Fundamentals of Statistical Reasoning in Education

ISBN-10: 0470084065
ISBN-13: 9780470084069
Edition: 2nd 2008 (Revised)
List price: $160.95
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Description: This volume gives educators the statistical knowledge and skills necessary in everyday classroom teaching, in running schools and in professional development pursuits.

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Book details

List price: $160.95
Edition: 2nd
Copyright year: 2008
Publisher: John Wiley & Sons, Incorporated
Publication date: 9/9/2008
Binding: Paperback
Pages: 496
Size: 7.50" wide x 9.25" long x 0.75" tall
Weight: 1.496
Language: English

This volume gives educators the statistical knowledge and skills necessary in everyday classroom teaching, in running schools and in professional development pursuits.

Casey Cobb is Associate Professor of Education Policy and Director of the Center for Education Policy Analysis at the University of Connecticut. His current research interests include policies on accountability, school choice, and bilingual education, where he examines the implications for equity among historically marginalized populations. He teaches courses in policy studies, research methods and evaluation. Casey has also served as evaluator on several projects, most recently working with the Connecticut Department of Education to study inter-district magnet programs.

Introduction
Why Statistics?
Descriptive Statistics
Inferential Statistics
The Role of Statistics in Educational Research
Variables and Their Measurement
Some Tips on Studying Statistics
Descriptive Statistics
Frequency Distributions
Why Organize Data?
Frequency Distributions for Quantitative Variables
Grouped Scores
Some Guidelines for Forming Class Intervals
Constructing a Grouped-Data Frequency Distribution
The Relative Frequency Distribution
Exact Limits
The Cumulative Percentage Frequency Distribution
Percentile Ranks
Frequency Distributions for Qualitative Variables
Summary
Graphic Representation
Why Graph Data?
Graphing Qualitative Data: The Bar Chart
Graphing Quantitative Data: The Histogram
The Frequency Polygon
Comparing Different Distributions
Relative Frequency and Proportional Area
Characteristics of Frequency Distributions
The Box Plot
Summary
Central Tendency
The Concept of Central Tendency
The Mode
The Median
The Arithmetic Mean
Central Tendency and Distribution Symmetry
Which Measure of Central Tendency to Use?
Summary
Variability
Central Tendency Is Not Enough: The Importance of Variability
The Range
Variability and Deviations from the Mean
The Variance
The Standard Deviation
The Predominance of the Variance and Standard Deviation
The Standard Deviation and the Normal Distribution
Comparing Means of Two Distributions: The Relevance of Variability
In the Denominator: n vs. n - 1
Summary
Normal Distributions and Standard Scores
A Little History: Sir Francis Galton and the Normal Curve
Properties of the Normal Curve
More on the Standard Deviation and the Normal Distribution
z Scores
The Normal Curve Table
Finding Area When the Score Is Known
Reversing the Process: Finding Scores When the Area Is Known
Comparing Scores from Different Distributions
Interpreting Effect Size
Percentile Ranks and the Normal Distribution
Other Standard Scores
Standard Scores Do Not "Normalize" a Distribution
The Normal Curve and Probability
Summary
Correlation
The Concept of Association
Bivariate Distributions and Scatterplots
The Covariance
The Pearson r
Computation of r: The Calculating Formula
Correlation and Causation
Factors Influencing Pearson r
Judging the Strength of Association: r[superscript 2]
Other Correlation Coefficients
Summary
Regression and Prediction
Correlation versus Prediction
Determining the Line of Best Fit
The Regression Equation in Terms of Raw Scores
Interpreting the Raw-Score Slope
The Regression Equation in Terms of z Scores
Some Insights Regarding Correlation and Prediction
Regression and Sums of Squares
Measuring the Margin of Prediction Error: The Standard Error of Estimate
Correlation and Causality (Revisited)
Summary
Inferential Statistics
Probability and Probability Distributions
Statistical Inference: Accounting for Chance in Sample Results
Probability: The Study of Chance
Definition of Probability
Probability Distributions
The Or/addition Rule
The And/multiplication Rule
The Normal Curve as a Probability Distribution
"So What?" Probability Distributions as the Basis for Statistical Inference
Summary
Sampling Distributions
From Coins to Means
Samples and Populations
Statistics and Parameters
Random Sampling Model
Random Sampling in Practice
Sampling Distributions of Means
Characteristics of a Sampling Distribution of Means
Using a Sampling Distribution of Means to Determine Probabilities
The Importance of Sample Size (n)
