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More About This Textbook
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Meet the Author
Janie Wilson began her adventure in teaching during graduate school and continued in a fulltime 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
PART I: INTRODUCTION.
Chapter 1. Welcome to Statistics.
Building competence.
Rationale for learning statistics.
Math.
Proportion and percent. Rounding.
Symbols.
APA style.
Conducting research.
Experiments. Correlations. The usefulness of correlations.
How to pick a sample.
Analyzing data using SPSS.
Preview of Chapter 2.
Conceptual Items.
Application Items.
PART II: DESCRIPTIVE STATISTICS.
Chapter 2. Variables and Graphing.
Measurement scales.
Nominal variables. Ordinal variables. Interval variables. Ratio variables. Special case of rating scales.
Qualitative vs. quantitative variables.
Discrete vs. continuous variables.
Picturing data: Simple frequency tables and graphs.
Nominal and ordinal data. Discrete interval and ratio data. Continuous interval and ratio data. Grouped frequency distributions.
Shapes of distributions.
Normal distributions. Skewed distributions. Kurtosis. Bimodal and trimodal distributions.
Preview of Chapter 3.
Conceptual Items.
Application Items.
Chapter 3. Measures of Central Tendency.
Summarizing data.
Median.
Mean.
Mean vs. median.
Introduction to SPSS.
Measures of central tendency on SPSS.
Summarizing experiments using means.
Graphing means.
Graphing means on SPSS.
Preview of Chapter 4.
Conceptual Items.
Application Items.
Computational formula in this chapter.
Chapter 4: Measures of Variability.
Spread of scores.
Range.
Sample variance.
Sample standard deviation.
Estimated population standard deviation.
Estimated population variance.
Measures of variability on SPSS.
Graphing sample standard deviation.
Graphs of standard deviation on SPSS.
Preview of Chapter 5.
Conceptual Items.
Application Items.
Computational formulas in this chapter.
Chapter 5. Descriptive zscores.
Standardized scores.
Comparing values from different samples.
Standardized distribution.
Proportion and percent.
Evaluations based on zscores. Comparing two values and probability. Percentile.
Logical limits.
Preview of Chapter 6.
Conceptual Items.
Application Items.
Computational formula in this chapter.
PART III: INFERENTIAL STATISTICS: EXPERIMENTS AND QUASIEXPERIMENTS.
Chapter 6. Inferential zscores and probability.
Probability.
Sampling distribution of means.
Creating a sampling distribution of means for your research.
Standardizing the sampling distribution of means.
Critical value and critical region.
Manipulating a sample.
Not different from normal. Higher than normal. Lower than normal. Decreasing the critical region.
Preview of Chapter 7.
Conceptual Items.
Application Items.
Computational formulas in this chapter.
References.
Chapter 7. Hypothesis Testing.
Formalizing the inferential z.
Lay out expectations.
Null hypothesis. Alternate hypothesis. Twotailed ztest. µ rather than.
Choose a statistic.
Sketch the normal distribution.
Collect data.
Calculate a statistic. Significance. APA style. Reject or fail to reject the null hypothesis. Inferential wording. Effect size. Plain English. Confidence intervals.
Onetailed test in the positive direction.
Onetailed test in the negative direction.
Hypothesis testing, truth, and power.
Preview of Chapter 8.
Conceptual Items.
Application Items.
Conceptual formulas in this chapter. Chapter 8. Three ttests.
ztest vs. ttest.
The singlesample ttest.
Hypothesis testing using the singlesample ttest.
The relatedsamples ttest.
The sampling distribution of mean differences. Hypothesis testing using the relatedsamples ttest. Relatedsamples ttest on SPSS. APAstyle results section.
Independentsamples ttest.
The sampling distribution of differences between means. Hypothesis testing using the independentsamples ttest.
Independentsamples ttest on SPSS.
APAstyle results section.
Preview of Chapter 9.
Conceptual Items.
Application Items.
Computational formulas in this chapter.
References.
Chapter 9: ANOVA. OneWay, BetweenGroups.
ttest vs. ANOVA.
Logic of ANOVA: Hypothesis testing.
Oneway, betweengroups ANOVA: Equal n.
Organizing ANOVA results. APA style. Effect size. Posthoc testing: Tukey's HSD. Plain English. Confidence intervals.
Oneway, betweengroups ANOVA: Unequal n.
Summary table. Effect size. Posthoc testing: Fisher's protected ttests. Plain English. Confidence intervals.
Oneway, betweengroups ANOVA on SPSS.
APAstyle results section. <
Application Items.
Computational formulas in this chapter.
References.
Chapter 10. ANOVA: TwoWay, BetweenGroups.
Oneway vs. twoway ANOVA.
Logic of the twoway, betweengroups ANOVA.
Twoway ANOVA effects.
Calculating the twoway, betweengroups ANOVA.
S_{tot.} SS_{BG.} and SS_{WG.} Separating SS_{BG} into three portions. Ftests for each effect.
Hypothesis testing and ANOVA results.
First main effect. Second main effect. Interaction effect.
Posthoc testing.
Post hoc for a significant main effect. Post hoc for a significant interaction effect.
