Statistical Imagination

ISBN-10: 0072943041
ISBN-13: 9780072943047
Edition: 2nd 2008
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Description: This text offers a successful new approach to teaching statistics without anxiety, but without sacrificing clear understanding of basic statistical princples.

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Book details

List price: $247.33
Edition: 2nd
Copyright year: 2008
Publisher: McGraw-Hill Companies, The
Publication date: 1/26/2007
Binding: Hardcover
Pages: 672
Size: 7.75" wide x 9.75" long x 1.25" tall
Weight: 2.838
Language: English

This text offers a successful new approach to teaching statistics without anxiety, but without sacrificing clear understanding of basic statistical princples.

Preface
The Statistical Imagination
Introduction
The Statistical Imagination
Linking the Statistical Imagination to the Sociological Imagination
Statistical Norms and Social Norms
Statistical Ideals and Social Values
Statistics and Science: Tools for Proportional Thinking
Descriptive and Inferential Statistics
What Is Science?
Scientific Skepticism and the Statistical Imagination
Conceiving of Data
The Research Process
Proportional Thinking: Calculating Proportions, Percentages, and Rates
How to Succeed in This Course and Enjoy It
Statistical Follies and Fallacies: The Problem of Small Denominators
Organizing Data to Minimize Statistical Error
Introduction
Controlling Sampling Error
Careful Statistical Estimation versus Hasty Guesstimation
Sampling Error and Its Management with Probability Theory
Controlling Measurement Error
Levels of Measurement: Careful Selection of Statistical Procedures
Measurement
Nominal Variables
Ordinal Variables
Interval Variables
Ratio Variables
Improving the Level of Measurement
Distinguishing Level of Measurement and Unit of Measure
Coding and Counting Observations
Frequency Distributions
Standardizing Score Distributions
Coding and Counting Interval/Ratio Data
Rounding Interval/Ratio Observations
The Real Limits of Rounded Scores
Proportional and Percentage Frequency Distributions for Interval/Ratio Variables
Cumulative Percentage Frequency Distributions
Percentiles and Quartiles
Grouping Interval/Ratio Data
Statistical Follies and Fallacies: The Importance of Having a Representative Sample
Charts and Graphs: A Picture Says a Thousand Words
Introduction: Pictorial Presentation of Data
Graphing and Table Construction Guidelines
Graphing Nominal/Ordinal Data
Pie Charts
Bar Charts
Graphing Interval/Ratio Variables
Histograms
Polygons and Line Graphs
Using Graphs with Inferential Statistics and Research Applications
Statistical Follies and Fallacies: Graphical Distortion
Measuring Averages
Introduction
The Mean
Proportional Thinking about the Mean
Potential Weaknesses of the Mean: Situations Where Reporting It Alone May Mislead
The Median
Potential Weaknesses of the Median: Situations Where Reporting It Alone May Mislead
The Mode
Potential Weaknesses of the Mode: Situations Where Reporting It Alone May Mislead
Central Tendency Statistics and the Appropriate Level of Measurement
Frequency Distribution Curves: Relationships Among the Mean, Median, and Mode
The Normal Distribution
Skewed Distributions
Using Sample Data to Estimate the Shape of a Score Distribution in a Population
Organizing Data for Calculating Central Tendency Statistics
Spreadsheet Format for Calculating Central Tendency Statistics
Frequency Distribution Format for Calculating the Mode
Statistical Follies and Fallacies: Mixing Subgroups in the Calculation of the Mean
Measuring Dispersion or Spread in a Distribution of Scores
Introduction
The Range
Limitations of the Range: Situations Where Reporting It Alone May Mislead
The Standard Deviation
Proportional and Linear Thinking about the Standard Deviation
Limitations of the Standard Deviation
The Standard Deviation as an Integral Part of Inferential Statistics
Why Is It Called the "Standard" Deviation?
Standardized Scores (Z-Scores)
The Standard Deviation and the Normal Distribution
Tabular Presentation of Results
Statistical Follies and Fallacies: What Does It Indicate When the Standard Deviation Is Larger than the Mean?
Probability Theory and the Normal Probability Distribution
Introduction: The Human Urge to Predict the Future
What Is a Probability?
Basic Rules of Probability Theory
Probabilities Always Range Between 0 and 1
The Addition Rule for Alternative Events
Adjust for Joint Occurrences
The Multiplication Rule for Compound Events
Account for Replacement with Compound Events
Using the Normal Curve as a Probability Distribution
Proportional Thinking about a Group of Cases and Single Cases
Partitioning Areas Under the Normal Curve
