Statistics

Preface V


Acknowledgments VII


1 Introduction 3


1.1 Why Study Statistics? 4


1.2 What Is Statistics? 4


1.3 More About Inferential Statistics 6


1.4 Three Types Of Data 9


1.5 Levels Of Measurement 10


1.6 Types Of Variables 14


1.7 How To Use This Book 19


Summary20


Important Terms 21


Review Questions 21


Part 1 Descriptive Statistics: Organizing And Summarizing Data 25


2 Describing Data With Tables And Graphs 27


Tables (Frequency Distributions) 28


2.1 Frequency Distributions For Quantitative Data 28


2.2 Guidelines 29


2.3 Outliers 34


2.4 Relative Frequency Distributions 35


2.5 Cumulative Frequency Distributions 36


2.6 Frequency Distributions For Qualitative (Nominal) Data 38


2.7 Interpreting Distributions Constructed By Others 39


Graphs 40


2.8 Graphs For Quantitative Data 40


2.9 Typical Shapes 45


2.10 A Graph For Qualitative (Nominal) Data 47


2.11 Misleading Graphs 48


2.12 Doing It Yourself 50


Summary 50


Important Terms 52


Review Questions 53


3 Describing Data With Averages 57


3.1 Mode 58


3.2 Median 59


3.3 Mean 61


3.4 Which Average? 63


3.5 Averages For Qualitative And Ranked Data 66


Summary 68


Important Terms 68


Key Equation 69


Review Questions 69


4 Describing Variability 73


4.1 Intuitive Approach 74


4.2 Range 76


4.3 Variance 76


4.4 Standard Deviation 77


4.5 Details: Standard Deviation 82


4.6 Degrees Of Freedom(Df) 90


4.7 Interquartile Range (Iqr) 92


4.8 Measures Of Variability For Qualitative And Ranked Data 93


Summary 93


Important Terms 94


Key Equations 95


Review Questions 95


5 Normal Distributions And Standard (Z) Scores 99


5.1 The Normal Curve 101


5.2 Z Scores 103


5.3 Standard Normal Curve 104


5.4 Solving Normal Curve Problems 107


5.5 Finding Proportions 108


5.6 Finding Scores 114


5.7 More About Z Scores 119


Summary 122


Important Terms 123


Key Equations 123


Review Questions 123


6 Describing Relationships: Correlation 127


6.1 An Intuitive Approach 128


6.2 Scatterplots 130


6.3 A Correlation Coefficient For Quantitative Data: R 133


6.4 Details: Computation Formula For R 141


6.5 Outliers Again 143


6.6 Other Types Of Correlation Coefficients 144


6.7 Computer Output 144


Summary 148


Important Terms 149


Key Equations 149


Review Questions 149


7 Regression 153


7.1 Two Rough Predictions 154


7.2 A Regression Line 155


7.3 Least Squares Regression Line 157


7.4 Standard Error Of Estimate, Sy|X 161


7.5 Assumptions 164


7.6 Interpretation Of


7.7 Multiple Regression Equations 164


7.8 Regression Toward The Mean 165


Summary 167


Important Terms 168


Key Equations 168


Review Questions 168


Part 2 Inferential Statistics: Generalizing Beyond Data 171


8 Populations, Samples, And Probability 173


Populations And Samples 174


8.1 Populations 174


8.2 Samples 175


8.3 Random Sampling 176


8.4 Tables Of Random Numbers 177


8.5 Random Assignment Of Subjects 179


8.6 Surveys Or Experiments? 180


Probability 181


8.7 Definition 181


8.8 Addition Rule 182


8.9 Multiplication Rule 183


8.10 Probability And Statistics 186


Summary 188


Important Terms 188


Key Equations 189


Review Questions 189


9 Sampling Distribution Of The Mean 193


9.1 What Is A Sampling Distribution? 194


9.2 Creating A Sampling Distribution From Scratch 195


9.3 Some Important Symbols 197


9.4 Mean Of All Sample Means () 199


9.5 Standard Error Of The Mean () 200


9.6 Shape Of The Sampling Distribution 202


9.7 Other Sampling Distributions 204


Summary 205


Important Terms 205


Key Equations 205


Review Questions 206


10 Introduction To Hypothesis Testing: The Z Test 209


10.1 Testing A Hypothesis About Sat Scores 210


10.2 Z Test For A Population Mean 212


10.3 Step–By–Step Procedure 214


10.4 Statement Of The Research Problem 214


10.5 Null Hypothesis (H0) 215


10.6 Alternative Hypothesis (H1) 216


10.7 Decision Rule 217


10.8 Calculations 218


10.9 Decision 218


10.10 Interpretation 219


Summary 220


Important Terms 221


Key Equations 221


Review Questions 221


11 More About Hypothesis Testing 225


11.1 Why Hypothesis Tests? 226


11.2 Strong Or Weak Decisions 228


11.3 One–Tailed And Two–Tailed Tests 229


11.4 Choosing A Level Of Significance (a) 233


11.5 Testing A Hypothesis About Vitamin C 235


11.6 Four Possible Outcomes 235


11.7 If H0 Really Is True 238


11.8 If H0 Really Is False Because Of A Large Effect 239


11.9 If H0 Really Is False Because Of A Small Effect 242


11.10 Influence Of Sample Size 243


11.11 Power And Sample Size 246


Summary 249


Important Terms 251


Review Questions 251


12 Estimation (Confidence Intervals) 255


12.1 Point Estimate For m 256


12.2 Confidence Interval (Ci) For m 256


12.3 Interpretation Of A Confidence Interval 260


12.4 Level Of Confidence 261


12.5 Effect Of Sample Size 262


12.6 Hypothesis Tests Or Confidence Intervals? 263


