Essential Statistics

by Wilson, Janie H., Ph.D.

• ISBN13: 9780130994226
• ISBN10: 0130994227
• Edition: 1st
• Format: Paperback
• Copyright: 2004-07-15
• Publisher: Pearson

Summary

This reader-friendly book covers all information essential to statistics in the social sciences, from z-tests to the two-way ANOVA. It presents material through a conversational style approach, focusing on reducing anxiety about statistics, making statistics relevant and interesting, and incorporating SPSS to show users how to analyze data efficiently. To encourage readers¿ enthusiasm of statistics and hold their interest, this book includes only those analyses that are necessary to build skills or will likely be used by them in the future.Part I, the Introduction, defines many research terms, and introduces math. The second part, DESCRIPTIVE STATISTICS, introduces classifications of variables, simple frequency tables and graphs, shapes of distributions, measures of central tendency and variability, descriptive z-scores , and simple frequency distributions. Part III, INFERENTIAL STATISTICS: EXPERIMENTS AND QUASI-EXPERIMENTS covers probability, hypothesis testing, t-tests, and ANOVAs by hand and using SPSS. The fourth section, INFERENTIAL STATISTICS: CORRELATIONAL RESEARCH, covers correlation, linear regression, and chi squared. The fifth section offers APPENDICES to cover additional designs: the one-way repeated-measures ANOVA, as well as multiple linear regression. SPSS layout, data analysis, and output for these designs are also covered.For statisticians in the social sciences.

Author Biography

Janie Wilson began her adventure in teaching during graduate school and continued in a full-time teaching position at Columbia College before receiving her Ph.D. in Experimental Psychology from the University of South Carolina in 1994. Since that time, she has been teaching and conducting research at Georgia Southern University. Her teaching includes courses in statistics, research methods, large sections of introductory psychology, and physiological psychology. Teaching and research merged when she was awarded a National Science Foundation grant as principal investigator for a physiological teaching laboratory, and a recent grant from the National Institute of Mental Health continues to fund her research program. She works with both undergraduates and graduate students on research projects involving social buffering of stress responses in rats and human adults and children. Dr. Wilson also conducts research on student evaluations of instructor immediacy and their ability to predict students' attitudes, motivation, and grades. She was honored with the College of Liberal Arts and Social Sciences Award for Excellence in 1997, the Award of Distinction in Teaching in 2003, and the Georgia Southern University Award for Excellence in Contributions to Instruction in 2004.

