Statistical reasoning in psychology and education/ Edward W. Minium, Bruce M. King, Gordon Bear.

1.1 Descriptive Statistics
1.2 Inferential Statistics
1.3 Relationship and Prediction
1.4 Our Concern: Applied Statistics
1.5 The Role of Applied Statistics
1.6 Do Statistics Lie?
1.7 Other Concerns about Statistics
Point of Controversy: Are Statistics
Necessary?
1.8 Some Tips on Studying Statistics
1.9 Summary
CHAPTER 2
PRELIMINARY CONCEPTS
2.1 Random Samples
2.2 Variables and Constants
2.3 Scales of Measurement
2.4 Scales of Measurement and Problems
of Statistical Treatment
2.5 Computational Accuracy with
Continuous Variables
2.6 Summary
CHAPTER 3
FREQUENCY DISTRIBUTIONS,
PERCENTIIES, AND
PERCENTILE RANKS

Organizing Qualitative Dau
Grouped Scores
How to Construct a Grouped
Frequency Distribution
Apparent versus Real Limits

The Relative Frequency Distribution
Stem-and-Leaf Displays
The Cumulative Frequency
Distribution
Percentiles and Percentile Ranks
Computing Percentiles from
Grouped Data
3.10 Computation of Percentile Rank
3.11 Summary
CHAPTER 4
GRAPHIC REPRESENTATION OF
FREQUENCY DISTRIBUTIONS
4.1 Basic Procedures
4.2 The Histogram
4.3 The Frequency Polygon
4.4 Choosing Between a Histogram and
a Polygon
4.5 The Bar Diagram and the Pie Chart
4.6 The Cumulative Percentage Curve
4.7 Factors Affecting the Shape of Graphs
4.8 Characteristics of Frequency
Distributions
4.9 Summary
CHAPTER 5
CENTRAL TENDENCY
5.1 The Mode
5.2 The Median
5.3 The Arithmetic Mean
5.4 Properties of the Mode
5.5 Properties of the Mean
Point of Controversy: Is It Permissible to
Calculate the Mean for Psychological and
Educational Tests?
5.6 Properties of the Median
5.7 Measures of Central Tendency in
Symmetrical and Asymmetrical
Distributions
5-8 The Effects of Score Transformations
5.9 Summary
CHAPTER 6
VARIABILITY

The Range
The Semi-Interquanile Range
Deviation Scores
Deviational Measures: The Variance
Deviational Measures: The Standard
Deviation
Point of Controversy: Calculating the
Sample Variance: Should We
Divide by n or (w — 1)?
6.6 Calculation of the Variance and

Standard Deviation: Raw-Score
Method
Properties of the Range
Properties of the Semi-Interquartile
Range
Properties of the Standard Deviation
6.10 Score Transformations and Measures
of Variability
6.11 Standard Scores (z Scores)
6.12 Measures of Variability and the
Normal Distribution
6.13 Comparing the Means of Two
Distributions
6.14 Summary
CHAPTER 7
the_normal curve
7.1 Historical Aspects of the Normal Curve
The Nature of the Normal Curve
7.3 Standard Scores and the Normal Curve
7.4 The Standard Normal Curve: Finding
Areas When the Score is Known
7.5 The Standard Normal Curve: Finding
Scores When the Area is Known

