Statistics in context

Cover
STATISTICS IN CONTEXT
CONTENTS IN BRIEF
CONTENTS
FIGURES, TABLES, AND BOXES
PREFACE
INTRODUCING . . . Statistics in Context
ACKNOWLEDGMENTS
CONTENTS OVERVIEW
CHAPTER ONE: INTRODUCTION: STATISTICS-WHO NEEDS THEM?
OVERVIEW
LEARNING OBJECTIVES
Everyday Statistics
WHAT ARE STATISTICS?
TYPES OF STATISTICS
The Historical Context: ROLL THEM BONES
DESCRIPTIVE STATISTICS
INFERENTIAL STATISTICS
VARIABLES
INDEPENDENT AND DEPENDENT VARIABLES
Think About It . . . : HOW A TAN AFFECTS ATTRACTIVENESS
CHANCE ERROR
USING STATISTICS
SOME CAUTIONARY NOTES ABOUT STATISTICS
STATISTICS IN CONTEXT
SUMMARY
TERMS YOU SHOULD KNOW
WRITING ASSIGNMENT
PRACTICE PROBLEMS
Think About It . . .
REFERENCES
Introducing SPSS: The Statistical Package for the Social Sciences
CHAPTER TWO: TYPES OF DATA
OVERVIEW
LEARNING OBJECTIVES
Everyday Statistics
DATA, DATA EVERYWHERE
SCALES OF MEASUREMENT
QUALITATIVE DATA
The Historical Context: S. S. STEVENS AND HIS POWER LAW
QUANTITATIVE DATA
Think About It . . .: SCALES OF MEASUREMENT
ORGANIZING DATA
FREQUENCY DISTRIBUTIONS
UNGROUPED FREQUENCY DISTRIBUTIONS
Think About It . . . FREQUENCY DISTRIBUTIONS (PART 1)
GROUPED FREQUENCY DISTRIBUTIONS
Think About It . . .: FREQUENCY DISTRIBUTIONS (PART 2)
SCALES OF MEASUREMENT IN CONTEXT
. . . AND FREQUENCY DISTRIBUTIONS
SUMMARY
TERMS YOU SHOULD KNOW
GLOSSARY OF EQUATIONS
WRITING ASSIGNMENT
PRACTICE PROBLEMS
Think About It . . .
REFERENCES
Getting Data into Your Stats Program
Reading in Data with SPSS
Reading in Data with R
CHAPTER THREE: A PICTURE IS WORTH A THOUSAND WORDS: CREATING AND INTERPRETING GRAPHICS
OVERVIEW
LEARNING OBJECTIVES
Everyday Statistics
VISUALIZING PATTERNS IN DATA
The Historical Context WILLIAM PLAYFAIR AND THE USE OF GRAPHICS IN PUBLISHING
BAR CHARTS AND HISTOGRAMS
DISCRETE DATA
CONTINUOUS DATA
STEM-AND-LEAF GRAPHS
FREQUENCY POLYGONS
PIE CHARTS
Think About It . . . INTERPRETING GRAPHICS
OTHER GRAPHICS
GRAPHING MEANS
GRAPHING RELATIONSHIPS
GRAPHING TIME
GRAPHICS IN CONTEXT: RULES FOR CREATING GOOD GRAPHS
RULES FOR CREATING A GOOD GRAPH
SUMMARY
TERMS YOU SHOULD KNOW
WRITING ASSIGNMENT
A NOTE ON GRAPHING WITH STATISTICAL SOFTWARE
PRACTICE PROBLEMS
Think About It . . .
REFERENCES
GRAPHING WITH SPSS AND R
Graphing with SPSS
Graphing with R
CHAPTER FOUR: MEASURES OF CENTRAL TENDENCY: WHAT’S SO AVERAGE ABOUT THE MEAN?
OVERVIEW
LEARNING OBJECTIVES
Everyday Statistics
MEASURES OF CENTER
MEASURES OF CENTER: WHAT IS TYPICAL?