Table of Contents

Preface	xii
About the Author	xx
PART I INTRODUCTION
Chapter 1 Welcome to Statistics	1	(10)
Building Competence	1	(1)
Rationale for Learning Statistics	1	(1)
Math	2	(1)
Proportion and Percent	2	(1)
Rounding	3	(1)
Symbols	3	(1)
APA Style	4	(1)
Conducting Research	4	(3)
Experiments	5	(1)
Correlations	6	(1)
The Usefulness of Correlations	6	(1)
How to Pick a Sample	7	(1)
Analyzing Data Using SPSS	7	(1)
Preview of Chapter 2	8	(3)
Conceptual Items	8	(1)
Application Items	8	(3)
PART II DESCRIPTIVE STATISTICS
Chapter 2 Variables and Graphing	11	(15)
Measurement Scales	11	(2)
Nominal Variables	11	(1)
Ordinal Variables	11	(1)
Interval Variables	12	(1)
Ratio Variables	12	(1)
Special Case of Rating Scales	12	(1)
Qualitative Versus Quantitative Variables	13	(1)
Discrete Versus Continuous Variables	14	(1)
Picturing Data: Simple Frequency Tables and Graphs	14	(7)
Nominal and Ordinal Data	15	(3)
Discrete Interval and Ratio Data	18	(1)
Continuous Interval and Ratio Data	19	(1)
Grouped Frequency Distributions	20	(1)
Shapes of Distributions	21	(2)
Normal Distributions	21	(1)
Skewed Distributions	22	(1)
Kurtosis	22	(1)
Bimodal and Trimodal Distributions	23	(1)
Preview of Chapter 3	23	(3)
Conceptual Items	24	(1)
Application Items	24	(2)
Chapter 3 Measures of Central Tendency	26	(25)
Summarizing Data	26	(1)
Mode	26	(2)
Median	28	(1)
Mean	29	(2)
Mean Versus Median	30	(1)
Introduction to SPSS	31	(2)
Measures of Central Tendency on SPSS	33	(7)
Summarizing Experiments Using Means	40	(1)
Graphing Means	41	(1)
Graphing Means on SPSS	42	(5)
Preview of Chapter 4	47	(3)
Conceptual Items	47	(1)
Application Items	48	(2)
Computational Formula in This Chapter	50	(1)
Chapter 4 Measures of Variability	51	(19)
Spread of Scores	51	(1)
Range	51	(1)
Sample Variance	52	(3)
Sample Standard Deviation	55	(1)
Estimated Population Standard Deviation	56	(1)
Estimated Population Variance	57	(1)
Measures of Variability on SPSS	58	(3)
Graphing Sample Standard Deviation	61	(2)
Graphs of Standard Deviation on SPSS	63	(3)
Preview of Chapter 5	66	(3)
Conceptual Items	66	(1)
Application Items	67	(2)
Computational Formulas in This Chapter	69	(1)
Chapter 5 Descriptive z-Scores	70	(12)
Standardized Scores	70	(1)
Comparing Values From Different Samples	70	(2)
Standardized Distribution	72	(1)
Proportion and Percent	73	(5)
Evaluations Based on Scores	75	(1)
Comparing Two Values and Probability	76	(1)
Percentile	77	(1)
Logical Limits	78	(1)
Preview of Chapter 6	79	(2)
Conceptual Items	79	(1)
Application Items	79	(2)
Computational Formula in This Chapter	81	(1)
PART III INFERENTIAL STATISTICS: EXPERIMENTS
Chapter 6 Inferential z-Scores and Probability	82	(16)
Probability	82	(2)
Sampling Distribution of Means	84	(2)
Creating a Sampling Distribution of Means for Your Research	86	(1)
Standardizing the Sampling Distribution of Means	86	(2)
Critical Value and Critical Region	87	(1)
Manipulating a Sample	88	(5)
Not Different From Normal	89	(1)
Higher Than Normal	89	(2)
Lower Than Normal	91	(1)
Decreasing the Critical Region	92	(1)
Preview of Chapter 7	93	(3)
Conceptual Items	94	(1)
Application Items	94	(2)
Computational Formulas in This Chapter	96	(1)
References	97	(1)
Chapter 7 Hypothesis Testing	98	(16)
Formalizing the Inferential z	98	(1)
Lay Out Expectations	98	(2)
Null Hypothesis	98	(1)
Alternative Hypothesis	99	(1)
Two-Tailed z-Test	99	(1)
μ Rather Than Χ	100	(1)
Choose a Statistic	100	(1)
Sketch the Normal Distribution	101	(1)
Collect Data	101	(4)
Calculate a Statistic	101	(1)
Significance	102	(1)
APA Style	102	(1)
Reject Or Fail to Reject the Null Hypothesis	102	(1)
Inferential Wording	102	(1)
Effect Size	103	(1)
Plain English	104	(1)
Confidence Intervals	104	(1)
One-tailed Test in the Positive Direction	105	(2)
One-tailed Test in the Negative Direction	107	(1)
Hypothesis Testing, Truth, and Power	108	(3)
Preview of Chapter 8	111	(2)
Conceptual Items	111	(1)
Application Items	111	(2)
Conceptual Formulas in This Chapter	113	(1)
Chapter 8 Three t-Tests	114	(29)
z-Test Versus t-Test	114	(1)
The Single-Sample t-Test	114	(4)
Hypothesis Testing Using the Single-sample t-Test	116	(2)
The Related-samples t-Test	118	(8)
The Sampling Distribution of Mean Differences	119	(1)
Hypothesis Testing Using the Related-samples t-Test	120	(3)
Related-samples t-Test on SPSS	123	(2)
APA-style Results Section	125	(1)
Independent-samples t-Test	126	(4)
The Sampling Distribution of Differences Between Means	126	(1)
Hypothesis Testing Using the Independent-samples t-Test	126	(4)
Independent-samples t-Test on SPSS	130	(5)
APA-style Results Section	135	(1)
Preview of Chapter 9	136	(4)
Conceptual Items	136	(1)
Application Items	136	(4)
