Statistics for the Life Sciences 1st edition by Myra Samuels 9780321989581 0321989589

Chapter 1 Introduction

Objectives

1.1 Statistics and the Life Sciences

Example 1.1.1 Vaccine for Anthrax

Example 1.1.2 Bacteria and Cancer

Example 1.1.3 Flooding and ATP

Example 1.1.4 MAO and Schizophrenia

Example 1.1.5 Food Choice by Insect Larvae

Example 1.1.6 Body Size and Energy Expenditure

A Look Ahead

1.2 Types of Evidence

Example 1.2.1 Lightning and Deafness

Example 1.2.2 Sexual Orientation

Example 1.2.3 Health and Marriage

Example 1.2.4 Toxicity in Dogs

Example 1.2.5 Autism

Example 1.2.6 Bronchial Asthma

Example 1.2.7 Renal Denervation

Blinding

The Need for Control Groups

Example 1.2.8 Clofibrate

Example 1.2.9 The Common Cold

Example 1.2.10 Diet and Cancer Prevention

Historical Controls

Example 1.2.11 Coronary Artery Disease

Example 1.2.12 Healthcare Trials

Exercises 1.2.1–1.2.10

1.3 Random Sampling

Samples and Populations

Remark

Definition of a Simple Random Sample

Employing Randomness

How to Choose a Random Sample

Example 1.3.1

Remark

Remark

Practical Concerns When Random Sampling

Nonsimple Random Sampling Methods

Example 1.3.2 La Graciosa Thistle

Example 1.3.3 Sand Crabs

Sampling Error

Example 1.3.4 Lengths of Fish

Example 1.3.5 Sizes of Nerve Cells

Example 1.3.6 Sucrose in Beet Roots

Example 1.3.7 Fungus Resistance in Corn

Example 1.3.8 Nitrite Metabolism

Example 1.3.9 Treatment of Ulcerative Colitis

Nonsampling Errors

Example 1.3.10 Abortion Funding

Example 1.3.11 HIV Testing

Example 1.3.12 Sugar and Hyperactivity

Exercises 1.3.1–1.3.7

Chapter 2 Description of Samples and Populations

Objectives

2.1 Introduction

Variables

Observational Units

Notation for Variables and Observations

Exercises 2.1.1–2.1.5

2.2 Frequency Distributions

Example 2.2.1 Color of Poinsettias

Example 2.2.2 School Bags and Neck Pain

Example 2.2.3 Infant Mortality

Example 2.2.4 Litter Size of Sows

Relative Frequency

Example 2.2.5 Color of Poinsettias

Grouped Frequency Distributions

Example 2.2.6 Serum CK

Example 2.2.7 Heights of Students

Interpreting Areas in a Histogram

Shapes of Distributions

Example 2.2.8 Microfossils

Example 2.2.9 Cell Firing Times

Example 2.2.10 Brain Weight

Sources of Variation

Example 2.2.11 Weights of Seeds

Example 2.2.12 Serum ALT

Exercises 2.2.1–2.2.9

2.3 Descriptive Statistics: Measures of Center

The Median

Example 2.3.1 Weight Gain of Lambs

Example 2.3.2 Weight Gain of Lambs

The Mean

Example 2.3.3 Weight Gain of Lambs

Example 2.3.4 Weight Gain of Lambs

Robustness

Example 2.3.5 Weight Gain of Lambs

Visualizing the Mean and Median

Example 2.3.6 Cricket Singing Times

Mean versus Median

Exercises 2.3.1–2.3.14

2.4 Boxplots

Quartiles and the Interquartile Range

Example 2.4.1 Blood Pressure

Example 2.4.2 Pulse

Outliers

Example 2.4.3 Pulse

Example 2.4.4 Radish Growth in Light

Boxplots for data with no outliers

Example 2.4.5 Radish Growth

Boxplots for data with Outliers

Exercises 2.4.1–2.4.8

2.5 Relationships between Variables

Categorical–Categorical Relationships

Example 2.5.1 E. Coli Watershed Contamination

Example 2.5.2 E. Coli Watershed Contamination

Numeric–Categorical Relationships

Example 2.5.3 Radish Growth

Numeric–Numeric Relationships

Example 2.5.4 Whale Selenium

Exercises 2.5.1–2.5.4

2.6 Measures of Dispersion

The Range

Example 2.6.1 Blood Pressure

The Standard Deviation

Example 2.6.2 Chrysanthemum Growth

Example 2.6.3 Chrysanthemum Growth

An abbreviation

Interpretation of the Definition of s

Example 2.6.4 Chrysanthemum Growth

Why n − 1?