The Historical ContextADOLPHE QUETELET AND THE “AVERAGE MAN”
THE MODE AND THE MEDIAN
FINDING THE POSITION OF THE MODE
FINDING THE POSITION OF THE MEDIAN
THE MEAN
MODE, MEDIAN, AND MEAN: WHICH IS THE “BEST” MEASURE OF CENTER?
Think About It . . . ESTIMATING MEASURES OF CENTER
SHAPES OF DISTRIBUTIONS
NORMAL DISTRIBUTIONS
FINDING CENTER WITH GROUPED DATA
Think About It . . . SHAPES OF DISTRIBUTIONS
MEASURES OF CENTER IN CONTEXT
SUMMARY
TERMS YOU SHOULD KNOW
GLOSSARY OF EQUATIONS
WRITING ASSIGNMENT
PRACTICE PROBLEMS
Think About It . . .
REFERENCES
CHAPTER FIVE: VARIABILITY: THE “LAW OF LIFE”
OVERVIEW
LEARNING OBJECTIVES
Everyday Statistics
MEASURING VARIABILITY
CONSISTENCY AND INCONSISTENCY IN DATA
The Historical Context WHAT IS THE SHAPE OF THE EARTH?
MEASURES OF VARIABILITY
THE RANGE
THE INTERQUARTILE RANGE
GRAPHING THE IQR
THE VARIANCE
AVERAGE DEVIATION FROM THE MEAN
THE STANDARD DEVIATION
FINDING THE VARIANCE IN A POPULATION
FINDING THE STANDARD DEVIATION IN A POPULATION
FINDING STANDARD DEVIATION IN A POPULATION VERSUS A SAMPLE
FINDING VARIANCE AND STANDARD DEVIATION: AN EXAMPLE
Think About It . . . THE RANGE RULE
STANDARD DEVIATION IN CONTEXT
DESCRIPTIVE STATISTICS IN CONTEXT
SUMMARY
TERMS YOU SHOULD KNOW
GLOSSARY OF EQUATIONS
WRITING ASSIGNMENT
PRACTICE PROBLEMS
Think About It . . .
REFERENCES
DESCRIPTIVE STATISTICS WITH SPSS AND R
Descriptive Statistics with SPSS
Descriptive Statistics with R
CHAPTER SIX: WHERE AM I? NORMAL DISTRIBUTIONS AND STANDARD SCORES
OVERVIEW
LEARNING OBJECTIVES
Everyday Statistics
STATISTICS SO FAR
STANDARD SCORES
The Historical Context ALFRED BINET AND INTELLIGENCE TESTING
THE Z-SCORE
THE “3-SIGMA RULE”
PROPORTIONS IN THE STANDARD NORMAL CURVE
THE BENEFITS OF STANDARD SCORES
COMPARING SCORES FROM DIFFERENT DISTRIBUTIONS
CONVERTING A Z-SCORE INTO A RAW SCORE
CONVERTING A PERCENTILE RANK INTO A RAW SCORE
Think About It . . . THE RANGE RULE REVISITED
STANDARD SCORES IN CONTEXT
SUMMARY
TERMS YOU SHOULD KNOW
GLOSSARY OF EQUATIONS
WRITING ASSIGNMENT
PRACTICE PROBLEMS
Think About It . . .
REFERENCES
CHAPTER SEVEN: BASIC PROBABILITY THEORY
OVERVIEW
LEARNING OBJECTIVES
Everyday Statistics
PROBABILITY
PROBABILITY AND FREQUENCY
BASIC SET THEORY
The Historical Context: THE GAMBLER’S FALLACY
CONDITIONAL PROBABILITY
COMBINING PROBABILITIES
USING PROBABILITY
Think About It . . . PROBABILITY THEORY AND CARD GAMES
PROBABILITY IN CONTEXT
SUMMARY
TERMS YOU SHOULD KNOW
GLOSSARY OF EQUATIONS
PRACTICE PROBLEMS
Think About It . . .