Sample Problems Using the Normal Curve
Computing Percentiles for Normally Distributed Populations
The Normal Curve as a Tool for Proportional Thinking
Statistical Follies and Fallacies: The Gambler's Fallacy: Independence of Probability Events
Using Probability Theory to Produce Sampling Distributions
Introduction: Estimating Parameters
Point Estimates
Predicting Sampling Error
Sampling Distributions
Sampling Distributions for Interval/Ratio Variables
The Standard Error
The Law of Large Numbers
The Central Limit Theorem
Sampling Distributions for Nominal Variables
Rules Concerning a Sampling Distribution of Proportions
Bean Counting as a Way of Grasping the Statistical Imagination
Distinguishing Among Populations, Samples, and Sampling Distributions
Statistical Follies and Fallacies: Treating a Point Estimate as Though It Were Absolutely True
Parameter Estimation Using Confidence Intervals
Introduction
Confidence Interval of a Population Mean
Calculating the Standard Error for a Confidence Interval of a Population Mean
Choosing the Critical Z-Score, Z[subscript Alpha]
Calculating the Error Term
Calculating the Confidence Interval
The Five Steps for Computing a Confidence Interval of a Population Mean, Mu[subscript x]
Proper Interpretation of Confidence Intervals
Common Misinterpretations of Confidence Intervals
The Chosen Level of Confidence and the Precision of the Confidence Interval
Sample Size and the Precision of the Confidence Interval
Large-Sample Confidence Interval of a Population Proportion
Choosing a Sample Size for Polls, Surveys, and Research Studies
Sample Size for a Confidence Interval of a Population Proportion
Statistical Follies and Fallacies: It Is Plus and Minus the Error Term
Hypothesis Testing I: The Six Steps of Statistical Inference
Introduction: Scientific Theory and the Development of Testable Hypotheses
Making Empirical Predictions
Statistical Inference
The Importance of Sampling Distributions for Hypothesis Testing
The Six Steps of Statistical Inference for a Large Single-Sample Means Test
Test Preparation
The Six Steps
Special Note on Symbols
Understanding the Place of Probability Theory in Hypothesis Testing
A Focus on p-Values
The Level of Significance and Critical Regions of the Sampling Distribution Curve
The Level of Confidence
Study Hints: Organizing Problem Solutions
Solution Boxes Using the Six Steps
Interpreting Results When the Null Hypothesis Is Rejected: The Hypothetical Framework of Hypothesis Testing
Selecting Which Statistical Test to Use
Statistical Follies and Fallacies: Informed Common Sense: Going Beyond Common Sense by Observing Data
Hypothesis Testing II: Single-Sample Hypothesis Tests: Establishing the Representativeness of Samples
Introduction
The Small Single-Sample Means Test
The "Students' t" Sampling Distribution
Selecting the Critical Probability Score, t[subscript Alpha], from the t-distribution Table
Special Note on Symbols
What Are Degrees of Freedom?
The Six Steps of Statistical Inference for a Small Single-Sample Means Test
Gaining a Sense of Proportion About the Dynamics of a Means Test
Relationships among Hypothesized Parameters, Observed Sample Statistics, Computed Test Statistics, p-Values, and Alpha Levels
Using Single-Sample Hypothesis Tests to Establish Sample Representativeness
Target Values for Hypothesis Tests of Sample Representativeness
Large Single-Sample Proportions Test
The Six Steps of Statistical Inference for a Large Single-Sample Proportions Test
What to Do If a Sample Is Found Not to Be Representative?
Presentation of Data from Single-Sample Hypothesis Tests
A Confidence Interval of the Population Mean When n Is Small
Statistical Follies and Fallacies: Issues of Sample Size and Sample Representativeness
Bivariate Relationships: t-Test for Comparing the Means of Two Groups
Introduction: Bivariate Analysis
Difference of Means Tests
Joint Occurrences of Attributes
Correlation
Two-Group Difference of Means Test (t-Test) for Independent Samples
The Standard Error and Sampling Distribution for the t-Test of the Difference Between Two Means
The Six Steps of Statistical Inference for the Two-Group Difference of Means Test
When the Population Variances (or Standard Deviations) Appear Radically Different
The Two-Group Difference of Means Test for Nonindependent or Matched-Pair Samples
The Six Steps of Statistical Inference for the Two-Group Difference of Means Test for Nonindependent or Matched-Pair Samples
Practical versus Statistical Significance
The Four Aspects of Statistical Relationships
Existence of a Relationship
Direction of the Relationship
Strength of the Relationship, Predictive Power, and Proportional Reduction in Error
