma superscript 2] of a Normally Distributed Population | |
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| Presenting Confidence Limits | |
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| Precision of the Confidence Interval for the Variance | |
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| Determining Sample Size Necessary to Achieve a Desired Quality-of-Estimate for the Variance | |
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| Using Normal-Approximation Techniques To Determine Confidence Intervals for the Variance | |
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| Using the Sampling Distribution of the Sample Variance to Approximate a Confidence Interval for the Population Variance | |
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| Confidence Interval for the Standard Deviation [sigma] of a Normally Distributed Population | |
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| Using the Sampling Distribution of the Sample Standard Deviation to Approximate a Confidence Interval for the Population Standard Deviation | |
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| The Optimal Estimator for the Proportion p of a Binomial Population | |
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| Deriving the Approximate Confidence Interval for the Proportion p of a Binomial Population | |
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| Estimating the Parameter p | |
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| Deciding when n is "Sufficiently Large", p not known | |
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| Approximate Confidence Intervals for the Binomial Parameter p When Sampling From a Finite Population without Replacement | |
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| The Exact Confidence Interval for the Binomial Parameter p | |
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| Precision of the Approximate Confidence-Interval Estimate of the Binomial Parameter p | |
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| Determining Sample Size for the Confidence Interval of the Binomial Parameter p | |
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| Approximate Confidence Interval for the Percentage of a Binomial Population | |
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| Approximate Confidence Interval for the Total Number in a Category of a Binomial Population | |
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| The Capture--Recapture Method for Estimating Population Size N | |
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| One-Sample Hypothesis Testing | |
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| Statistical Hypothesis Testing | |
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| The Null Hypothesis and the Alternative Hypothesis | |
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| Testing the Null Hypothesis | |
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| Two-Sided Versus One-Sided Hypothesis Tests | |
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| Testing Hypotheses about the Population Mean [mu]: Known Standard Deviation [sigma], Normally Distributed Population | |
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| The P Value | |
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| Type I Error versus Type II Error | |
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| Critical Values and Critical Regions | |
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| The Level of Significance | |
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| Decision Rules for Statistical Hypothesis Tests | |
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| Selecting Statistical Hypotheses | |
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| The Probability of a Type II Error | |
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| Consumer's Risk and Producer's Risk | |
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| Why It is Not Possible to Prove the Null Hypothesis | |
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| Classical Inference Versus Bayesian Inference | |
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| Procedure for Testing the Null Hypothesis | |
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| Hypothesis Testing Using X as the Test Statistic | |
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| The Power of a Test, Operating Characteristic Curves, and Power Curves | |
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| Testing Hypothesis about the Population Mean [mu]: Standard Deviation [sigma] Not Known, Small Sample (n [ 30) from a Normally Distributed Population | |
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| The P Value for the t Statistic | |
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| Decision Rules for Hypothesis Tests with the t Statistic | |
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| [beta], 1 - [beta], Power Curves, and OC Curves | |
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| Testing Hypotheses about the Population Mean [mu]: Large Sample (n [greater than or equal] 30) from any Population Distribution | |
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| Assumptions of One-Sample Parametric Hypothesis Testing | |
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| When the Assumptions are Violated | |
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| Testing Hypothesis about the Variance [sigma superscript 2] of a Normally Distributed Population | |
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| Testing Hypotheses about the Standard Deviation [sigma] of a Normally Distributed Population | |
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| Testing Hypotheses about the Proportion p of a Binomial Population: Large Samples | |
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| Testing Hypotheses about the Proportion p of a Binomial Population: Small Samples | |
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| Two-Sample Estimation and Hypothesis Testing | |
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| Independent Samples Versus Paired Samples | |
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| The Optimal Estimator of the Difference Between Two Population Means ([mu subscript 1] - [mu subscript 2]) | |