REFERENCES
CHAPTER EIGHT: THE CENTRAL LIMIT THEOREM AND HYPOTHESIS TESTING
OVERVIEW
LEARNING OBJECTIVES
Everyday Statistics
INTRODUCTION: ERROR IN STATISTICS
INFERENTIAL STATISTICS
THE SCIENTIFIC METHOD
The Historical Context: KINNEBROOK’S ERROR AND STATISTICS
THE CENTRAL LIMIT THEOREM
MEASURING THE DISTRIBUTION OF LARGE SETS OF EVENTS
THE LAW OF LARGE NUMBERS AND THE CENTRAL LIMIT THEOREM
Think About It . . . THE LAW OF LARGE NUMBERS AND DICE GAMES
DRAWING SAMPLES FROM POPULATIONS
THE SAMPLING DISTRIBUTION OF THE MEANS
THE THREE STATEMENTS THAT MAKE UP THE CENTRAL LIMIT THEOREM
RANDOM SAMPLING
USING THE CENTRAL LIMIT THEOREM
ESTIMATING PARAMETERS AND HYPOTHESIS TESTING
THE NULL AND ALTERNATIVE HYPOTHESES
DIRECTIONAL HYPOTHESES
HYPOTHESIS TESTING IN CONTEXT
SUMMARY
TERMS YOU SHOULD KNOW
GLOSSARY OF EQUATIONS
PRACTICE PROBLEMS
Think About It . . .
REFERENCES
CHAPTER NINE: THE Z-TEST
OVERVIEW
LEARNING OBJECTIVES
Everyday Statistics
ERROR REVISITED
The Historical Context: THE TRIAL OF THE PYX
HOW DIFFERENT IS DIFFERENT ENOUGH? CRITICAL VALUES AND P
ASSUMPTIONS IN HYPOTHESIS TESTING
THE OUTER 5%: THE REJECTION REGION
Think About It . . . P-VALUES AND ALPHA LEVELS
FINDING THE Z-VALUE IN A NONDIRECTIONAL HYPOTHESIS
THE Z-TEST
ANOTHER EXAMPLE
STATISTICS AS ESTIMATES
ON BEING RIGHT: TYPE I AND TYPE II ERRORS
AN EXAMPLE
p-VALUES
INFERENTIAL STATISTICS IN CONTEXT: GALTON AND THE QUINCUNX
SUMMARY
TERMS YOU SHOULD KNOW
GLOSSARY OF EQUATIONS
WRITING ASSIGNMENT
PRACTICE PROBLEMS
Think About It . . .
REFERENCES
CHAPTER TEN: T-TESTS
OVERVIEW
LEARNING OBJECTIVES
Everyday Statistics
INFERENTIAL TESTING SO FAR
WILLIAM GOSSET AND THE DEVELOPMENT OF THE T-TEST
“STUDENT’S” FAMOUS TEST
The Historical Context STATISTICS AND BEER
THE SINGLE-SAMPLE T-TEST
DEGREES OF FREEDOM
WHEN BOTH σ AND μ ARE UNKNOWN
INDEPENDENT-SAMPLES T-TEST
THE STANDARD ERROR OF THE DIFFERENCE
FINDING THE DIFFERENCE BETWEEN TWO MEANS: AN EXAMPLE
FINDING THE DIFFERENCE BETWEEN MEANS WITH UNEQUAL SAMPLES
ASSUMPTIONS
Think About It . . . T-TESTS AND SAMPLE SIZE
DEPENDENT-SAMPLES T-TESTS
INTRODUCTION
USING A DEPENDENT-SAMPLES T-TEST: AN EXAMPLE
CALCULATIONS AND RESULTS
Think About It . . . T-TESTS AND VARIABILITY
T-TESTS IN CONTEXT: “GARBAGE IN, GARBAGE OUT”
SUMMARY
TERMS YOU SHOULD KNOW
GLOSSARY OF EQUATIONS
WRITING ASSIGNMENT
PRACTICE PROBLEMS
USING THE FORMULA FOR UNEQUAL N’S WITH EQUAL N’S
Think About It . . .
REFERENCES
Conducting t-Tests with SPSS and R
t-Tests with SPSS
t-Tests with R
CHAPTER ELEVEN: ANALYSIS OF VARIANCE
OVERVIEW
LEARNING OBJECTIVES
Everyday Statistics
COMPARING MORE THAN TWO GROUPS
ANALYSIS OF VARIANCE: WHAT DOES IT MEAN?
