BASIC STATISTICS FOR THE BEHAVIORAL SCIENCES 4E

by Heiman, Gary

• ISBN13: 9780618220175
• ISBN10: 0618220178
• Edition: 4th
• Format: Hardcover
• Copyright: 2002-07-30
• Publisher: Wadsworth Publishing

Summary

Each statistical procedure in this text is presented in a conceptual, intuitive manner to illustrate how it fills a need in the process. Students anxious about math will benefit from a scaled back emphasis on the discipline, plain language, and a step-by-step approach that reintroduces, reviews, and reinforces procedures. In addition, references to psychology have been reduced to make the text more inclusive of all behavioral sciences. The text has been revised to streamline the narrative without reducing content, make presentations more concise, and add more explanatory techniques. Nearly all examples include specific variables and questions rather than generic data, and most are taken from everyday life so that students gain an intuitive feel for the meaning of scores and develop an ability to think in statistical terms.

Table of Contents

Preface	xxi
part 1 INTRODUCTION	1	(38)
Approaching Statistics	2	(13)
Getting Started	2	(1)
Some Commonly Asked Questions about Statistics	2	(4)
What Are Statistics?	2	(1)
What Do Researchers Do with Statistics?	3	(1)
But I'm Not Interested in Research; I Just Want to Help People!	3	(1)
But I Don't Know Anything about Research!	3	(1)
What if I'm Not Very Good at Statistics?	3	(1)
But Statistics Aren't Written in English!	4	(1)
What if I'm Not Very Good at Math?	4	(1)
So All I Have to Do Is Learn How to Compute the Answers?	4	(1)
All Right, So How Do I Learn Statistics?	4	(1)
What's with This Book?	5	(1)
Review of Mathematics Used in Statistics	6	(5)
Basic Statistical Notation	6	(1)
Identifying Mathematical Operations	6	(1)
Determining the Order of Mathematical Operations	6	(1)
Working with Formulas	7	(1)
Rounding	8	(1)
Transformations	8	(1)
Proportions	8	(1)
Percents	9	(1)
Creating Graphs	9	(2)
Putting It All Together	11	(1)
Chapter Summary	11	(1)
Key Terms	12	(1)
Review Questions	12	(1)
Application Questions	13	(2)
Statistics and the Research Process	15	(24)
Getting Started	15	(1)
The Logic of Scientific Research	16	(6)
Obtaining Data by Measuring Variables	16	(1)
Examining the Relationships Between Variables	17	(1)
Strength of a Relationship	18	(1)
No Relationship	19	(1)
Graphing Relationships	20	(1)
Using Relationships to Discover Laws	21	(1)
Samples and Populations	22	(2)
Drawing Inferences about a Population	22	(1)
Representativeness of a Sample	23	(1)
Random Sampling	23	(1)
Unrepresentative Samples	24	(1)
Using Statistical Procedures to Analyze Data	24	(3)
Descriptive Statistics	25	(1)
Inferential Statistics	26	(1)
Statistics and Parameters	26	(1)
The Characteristics of a Study	27	(4)
Experiments	27	(1)
The Independent Variable	27	(1)
Conditions of the Independent Variable	28	(1)
The Dependent Variable	28	(1)
Drawing Conclusions from Experiments	29	(1)
The Problem of Causality	29	(1)
Correlational Studies	30	(1)
Again, the Problem of Causality	31	(1)
The Characteristics of the Scores	31	(3)
The Four Types of Measurement Scales	31	(2)
Discrete and Continuous Scales	33	(1)
Putting It All Together	34	(1)
Chapter Summary	34	(1)
Key Terms	35	(1)
Review Questions	36	(1)
Application Questions	36	(3)
part 2 DESCRIPTIVE STATISTICS: DESCRIBING SAMPLES AND POPULATIONS	39	(118)
Summarizing Scores Using Frequency Distributions and Percentiles	40	(27)
Getting Started	40	(1)
More Statistical Notation	41	(1)
Why Is It Important to Know about Frequency Distributions?	41	(1)
Creating Simple Frequency Distributions	42	(4)