7.6 The Normal Curve as a Model for
Real Variables
7.7 The Normal Curve as a Model for
Sampling Distributions
Point of Controversy: How Normal Is the
Normal Curve?
7.8 Summary
CHAPTER 8
DERIVED SCORES
8.1 The Need for Derived Scores
8.2 Standard Scores
8.3 Translating Raw Scores to Standard
Scores
8.4 Standard Scores as Linear
Transformations of Raw Scores
8.5 Percentile Scores
8.6 Comparability of Scores
8.7 Normalized Standard Scores
8.8 Combining Measures from Different
Distributions
8.9 Summary
CHAPTER 9
CORRELATION
9.1 Some History
9.2 Graphing Bivariate Distributions:
The Scatter Diagram
9.3 Correlation: A Matter of Direction
9.4 Correlation: A Matter of Degree
9.5 Understanding the Meaning of
Degree of Correlation
9.6 Formulas for Pearson's Coefficient
of Correlation ~
9.7 Calculating rlrom Raw Scores
9.8 Correlation Does Not Establish
Causation
9 9 The Effects of Score Transformations
9.10 Cautions Concerning Correlation
Coefficients
9.11 Other Ways to Measure Association
9.12 Summary
CHAPTER 10
PREDICTION :
10.1 The Problem of Prediction
10.2 The Criterion of Best Fit
Point of Controversy: Least-Squares
Regression versus the Resistant Line
10.3 The Regression Equation:
Standard-Score Form
10.4 The Regression Equation: Raw-Score
Form
10.5 Error of Prediction: The Standard
Error of Estimate
10.6 An Alternative (and Preferred)
Formula for 5^
10.7 Error in Estimating Tfrom X
10.8 Cautions Concerning Estimation of
Predictive Error
10.9 Summary
CHAPTER 11
INTERPRETIVE ASPECTS OF
CORRELATION AND REGRESSION
11.1 Factors Influencing r: Range of
Talent
11.2 The Correlation Coefficient in
Discontinuous Distributions
11.3 Factors Influencing r:
Heterogeneity of Samples
11.4 Interpretation of r: The Regression
Equation I
11.5 Interpretation of r: The Regression
Equation II
11.6 Regression Problems in Research
11.7 An Apparent Paradox in Regression
11.8 Interpretation of r: Proportion of
Variation in Y
Not Associated with Variation in X
11.9 Interpretation of r: Proportion of
Variance in Y
Associated with Variance in X
11.10 Interpretation of r: Proportion of
Correct Placements
11.11 Summary
CHAPTER 12
PROBABILITY
12.1 Defining Probability
12.2 A Mathematical Model of Probability
12.3 Two Theorems in Probability
12.4 An Example of a Probability
Distribution: The Binomial
12.5 Applying the Binomial
12.6 The Frequency Distribution (and
Normal Curve) as a Probability
Distribution
12.7 Are Amazing Coincidences Really
that Amazing?
12.8 Summary
CHAPTER 13
THE BASIS OF
STATISTICAL INFERENCE
13.1 A Problem in Inference: Testing
Hypotheses
13.2 A Problem in Inference: Estimation
13.3 Basic Issues in Inference
13.4 Random Sampling
13.5 Using a Table of Random Numbers
13.6 The Random Sampling Distribution
of the Mean: An Introduction
13.7 Characteristics of the Random
Sampling Distribution of the Mean
13.8 Putting the Sampling Distribution of
the Mean to Use
13.9 Summary
CHAPTER 14
TESTING HYPOTHESES ABOUT
SINGLE MEANS {z and t)
14.1 Testing a Hypothesis About a
Single Mean
