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1st Edition

Introductory Statistics for the Health Sciences

By

,

Larry E. Toothaker

ISBN 9781466565333
Published March 23, 2015 by Chapman and Hall/CRC
603 Pages 151 Color Illustrations

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Book Description

Introductory Statistics for the Health Sciences takes students on a journey to a wilderness where science explores the unknown, providing students with a strong, practical foundation in statistics. Using a color format throughout, the book contains engaging figures that illustrate real data sets from published research. Examples come from many areas of the health sciences, including medicine, nursing, pharmacy, dentistry, and physical therapy, but are understandable to students in any field. The book can be used in a first-semester course in a health sciences program or in a service course for undergraduate students who plan to enter a health sciences program.

The book begins by explaining the research context for statistics in the health sciences, which provides students with a framework for understanding why they need statistics as well as a foundation for the remainder of the text. It emphasizes kinds of variables and their relationships throughout, giving a substantive context for descriptive statistics, graphs, probability, inferential statistics, and interval estimation. The final chapter organizes the statistical procedures in a decision tree and leads students through a process of assessing research scenarios.

Web Resource
The authors have partnered with William Howard Beasley, who created the illustrations in the book, to offer all of the data sets, graphs, and graphing code in an online data repository via GitHub. A dedicated website gives information about the data sets and the authors’ electronic flashcards for iOS and Android devices. These flashcards help students learn new terms and concepts.

The Frontier between Knowledge and Ignorance
Introduction
The Context for Statistics: Science and Research
Definition of Statistics
The Big Picture: Populations, Samples, and Variables
Generalizing from the Sample to the Population
Experimental Research
Blinding and Randomized Block Design
Nonexperimental Research
Quasi-Experimental Research
Inferences and Kinds of Validity

Describing Distributions with Statistics: Middle, Spread, and Skewness
Introduction
Measures of Location
Measure of Skewness or Departure from Symmetry

Exploring Data Visually
Introduction
Why Graph Our Data?
Pie Charts and Bar Graphs
Two Kinds of Dot Plots
Scatterplots
Histograms
Time Plots (Line Graphs)
Boxplots
Beyond These Graphs

Relative Location and Normal Distributions
Introduction
Standardizing Scores
Computing a z Score in a Sample
Computing a z Score in a Population
Comparing z Scores for Different Variables
A Different Kind of Standard Score
Distributions and Proportions
Areas under the Standard Normal Curve

Bivariate Correlation
Introduction
Pearson’s Correlation Coefficient
Verbal Definition of Pearson’s r
Judging the Strength of a Correlation
What Most Introductory Statistics Texts Say about Correlation
Pearson’s r Measures Linear Relationships Only
Correlations Can Be Influenced by Outliers
Correlations and Restriction of Range
Combining Groups of Scores Can Affect Correlations
Missing Data Are Omitted from Correlations
Pearson’s r Does Not Specify Which Variable Is the Predictor

Probability and Risk
Introduction
Relative Frequency of Occurrence
Conditional Probability
Special Names for Certain Conditional Probabilities
Statistics Often Accompanying Sensitivity and Specificity
Two Other Probabilities: "And" and "Or"
Risk and Relative Risk
Other Statistics Associated with Probability

Sampling Distributions and Estimation
Introduction
Quantifying Variability from Sample to Sample
Kinds of Distributions
Why We Need Sampling Distributions
Comparing Three Distributions: What We Know So Far
Central Limit Theorem
Unbiased Estimators
Standardizing the Sample Mean
Interval Estimation
Calculating a Confidence Interval Estimate of μ

Hypothesis Testing and Interval Estimation
Introduction
Testable Guesses
The Rat Shipment Story
Overview of Hypothesis Testing
Two Competing Statements about What May Be True
Writing Statistical Hypotheses
Directional and Nondirectional Alternative Hypotheses
Choosing a Small Probability as a Standard
Compute the Test Statistic and a Certain Probability
Decision Rules When H1 Predicts a Direction
Decision Rules When H1 Is Nondirectional
Assumptions
Testing Hypotheses with Confidence Intervals: Nondirectional H1
Testing Hypotheses with Confidence Intervals: Directional H1