Presenting Simple Frequency in a Table	42	(1)
Graphing a Simple Frequency Distribution	43	(1)
Bar Graphs	43	(1)
Histograms	44	(1)
Frequency Polygons	44	(2)
Types of Simple Frequency Distributions	46	(6)
The Normal Distribution	46	(2)
Overlapping Distributions	48	(1)
Variations in the Normal Distribution	49	(1)
Other Common Frequency Polygons	50	(1)
Skewed Distributions	50	(1)
Bimodal and Rectangular Distributions	51	(1)
On the Importance of Frequency	51	(1)
Creating Relative Frequency Distributions	52	(5)
Presenting Relative Frequency in a Table	53	(1)
Graphing a Relative Frequency Distribution	54	(1)
Finding Relative Frequency Using the Normal Curve	54	(3)
Creating Cumulative Frequency Distributions	57	(1)
Presenting Cumulative Frequency in a Table	57	(1)
Graphing a Cumulative Frequency Distribution	58	(1)
Computing Percentile	58	(3)
Finding Percentile Using the Area Under the Normal Curve	60	(1)
A Word about Grouped Frequency Distributions	61	(1)
Putting It All Together	62	(1)
Chapter Summary	62	(1)
Key Terms	63	(1)
Review Questions	63	(1)
Application Questions	64	(2)
Summary of Formulas	66	(1)
Summarizing Scores Using Measures of Central Tendency: The Mean, Median, and Mode	67	(28)
Getting Started	67	(1)
More Statistical Notation	68	(1)
Why Is It Important to Know about Central Tendency?	68	(1)
What Is Central Tendency?	68	(2)
The Mode	70	(2)
Uses of the Mode	71	(1)
The Median	72	(2)
Uses of the Median	74	(1)
The Mean	74	(4)
Uses of the Mean	75	(3)
Transformations and the Mean	78	(1)
Deviations Around the Mean	78	(2)
Using the Mean to Interpret Data	80	(4)
Using the Mean to Predict Scores	80	(2)
Using the Mean to Describe a Score's Location	82	(1)
Using the Sample Mean to Describe the Population Mean	83	(1)
Summarizing the Results of an Experiment	84	(6)
Summarizing a Relationship Using Measures of Central Tendency	85	(1)
Graphing the Results of an Experiment	86	(1)
Line Graphs	87	(1)
Bar Graphs	88	(1)
Inferring the Relationship in the Population	89	(1)
Putting It All Together	90	(1)
Chapter Summary	91	(1)
Key Terms	92	(1)
Review Questions	92	(1)
Application Questions	92	(2)
Summary of Formulas	94	(1)
Summarizing Scores with Measures of Variability: Range, Variance, and Standard Deviation	95	(32)
Getting Started	95	(1)
More Statistical Notation	96	(1)
Why Is It Important to Know about Measures of Variability?	96	(3)
The Range	99	(2)
The Semi-Interquartile Range	100	(1)
Understanding the Variance and Standard Deviation	101	(1)
Describing the Sample Variance	102	(3)
Computational Formula for the Sample Variance	103	(1)
Interpreting Variance	104	(1)
Describing the Sample Standard Deviation	105	(5)
Computational Formula for the Sample Standard Deviation	105	(1)
Interpreting the Standard Deviation	106	(1)
Applying the Standard Deviation to a Normal Distribution	107	(1)
Describing Different Normal Curves Using the Standard Deviation	108	(2)
Mathematical Constants and the Standard Deviation	110	(1)
The Population Variance and the Population Standard Deviation	110	(5)
Estimating the Population Variance and Population Standard Deviation	111	(2)
Computational Formula for the Estimated Population Variance and Standard Deviation	113	(1)
Interpreting the Estimated Population Variance and Standard Deviation	114	(1)
Variance Is the Error in Predictions	115	(2)
Summarizing Research Using Measures of Variability	117	(2)
Understanding the Proportion of Variance Accounted For	119	(2)
Putting It All Together	121	(1)
Chapter Summary	122	(1)
Key Terms	123	(1)
Review Questions	123	(1)
Application Questions	124	(2)
Summary of Formulas	126	(1)
