This engaging text shows how statistics and methods work together, demonstrating a variety of techniques for evaluating statistical results against the specifics of the methodological design. Richard Gonzalez elucidates the fundamental concepts involved in analysis of variance (ANOVA), focusing on single degree-of-freedom tests, or comparisons, wherever possible. Potential threats to making a causal inference from an experimental design are highlighted. With an emphasis on basic between-subjects and within-subjects designs, Gonzalez resists presenting the countless ""exceptions to the rule""…mehr
This engaging text shows how statistics and methods work together, demonstrating a variety of techniques for evaluating statistical results against the specifics of the methodological design. Richard Gonzalez elucidates the fundamental concepts involved in analysis of variance (ANOVA), focusing on single degree-of-freedom tests, or comparisons, wherever possible. Potential threats to making a causal inference from an experimental design are highlighted. With an emphasis on basic between-subjects and within-subjects designs, Gonzalez resists presenting the countless ""exceptions to the rule"" that make many statistics textbooks so unwieldy and confusing for students and beginning researchers. Ideal for graduate courses in experimental design or data analysis, the text may also be used by advanced undergraduates preparing to do senior theses. &
1. The Nature of Research 1.1 Introduction 1.2 Observations and Variables 1.3 Behavioral Variables 1.4 Stimulus Variables 1.5 Individual Difference Variables 1.6 Discrete and Continuous Variables 1.7 Levels of Measurement 1.8 Summarizing Observations in Research 1.9 Questions and Problems 2. Principles of Experimental Design 2.1 The Farmer from Whidbey Island 2.2 The Experiment 2.3 The Question of Interest 2.4 Sample Space and Probability 2.5 Simulation of the Experiment 2.6 Permutations 2.7 Combinations 2.8 Probabilities of Possible Outcomes 2.9 A Sample Space for the Experiment 2.10 Testing a Null Hypothesis 2.11 Type I and Type II Errors 2.12 Experimental Controls 2.13 The Importance of Randomization 2.14 A Variation in Design 2.15 Summary 2.16 Questions and Problems 3. The Standard Normal Distribution: An Amazing Approximation 3.1 Introduction 3.2 Binomial Populations and Binomial Variables 3.3 Mean of a Population 3.4 Variance and Standard Deviation of a Population 3.5 The Average of a Sum and the Variance of a Sum 3.6 The Average and Variance of Repeated Samples 3.7 The Second Experiment with the Farmer: µT and sT 3.8 Representing Probabilities by Areas 3.9 The Standard Normal Distribution 3.10 The Second Experiment with the Farmer: A Normal Distribution Test 3.11 The First Experiment with the Farmer: A Normal Distribution Test 3.12 Examples of Binomial Models 3.13 Populations That Have Several Possible Values 3.14 The Distribution of the Sum from a Uniform Distribution 3.15 The Distribution of the Sum T from a U-Shaped Population 3.16 The Distribution of the Sum T from a Skewed Population 3.17 Summary and Sermon 3.18 Questions and Problems 4. Tests for Means from Random Samples 4.1 Transforming a Sample Mean into a Standard Normal Variable 4.2 The Variance and Standard Error of the Mean When the Population Variance s2 Is Known 4.3 The Variance and Standard Error of the Mean When Population s2 Is Unknown 4.4 The t Distribution and the One-Sample t Test 4.5 Confidence Interval for a Mean 4.6 Standard Error of the Difference between Two Means 4.7 Confidence Interval for a Difference between Two Means 4.8 Test of Significance for a Difference between Two Means: The Two-Sample t Test 4.9 Using a Computer Program 4.10 Returning to the Farmer Example in Chapter 2 4.11 Effect Size for a Difference between Two Independent Means 4.12 The Null Hypothesis and Alternatives 4.13 The Power of the t Test against a Specified Alternative 4.14 Estimating the Number of Observations Needed in Comparing Two Treatment Means 4.15 Random Assignments of Participants 4.16 Attrition in Behavioral Science Experiments 4.17 Summary 4.18 Questions and Problems 5. Homogeneity and Normality Assumptions 5.1 Introduction 5.2 Testing Two Variances: The F Distribution 5.3 An Example of Testing the Homogeneity of Two Variances 5.4 Caveats 5.5 Boxplots 5.6 A t Test for Two Independent Means When the Population Variances Are Not Equal 5.7 Nonrandom Assignment of Subjects 5.8 Treatments That Operate Differentially on Individual Difference Variables 5.9 Nonadditivity of a Treatment Effect 5.10 Transformations of Raw Data 5.11 Normality 5.12 Summary 5.13 Questions and Problems 6. The Analysis of Variance: One Between-Subjects Factor 6.1 Introduction 6.2 Notation for a One-Way Between-Subjects Design 6.3 Sums of Squares for the One-Way Between-Subjects Design 6.4 One-Way Between-Subjects Design: An Example 6.5 Test of Significance for a One-Way Between-Subjects Design 6.6 Weighted Means Analysis with Unequal n's 6.7 Summary 6.8 Questions and Problems 7. Pairwise Comparisons 7.1 Introduction 7.2 A One-Way Between-Subjects Experiment with 4 Treatments 7.3 Protection Levels and the Bonferroni Significant Difference (BSD) Test 7.4 Fisher's Significant Difference (FSD) Test 7.5 The Tukey Significant Difference (TSD) Test 7.6 Scheffé's Significant Difference (SSD) Test 7.7 The Four Methods: General Considerations 7.8 Questions and Problems 8. Orthogonal, Planned and Unplanned Comparisons 8.1 Introduction 8.2 Comparisons on Treatment Means 8.3 Standard Error of a Comparison 8.4 The t Test of Significance for a Comparison 8.5 Orthogonal Comparisons 8.6 Choosing a Set of Orthogonal Comparisons 8.7 Protection Levels with Orthogonal Comparisons 8.8 Treatments as Values of an Ordered Variable 8.9 Coefficients for Orthogonal Polynomials 8.10 Tests of Significance for Trend Comparisons 8.11 The Relation between a Set of Orthogonal Comparisons and the Treatment Sum of Squares 8.12 Tests of Significance for Planned Comparisons 8.13 Effect Size for Comparisons 8.14 The Equality of Variance Assumption 8.15 Unequal
