Table of Contents Index List of Figures List of Tables Definitions
Table of Contents

+ Preface
History of the Text
Conceptual Framework of the Text
Computation
Assumptions
Probability Theory
Hypothesis Testing
Who Should Take This Course
A Brief History of the Teaching of Statistics
Teaching Statistics
Using Technology
Feelings about the Course
Statistical Calculators and Statistical Packages
Statistical Calculators
Statistical Packages
Notation for Statistical Packages
Objectives of the Text
ICONS
The Author
Acknowledgments
+ A Mayoral Fantasy
A Full-Blown Fiasco
Organizing and Describing the Data - An Alternative Ending
Sampling - An Alternative Approach and a Happy Ending
+ Models
Definition of a Model
Characteristics of Models
The Language of Models
Model-Building in Science
Power and Simplicity of Models
Mathematical Models
Building a Better Boat - Example of Model-Building
Conclusion
+ The Language of Algebra
The Symbol Set of Algebra
Numbers
Variables
Operators
Delimiters
Syntax of the Language of Algebra
Creating sentences
Eliminating Parentheses
Transformations
Numbers
Fractions
Exponential Notation
Binomial Expansion
Multiplication of Phrases
Factoring
Sequential Application of Rewriting Rules to Simplify an Expression
Evaluating Algebraic Sentences
+ Measurement
Definition
Properties of Measurement Systems
Magnitude
Intervals
Rational Zero
SCALE TYPES
Nominal Scales
Ordinal Scales
Interval Scales
Ratio Scales
Exercises in Classifying Scale Types
The Myth of Scale Types
The Ruler and Scale Types
Toward a Reconceptualization of Scale Types
+ Frequency Distributions
Frequency Tables
Frequency Distributions
Histograms
Absolute Frequency Polygons
Relative Frequency Polygon
Absolute Cumulative Frequency Polygons
Relative Cumulative Polygon
+ Comparing Frequency Distributions
Overlapping Frequency Distributions
Overlapping Relative Frequency Polygons
Contingency Tables
Conclusion
+ Grouped Frequency Distributions
Why Intervals are Necessary
Selecting the Interval Size
Computing the Frequency Table
Drawing the Frequency Polygon or Histogram
Selecting Another Interval Size
Selecting the Appropriate Interval Size
+ Models of Distributions
Models of Distributions
Variations of Probability Models
The Uniform or Rectangular Distribution
The Negative Exponential Distribution
The Triangular Distribution
The Normal Distribution or Normal Curve
Properties of Probability Distributions
+ The Normal Curve
A Family of Distributions
Similarity of Members of the Family of Normal Curves
Area Under a Curve
Drawing a Member of the Family of Normal Curves
Differences in Members of the Family of Normal Curves
Finding Area Under Normal Curves
Area below a Score
Area between Scores
Area Above a Score
Finding Probabilities in Both Tails
Finding Scores from Area
Finding Scores that Cut Off Middle Area
Finding Scores that Cut off Bottom Area
The Standard Normal Curve
Summary
+ Summation Notation
Subscripted Variables
Summation Notation
Summation of Algebraic Expressions
The General Rule
Exceptions to the General Rule
Solving Algebraic Expressions with Summation Notation
Summary
+ Statistics
Measures of Central Tendency
The Mode
The Median
The Mean
Kiwi Bird Problem
Skewed Distributions and Measures of Central Tendency
Measures of Variability
The Range
The Variance and The Standard Deviation
Calculating Statistics with a Statistical Calculator
Calculating Statistics using SPSS
INTERPRETING A MEAN AND STANDARD DEVIATION
Summary
+ Score Transformations
Why Do We Need to Transform Scores?