Describing Data with z-Scores and the Normal Curve Model	127	(30)
Getting Started	127	(1)
More Statistical Notation	128	(1)
Why Is It Important to Know about z-Scores?	128	(1)
Understanding z-Scores	128	(5)
Describing a Score's Relative Location as a z-Score	130	(1)
Computing z-Scores	131	(1)
Computing a Raw Score When z Is Known	132	(1)
How Variability Influences z-Scores	133	(1)
Interpreting z-Scores: The z-Distribution	133	(2)
Characteristics of the z-Distribution	135	(1)
Using the z-Distribution to Compare Different Variables	135	(2)
Plotting Different z-Distributions on the Same Graph	136	(1)
Using the z-Distribution to Determine the Relative Frequency of Raw Scores	137	(8)
The Standard Normal Curve	138	(2)
Applying the Standard Normal Curve Model	140	(1)
Finding Percentile Rank for a Raw Score	141	(1)
Finding a Raw Score at a Given Percentile	142	(1)
Using the z-Table	143	(2)
Using z-Scores to Define Psychological Attributes	145	(1)
Using z-Scores to Describe Sample Means	145	(7)
The Sampling Distribution of Means	146	(2)
The Standard Error of the Mean	148	(2)
Calculating a z-Score for a Sample Mean	150	(1)
Using the Sampling Distribution to Determine Relative Frequency of Sample Means	150	(2)
Putting It All Together	152	(1)
Chapter Summary	152	(1)
Key Terms	153	(1)
Review Questions	154	(1)
Application Questions	154	(2)
Summary of Formulas	156	(1)
part 3 DESCRIBING RELATIONSHIPS	157	(58)
Describing Relationships Using Correlations	158	(30)
Getting Started	158	(1)
More Statistical Notation	159	(1)
Why Is It Important to Know about Correlation Coefficients?	159	(1)
Understanding Correlational Research	160	(4)
Drawing Conclusions from Correlational Research	160	(1)
Distinguishing Characteristics of Correlational Analysis	161	(1)
Plotting Correlational Data: The Scatterplot	162	(1)
What the Correlation Coefficient Indicates	163	(1)
Types of Relationships	164	(2)
Linear Relationships	164	(1)
Nonlinear Relationships	165	(1)
How the Correlation Coefficient Describes the Type of Relationship	166	(1)
Strength of the Relationship	166	(5)
Perfect Association	167	(1)
Intermediate Association	168	(2)
Zero Association	170	(1)
Correlation Coefficients in Real Research	171	(1)
Computing the Correlation Coefficient	171	(8)
The Pearson Correlation Coefficient	171	(3)
The Spearman Rank-Order Correlation Coefficient	174	(2)
Tied Ranks	176	(1)
The Point-Biserial Correlation Coefficient	177	(2)
The Restriction of Range Problem	179	(1)
Correlations in the Population	180	(1)
Putting It All Together	181	(1)
Chapter Summary	181	(1)
Key Terms	182	(1)
Review Questions	183	(1)
Application Questions	183	(3)
Summary of Formulas	186	(2)
Using Linear Regression to Predict Scores	188	(27)
Getting Started	188	(1)
More Statistical Notation	189	(1)
Why Is It Important to Know about Linear Regression?	189	(1)
Understanding Linear Regression	189	(2)
Summarizing the Scatterplot Using the Regression Line	190	(1)
Predicting Scores Using the Regression Line	191	(1)
The Linear Regression Equation	191	(6)
Computing the Slope	194	(1)
Computing the Y Intercept	195	(1)
Describing the Linear Regression Equation	195	(1)
Plotting the Regression Line	196	(1)
Using the Regression Equation to Predict Y Scores	196	(1)
Error When the Linear Regression Equation Is Used to Predict Scores	197	(6)
Computing the Variance of the Y Scores Around Y'	197	(2)
Computing the Standard Error of the Estimate	199	(2)
The Strength of a Relationship and Prediction Error	201	(1)
Assumptions of Linear-Regression	202	(1)
The Proportion of Variance Accounted For	203	(6)