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| The Theoretical Sampling Distribution of the Difference Between Two Means | |
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| Confidence Interval for the Difference Between Means ([mu subscript 1] - [mu subscript 2]): Standard Deviations ([sigma subscript 1] and [sigma subscript 2]) Known, Independent Samples from Normally Distributed Populations | |
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| Testing Hypotheses about the Difference Between Means ([mu subscript 1] - [mu subscript 2]): Standard Deviations ([sigma subscript 1] and [sigma subscript 2]) known, Independent Samples from Normally Distributed Populations | |
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| The Estimated Standard Error of the Difference Between Two Means | |
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| Confidence Interval for the Difference Between Means ([mu subscript 1] - [mu subscript 2]): Standard Deviations not known but Assumed Equal ([sigma subscript 1] = [sigma subscript 2]), Small (n[subscript 1] [ 30 and n[subscript 2] [ 30) Independent Samples from Normally Distributed Populations | |
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| Testing Hypotheses about the Difference Between Means ([mu subscript 1] - [mu subscript 2]): Standard Deviations not Known but Assumed Equal ([sigma subscript 1] = [sigma subscript 2]), Small (n[subscript 1] [ 30 and n[subscript 2] [ 30) Independent Samples from Normally Distributed Populations | |
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| Confidence Interval for the Difference Between Means ([mu subscript 1] - [mu subscript 2]): Standard Deviations ([sigma subscript 1] and [sigma subscript 2]) not Known, Large (n[subscript 1] [greater than or equal] 30 and n[subscript 2] [greater than or equal] 30) Independent Samples from any Populations Distributions | |
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| Testing Hypotheses about the Difference Between Means ([mu subscript 1] - [mu subscript 2]): Standard Deviations ([sigma subscript 1] and [sigma subscript 2]), not known, Large (n[subscript 1] [greater than or equal] 30 and n[subscript 2] [greater than or equal] 30) Independent Samples from any Populations Distributions | |
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| Confidence Interval for the Difference Between Means ([mu subscript 1] - [mu subscript 2]): Paired Samples | |
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| Testing Hypotheses about the Difference Between Means ([mu subscript 1] - [mu subscript 2]): Paired Samples | |
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| Assumptions of Two-Sample Parametric Estimation and Hypothesis Testing about Means | |
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| When the Assumptions are Violated | |
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| Comparing Independent-Sampling and Paired-Sampling Techniques on Precision and Power | |
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| The F Statistic | |
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| The F Distribution | |
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| Critical Values of the F Distribution | |
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| Table A.8: Critical Values of the F Distribution | |
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| Confidence Interval for the Ratio of Variances ([sigma superscript 2 subscript 1]/[sigma superscript 2 subscript 2]): Parameters ([sigma superscript 2 subscript 1], [sigma subscript 1], [mu subscript 1] and [sigma superscript 2 subscript 2], [sigma subscript 2], [mu subscript 2]) Not Known, Independent Samples From Normally Distributed Populations | |
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| Testing Hypotheses about the Ratio of Variances ([sigma superscript 2 subscript 1]/[sigma superscript 2 subscript 2]): Parameters ([sigma superscript 2 subscript 1], [sigma subscript 1], [mu subscript 1] and [sigma superscript 2 subscript 2], [sigma subscript 2], [mu subscript 2]) not known, Independent Samples from Normally Distributed Populations | |
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| When to Test for Homogeneity of Variance | |
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| The Optimal Estimator of the Difference Between Proportions (p[subscript 1] - p[subscript 2]): Large Independent Samples | |
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| The Theoretical Sampling Distribution of the Difference Between Two Proportions | |
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| Approximate Confidence Interval for the Difference Between Proportions from Two Binomial Populations (p[subscript 1] - p[subscript 2]): Large Independent Samples | |
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| Testing Hypotheses about the Difference Between Proportions from Two Binomial Populations (p[subscript 1] - p[subscript 2]): Large Independent Samples | |
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| Multisample Estimation and Hypothesis Testing | |
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| Multisample Inferences | |
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| The Analysis of Variance | |
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| Anova: One-Way, Two-Way, or Multiway | |
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| One-Way Anova: Fixed-Effects or Random Effects | |
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| One-way, Fixed-Effects Anova: The Assumptions | |
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| Equal-Samples, One-Way, Fixed-Effects Anova: H[subscript 0] and H[subscript 1] | |
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| Equal-Samples, One-Way, Fixed-Effects Anova: Organizing the Data | |
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| Equal-Samples, One-Way, Fixed-Effects Anova: the Basic Rationale | |
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| SST = SSA + SSW | |
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| Computational Formulas for SST and SSA | |
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| Degrees of Freedom and Mean Squares | |
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| The F Test | |
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| The Anova Table | |