Plain English.
Applying results.
Twoway, betweengroups ANOVA on SPSS.
APAstyle results section.
Graphing the twoway ANOVA.
Preview of Chapter 11.
Conceptual Items.
Application Items.
Computational formulas in this chapter.
References.
PART IV: INFERENTIAL STATISTICS: CORRELATIONAL RESEARCH.
Chapter 11. Correlational Data.
Relationships between variables.
Logic of Pearson's r.
Perfect relationships. Lessthanperfect relationships.
Pearson's r calculations.
Correlations on SPSS.
Scatterplot on SPSS. Pearson's r on SPSS.
APAstyle results section.
Inaccurate correlations.
Artificially low correlations. Artificially high correlations.
Preview of Chapter 12.
Conceptual Items.
Application Items.
Computational formula in this chapter.
References.
Chapter 12: Linear Regression.
Correlation before prediction.
Linear regression theory.
Prediction. Error in predictions.
Calculating the regression equation.
Graphing the regression line.
Standard error of the estimate.
Standard error calculations.
Prediction on SPSS.
Correlation on SPSS. Linear regression on SPSS.
APAstyle results section.
Preview of Chapter 13.
Conceptual Items.
Application Items.
Computational formulas in this chapter.
References.
Chapter 13. Chisquare Analyses.
Simple frequency counts.
Oneway x ^{2}: Goodnessoffit test.
Null and alternate hypotheses. Chosen statistic. Sampling distribution for X ^{2.} X ^{2} _{obt} above zero. APA style. Plain English. Inferring
Goodness of fit for three levels.
Goodness of fit with unequal expectations.
Oneway X ^{2} on SPSS.
APAstyle results section.
Twoway X ^{2}: Test of independence.
Null and alternate hypotheses. Chosen statistic. Sampling distribution. Significantly related. APA style. Strength of effect. Plain English. Inference to the real population.
Twoway X ^{2} in SPSS.
APAstyle results section.
Conceptual Items.
Application Items.
Computational formulas in this chapter.
References.
PART V: APPENDICES.
Appendix A. ANOVA: OneWay, RepeatedMeasures Using SPSS.
Testing the same participants.
Oneway, repeatedmeasures ANOVA on SPSS.
Posthoc testing.
APAstyle results section.
Conceptual Items.
Application Items.
Computational formula in this appendix.
Appendix B. Multiple Regression.
More than one predictor variable.
Multiple regression on SPSS.
APAstyle results section.
Summary of multiple regression.
Conceptual Items.
Application Items.
ztable.
ttable.
Ftable.
qtable.
Correlation table.
X table.
Preface
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
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 readerfriendly supplemental statistics texts have become available over the past few years, this book is thefirst that offers the same readability and covers all information essential to a statistics course, from ztests to the twoway ANOVA. In fact, I have also included brief Appendices on the repeatedmeasures 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.
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 oddnumbered items are located at the back of the book. Answers to all evennumbered items are found in the instructor's manual, and the student workbook provides 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 encouraging student enthusiasm is a primary goal. Discussions have centered around getting and keeping students' attention in order to teach effectively, and we have begun to embrace the idea of entertaining while teaching. In this text, I have tried to entertain through examples that are relevant to most college students, including examples that have made my students laugh, nod their heads in agreement, or analyze enthusiastically to reach the answer. Because students should recognize that scientific knowledge is established through research, several examples are based on the results of published studies, and references are found at the end of relevant chapters.
In addition to interesting examples, the text includes only analyses that (a) are necessary to build skills or (b) will likely be used by students in the future. Many of us can attest to the frustration (and boredom) associated with learning more than we want to know. I had this experience when I was taught how to build a website; to my dismay, I was also taught the inner workings of my computer. I found myself tuning out the information that, by my teacher's own admission, would not be relevant to me. This text presents statistics chosen as highly relevant based on talking with colleagues, reading their research, and experiencing my own needs when analyzing data from my lab. Further, each discussion of inferential statistics contains information that students are likely to need, including effect size, confidence intervals, and a model APAstyle results section.
A third goal of this text is to teach SPSS. Most campuses have access to this computer program, and it is currently the most popular program for data analysis. I require my students to learn how to conduct analyses by hand before turning to computers because hand calculations allow students to play an active role in finding the result of an example. Formulas also tend to reflect the logic behind analyses. I've also noticed that the majority of my students have difficulty relating to the material when they stare at a computer screen. However, SPSS offers a level of efficiency students would never enjoy if they continued to rely on hand calculations. To ease the transition from hand computations to computer analysis, SPSS is thoroughly integrated in the text. After each analysis is conducted by hand, the same example is analyzed using SPSS. That way, students can clearly see that the computer provides the same output they calculated by hand. As an added bonus, students will not need to purchase an additional manual on the use of SPSS; every relevant aspect is covered in the current textbook, from data entry to output. Topics and Organization
This text covers statistics essential to students in the social sciences. I have chosen a slightly unusual chapter organization, with correlation and regression analyses found under Inferential Statistics. Traditionally, these analyses are discussed early in the course as descriptive statistics, and students never hear of pvalues or significant effects. When I taught correlation and regression as descriptive statistics, it was always awkward for me to try to revisit them at the end of the term to let students know these analyses could actually be inferential statistics. I also wanted to avoid putting correlation and regression in the middle of zscores because the arrangement breaks up the natural flow of discussion from descriptive to inferential statistics.