Using r to Compute the Proportion of Variance Accounted For	206	(1)
Using the Variance Accounted For	207	(2)
A Word about Multiple Correlation and Regression	209	(1)
Putting It All Together	209	(1)
Chapter Summary	209	(1)
Key Terms	210	(1)
Review Questions	211	(1)
Application Questions	211	(2)
Summary of Formulas	213	(2)
part 4 INFERENTIAL STATISTICS	215	(218)
Probability: Making Decisions about Chance Events	216	(23)
Getting Started	216	(1)
More Statistical Notation	217	(1)
Why Is It Important to Know about Probability?	217	(1)
The Logic of Probability	217	(2)
Computing Probability	219	(2)
Creating Probability Distributions	219	(1)
Factors Affecting the Probability of an Event	220	(1)
Obtaining Probability from the Standard Normal Curve	221	(3)
Determining the Probability of Individual Scores	221	(2)
Determining the Probability of Sample Means	223	(1)
Making Decisions Based on Probability	224	(10)
Deciding Whether a Sample Represents a Population	225	(1)
Making Decisions about a Sample Mean	226	(2)
Setting Up the Sampling Distribution	228	(1)
Identifying the Critical Value	229	(1)
Deciding if the Sample Represents the Population	230	(2)
Other Ways to Set Up the Sampling Distribution	232	(1)
On Being Wrong When We Decide about a Sample	233	(1)
Putting It All Together	234	(1)
Chapter Summary	234	(1)
Key Terms	235	(1)
Review Questions	235	(1)
Application Questions	236	(2)
Summary of Formulas	238	(1)
Overview of Statistical Hypothesis Testing: The z-Test	239	(30)
Getting Started	239	(1)
More Statistical Notation	240	(1)
Why Is It Important to Know about the z-Tests?	240	(1)
The Role of Inferential Statistics in Research	240	(2)
Setting Up Inferential Procedures	242	(6)
Creating the Experimental Hypotheses	242	(1)
Designing a One-Sample Experiment	243	(1)
Creating the Statistical Hypotheses	243	(1)
The Alternative Hypothesis	243	(1)
The Null Hypothesis	244	(2)
The Logic of Statistical Hypothesis Testing	246	(2)
Testing a Mean When σx Is Known: The z-Test	248	(2)
Setting Up the Sampling Distribution for a Two-Tailed Test	248	(2)
Computing z	250	(1)
Interpreting z	250	(5)
Reporting Significant Results	251	(1)
Interpreting Significant Results	252	(1)
Retaining H0	253	(1)
Interpreting Nonsignificant Results	254	(1)
Summary of Statistical Hypothesis Testing	255	(1)
The One-Tailed Test	255	(3)
The One-Tailed Test for Increasing Scores	255	(2)
The One-Tailed Test for Decreasing Scores	257	(1)
Choosing One-Tailed versus Two-Tailed Tests	257	(1)
Errors in Statistical Decision Making	258	(6)
Type I Errors: Rejecting H0 When H0 Is True	258	(3)
Type II Errors: Retaining H0 When H0 Is False	261	(1)
Comparing Type I and Type II Errors	261	(1)
Power	262	(2)
Putting It All Together	264	(1)
Chapter Summary	264	(1)
Key Terms	265	(1)
Review Questions	266	(1)
Application Questions	266	(2)
Summary of Formulas	268	(1)
Hypothesis Testing for a Single Mean or a Correlation Coefficient: The t-Test	269	(31)
Getting Started	269	(1)
More Statistical Notation	270	(1)
Why Is It Important to Know about t-Tests?	270	(1)
Setting Up the t-Test	271	(1)
Calculating the One-Sample t-Test	272	(2)
Computational Formulas for the One-Sample t-Test	273	(1)
The t-Distribution	274	(3)
The Degrees of Freedom	276	(1)
Using the t-Tables	277	(1)
Interpreting the t-Test	277	(3)
One-Tailed Hypotheses in the One-Sample t-Test	278	(1)
Some Help When Using the t-Tables	279	(1)
Estimating the Population μ by Computing a Confidence Interval	280	(3)
Computing the Confidence Interval for a Single μ	281	(1)
Confidence Intervals and the Size of Alpha	282	(1)
Significance Tests for Correlation Coefficients	283	(3)