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| Multiple Comparison Tests | |
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| Duncan's Multiple-Range Test | |
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| Confidence-Interval Calculations Following Multiple Comparisons | |
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| Testing for Homogeneity of Variance | |
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| One-Way, Fixed-Effects ANOVA: Equal or Unequal Sample Sizes | |
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| General-Procedure, One-Way, Fixed-effects ANOVA: Organizing the Data | |
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| General-Procedure, One-Way, Fixed-effects ANOVA: Sum of Squares | |
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| General-Procedure, One-Way, Fixed-Effects ANOVA Degrees of Freedom and Mean Squares | |
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| General-Procedure, One-Way, Fixed-Effects ANOVA: the F Test | |
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| General-Procedure, One-Way, Fixed-Effects ANOVA: Multiple Comparisons | |
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| General-Procedure, One-Way, Fixed-Effects ANOVA: Calculating Confidence Intervals and Testing for Homogeneity of Variance | |
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| Violations of ANOVA Assumptions | |
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| Regression and Correlation | |
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| Analyzing the Relationship between Two Variables | |
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| The Simple Linear Regression Model | |
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| The Least-Squares Regression Line | |
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| The Estimator of the Variance [sigma superscript 2 subscript Y times X] | |
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| Mean and Variance of the y Intercept a and the Slope b | |
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| Confidence Intervals for the y Intercept a and the Slope b | |
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| Confidence Interval for the Variance [sigma superscript 2 subscript Y times X] | |
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| Prediction Intervals for Expected Values of Y | |
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| Testing Hypotheses about the Slope b | |
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| Comparing Simple Linear Regression Equations from Two or More Samples | |
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| Multiple Linear Regression | |
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| Simple Linear Correlation | |
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| Derivation of the Correlation Coefficient r | |
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| Confidence Intervals for the Population Correlation Coefficient [rho] | |
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| Using the r Distribution to Test Hypotheses about the Population Correlation Coefficient [rho] | |
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| Using the t Distribution to Test Hypotheses about p | |
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| Using the Z Distribution to Test the Hypothesis [rho] = c | |
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| Interpreting the Sample Correlation Coefficient r | |
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| Multiple Correlation and Partial Correlation | |
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| Nonparametric Techniques | |
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| Nonparametric vs. Parametric Techniques | |
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| Chi-Square Tests | |
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| Chi-Square Test for Goodness-of-fit | |
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| Chi-Square Test for Independence: Contingency Table Analysis | |
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| Chi-Square Test for Homogeneity Among k Binomial Proportions | |
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| Rank Order Tests | |
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| One-Sample Tests: The Wilcoxon Signed-Rank Test | |
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| Two-Sample Tests: the Wilcoxon Signed-Rank Test for Dependent Samples | |
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| Two-Sample Tests: the Mann-Whitney U Test for Independent Samples | |
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| Multisample Tests: the Kruskal-Wallis H Test for k Independent Samples | |
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| The Spearman Test of Rank Correlation | |
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| Appendix | |
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| Cumulative Binomial Probabilities | |
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| Cumulative Poisson Probabilities | |
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| Areas of the Standard Normal Distribution | |
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| Critical Values of the t Distribution | |
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| Critical Values of the Chi-Square Distribution | |
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| Critical Values of the F Distribution | |
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| Least Significant Studentized Ranges r[subscript p] | |
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| Transformation of r to z[subscript r] | |
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| Critical Values of the Pearson Product-Moment Correlation Coefficient r | |
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| Critical Values of the Wilcoxon W | |
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| Critical Values of the Mann-Whitney U | |
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| Critical Values of the Kruskal-Wallis H | |
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| Critical Values of the Spearman r[subscript S] | |
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| Index | |