Introduction | |

Descriptive Statistics | |

Inferential Statistics | |

Our Concern: Applied Statistics | |

Variables and Constants | |

Scales of Measurement | |

Scales of Measurement and Problems of Statistical Treatment | |

Do Statistics Lie? | |

Point of Controversy: Are Statistical Procedures Necessary? | |

Some Tips on Studying Statistics | |

Statistics and Computers | |

Summary | |

Frequency Distributions, Percentiles, and Percentile Ranks | |

Organizing Qualitative Data | |

Grouped Scores | |

How to Construct a Grouped Frequency Distribution | |

Apparent versus Real Limits | |

The Relative Frequency Distribution | |

The Cumulative Frequency Distribution | |

Percentiles and Percentile Ranks | |

Computing Percentiles from Grouped Data | |

Computation of Percentile Rank | |

Summary | |

Graphic Representation of Frequency Distributions | |

Basic Procedures | |

The Histogram | |

The Frequency Polygon | |

Choosing between a Histogram and a Polygon | |

The Bar Diagram and the Pie Chart | |

The Cumulative Percentage Curve | |

Factors Affecting the Shape of Graphs | |

Shape of Frequency Distributions | |

Summary | |

Central Tendency | |

The Mode | |

The Median | |

The Mean | |

Properties of the Mode | |

Properties of the Mean | |

Point of Controversy: Is It Permissible to Calculate the Mean for Tests in the Behavioral Sciences? | |

Properties of the Median | |

Measures of Central Tendency in Symmetrical and Asymmetrical Distributions | |

The Effects of Score Transformations | |

Summary | |

Variability and Standard (z) Scores | |

The Range and Semi-Interquartile Range | |

Deviation Scores | |

Deviational Measures: The Variance | |

Deviational Measures: The Standard Deviation | |

Calculation of the Variance and Standard Deviation: Raw-Score Method | |

Calculation of the Standard Deviation with IBM SPSS (formerly SPSS) | |

Point of Controversy: Calculating the Sample Variance: Should We Divide by n or (n - 1)? | |

Properties of the Range and Semi-Interquartile Range | |

Properties of the Standard Deviation | |

How Big Is a Standard Deviation? | |

Score Transformations and Measures of Variability | |

Standard Scores (z Scores) | |

A Comparison of z Scores and Percentile Ranks | |

Summary | |

Standard Scores and the Normal Curve | |

Historical Aspects of the Normal Curve | |

The Nature of the Normal Curve | |

Standard Scores and the Normal Curve | |

The Standard Normal Curve: Finding Areas When the Score Is Known | |

The Standard Normal Curve: Finding Scores When the Area Is Known | |

The Normal Curve as a Model for Real Variables | |

The Normal Curve as a Model for Sampling Distributions | |

Summary | |

Point of Controversy: How Normal Is the Normal Curve? | |

Correlation | |

Some History | |

Graphing Bivariate Distributions: The Scatter Diagram | |

Correlation: A Matter of Direction | |

Correlation: A Matter of Degree | |

Understanding the Meaning of Degree of Correlation | |

Formulas for Pearson's Coefficient of Correlation | |

Calculating r from Raw Scores | |

Calculating r with IBM SPSS | |

Spearman's Rank-Order Correlation Coefficient | |

Correlation Does Not Prove Causation | |

The Effects of Score Transformations | |

Cautions Concerning Correlation Coefficients | |

Summary | |

Prediction | |

The Problem of Prediction | |

The Criterion of Best Fit | |

Point of Controversy: Least-Squares Regression versus the Resistant Line | |

The Regression Equation: Standard-Score Form | |

The Regression Equation: Raw-Score Form | |

Error of Prediction: The Standard Error of Estimate | |

An Alternative (and Preferred) Formula for S_{YX} | |

Calculating the "Raw-Score" Regression Equation and Standard Error of Estimate with IBM SPSS | |

Error in Estimating Y from X | |

Cautions Concerning Estimation of Predictive Error | |

Prediction Does Not Prove Causation | |

Summary | |

Interpretive Aspects of Correlation and Regression | |

Factors Influencing r: Degree of Variability in Each Variable | |

Interpretation of r: The Regression Equation I | |

Interpretation of r: The Regression Equation II | |

Interpretation of r: Proportion of Variation in Y Not Associated with | |

Variation in X | |

Interpretation of r: Proportion of Variation in Y Associated with | |

Variation in X | |

Interpretation of r: Proportion of Correct Placements | |

Summary | |

Probability | |

Defining Probability | |

A Mathematical Model of Probability | |

Two Theorems in Probability | |

An Example of a Probability Distribution: The Binomial | |

Applying the Binomial | |

Probability and Odds | |

Are Amazing Coincidences Really That Amazing? | |

Summary | |

Random Sampling and Sampling Distributions | |

Random Sampling | |

Using a Table of Random Numbers | |

The Random Sampling Distribution of the Mean: An Introduction | |

Characteristics of the Random Sampling Distribution of the Mean | |

Using the Sampling Distribution of X to Determine the Probability for Different Ranges of Values of X | |

