Statistical Reasoning in the Behavioral Sciences, 6th Edition

by Bruce M. King (Clemson University ); Patrick J. Rosopa (Clemson University ); Edward W. Minium (San Jose State Univ.)

• ISBN13: 9780470643822
• ISBN10: 047064382X
• Edition: 6th
• Format: Hardcover
• Copyright: 2010-08-01
• Publisher: Wiley
• More Book Details

Summary

Statistical Reasoning continues to provide a streamlined and easy-to-understand text on statistics of the behavioral sciences for business professionals. The sixth edition includes new information about the use of computers in statistics and offers an SPSS printout page in selected chapters. The example problems have been updated to reflect more current topics. The latest research and new photos have been integrated throughout the book to make the material more accessible. With these changes, business professionals will develop an understanding of statistical logic and procedures, the properties of statistical devices, and the importance of the assumptions underlying statistical tools.

Table of Contents

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 H₀: 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

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