Types of Errors and Power
Introduction
Possible Errors in Hypothesis Testing
Probability of a Type I Error
Probability of Correctly Retaining the Null Hypothesis
Type I Errors and Confidence Intervals
Probability of a Type II Error and Power
Factors Influencing Power: Effect Size
Factors Influencing Power: Sample Size
Factors Influencing Power: Directional Alternative Hypotheses
Factors Influencing Power: Significance Level
Factors Influencing Power: Variability
Factors Influencing Power: Relation to Confidence Intervals

One-Sample Tests and Estimates
Introduction
One-Sample t Test
Distribution for Critical Values and p Values
Critical Values for the One-Sample t Test
Completing the Sleep Quality Example
Assumptions
Confidence Interval for μ Using One-Sample t Critical Value
Graphing Confidence Intervals and Sample Means

Two-Sample Tests and Estimates
Introduction
Pairs of Scores and the Paired t Test
Two Other Ways of Getting Pairs of Scores
Fun Fact Associated with Paired Means
Paired t Hypotheses When Direction Is Not Predicted
Paired t Hypotheses When Direction Is Predicted
Formula for the Paired t Test
Confidence Interval for the Difference in Paired Means
Comparing Means of Two Independent Groups
Independent t Hypotheses When Direction Is Not Predicted
Independent t Hypotheses When Direction Is Predicted
Formula for the Independent-Samples t Test
Assumptions
Confidence Intervals for a Difference in Independent Means
Limitations on Using the t Statistics in This Chapter

Tests and Estimates for Two or More Samples
Introduction
Going beyond the Independent-Samples t Test
Variance between Groups and Within Groups
One-Way ANOVA F Test: Logic and Hypotheses
Computing the One-Way ANOVA F Test
Critical Values and Decision Rules
Numeric Example of a One-Way ANOVA F Test
Testing the Null Hypothesis
Assumptions and Robustness
How to Tell Which Group Is Best
Multiple Comparison Procedures and Hypotheses
Many Statistics Possible for Multiple Comparisons
Confidence Intervals in a One-Way ANOVA Design

Tests and Estimates for Bivariate Linear Relationships
Introduction
Testing a Null Hypothesis about a Correlation
Assumptions of Pearson’s r
Using a Straight Line for Prediction
Linear Regression Analysis
Determining the Best-Fitting Line
Hypothesis Testing in Bivariate Regression
Confidence Intervals in Simple Regression
Limitations on Using Regression

Analysis of Frequencies and Ranks
Introduction
One-Sample Proportion
Confidence Interval for a Proportion
Goodness of Fit Hypotheses
Goodness of Fit Statistic
Computing the Chi-Square Test for Goodness of Fit
Goodness of Fit: Assumptions and Robustness
Chi-Square for Independence
Hypotheses for Chi-Square for Independence
Computing Chi-Square for Independence
Relative Risk
Odds Ratios
Analysis of Ranks

Choosing an Analysis Plan
Introduction
Statistics That We Have Covered
Organizing Our List: Kind of Outcomes, Number of Samples
Adding to the Tree: Two Samples
Adding Again to the Tree: More Than Two Samples
Completing the Tree: Analysis of Categories
Completing the Tree: The Remaining Categorical Analyses

Appendix

Index

References appear at the end of each chapter.

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Author(s)

Biography

Lise DeShea is the senior research biostatistician in the College of Nursing at the University of Oklahoma Health Sciences Center. She has served on the faculty of the University of Kentucky and worked as a statistician for a Medicaid agency. She has conducted research on emergency room utilization, bootstrapping, and forgiveness.

Larry E. Toothaker is an emeritus David Ross Boyd Professor, the highest honor for teaching excellence at the University of Oklahoma. He has conducted research on multiple comparison procedures and nonparametric methods. He retired in 2008 after teaching statistics in the Department of Psychology for 40 years.

Reviews

"… well-written and easy to understand … the examples and exercises are very nicely done. I found myself wanting to work through all of them! … the figures and tables are visually appealing and useful. … many students in the health sciences will find the text to be interesting and useful.
I think that the material is perfect for those who are math-phobic and those who have not taken any math classes in several years. … The figures illustrate the concepts well, and the practice scenarios are very helpful for students to assess what they have learned …"
—Robert A. Oster, PhD, Department of Medicine, University of Alabama at Birmingham, and Former Chair and Program Chair of the American Statistical Association Section on Teaching of Statistics in the Health Sciences

Support Material

Ancillaries

• Instructor Resources