The first part of the text, INTRODUCTION, welcomes the student, defines many research terms, and introduces math. Chapter 1 shows students that calculations for this course are not difficult; math is simply a tool we use to make sense of data and hopefully learn something new about behavior.
The second part, DESCRIPTIVE STATISTICS, introduces in Chapter 2 classifications of variables, simple frequency tables and graphs, and shapes of distributions. In Chapters 3 and 4, measures of central tendency and variability are explained in detail using examples, and SPSS output is provided where appropriate. In Chapter 5, descriptive zscores are introduced, and simple frequency distributions are revisited.
Part III, INFERENTIAL STATISTICS: EXPERIMENTS AND QUASIEXPERIMENTS covers probability, hypothesis testing, ttests, and ANOVAs by hand and using SPSS. In Chapter 6, probability and inferential zscores flow naturally from the Chapter 5 topic of descriptive zscores. Chapter 7 then relies on inferential zscores to introduce the logic of hypothesis testing. Chapter 8 takes one more step, beginning with the singlesample ttest and moving through the dependentsamples ttest, then to the independentsamples ttest. The oneway, betweengroups ANOVA in Chapter 9 is a logical extension of the independentsamples ttest. A significant ANOVA is followed by post hoc testing. Chapter 10 covers the twoway, betweengroups ANOVA and post hoc testing of main effects and the interaction. Within this part of the text, I point out that we have true experiments only when participants are manipulated; without manipulation, we only know if variables are related. This point is illustrated by several Application Items in which a quasiIV (e.g., gender) is used in a study, and students much decide if causation can be established.
The fourth section, INFERENTIAL STATISTICS: CORRELATIONAL RESEARCH, covers correlation, linear regression, and chi squared. My students generally perform well on these topics, easing their stress toward the end of the term and allowing them to get their second wind for the final exam. Just as with Part III of the book, I point out here that cause and effect can in fact be established in correlational research if one variable has been manipulated.
The fifth section offers APPENDICES to cover additional designs students are likely to use as undergraduates. Instructors may choose to discuss the logic of the oneway, repeatedmeasures ANOVA as well as multiple linear regression. SPSS layout, data analysis, and output for these designs are also covered. To the Student How to Use This Book
While I wrote this book, I tried to always keep in mind how I would talk with you if we were discussing statistics face to face. As a result, I hope you find the conversational style enjoyable and easy to read. For many of us, statistics can be a bit overwhelming, and I didn't want the wording to get in the way of learning the material.
Each chapter begins with a brief overview of what is found in the chapter. It is really the theory of when and why we run certain statistics. Terms that are particularly important are in bold type. Next, formulas are introduced with examples rather than alone because using the formulas is more important than just looking at them or trying to memorize them with no application. It is useful for you to calculate statistics by hand for at least two reasons: Hand calculations offer an active role in conducting statistics that reinforces the logic behind each calculation, and later, computer output can be examined for errors. The examples calculated by hand should be of interest to most college students. In fact, many examples are based on suggestions from my own students.
As soon as you calculate the answer to an example, you'll learn to make sense of the result and write it in plain English. After all, a statistic is not useful unless it brings us knowledge to share with the world. In fact, psychologists rely on the American Psychological Association to set guidelines for reporting results, and your instructor might ask you to review the APAstyle results section in relevant chapters.
At the end of each analysis, SPSS is offered as a way to calculate answers more quickly. SPSS, a computer program used to analyze numerous types of data, was chosen for this text based on its popularity and availability. For every analysis on SPSS, an example that was recently calculated by hand is entered into the computer. The text begins with how to enter numbers in a spreadsheet and covers which options to choose from pulldown menus as well as how to read the output. It might be useful to highlight relevant information on the output to avoid focusing on information you don't need to report.
Because each example on SPSS will have been calculated by hand first, you will be able to check the output from SPSS for reasonable answers. For example, the text indicates that SPSS offers a way to describe a sample that in fact is an estimate of the population. This type of error will not be understood unless you first complete calculations to describe a sample by hand. Of course, computers are not thinking creatures, so we have to make sure we doublecheck the logic of all output based on our own experiences with hand calculations. After you feel comfortable with assessing computer output, SPSS will probably replace hand calculations as an efficient way to analyze data. This will certainly be true in later courses like research methods and when you conduct your own research in the future.
Finally, each chapter ends with a preview of the next chapter, but this section also contains a summary of the current chapter. Reading this section carefully will give you an idea of whether or not the overall picture of thechapter is clear.
To further check your grasp of the material, Conceptual Items will test your memory of information found in the chapter. Next, Application Items present examples to be analyzed by hand and on SPSS.
Even if your instructor does not assign practice items, you might want to make a habit of completing them to become competent with the material before a test. Additional examples can be found in the student workbook, and the workbook also showcases research articles published by undergraduates.