Random Sampling Without Replacement | |

Summary | |

Introduction to Statistical Inference: Testing Hypotheses about Single Means (z and t) | |

Testing a Hypothesis about a Single Mean | |

The Null and Alternative Hypotheses | |

When Do We Retain and When Do We Reject the Null Hypothesis? | |

Review of the Procedure for Hypothesis Testing | |

Dr. Brown's Problem: Conclusion | |

The Statistical Decision | |

Choice of H_{A}: One-Tailed and Two-Tailed Tests | |

Review of Assumptions in Testing Hypotheses about a Single Mean | |

Point of Controversy: The Single-Subject Research Design | |

Estimating the Standard Error of the Mean When ¿ Is Unknown | |

The t Distribution | |

Characteristics of Student's Distribution of t | |

Degrees of Freedom and Student's Distribution of t | |

An Example: Has the Violent Content of Television Programs Increased? | |

Calculating t from Raw Scores | |

Calculating t with IBM SPSS | |

Levels of Significance versus p-Values | |

Summary | |

Interpreting the Results of Hypothesis Testing: Effect Size, Type I and Type II Errors, and Power | |

A Statistically Significant Difference versus a Practically Important Difference | |

Point of Controversy: The Failure to Publish "Nonsignificant" Results | |

Effect Size | |

Errors in Hypothesis Testing | |

The Power of a Test | |

Factors Affecting Power: Difference between the True Population Mean and the Hypothesized Mean (Size of Effect) | |

Factors Affecting Power: Sample Size | |

Factors Affecting Power:Variability of the Measure | |

Factors Affecting Power: Level of Significance (¿) | |

Factors Affecting Power: One-Tailed versus Two-Tailed Tests | |

Calculating the Power of a Test | |

Point of Controversy: Meta-Analysis | |

Estimating Power and Sample Size for Tests of Hypotheses about Means | |

Problems in Selecting a Random Sample and in Drawing Conclusions | |

Summary | |

Testing Hypotheses about the Difference between Two Independent Groups | |

The Null and Alternative Hypotheses | |

The Random Sampling Distribution of the Difference between Two Sample Means | |

Properties of the Sampling Distribution of the Difference between Means | |

Determining a Formula for t | |

Testing the Hypothesis of No Difference between Two Independent Means: The Dyslexic Children Experiment | |

Use of a One-Tailed Test | |

Calculation of t with IBM SPSS | |

Sample Size in Inference about Two Means | |

Effect Size | |

Estimating Power and Sample Size for Tests of Hypotheses about the Difference between Two Independent Means | |

Assumptions Associated with Inference about the Difference between Two Independent Means | |

The Random-Sampling Model versus the Random-Assignment Model | |

Random Sampling and Random Assignment as Experimental Controls | |

Summary | |

Testing for a Difference between Two Dependent (Correlated) Groups | |

Determining a Formula for t | |

Degrees of Freedom for Tests of No Difference between Dependent Means | |

An Alternative Approach to the Problem of Two Dependent Means | |

Testing a Hypothesis about Two Dependent Means: Does Text Messaging Impair Driving? | |

Calculating t with IBM SPSS | |

Effect Size | |

Power | |

Assumptions When Testing a Hypothesis about the Difference between Two Dependent Means | |

Problems with Using the Dependent-Samples Design | |

Summary | |

Inference about Correlation Coefficients | |

The Random Sampling Distribution of r | |

Testing the Hypothesis that r = 0 | |

Fisher's z' Transformation | |

Strength of Relationship | |

A Note about Assumptions | |

Inference When Using Spearman's r_{S} | |

Summary | |

An Alternative to Hypothesis Testing: Confidence Intervals | |

Examples of Estimation | |

Confidence Intervals for ¿_{X} | |

The Relation between Confidence Intervals and Hypothesis Testing | |

The Advantages of Confidence Intervals | |

Random Sampling and Generalizing Results | |

Evaluating a Confidence Interval | |

Point of Controversy: Objectivity and Subjectivity in Inferential Statistics: Bayesian Statistics | |