Generality of the Concept of a Sampling Distribution
Summary
Testing Statistical Hypotheses about [Mu] When [sigma] Is Known: The One-Sample z Test
Testing a Hypothesis about [Mu]: Does "Homeschooling" Make a Difference?
Dr. Meyer's Problem in a Nutshell
The Statistical Hypotheses: H[subscript 0] and H[subscript 1]
The Test Statistic z
The Probability of the Test Statistic: The p Value
The Decision Criterion: Level of Significance ([alpha])
The Level of Significance and Decision Error
The Nature and Role of H[subscript 0] and H[subscript 1]
Rejection versus Retention of H[subscript 0]
Statistical Significance versus Importance
Directional and Nondirectional Alternative Hypotheses
Prologue: The Substantive versus the Statistical
Summary
Estimation
Hypothesis Testing versus Estimation
Point Estimation versus Interval Estimation
Constructing an Interval Estimate of [Mu]
Interval Width and Level of Confidence
Interval Width and Sample Size
Interval Estimation and Hypothesis Testing
Advantages of Interval Estimation
Summary
Testing Statistical Hypotheses about [Mu] When [sigma] Is Not Known: The One-Sample t Test
Reality: [sigma] Often Is Unknown
Estimating the Standard Error of the Mean
The Test Statistic t
Degrees of Freedom
The Sampling Distribution of Student's t
An Application of Student's t
Assumption of Population Normality
Levels of Significance versus p Values
Constructing a Confidence Interval for [Mu] When [sigma] Is Not Known
Summary
Comparing the Means of Two Populations: Independent Samples
From One Mu to Two
Statistical Hypotheses
The Sampling Distribution of Differences Between Means
Estimating [Characters not reproducible]
The t Test for Two Independent Samples
Testing Hypotheses about Two Independent Means: An Example
Interval Estimation of [Mu subscript 1] - [Mu subscript 2]
Appraising the Magnitude of a Difference: Measures of Effect Size for X[subscript 1]-X[subscript 2]
How Were Groups Formed? The Role of Randomization
Statistical Inferences and Nonstatistical Generalizations
Summary
Comparing the Means of Dependent Samples
The Meaning of "Dependent"
Standard Error of the Difference Between Dependent Means
Degrees of Freedom
The t Test for Two Dependent Samples
Testing Hypotheses about Two Dependent Means: An Example
Interval Estimation of [Mu subscript D]
Summary
Comparing the Means of Three or More Independent Samples: One-Way Analysis of Variance
Comparing More Than Two Groups: Why Not Multiple t Tests?
The Statistical Hypotheses in One-Way ANOVA
The Logic of One-Way ANOVA: An Overview
Alison's Reply to Gregory
Partitioning the Sums of Squares
Within-Groups and Between-Groups Variance Estimates
The F Test
Tukey's "HSD" Test
Interval Estimation of [Mu subscript i] - [Mu subscript j]
One-Way ANOVA: Summarizing the Steps
Estimating the Strength of the Treatment Effect: Effect Size ([Omega superscript 2])
ANOVA Assumptions (and Other Considerations)
Summary
Inferences about the Pearson Correlation Coefficient
From [Mu] to [rho]
The Sampling Distribution of r When [rho] = 0
Testing the Statistical Hypothesis That [rho] = 0
An Example
Table E
The Role of n in the Statistical Significance of r
Statistical Significance versus Importance (Again)
Testing Hypotheses Other Than [rho] = 0
Interval Estimation of [rho]
Summary
Making Inferences from Frequency Data
Frequency Data versus Score Data
A Problem Involving Frequencies: The One-Variable Case
X[superscript 2]: A Measure of Discrepancy Between Expected and Observed Frequencies
The Sampling Distribution of X[superscript 2]
Completion of the Voter Survey Problem: The X[superscript 2] Goodness-of-Fit Test
The X[superscript 2] Test of a Single Proportion
Interval Estimate of a Single Proportion
When There Are Two Variables: The X[superscript 2] Test of Independence
Finding Expected Frequencies in the Two-Variable Case
Calculating the Two-Variable X[superscript 2]
The X[superscript 2] Test of Independence: Summarizing the Steps
The 2 x 2 Contingency Table
Testing a Difference Between Two Proportions
The Independence of Observations
X[superscript 2] and Quantitative Variables
Other Considerations
Summary
Statistical "Power" (and How to Increase It)
The Power of a Statistical Test
Power and Type II Error
Effect Size (Revisited)
Factors Affected Power: The Effect Size
Factors Affecting Power: Sample Size
Additional Factors Affecting Power
Significance versus Importance
Selecting an Appropriate Sample Size
Summary
References
Review of Basic Mathematics
Introduction
Symbols and Their Meaning
Arithmetic Operations Involving Positive and Negative Numbers
Squares and Square Roots
Fractions
Operations Involving Parentheses
Approximate Numbers, Computational Accuracy, and Rounding
Answers to Selected End-of-Chapter Problems
Statistical Tables
Index
Useful Formulas

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