The Historical Context: FERTILIZER, POTATOES, AND FISHER’S ANALYSIS OF VARIANCE
A HYPOTHETICAL STUDY OF BLOOD DOPING
ASSESSING BETWEEN-GROUP AND WITHIN-GROUP VARIABILITY IN OUR HYPOTHETICAL RESULTS
ANOVA TERMINOLOGY
THE ONE-WAY ANOVA PROCEDURE
SUMS OF SQUARES
Think About It . . . T FOR TWO AND F FOR MANY
Think About It . . . THE F-STATISTIC
POST-HOC TESTING
THE TUKEY HSD TEST WITH EQUAL N’S
THE TUKEY HSD TEST WITH UNEQUAL N’S
MODELS OF F
ONE-WAY ANOVA ASSUMPTIONS
FACTORIAL DESIGNS OR TWO-WAY ANOVAS
AN EXAMPLE: ALBERT BANDURA’S STUDY OF IMITATING VIOLENCE
GRAPHING THE MAIN EFFECTS
THE LOGIC OF THE TWO-WAY ANOVA
USING THE TWO-WAY ANOVA SOURCE TABLE
INTERPRETING THE RESULTS
ANOVA IN CONTEXT: INTERPRETATION AND MISINTERPRETATION
SUMMARY
TERMS YOU SHOULD KNOW
GLOSSARY OF EQUATIONS
WRITING ASSIGNMENT
PRACTICE PROBLEMS
Think About It . . .
REFERENCES
Using SPSS and R for ANOVA
One-Way ANOVA in SPSS
Two-Way ANOVA in SPSS
One-Way ANOVA in R
Two-Way ANOVA in R
CHAPTER TWELVE: CONFIDENCE INTERVALS AND EFFECT SIZE: BUILDING A BETTER MOUSETRAP
OVERVIEW
LEARNING OBJECTIVES
Everyday Statistics
USING ESTIMATIONS
ESTIMATES AND CONFIDENCE INTERVALS
The Historical Context: JERZY NEYMAN: WHAT’S A LEMMA?
CIS AND THE Z-TEST
Think About It . . . WHAT DOES A CONFIDENCE INTERVAL REALLY MEAN? (PART 1)
CIS AND THE SINGLE-SAMPLE T-TEST
CIS AND INDEPENDENT- AND DEPENDENT-SAMPLES T-TESTS
Think About It . . . WHAT DOES A CONFIDENCE INTERVAL REALLY MEAN? (PART 2)
EFFECT SIZE: HOW DIFFERENT ARE THESE MEANS, REALLY?
EFFECT SIZE AND ANOVA
STATISTICS IN CONTEXT: THE CI VERSUS THE INFERENTIAL TEST
SUMMARY
TERMS YOU SHOULD KNOW
GLOSSARY OF EQUATIONS
WRITING ASSIGNMENT
PRACTICE PROBLEMS
Think About It . . .
REFERENCES
CHAPTER THIRTEEN: CORRELATION AND REGRESSION: ARE WE RELATED?
OVERVIEW
LEARNING OBJECTIVES
Everyday Statistics
THE CORRELATION COEFFICIENT
The Historical Context STATISTICS AND SWEET PEAS
POSITIVE AND NEGATIVE CORRELATIONS
WEAK AND STRONG CORRELATIONS
CALCULATING R
TESTING HYPOTHESES ABOUT R
THE LEAST SQUARES REGRESSION LINE, A.K.A. THE LINE OF BEST FIT
CONNECTING THE DOTS
FINDING THE REGRESSION LINE
Think About It . . . WHAT DOES PERFECT MEAN?
SOME CAUTIONARY NOTES
LINEAR VERSUS CURVILINEAR RELATIONSHIPS
TRUNCATED RANGE
COEFFICIENT OF DETERMINATION
Think About It . . . SHARED VARIABILITY AND RESTRICTED RANGE
STATISTICS IN CONTEXT: CORRELATIONS AND CAUSATION
SUMMARY
TERMS YOU SHOULD KNOW
GLOSSARY OF EQUATIONS
WRITING ASSIGNMENT
PRACTICE PROBLEMS
Think About It . . .