Statistical Hypotheses for the Correlation Coefficient	284	(2)
The Significance Test for the Pearson r	286	(6)
The Sampling Distribution of r	286	(1)
Interpreting a Significant r	287	(2)
One-Tailed Tests of r	289	(1)
Testing the Spearman rs and the Point-Biserial rpb	289	(1)
Testing rs	290	(1)
Testing rpb	291	(1)
Summary of Testing a Correlation Coefficient	292	(1)
Maximizing the Power of a Statistical Test	292	(2)
Maximizing the Power of the t-Test	293	(1)
Maximizing the Power of a Correlation Coefficient	294	(1)
Putting It All Together	294	(1)
Chapter Summary	294	(1)
Key Terms	295	(1)
Review Questions	296	(1)
Application Questions	296	(2)
Summary of Formulas	298	(2)
Hypothesis Testing for Two-Sample Means: The t-Test	300	(33)
Getting Started	300	(1)
More Statistical Notation	301	(1)
Why Is It Important to Know about the Two-Sample t-Test?	301	(1)
Understanding the Two-Sample Experiment	301	(2)
The Independent Samples t-Test	303	(9)
Assumptions of the Independent Samples t-Test	304	(1)
Statistical Hypotheses for the Independent Samples t-Test	304	(1)
The Sampling Distribution for the Independent Samples t-Test	305	(1)
Computing the Independent Samples t-Test	306	(1)
Estimating the Population Variance	306	(1)
Computing the Standard Error of the Difference	307	(1)
Computing t for Two Independent Samples	308	(1)
Computational Formulas for the Independent Samples t-Test	309	(1)
Interpreting tobt in the Independent Samples t-Test	309	(2)
Confidence Interval for the Difference Between Two μs	311	(1)
Additional Aspects of the Independent Samples t-Test	312	(1)
Performing One-Tailed Tests on Independent Samples	312	(1)
Testing Hypotheses about Nonzero Differences	312	(1)
Power and the Independent Samples t-Test	313	(1)
The Related Samples t-Test	313	(8)
Assumptions of the Related Samples t-Test	314	(1)
The Logic of Hypotheses Testing in the Related Samples t-Test	315	(1)
Statistical Hypotheses for the Related Samples t-Test	316	(1)
Computing the Related Samples t-Test	317	(1)
Computational Formula for the Related Samples t-Test	318	(1)
Interpreting the Related Samples t-Test	318	(2)
Computing the Confidence Interval for μD	320	(1)
Testing Other Hypotheses with the Related Samples t-Test	320	(1)
Power and the Related Samples t-Test	321	(1)
Describing the Relationship in a Two-Sample Experiment	321	(4)
Graphing the Results of a Two-Sample Experiment	322	(1)
Describing the Strength of the Relationship in a Two-Sample Experiment Using rpb	323	(1)
Describing Effect Size in a Two-Sample Experiment	324	(1)
Putting It All Together	325	(1)
Chapter Summary	326	(1)
Key Terms	327	(1)
Review Questions	327	(1)
Application Questions	328	(3)
Summary of Formulas	331	(2)
Hypothesis Testing for Two or More Means: The One-Way Analysis of Variance	333	(31)
Getting Started	333	(1)
More Statistical Notation	334	(1)
Why Is It Important to Know about ANOVA?	334	(1)
An Overview of ANOVA	334	(4)
How ANOVA Controls the Experiment-Wise Error Rate	336	(1)
Assumptions of the One-Way Between-Subjects ANOVA	336	(1)
Statistical Hypotheses in ANOVA	337	(1)
The Order of Operations in ANOVA: The F Statistic and Post Hoc Comparisons	337	(1)
Components of the ANOVA	338	(13)
The Mean Square Within Groups	339	(1)
The Mean Square Between Groups	339	(3)
Comparing the Mean Squares: The Logic of the F-Ratio	342	(1)
The F-Distribution	343	(1)
Degrees of Freedom and the Critical Value	344	(1)
Computing the F-Ratio	345	(1)
Computational Formulas for the One-Way Between-Subjects ANOVA	346	(1)
Computing the Sums of Squares	346	(2)
Computing the Degrees of Freedom	348	(1)
Computing the Mean Squares	348	(1)