Example 2.6.5 Chrysanthemum Growth

Visualizing Measures of Dispersion

Example 2.6.6 Daily Gain of Cattle

Visualizing the Standard Deviation

Example 2.6.7 Daily Gain of Cattle

Estimating the SD from a Histogram

Example 2.6.8 Pulse after Exercise

Comparison of Measures of Dispersion

Exercises 2.6.1–2.6.17

2.7 Effect of Transformation of Variables (Optional)

Example 2.7.1 Weight

Example 2.7.2 Body Temperature

How Linear Transformations Affect the Frequency Distribution

Example 2.7.3 Body Temperature

How Linear Transformations Affect y¯ and s

Example 2.7.4 Additive Transformation

Other Statistics

Nonlinear Transformations

Example 2.7.5 Cricket Singing Times

Exercises 2.7.1–2.7.6

2.8 Statistical Inference

Example 2.8.1 Blood Types

Specifying the Population

Example 2.8.2 Blood Types

Example 2.8.3 Alcohol and MOPEG

Describing a Population

Proportions

Example 2.8.4 Oat Plants

Remark

Example 2.8.5 Lung Cancer

Other Descriptive Measures

Example 2.8.6 Tobacco Leaves

2.9 Perspective

Parameters and Statistics

A Look Ahead

Supplementary Exercises 2.S.1–2.S.24

Chapter 3 Probability and the Binomial Distribution

Objectives

3.1 Probability and the Life Sciences

3.2 Introduction to Probability

Basic Concepts

Example 3.2.1 Coin Tossing

Example 3.2.2 Coin Tossing

Example 3.2.3 Sampling Fruitflies

Frequency Interpretation of Probability

Example 3.2.4 Coin Tossing

Example 3.2.5 Coin Tossing

Example 3.2.6 Sampling Fruitflies

Probability Trees

Example 3.2.7 Coin Tossing

Combination of Probabilities

Example 3.2.8 Sampling Fruitflies

Example 3.2.9 Nitric Oxide

Hypothetical 1,000

Example 3.2.10 Nitric Oxide

Example 3.2.11 Medical Testing

Example 3.2.12 False Positives

Exercises 3.2.1–3.2.8

3.3 Probability Rules (Optional)

Basic Rules

Example 3.3.1 Blood Type

Addition Rules

Example 3.3.2 Hair Color and Eye Color

Example 3.3.3 Hair Color and Eye Color

Example 3.3.4 Hair Color and Eye Color

Multiplication Rules

Example 3.3.5 Coin Tossing

Example 3.3.6 Blood Type

Example 3.3.7 Hair Color and Eye Color

Example 3.3.8 Hand Size

Exercises 3.3.1–3.3.5

3.4 Density Curves

Relative Frequency Histograms and Density Curves

Example 3.4.1 Blood Glucose

Example 3.4.2 Blood Glucose

The Continuum Paradox

Probabilities and Density Curves

Example 3.4.3 Blood Glucose

Example 3.4.4 Tree Diameters

Exercises 3.4.1–3.4.5

3.5 Random Variables

Example 3.5.1 Dice

Example 3.5.2 Family Size

Example 3.5.3 Medications

Example 3.5.4 Heights of Men

Mean and Variance of a Random Variable

Example 3.5.5 Fish Vertebrae

Example 3.5.6 Dice

Example 3.5.7 Fish Vertebrae

Example 3.5.8 Dice

Adding and Subtracting Random Variables (Optional)