12.7 Confidence Interval For Population Percent 263


Summary 265


Important Terms 266


Key Equation 266


Review Questions 266


13 T Test For One Sample 269


13.1 Gas Mileage Investigation 270


13.2 Sampling Distribution Of T 270


13.3 T Test 274


13.4 Common Theme Of Hypothesis Tests 275


13.5 Reminder About Degrees Of Freedom 275


13.6 Details: Estimating The Standard Error 275


13.7 Details: Calculations For The T Test 276


13.8 Confidence Intervals For M Based On T 278


13.9 Assumptions 279


Summary 280


Important Terms 280


Key Equations 280


Review Questions 280


14 T Test For Two Independent Samples 285


14.1 Epo Experiment 286


14.2 Statistical Hypotheses 287


14.3 Sampling Distribution Of 289


14.4 T Test 91


14.5 Details: Calculations For The T Test 292


14.6 P–Values 296


14.7 Statistically Significant Results 299


14.8 Estimating Effect Size: Point Estimates And Confidence Intervals 300


14.9 Estimating Effect Size: Cohen s D 303


14.10 Meta–Analysis


14.11 Reports In The Literature 306


14.12 Assumptions 308


14.13 Computer Output 308


Summary 309


Important Terms 310


Key Equations 310


Review Questions 311


15 T Test For Two Related Samples (Repeated Measures) 315


15.1 Epo Experiment With Repeated Measures 316


15.2 Statistical Hypotheses 319


15.3 Sampling Distribution Of 320


15.4 T Test 320


15.5 Details: Calculations For The T Test 321


15.6 Estimating Effect Size 324


15.7 Assumptions 326


15.8 Overview: Three T Tests For Population Means 326


15.9 T Test For The Population Correlation Coefficient, r 329


Summary 331


Important Terms 332


Key Equations 332


Review Questions 333


16 Analysis Of Variance (One Factor) 337


16.1 Testing A Hypothesis About Sleep Deprivation And Aggression 338


16.2 Two Sources Of Variability 340


16.3 F Test 342


16.4 Details: Variance Estimates 344


16.5 Details: Mean Squares (Ms) And The F Ratio 350


16.6 Table For The F Distribution 352


16.7 Anova Summary Tables 353


16.8 F Test Is Nondirectional 355


16.9 Estimating Effect Size 355


16.10 Multiple Comparisons 358


16.11 Overview: Flow Chart For Anova 362


16.12 Reports In The Literature 362


16.13 Assumptions 364


16.14 Computer Output 364


Summary 364


Important Terms 366


Key Equations 366


Review Questions 366


17 Analysis Of Variance (Repeated Measures) 371


17.1 Sleep Deprivation Experiment With Repeated Measures 372


17.2 F Test 373


17.3 Two Complications 375


17.4 Details: Variance Estimates 375


17.5 Details: Mean Square (Ms) And The F Ratio 379


17.6 Table For The F Distribution 381


17.7 Anova Summary Tables 381


17.8 Estimating Effect Size 383


17.9 Multiple Comparisons 384


17.10 Reports In The Literature 386


17.11 Assumptions 387


Summary 387


Important Terms 388


Key Equations 388


Review Questions 388


18 Analysis Of Variance (Two Factors) 393


18.1 A Two–Factor Experiment: Responsibility In Crowds 394


18.2 Three F Tests 397


18.3 Interaction 398


18.4 Details: Variance Estimates 402


18.5 Details: Mean Squares (Ms) And F Ratios 406


18.6 Table For The F Distribution 408


18.7 Estimating Effect Size 408


18.8 Multiple Comparisons 409


18.9 Simple Effects 410


18.10 Overview: Flow Chart For Two–Factor Anova 414


18.11 Reports In The Literature 415


18.12 Assumptions 416


18.13 Other Types Of Anova 416


Summary 417


Important Terms 417


Key Equations 417


Review Questions 418


19 Chi–Square (c2) Test For Qualitative (Nominal) Data 423


One–Variable c2 Test 424


19.1 Survey Of Blood Types 424


19.2 Statistical Hypotheses 424


19.3 Details: Calculating c2 425


19.4 Table For The c 2 Distribution 428


19.5 c2 Test 428


Two–Variable c2 Test 431


19.6 Lost Letter Study 431


19.7 Statistical Hypotheses 432


19.8 Details: Calculating c2 433


19.9 Table For The c2 Distribution 434


19.10 c2 Test 436


19.11 Estimating Effect Size 437


19.12 Odds Ratios 438


19.13 Reports In The Literature 440


19.14 Some Precautions 441


19.15 Computer Output 442


Summary 443


Important Terms 443


Key Equations 443


Review Questions 444


20 Tests For Ranked (Ordinal) Data 449


20.1 Use Only When Appropriate 450


20.2 A Note On Terminology 450


20.3 Mann–Whitney U Test (Two Independent Samples) 451


20.4 Wilcoxon T Test (Two Related Samples) 456


20.5 Kruskal–Wallis H Test (Three Or More Independent Samples) 460


20.6 General Comment: Ties 464


Summary 464


Important Terms 465


Review Questions 465


21 Postscript: Which Test? 469


21.1 Descriptive Or Inferential Statistics? 470


21.2 Hypothesis Tests Or Confidence Intervals? 470


21.3 Quantitative Or Qualitative Data? 472


21.4 Distinguishing Between The Two Types Of Data 472


21.5 One, Two, Or More Groups? 473


21.6 Concluding Comments 474


Review Questions 474


Appendices 479


A Math Review 479


B Answers To Selected Questions 487


C Tables 529


D Glossary 543


Photo Credits 550


Index 551