Computing the F	349	(1)
Interpreting Fobt in a One-Way ANOVA	350	(1)
Performing Post Hoc Comparisons	351	(2)
Fisher's Protected t-Test	351	(1)
Tukey's HSD Multiple Comparisons Test	352	(1)
Summary of Steps in Performing a One-Way ANOVA	353	(1)
Describing the Relationship in a One-Way ANOVA	354	(2)
The Confidence Interval for Each Population μ	354	(1)
Graphing the Results in ANOVA	355	(1)
Eta Squared: The Proportion of Variance Accounted For	355	(1)
Other Considerations When Using ANOVA	356	(1)
The Within-Subjects ANOVA	356	(1)
Power and ANOVA	357	(1)
Putting It All Together	357	(1)
Chapter Summary	358	(1)
Key Terms	359	(1)
Review Questions	359	(1)
Application Questions	360	(2)
Summary of Formulas	362	(2)
Hypothesis Testing for Means from Two Independent Variables: The Two-Way Analysis of Variance	364	(38)
Getting Started	364	(1)
More Statistical Notation	365	(1)
Why Is It Important to Know about the Two-Way ANOVA?	365	(1)
Understanding the Two-Way Design	366	(2)
Overview of the Two-Way Between-Subjects ANOVA	368	(7)
Assumptions of the Two-Way Between-Subjects ANOVA	368	(1)
Logic of the Two-Way ANOVA	368	(1)
Main Effects	369	(2)
Interaction Effects	371	(2)
Overview of the Computations of the Two-Way ANOVA	373	(2)
Computing the Two-Way ANOVA	375	(8)
Computing the Sums of Squares	376	(3)
Computing the Degrees of Freedom	379	(1)
Computing the Mean Squares	379	(2)
Computing F	381	(1)
Interpreting Each F	382	(1)
Interpreting the Two-Way Experiment	383	(9)
Graphing Main Effects	383	(1)
Graphing the Interaction Effect	384	(2)
Performing Post Hoc Comparisons	386	(1)
Performing Tukey's HSD for Main Effects	387	(1)
Performing Tukey's HSD for the Interaction	388	(2)
Interpreting the Overall Results of the Experiment	390	(1)
Describing the Effect Size: Eta Squared	391	(1)
Confidence Intervals for a Single μ	392	(1)
Summary of the Steps in Performing a Two-Way ANOVA	392	(1)
Within-Subjects and Mixed Designs	393	(1)
Putting It All Together	393	(1)
Chapter Summary	394	(1)
Key Terms	395	(1)
Review Questions	395	(1)
Application Questions	395	(3)
Summary of Formulas	398	(4)
Chi Square and Other Nonparametric Procedures	402	(31)
Getting Started	402	(1)
Why Is It Important to Know about Nonparametric Procedures?	403	(1)
Chi Square Procedures	403	(1)
One-Way Chi Square: The Goodness of Fit Test	404	(6)
Creating the Statistical Hypotheses for the One-Way Chi Square	405	(1)
Computing the Expected Frequencies for the One-Way Chi Square	406	(1)
Assumptions of the One-Way Chi Square	406	(1)
Computing x2	407	(1)
Interpreting x2	408	(1)
Other Uses of the Goodness of Fit Test	409	(1)
Additional Procedures in a One-Way Chi Square	410	(1)
The Two-Way Chi Square: The Test of Independence	410	(7)
Logic of the Two-Way Chi Square	411	(2)
Computing the Expected Frequencies in the Two-Way Chi Square	413	(1)
Computing the Two-Way Chi Square	414	(1)
Additional Procedures in the Two-Way Chi Square	415	(1)
Graphing the Two-Way Chi Square	415	(1)
Describing the Relationship in a Two-Way Chi Square	415	(2)
Nonparametric Procedures for Ranked Data	417	(11)
The Logic of Nonparametric Procedures for Ranked Data	417	(1)
Choosing a Nonparametric Procedure	418	(1)
Tests for Two Independent Samples: The Mann-Whitney U Test and the Rank Sums Test	419	(1)
The Mann-Whitney U Test	419	(2)
The Rank Sums Test	421	(1)
The Wilcoxon T Test for Two Related Samples	422	(1)
The Kruskal-Wallis H Test	423	(3)
The Friedman x2 Test	426	(2)
Putting It All Together	428	(1)
Chapter Summary	428	(1)
Key Terms	429	(1)
Review Questions	429	(1)
Application Questions	430	(3)
Summary of Formulas	433