Confidence Intervals for ¿_{X} - ¿_{Y} | |

Sample Size Required for Confidence Intervals of ¿_{X} and ¿_{X} - ¿_{Y} | |

Confidence Intervals for ¿ | |

Where are We in Statistical Reform? | |

Summary | |

Testing for Differences among Three or More Groups: One-Way Analysis of Variance (and Some Alternatives) | |

The Null Hypothesis | |

The Basis of One-Way Analysis of Variance:Variation within and between Groups | |

Partition of the Sums of Squares | |

Degrees of Freedom | |

Variance Estimates and the F Ratio | |

The Summary Table | |

Example: Does Playing Violent Video Games Desensitize People to Real-Life Aggression? | |

Comparison of t and F | |

Raw-Score Formulas for Analysis of Variance | |

Calculation of ANOVA for Independent Measures with IBM SPSS | |

Assumptions Associated with ANOVA | |

Effect Size | |

ANOVA and Power | |

Post Hoc Comparisons | |

Some Concerns about Post Hoc Comparisons | |

An Alternative to the F Test: Planned Comparisons | |

How to Construct Planned Comparisons | |

Analysis of Variance for Repeated Measures | |

Calculation of ANOVA for Repeated Measures with IBM SPSS | |

Summary | |

Factorial Analysis of Variance: The Two-Factor Design | |

Main Effects | |

Interaction | |

The Importance of Interaction | |

Partition of the Sums of Squares for Two-Way ANOVA | |

Degrees of Freedom | |

Variance Estimates and F Tests | |

Studying the Outcome of Two-Factor Analysis of Variance | |

Effect Size | |

Calculation of Two-Factor ANOVA with IBM SPSS | |

Planned Comparisons | |

Assumptions of the Two-Factor Design and the Problem of Unequal Numbers of Scores | |

Mixed Two-Factor Within-Subjects Design | |

Calculation of the Mixed Two-Factor Within-Subjects Design with IBM SPSS | |

Summary | |

Chi-Square and Inference about Frequencies | |

The Chi-Squre Test for Goodness of Fit | |

Chi-Square (¿^{2}) as a Measure of the Difference between Observed and Expected Frequencies | |

The Logic of the Chi-Square Test | |

Interpretation of the Outcome of a Chi-Square Test | |

Different Hypothesized Proportions in the Test for Goodness of Fit | |

Effect Size for Goodness-of-Fit Problems | |

Assumptions in the Use of the Theoretical Distribution of Chi-Square | |

Chi-Square as a Test for Independence between Two Variables | |

Finding Expected Frequencies in a Contingency Table | |

Calculation of ¿^{2} and Determination of Significance in a Contingency Table | |

Measures of Effect Size (Strength of Association) for Tests of Independence | |

Point of Controversy: Yates' Correction for Continuity | |

Power and the Chi-Square Test of Independence | |

Summary | |

Some (Almost) Assumption-Free Tests | |

The Null Hypothesis in Assumption-Freer Tests | |

Randomization Tests | |

Rank-Order Tests | |

The Bootstrap Method of Statistical Inference | |

An Assumption-Freer Alternative to the t Test of a Difference between Two Independent Groups: The Mann-Whitney U Test | |

Point of Controversy: A Comparison of the t Test and Mann-Whitney U Test with Real-World Distributions | |

An Assumption-Freer Alternative to the t Test of a Difference between Two Dependent Groups: The Sign Test | |

Another Assumption-Freer Alternative to the t Test of a Difference between Two Dependent Groups: The Wilcoxon Signed-Ranks Test | |

An Assumption-Freer Alternative to One-Way ANOVA for Independent Groups: The Kruskal-Wallis Test | |

An Assumption-Freer Alternative to ANOVA for Repeated Measures: | |

Friedman's Rank Test for Correlated Samples | |

Summary | |

Review of Basic Mathematics | |

List of Symbols | |

Answers to Problems | |

Statistical Tables | |

Areas under the Normal Curve Corresponding to Given Values of z | |

The Binomial Distribution | |

Random Numbers | |

Student's t Distribution | |

The F Distribution | |

The Studentized Range Statistic | |

Values of the Correlation Coefficient Required for Different Levels of Significance When H_{0}: r= 0 | |

Values of Fisher's z' for Values of r | |

The ¿^{2} Distribution | |

Critical One-Tail Values of SR_{X} for the Mann-Whitney U Test | |

Critical Values for the Smaller of R_{+} or R_{-} for the Wilcoxon Signed-Ranks Test | |

Epilogue: The Realm of Statistics | |

ReferenceS | |

Index | |

Table of Contents provided by Publisher. All Rights Reserved. |