REFERENCES
Using SPSS and R for Correlation and Regression
Pearson Correlation Coefficient in SPSS
Conducting a Regression in SPSS
Pearson Correlation Coefficient in R
Conducting a Regression in R
CHAPTER FOURTEEN: THE CHI-SQUARE TEST
OVERVIEW
LEARNING OBJECTIVES
Everyday Statistics
THE CHI-SQUARE TEST AND WHY WE NEED IT
PARAMETRIC VERSUS NONPARAMETRIC TESTING
The Historical Context THE QUESTIONNAIRE
MAKING ASSUMPTIONS
THE ONE-WAY CHI-SQUARE TEST FOR GOODNESS OF FIT
THE TWO-WAY CHI-SQUARE TEST OF INDEPENDENCE
AN EXAMPLE OF THE TWO-WAY TEST: AMERICANS’ BELIEF IN GHOSTS BY REGION
A SHORTCUT
A SPECIAL CASE FOR CHI SQUARE: THE “2 BY 2” DESIGN
Think About It . . . THE RISK RATIO
NONPARAMETRIC TESTS IN CONTEXT: TYPES OF DATA REVISITED
SUMMARY
TERMS YOU SHOULD KNOW
GLOSSARY OF EQUATIONS
PRACTICE PROBLEMS
Think About It . . .
REFERENCES
Conducting Chi-Square Tests with SPSS and R
Chi-Square Test for Goodness-of-Fit in SPSS
Two-Way Chi-Square Test for Independence in SPSS
Chi-Square Test for Goodness-of-Fit in R
Two-Way Chi-Square Test for Independence in R
CHAPTER FIFTEEN: NONPARAMETRIC TESTS
OVERVIEW
LEARNING OBJECTIVES
Everyday Statistics
NONPARAMETRIC STATISTICS
REVIEW: HOW PARAMETRIC AND NONPARAMETRIC TESTS DIFFER
The Historical Context THE POWER OF STATISTICS IN SOCIETY
PERFORMING NONPARAMETRIC TESTS
RANKING THE DATA
THE SPEARMAN CORRELATION (Rs)
THE SPEARMAN CORRELATION: AN EXAMPLE
THE RESULTS
THE MANN-WHITNEY U-TEST
THE WILCOXON SIGNED-RANK, MATCHED-PAIRS T-TEST
THE WILCOXON TEST: AN EXAMPLE
OUR RESULTS
NON-NORMAL DISTRIBUTIONS
Think About It . . . THINKING AHEAD
NONPARAMETRIC TESTS IN CONTEXT
SUMMARY
TERMS YOU SHOULD KNOW
GLOSSARY OF EQUATIONS
WRITING ASSIGNMENT
PRACTICE PROBLEMS
Think About It . . .
REFERENCES
Conducting Nonparametric Tests with SPSS and R
Spearman’s Correlation in SPSS
Mann-Whitney U-Test in SPSS
Spearman’s Correlation in R
Mann-Whitney U-Test in R
CHAPTER SIXTEEN: WHICH TEST SHOULD I USE, AND WHY?
OVERVIEW
STATISTICS IN CONTEXT
EXAMPLES
ONE LAST WORD
REFERENCES
APPENDIX A: THE PROPORTIONS UNDER THE STANDARD NORMAL CURVE
APPENDIX B: THE STUDENT’S TABLE OF CRITICAL T-VALUES
APPENDIX C: CRITICAL F-VALUES
APPENDIX D: CRITICAL TUKEY HSD VALUES
APPENDIX E: CRITICAL VALUES OF CHI SQUARE
APPENDIX F: THE PEARSON CORRELATION COEFFICIENT: CRITICAL R-VALUES
APPENDIX G: CRITICAL RS VALUES FOR THE SPEARMAN CORRELATION COEFFICIENT
APPENDIX H: MANN-WHITNEY CRITICAL U-VALUES
APPENDIX I: CRITICAL VALUES FOR THE WILCOXON SIGNED-RANK, MATCHED-PAIRS T-TEST
ANSWERS TO ODDS END-OF-CHAPTER PRACTICE PROBLEMS
CREDIT
INDEX