Practical Applications of the Relationship
When to Apply the Various Aspects of Relationships
Relevant Aspects of a Relationship for Two-Group Difference of Means Tests
Statistical Follies and Fallacies: Fixating on Differences of Means While Ignoring Differences in Variances
Analysis of Variance: Differences Among Means of Three or More Groups
Introduction
Calculating Main Effects
The General Linear Model: Testing the Statistical Significance of Main Effects
Determining the Statistical Significance of Main Effects Using ANOVA
The F-Ratio Test Statistic
How the F-Ratio Turns Out When Group Means Are Not Significantly Different
The F-Ratio as a Sampling Distribution
Relevant Aspects of a Relationship for ANOVA
Existence of the Relationship
Direction of the Relationship
Strength of the Relationship
Practical Applications of the Relationship
The Six Steps of Statistical Inference for One-Way ANOVA
Tabular Presentation of Results
Multivariate Applications of the General Linear Model
Similarities Between the t-Test and the F-Ratio Test
Statistical Follies and Fallacies: Individualizing Group Findings
Nominal Variables: The Chi-Square and Binomial Distributions
Introduction: Proportional Thinking About Social Status
Crosstab Tables: Comparing the Frequencies of Two Nominal/Ordinal Variables
The Chi-Square Test: Focusing on the Frequencies of Joint Occurrences
Calculating Expected Frequencies
Differences Between Observed and Expected Cell Frequencies
Degrees of Freedom for the Chi-Square Test
The Chi-Square Sampling Distribution and Its Critical Regions
The Six Steps of Statistical Inference for the Chi-Square Test
Relevant Aspects of a Relationship for the Chi-Square Test
Using Chi-Square as a Difference of Proportions Test
Tabular Presentation of Data
Small Single-Sample Proportions Test: The Binomial Distribution
The Binomial Distribution Equation
Shortcut Formula for Expanding the Binomial Equation
The Six Steps of Statistical Inference for a Small Single-Sample Proportions Test: The Binomial Distribution Test
Statistical Follies and Fallacies: Low Statistical Power When the Sample Size Is Small
Bivariate Correlation and Regression: Part 1: Concepts and Calculations
Introduction: Improving Best Estimates of a Dependent Variable
A Correlation Between Two Interval/Ratio Variables
Identifying a Linear Relationship
Drawing the Scatterplot
Identifying a Linear Pattern
Using the Linear Regression Equation to Measure the Effects of X on Y
Pearson's r Bivariate Correlation Coefficient
Computational Spreadsheet for Calculating Bivariate Correlation and Regression Statistics
Characteristics of the Pearson's r Bivariate Correlation Coefficient
Understanding the Pearson's r Formulation
Regression Statistics
The Regression Coefficient or Slope, b
The Y-intercept, a
Calculating the Terms of the Regression Line Formula
For the Especially Inquisitive: The Mathematical Relationship Between Pearson's r Correlation Coefficient and the Regression Coefficient, b
Statistical Follies and Fallacies The Failure to Observe a Scatterplot Before Calculating Pearson's r
Linear Equations Work Only with a Linear Pattern in the Scatterplot
Outlier Coordinates and the Attenuation and Inflation of Correlation Coefficients
Bivariate Correlation and Regression: Part 2: Hypothesis Testing and Aspects of a Relationship
Introduction: Hypothesis Test and Aspects of a Relationship Between Two Interval/Ratio Variables
Organizing Data for the Hypothesis Test
The Six Steps of Statistical Inference and the Four Aspects of a Relationship
Existence of a Relationship
Direction of the Relationship
Strength of the Relationship
Practical Applications of the Relationship
Careful Interpretation of Correlation and Regression Statistics
Correlations Apply to a Population, Not to an Individual
Careful Interpretation of the Slope, b
Distinguishing Statistical Significance from Practical Significance
Tabular Presentation: Correlation Tables
Statistical Follies and Fallacies: Correlation Does Not Always Indicate Causation
Review of Basic Mathematical Operations
Statistical Probability Tables
Statistical Table A-Random Number Table
Statistical Table B-Normal Distribution Table
Statistical Table C-t-Distribution Table
Statistical Table D-Critical Values of the F-Ratio Distribution at the .05 Level of Significance
Statistical Table E-Critical Values of the F-Ratio Distribution at the .01 Level of Significance
Statistical Table F-q-Values of Range Tests at the .05 and .01 Levels of Significance
Statistical Table G-Critical Values of the Chi-Square Distribution
Answers to Selected Chapter Exercises
Guide to SPSS for Windows
References
Index

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