14.2 When Do We Retain and When Do
We Reject the Hypothesis?
14.3 Generality of the Procedure for
Hypothesis Testing
14.4 Dr. Frost's Problem: Conclusion
14.5 Review of Assumptions in
Inference about a Single Mean
14.6 Estimating the Standard Error of the
Mean When a is Unknown
14.7 The t Distribution
14.8 Characteristics of Student's
Distribution of t
14.9 Degrees of Freedom and Student's
Distribution of t
14.10 Using Student's Distribution of t
14.11 An Example: Professor Dyett's
Question
14.12 Computing / from Raw Scores
14.13 Directional and Nondirectional
Alternative Hypotheses
14.14 Reading Research Reports in
Behavioral Science
Point of Controversy: The Bootstrap
Method of Statistical Inference
14.15 Problems in Selecting a Random
Sample and in Drawing Conclusions
14.16 Summary
CHAPTER 15
FURTHER CONSIDERATIONS IN
HYPOTHESIS TESTING
15.1 Statement of the Hypothesis
15.2 Choice of H,,: One-Tailed and
Two-Tailed Tests
15.3 The Criterion for Rejecting or
Retaining Hq
15.4 The Statistical Decision
15.5 A Statistically Significant Difference
Versus a Practically Important
Difference
15.6 Errors in Hypothesis Testing
15.7 Levels of Significance Versus
p-Values
15.8 Summary
Point of Controversy: Dichotomous
Significance-testing Decisions
CHAPTER 16
TESTING HYPOTHESES ABOUT THE
DIFFERENCE BETWEEN TWO
INDEPENDENT MEANS
16.1 The Random Sampling
Distribution of the Difference
Between Two Sample Means
16.2 An Illustration of the Sampling
Distribution of the Difference
Between Means
16.3 Properties of the Sampling
Distribution of the Difference
Between Means
16.4 Determining a Formula for t
16.5 Testing the Hypothesis of No
Difference Between Two
Independent Means: The Dyslexic
Children Experiment
16.6 The Conduct of a One-Tailed Test
16.7 Sample Size in Inference about
Two Means
16.8 Assumptions Associated with
Inference about the Difference
Between Two Independent Means
16.9 The Random-Sampling Model
Versus the Random Assignment
Model
16.10 Random Sampling and Random
Assignment as Experimental
Controls
16.11 The Experiment Versus the In Situ
Study
16.12 Summary
CHAPTER 17
TESTING HYPOTHESES
DIFFERENCE BETWEEN
DEPENDENT MEANS
17.1 Determining a Formula for t
ABOUT THE
TWO
17.2 Degrees of Freedom for Tests of No
Difference Between Dependent
Means
17.3 Testing a Hypothesis about Two
Dependent Means
17.4 An Alternative Approach to the
Problem of Two Dependent Means
17.5 Advantages of the DependentSamples
Design
17.6 Hazards of the Dependent-Samples
Design
17.7 Summary
CHAPTER 18
ESTIMATION OF /i AND l^x-
18.1 Two Ways of Making Estimates
18.2 Interval Estimates of Hx
18.3 Interval Estimates of iix~I^y
18.4 Evaluating an Interval Estimate
18.5 Sample Size Required for Estimates
of Hx2^nd Hx- fir
18.6 The Relation Between Interval
Estimation and Hypothesis Testing
18.7 The Merits of Interval Estimation
18.8 Summary
CHAPTER 19
POWER AND MEASURE
OF EFFECT SIZE
19-1 Type I Error and Type II Error
19.2 The Power of a Test
Point of Controversy: Failure to Publish
"Nonsignificant" Results

