Elementary Statistics Looking at the Big Picture

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  • Edition: 1st
  • Format: Hardcover
  • Copyright: 2010-01-01
  • Publisher: Duxbury Press
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Using a successfully class-tested approach that gives coherence to a broad range of introductory topics, this innovative text provides students with a big picture view of statistics as well as problem-solving strategies that can be applied in many statistical problems. Author Nancy Pfenning organizes content around four basic processes of statistics: producing data, displaying and summarizing data, understanding probability, and performing statistical inference. Within this framework, the book progresses systematically through five basic problem situations involving values of variables (quantitative, categorical, or a blend). As a result, students learn to identify which situation applies to a specific problem and how to choose the correct display, summary, or inference tool. As students gain proficiency in specific statistical techniques, the author also points out connections among topics and techniques to help them gain a perspective on statistics as a whole. More than 1,000 real-life examples and categorized exercises support the approach, engaging students in practicing and developing a variety of skills.

Table of Contents

Introduction: Variables and Processes in Statistics
Types of Variables: Categorical or Quantitative
Students Talk Stats: Identifying Types of Variables
Data for Two Types of Variables
Roles of Variables: Explanatory or Response
Statistics as a Four-Stage Process
Data Production
Sampling: Which Individuals Are Studied
Sources of Bias in Sampling: When Selected Individuals Are Not Representative
Probability Sampling Plans: Relying on Randomness
Role of Sample Size: Bigger Is Better if the Sample Is Representative
From Sample to Population: To What Extent Can We Generalize?
Students Talk Stats: Seeking a Representative Sample
Design: How Individuals Are Studied
Various Designs for Studying Variables
Sample Surveys: When Individuals Report Their Own Values
Observational Studies: When Nature Takes Its Course
Experiments: When Researchers Take Control
Students Talk Stats: Does TV Cause ADHD?
Considering Study Design
Displaying and Summarizing Data
Displaying and Summarizing Data for a Single Variable
Single Categorical Variable
Students Talk Stats: Biased Sample, Biased Assessment
Single Quantitative Variables and the Shape of a Distribution
Center and Spread: What's Typical for Quantitative Values, and How They Vary
Normal Distributions: The Shape of Things to Come
Displaying and Summarizing Relationships
Relationship Between One Categorical and One Quantitative Variable
Students Talk Stats: Displaying and Summarizing Paired Data
Relationship Between Two Categorical Variables
Relationships Between Two Quantitative Variables
Students Talk Stats: How Outliers and Influential Observations Affect a Relationship
Students Talk Stats: Confounding in a Relationship Between Two Quantitative Variables
Finding Probabilities
The Meaning of "Probability" and Basic Rules
More General Probability Rules and Conditional Probability
Students Talk Stats: Probability as a Weighted Average of Conditional Probabilities
Random Variables
Discrete Random Variables
Binomial Random Variables
Students Talk Stats: Calculating and Interpreting the Mean and Standard Deviation of Count or Proportion
Continuous Random Variables and the Normal Distribution
Students Talk Stats: Means, Standard Deviations, and Below-Average Heights
Sampling Distributions
The Behavior of Sample Proportion in Repeated Random Samples
The Behavior of Sample Mean in Repeated Random Samples
Students Talk Stats: When Normal Approximations Are Appropriate
Statistical Inference
Inference for a Single Categorical Variable
Point Estimate and Confidence Interval: A Best Guess and a Range of Plausible Values for Population Proportion
Students Talk Stats: Interpreting a Confidence Interval
Test: Is a Proposed Population Proportion Plausible?
Students Talk Stats: Interpreting a P-value
Students Talk Stats: What Type of Error Was Made?
Students Talk Stats: The Correct Interpretation of a Small P-value
Students Talk Stats: The Correct Interpretation When a P-value Is Not Small
Inference for a Single Quantitative Variable
Inference for a Mean when Population Standard Deviation Is Known or Sample Size Is Large
Students Talk Stats: Confidence Interval for a Mean
Students Talk Stats: Interpreting a Confidence Interval for the Mean Correctly
Inference for a Mean When the Population Standard Deviation Is Unknown and the Sample Size Is Small
Students Talk Stats: Practical Application of a t Test
A Closer Look at Inference for Means
Inference for Relationships Between Categorical and Quantitative Variables
Inference for a Paired Design with t
Inference for a Two-Sample Design with t
Students Talk Stats: Ordinary vs. Pooled Two-Sample t
Inference for a Several-sample Design with F: Analysis of Variance
Students Talk Stats: Reviewing Relationships between Categorical and Quantitative Variables
Inference for Relationships Between Two Categorical Variables
Comparing Proportions with a z Test
Comparing Counts with a Chi-Square Test
Inference for Relationships Between Two Quantitative Variables
Inference for Regression: Focus on the Slope of the Regression Line
Students Talk Stats: No Evidence of a Relationship
Interval Estimates for an Individual or Mean Response
How Statistics Problems Fit into the Big Picture
The Big Picture in Problem-Solving
Students Talk Stats: Choosing the Appropriate Statistical Tools
Non-Parametric Methods (Online)
The Sign Test as an Alternative to the Paired t Test
The Rank-Sum Test as an Alternative to the Two-Sample t Test
Summary of Non-Parametrics
Two-Way ANOVA (Online)
Multiple Regression (Online)
Solutions to Selected Exercises
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