1. The Nature of Research 1.1 Introduction 1.2 Observations and Variables 1.3 Behavioral Variables 1.4 Stimulus Variables 1.5 Individual Difference Variables 1.6 Discrete and Continuous Variables 1.7 Levels of Measurement 1.8 Summarizing Observations in Research 1.9 Questions and Problems 2. Principles of Experimental Design 2.1 The Farmer from Whidbey Island 2.2 The Experiment 2.3 The Question of Interest 2.4 Sample Space and Probability 2.5 Simulation of the Experiment 2.6 Permutations 2.7 Combinations 2.8 Probabilities of Possible Outcomes 2.9 A Sample Space for the Experiment 2.10 Testing a Null Hypothesis 2.11 Type I and Type II Errors 2.12 Experimental Controls 2.13 The Importance of Randomization 2.14 A Variation in Design 2.15 Summary 2.16 Questions and Problems 3. The Standard Normal Distribution: An Amazing Approximation 3.1 Introduction 3.2 Binomial Populations and Binomial Variables 3.3 Mean of a Population 3.4 Variance and Standard Deviation of a Population 3.5 The Average of a Sum and the Variance of a Sum 3.6 The Average and Variance of Repeated Samples 3.7 The Second Experiment with the Farmer: µT and sT 3.8 Representing Probabilities by Areas 3.9 The Standard Normal Distribution 3.10 The Second Experiment with the Farmer: A Normal Distribution Test 3.11 The First Experiment with the Farmer: A Normal Distribution Test 3.12 Examples of Binomial Models 3.13 Populations That Have Several Possible Values 3.14 The Distribution of the Sum from a Uniform Distribution 3.15 The Distribution of the Sum T from a U-Shaped Population 3.16 The Distribution of the Sum T from a Skewed Population 3.17 Summary and Sermon 3.18 Questions and Problems 4. Tests for Means from Random Samples 4.1 Transforming a Sample Mean into a Standard Normal Variable 4.2 The Variance and Standard Error of the Mean When the Population Variance s2 Is Known 4.3 The Variance and Standard Error of the Mean When Population s2 Is Unknown 4.4 The t Distribution and the One-Sample t Test 4.5 Confidence Interval for a Mean 4.6 Standard Error of the Difference between Two Means 4.7 Confidence Interval for a Difference between Two Means 4.8 Test of Significance for a Difference between Two Means: The Two-Sample t Test 4.9 Using a Computer Program 4.10 Returning to the Farmer Example in Chapter 2 4.11 Effect Size for a Difference between Two Independent Means 4.12 The Null Hypothesis and Alternatives 4.13 The Power of the t Test against a Specified Alternative 4.14 Estimating the Number of Observations Needed in Comparing Two Treatment Means 4.15 Random Assignments of Participants 4.16 Attrition in Behavioral Science Experiments 4.17 Summary 4.18 Questions and Problems 5. Homogeneity and Normality Assumptions 5.1 Introduction 5.2 Testing Two Variances: The F Distribution 5.3 An Example of Testing the Homogeneity of Two Variances 5.4 Caveats 5.5 Boxplots 5.6 A t Test for Two Independent Means When the Population Variances Are Not Equal 5.7 Nonrandom Assignment of Subjects 5.8 Treatments That Operate Differentially on Individual Difference Variables 5.9 Nonadditivity of a Treatment Effect 5.10 Transformations of Raw Data 5.11 Normality 5.12 Summary 5.13 Questions and Problems 6. The Analysis of Variance: One Between-Subjects Factor 6.1 Introduction 6.2 Notation for a One-Way Between-Subjects Design 6.3 Sums of Squares for the One-Way Between-Subjects Design 6.4 One-Way Between-Subjects Design: An Example 6.5 Test of Significance for a One-Way Between-Subjects Design 6.6 Weighted Means Analysis with Unequal n's 6.7 Summary 6.8 Questions and Problems 7. Pairwise Comparisons 7.1 Introduction 7.2 A One-Way Between-Subjects Experiment with 4 Treatments 7.3 Protection Levels and the Bonferroni Significant Difference (BSD) Test 7.4 Fisher's Significant Difference (FSD) Test 7.5 The Tukey Significant Difference (TSD) Test 7.6 Scheffé's Significant Difference (SSD) Test 7.7 The Four Methods: General Considerations 7.8 Questions and Problems 8. Orthogonal, Planned and Unplanned Comparisons 8.1 Introduction 8.2 Comparisons on Treatment Means 8.3 Standard Error of a Comparison 8.4 The t Test of Significance for a Comparison 8.5 Orthogonal Comparisons 8.6 Choosing a Set of Orthogonal Comparisons 8.7 Protection Levels with Orthogonal Comparisons 8.8 Treatments as Values of an Ordered Variable 8.9 Coefficients for Orthogonal Polynomials 8.10 Tests of Significance for Trend Comparisons 8.11 The Relation between a Set of Orthogonal Comparisons and the Treatment Sum of Squares 8.12 Tests of Significance for Planned Comparisons 8.13 Effect Size for Comparisons 8.14 The Equality of Variance Assumption 8.15 Unequal
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