Percentile Ranks Based on the Sample
Percentile Ranks Based on the Normal Curve
Computing Percentile Ranks Based on the Normal Curve with SPSS
Comparing the Two Methods of Computing Percentile Ranks
An Unfortunate Property
Summary
+ Linear Transformations
The Additive Component
The Multiplicative Component
Linear Transformations: Affect on Mean and Standard Deviation
Linear Transformations: Finding a and b Given and s X'
Standard Score or z-Scores
Finding Linear Transformations Using SPSS
Summary
+ Regression Models
Example Uses of Regression Models
Selecting Colleges
Pregnancy
Selection and Placemen t During the World Wars
Manufacturing Widgets
Procedure for Construction of a Regression Model
The Least-Squares Criteria for Goodness-of-Fit
The Regression Model
Solving for Parameter Values that Satisfy the Least-Square Criterion
Using Statistical Calculators to Solve for Regression Parameters
Demonstration of Optimal Parameter Estimates
Scatter Plots and the Regression Line
The Standard Error of Estimate
Conditional Distributions
Interval Estimates
Regression Analysis Using SPSS
Summary
+ Correlation
Definition
Understanding and Interpreting the Correlation Coefficient
Scatter plots
Slope of the Regression Line of z-scores
Variance Interpretation
Calculation of the Correlation Coefficient
The Correlation Matrix
Cautions about Interpreting Correlation Coefficients
Appropriate Data Type
Effect of Outliers
Correlation and Causation
Summary
+ Hypothesis Testing and Probability Theory
Does Caffeine Make People More Alert?
Hypothesis Testing
Definition and Purpose of Hypothesis Tests
Rational Decisions
Effects
General Principles
The Model
Probability
Combining Probabilities of Independent Events
Combining Probabilities Using "or"
Conditional Probabilities
Including Cost in Making Decisions with Probabilities
Using Probability Models in Science
Establishing Probabilities
Equal Likelihood
Relative Frequency
Area Under Theoretical Models of Frequency Distributions
Subjective Probabilities
Inaccurate estimates of probabilities and their effect
Using Probabilities
In the Long Run
In the Short Run
Summary
+ The Sampling Distribution
The Sample Distribution
Probability Models: Population Distributions
The Sampling Distribution
The Sampling Distribution of the Mean
Computer Simulation of Sampling Distribution
Summary
+ Testing Hypotheses about Single Means
The Head-Start Study
The Head-Start Study Redone
Setting the value of Alpha
Practical Significance versus Statistical Significance
Summary
+ The T-Test
Experimental Designs
Crossed Designs
Example Design
Raw Scores
Analysis Step One: Find the Difference Scores
Analysis Step Two: Find the Mean and Standard Deviation of D i
The Model Under the Null Hypothesis
Analysis Step Three: Estimate the Standard Error
Analysis Step Four: Find the Degrees of Freedom
Analysis Step Five: Find the Significance Level
Using SPSS to Compute a Crossed t-test
Nested t-tests
Analysis and Logic Underlying Nested Designs
Computing a Nested t-test Using SPSS
An Example Without Explanations
The t distribution
Degrees of Freedom
Relationship to the Normal Curve
Testing Hypotheses with the T-Distribution
One- and Two-Tailed T-Tests
Two-Tailed t-tests
One-Tailed t-tests
A one-tailed t-test in the Positive Direction
A one-tailed t-test in the Negative Direction
Comparison of One and Two-tailed t-tests
Summary
+ Errors in Hypothesis Testing
A Second Chance
The Analysis Generalized to All Experiments
Summary
+ Analysis of Variance (ANOVA)
The Bottom Line: Results and Interpretation of ANOVA
Hypothesis Testing Theory Underlying ANOVA
Two Ways of Estimating the Population Parameter sigma sub X squared or the theoretical variance of scores images/sigma2a.gif 21 18 sigma sub X squared
The Within Method
The Between Method
The F-ratio
The F-distribution
Finding Exact Significance Levels for the F-ratio
The Distribution of F-ratios when there are Real Effects
Similarity of ANOVA and t-test
Computing the t-test
Computing the ANOVA
Example of a Non-Significant One-Way ANOVA
Example of a Significant One-Way ANOVA
Summary
+ Chi-Square and Tests of Contingency tables
Review of Contingency Tables
Hypothesis Testing with Contingency Tables
Computation of the Chi-Squared Statistic
The Theoretical Distribution of Chi-Squared When No Effects Are Present
Finding the Exact Significance Level for A Chi-Square Statistic
Interpreting a Significant Chi-Square
Summary
+ Testing a Single Correlation Coefficient
The Hypothesis and Nature of the Effects
The Model of No Effects
Comparing the Obtained Statistic with the Model
Summary
+ Relational Databases and Statistical Packages
Student Attitudes as a Function of Student Attributes, Teacher Attributes, and Environment
A Better Way: Relational Databases
Setting up the Database
Creating a New Database
Creating the Teacher Table in Access
Creating the Other Example Tables
Reading a Relational Database into an SPSS Data File
Adding a Data Source
Selecting Tables From a Data Source
Summary