Factors Affecting Power:
Discrepancy Between the True
Population Mean and the
Hypothesized Mean (Size of Effect)
Factors Affecting Power: Sample
Size
Factors Affecting Power: Variability
of the Measure and Dependent
Samples
Factors Affecting Power: Level of
Significance (a)
Factors Affecting Power: One-Tailed
Versus Two-Tailed Tests
Summary of Factors Affecting Power
Calculating the Power of a Test
19.10 Effect Size
19.11 Estimating Power and Sample Size
for Tests of Hypotheses about
Means
19.12 Some Implications of Power Curves
19.13 Reporting Inferential Statistics
Point of Controversy: Meta-Analysis
19.14 Summary
CHAPTER 20
ONE-WAY ANALYSIS OF VARIANCE
(AND SOME ALTERNATIVES)
20.1 The Null Hypothesis
20.2 The Logic of One Way Analysis of
Variance: Variation Within and
Between Groups
20.3 Partition of Sums of Squares
20.4 Degrees of Freedom
20.5 Variance Estimates and the F" Ratio
20.6 The Summary Table
20.7 An Example
20.8 Raw Score Formulas for Analysis of
Variance
20.9 Comparison of t and F
20.10 Assumptions Associated with
ANOVA
20.11 ANOVA and Power
20.12 Post Hoc Comparisons
20.13 An Alternative to the FTest:
Planned Comparisons
20.14 How to Construct Planned
Comparisons
20.15 An Alternative for Comparing One
Control Group with Several
Experimental Groups: Dunnett's
Test
Point of Controversy: Analysis of Variance
Versus A Priori Coraparisons
20.16 Analysis of Variance for
Repeated Measures
20.17 Summary
CHAPTER 21
FACTORIAL ANALYSIS
OF VARIANCE:
THE TWO-FACTOR DESIGN
21.1 Main Effects
21.2 Interaction
21.3 The Importance of Interaction
21.4 Partition of the Sum of Squares for
Two-way ANOVA
21.5 Degrees of Freedom
21.6 Variance Estimates and F Tests
21.7 Studying the Outcome of Two-Way
Analysis of Variance
21.8 Planned Comparisons
21.9 Assumptions of the Two-Factor
Design and the Problem of
Unequal Numbers of Scores
21.10 Mixed Two-Factor Within-Subjects
Design
21.11 Summary
CHAPTER 22
INFERENCE ABOUT PEARSON
CORRELATION COEFFICIENTS
22.1 The Random Sampling Distribution
of r
22.2 Testing the Hypothesis that /? = 0
22.3 Fisher's z' Transformation
22.4 Estimating p
22.5 Testing the Hypothesis of No
Difference Between and P2.
Independent Samples
22.6 A Note About Assumptions
22.7 Summary
CHAPTER 23
_CHL:SQ1IARE AND INFERENCE
ABOUT FREQUENCIES
23.1 A Problem in Discrepancy Between
Expected and Observed
Frequencies
23.2 Chi-Square as a Measure of
Discrepancy Between Expected
and Observed Frequencies
23.3 The Logic of the Chi-Square Test
23.4 Interpretation of the Outcome of a
Chi-Square Test
23.5 Different Hypothesized Proportions
in the Test for Goodness of Fit
23.6 Assumptions in the Use of the
Theoretical Distribution of
Chi-Square
23.7 Hypothesis Testing When df= 1
23.8 Two Variables; Contingency Tables
and the Hypothesis of
Independence
23.9 Finding Expected Frequencies in a
Contingency Table
23.10 Calculation of and
Determination of Significance in a
Contingency Table
Point of Controversy: Yates' Correction
for Continuity
23.11 Interval Estimates About
Proportions
23.12 Other Applications of Chi-Square
2313 Summary
CHAPTER 24
SOME (ALMOST)
ASSUMPTION-FREE TESTS
24.1 Randomization Tests
24.2 How to Place Scores in Rank Order
24.3 Test of Location for Two
Independent Groups: The Mann-
Whitney UTest
Point of Controversy: A Comparison of
the t test and Mann-Whitney 17 Test with
Real-World Distributions
24.4 Test of Location Among Several
Independent Groups: The Kruskal-
Wallis Test
24.5 Test of Location for Two Dependent
Groups: The Sign Test
24.6 Test of Location for Two Dependent
Groups: The Wilcoxon Signed-
Ranks Test
24.7 Spearman's Rank-Order Correlation
Coefficient
Point of Controversy: Objectivity and
Subjectivity in Inferential Statistics
24.8 Summary
EPILOGUE;
THE REALM OF STATISTICS
APPENDIX A REVIEW Of BASIC MATHEMATICS
APPENDIX B SUMMATION RULES
APPENDIX C LIST OF SYMBOLS
APPENDIX D ANSWERS TO ODD-NUMBERED
PROBLEMS
APPENDIX E STATISTICAL ANALYSIS BY
COMPUTER
APPENDIX F STATISTICAL TABLES

Areas Under the Normal Curve
Corresponding to Given Values of z
The Binomial Distribution
Random Numbers
Student's t Distribution
The F Distribution
The Studentized Range Statistic
Dunnett's Test: Distribution of t
Statistic in Comparing Several
Treatment Means with One Control
Values of the Correlation
Coefficient Required for Different
Levels of Significance When H^.
p = 0
Values of Fisher's z' for Values of r
The Distribution
Critical One-Tail Values of for
the Mann-Whitney C/Test
Critical Values for the Smaller of
W+ or W- for the Wilcoxon
Signed-Ranks Tests