Computational Formulas in This Chapter	140	(2)
References	142	(1)
Chapter 9 ANOVA One-Way, Between-Groups	143	(28)
t-Test Versus ANOVA	143	(1)
Logic of ANOVA: Hypothesis Testing	143	(3)
One-way, Between-groups ANOVA: Equal η	146	(8)
Organizing ANOVA Results	150	(1)
APA Style	150	(1)
Effect Size	150	(1)
Post-hoc Testing: Tukey's HSD	151	(1)
Plain English	152	(1)
Confidence Intervals	152	(2)
One-way, Between-groups ANOVA: Unequal η	154	(5)
Summary Table	156	(1)
Effect Size	156	(1)
Post-hoc Testing: Fisher's Protected t-Tests	157	(1)
Plain English	158	(1)
Confidence Intervals	158	(1)
One-way, Between-groups ANOVA on SPSS	159	(6)
APA-style Results Section	165	(1)
Preview of Chapter 10	165	(4)
Conceptual Items	166	(1)
Application Items	167	(2)
Computational Formulas in This Chapter	169	(1)
References	169	(2)
Chapter 10 ANOVA Two-Way, Between-Groups	171	(30)
One-way Versus Two-way ANOVA	171	(1)
Logic of the Two-way, Between-groups ANOVA	171	(3)
Two-way ANOVA Effects	171	(3)
Calculating the Two-way, Between-groups ANOVA	174	(4)
SStot	174	(1)
SSBG and SSwG	175	(1)
Separating SSBG Into Three Portions	176	(1)
F-Tests for Each Effect	177	(1)
Hypothesis Testing and ANOVA Results	178	(3)
First Main Effect	179	(1)
Second Main Effect	180	(1)
Interaction Effect	180	(1)
Post-hoc Testing	181	(3)
Post Hoc for a Significant Main Effect	181	(1)
Post Hoc for a Significant Interaction Effect	182	(2)
Plain English	184	(1)
Applying Results	184	(1)
Two-way, Between-groups ANOVA on SPSS	185	(7)
APA-style Results Section	192	(1)
Graphing the Two-way ANOVA	193	(3)
Preview of Chapter 11	196	(4)
Conceptual Items	197	(1)
Application Items	197	(3)
Computational Formulas in This Chapter	200	(1)
References	200	(1)
PART IV INFERENTIAL STATISTCS: CORRELATIONAL RESEARCH
Chapter 11 Correlational Data	201	(23)
Relationships Between Variables	201	(1)
Logic of Pearson's r	201	(4)
Perfect Linear Relationships	201	(3)
Less-than-perfect Relationships	204	(1)
Pearson's r Calculations	205	(2)
Inferential Correlations: Hypothesis Testing	207	(2)
Correlations on SPSS	209	(5)
Scatterplot on SPSS	210	(2)
Pearson's r on SPSS	212	(2)
APA-style Results Section	214	(1)
Inaccurate Correlations	214	(5)
Artificially Low Correlations	214	(3)
Artificially High Correlations	217	(2)
Preview of Chapter 12	219	(4)
Conceptual Items	220	(1)
Application Items	220	(3)
Computational Formula in This Chapter	223	(1)
References	223	(1)
Chapter 12 Linear Regression	224	(18)
Correlation Before Prediction	224	(1)
Linear Regression Theory	224	(2)
Prediction	225	(1)
Error in Predictions	226	(1)
Calculating the Regression Equation	226	(3)
Graphing the Regression Line	229	(1)
Standard Error of the Estimate	230	(3)
Standard Error Calculations	230	(3)
Prediction on SPSS	233	(3)
Correlation on SPSS	233	(1)
Linear Regression on SPSS	234	(2)
APA-style Results Section	236	(1)
Preview of Chapter 13	236	(5)
Conceptual Items	237	(1)
Application Items	237	(4)
Computational Formulas in This Chapter	241	(1)
References	241	(1)
Chapter 13 Chi-Square Analyses	242	(21)
Simple Frequency Counts	242	(1)
One-Way χ²: Goodness-of-fit Test	242	(4)
Null and Alternative Hypotheses	242	(1)
Chosen Statistic	243	(1)
Sampling Distribution for χ²	243	(1)
χ²obt Above Zero	244	(2)
APA Style	246	(1)
Plain English	246	(1)
Inferring Back to the Population	246	(1)
Goodness-of-fit for Three Levels	246	(2)
Goodness-of-fit with Unequal Expectations	248	(1)
One-way χ² on SPSS	249	(1)
APA-style Results Section	249	(1)
Two-way χ²: Test of Independence	250	(4)
Null and Alternative Hypotheses	250	(1)
Chosen Statistic	250	(1)
Sampling Distribution	250	(1)
Significantly Related	251	(1)
APA Style	252	(1)
Strength of Effect	252	(1)
Plain English	253	(1)
Inference to the Real Population	254	(1)
Two-way χ² in SPSS	254	(5)
APA-style Results Section	259	(1)
Conceptual Items	259	(1)
Application Items	260	(1)
Computational Formulas in This Chapter	261	(1)
References	262	(1)
Appendix A ANOVA: One-Way, Repeated-Measures Using SPSS	263	(11)
Testing the Same Participants	263	(1)
One-way, Repeated-measures ANOVA on SPSS	264	(7)
APA-style Results Section	271	(1)
Summary of the One-way, Repeated-measures ANOVA	271	(1)
Conceptual Items	271	(1)
Application Items	272	(2)
Appendix B Multiple Regression Using SPSS	274	(7)
More Than One Predictor Variable	274	(1)
Multiple Regression in SPSS	275	(3)
APA-style Results Section	278	(1)
Summary of Multiple Regression	278	(1)
Conceptual Items	278	(1)
Application Items	278	(3)
Table 1 z-Table	281	(4)
Table 2 t-Table	285	(1)
Table 3 F-Table	286	(3)
Table 4 q-Table	289	(2)
Table 5 r-Table	291	(2)
Table 6 χ² Table	293	(1)
Answers to Odd-Numbered Items	294	(49)
Index	343

Excerpts

To the Instructor Why Another Statistics Book?I have been teaching statistics for about ten years, and one thing remains consistent: The majority of psychology students are not overjoyed to learn statistics. When I ask them why, they often tell me they aren't good at math and statistics is a baring course. While I appreciate their candid replies, I don't think their perceptions are accurate. They can be good at math, and statistics doesn't have to be a boring course.In this textbook, every effort is made to reduce anxiety about statistics, make statistics relevant and interesting, and incorporate SPSS to show students how to analyze data efficiently.To reduce anxiety, Chapter 1 opens with pointers on how to become competent in the course, with the final point reminding students that we're on their side. We want them to succeed and are delighted to record high grades when they are earned. Chapter 1 also contains a section on math, and students can quickly see that calculations required in statistics are quite simple. To further demonstrate that the math required of them is not difficult, over 30 practice items are offered at the end of this chapter. Within the first few class meetings, students should begin to recognize that they can perform well in statistics if they apply themselves, and we are available to help if they need us.In addition to a simple introduction to the course in Chapter 1, the entire text is written in a conversational style to further reduce anxiety. Although several reader-friendly supplemental statistics texts have become available over the past few years, this book is the first that offers the same readability and covers all information essential to a statistics course, from z-tests to the two-way ANOVA. In fact, I have also included brief Appendices on the repeated-measures ANOVA and multiple regression for instructors who choose to cover them. Every chapter and appendix is written in a straightforward way that my students have found accessible.Within each chapter, the material is segmented into many sections and subsections to allow students to digest the material at their own pace without stopping in the middle of a long stretch of text. The final section of each chapter is a preview of the subsequent chapter. The Preview summarizes the current chapter and links the material with the next chapter to help students see connections between topics. Finally, anxiety is reduced by offering students many practice items, which have been divided into Conceptual and Application categories. Conceptual Items are definitional or based on theory presented in the chapter. "What measure of variability must be used with ordinal data?" "When designing an experiment, why do researchers prefer a dependent variable of interval or ratio values?" "Why is it illogical to compare diagonal cell means after discovering a significant interaction?"Answers to these items can easily be found within the chapter to help students test themselves on their memory of the material. Application Items are more involved, requiring students to analyze an example in detail, often including calculations.A second Application Item example allows students to explore the relationship between age and respect.For both Conceptual and Application Item sections, more challenging items tend to be found toward the end of each category, and answers to odd-numbered items are located at the back of the book. Answers to all even-numbered items are found in theinstructor's manual,and thestudent workbookprovides larger data sets and a look at studies published by undergraduates.To address students' concern that statistics is a boring course, I have tried to share my passion for teaching statistics in this textbook. For several years, passion in teaching has been a hot topic among instructors, and enc