Example 3.5.9 Temperature

Example 3.5.10 Feet to Inches

Example 3.5.11 Mass

Exercises 3.5.1–3.5.10

3.6 The Binomial Distribution

The Independent-Trials Model

Example 3.6.1 Albinism

Example 3.6.2 Mutant Cats

An Example of the Binomial Distribution

Example 3.6.3 Albinism

The Binomial Distribution Formula

Notes on Table 2

Example 3.6.4 Mutant Cats

Remark

Computational Note

Example 3.6.5 Sampling Fruitflies

Example 3.6.6 Blood Type

Example 3.6.7 Blood Type

Mean and Standard Deviation of a Binomial

Example 3.6.8 Blood Type

Applicability of the Binomial Distribution

Application to Sampling

Contagion

Example 3.6.9 Chickenpox

Exercises 3.6.1–3.6.12

3.7 Fitting a Binomial Distribution to Data (Optional)

Example 3.7.1 Sexes of Children

Exercises 3.7.1–3.7.3

Supplementary Exercises 3.S.1–3.S.12

Chapter 4 The Normal Distribution

Objectives

4.1 Introduction

Example 4.1.1 Serum Cholesterol

Further Examples

Example 4.1.2 Blue Jay Bill Length

Example 4.1.3 Interspike Times in Nerve Cells

Example 4.1.4 Measurement Error

4.2 The Normal Curves

4.3 Areas under a Normal Curve

The Standardized Scale

Determining Areas for a Normal Curve

Example 4.3.1 Lengths of Fish

Inverse Reading of Table 3

Example 4.3.2 Lengths of Fish

Problem-Solving Tip

Exercises 4.3.1–4.3.17

4.4 Assessing Normality

Example 4.4.1 Serum Cholesterol

Example 4.4.2 Moisture Content

Normal Quantile Plots

How Normal Quantile Plots Work

Example 4.4.3 Height of Eleven Women

Example 4.4.4 Heights of Eleven Women

Making Decisions about Normality

Transformations for Nonnormal Data

Example 4.4.5 Lentil Growth

An Objective Measure of Abnormality: The Shapiro–Wilk Test (optional)

Example 4.4.6 Lentil Growth

Caution

Exercises 4.4.1–4.4.8

4.5 Perspective

Supplementary Exercises 4.S.1–4.S.21

Chapter 5 Sampling Distributions

Objectives

5.1 Basic Ideas

Sampling Variability

The Meta-Study

Example 5.1.1 Rat Blood Pressure

Example 5.1.2 Bacterial Growth

Example 5.1.3 Knee Replacement

Relationship to Statistical Inference

Exercises 5.1.1–5.1.5

5.2 The Sample Mean

The Sampling Distribution of Y¯

Example 5.2.1 Serum Cholesterol

Example 5.2.2 Weights of Seeds

Remark

Dependence on Sample Size

Example 5.2.3 Weights of Seeds

Populations, Samples, and Sampling Distributions

Example 5.2.4 Weights of Seeds

Other Aspects of Sampling Variability

Example 5.2.5 Weights of Seeds

Exercises 5.2.1–5.2.19

5.3 Illustration of the Central Limit Theorem (Optional)

Example 5.3.1 Eye Facets

Example 5.3.2 Reaction Time

Example 5.3.3 Reaction Time

Exercises 5.3.1–5.3.3

5.4 The Normal Approximation to the Binomial Distribution (Optional)

Remarks

Example 5.4.1 Normal Approximation to Binomial

The Continuity Correction

Example 5.4.2

Example 5.4.3

Remark

Example 5.4.4

How Large Must n Be?

Exercises 5.4.1–5.4.14

5.5 Perspective

Supplementary Exercises 5.S.1–5.S.13

Unit I Highlights and Study (Reflections on Chapters 1–5)

Reflections on Chapter 1

Reflections on Chapters 2–4

Reflections on Chapter 5

Unit I Summary Exercises

Unit II Inference for Means

Chapter 6 Confidence Intervals

Objectives

6.1 Statistical Estimation

Example 6.1.1 Butterfly Wings

6.2 Standard Error of the Mean

Example 6.2.1 Butterfly Wings

Standard Error versus Standard Deviation

Example 6.2.2 Lamb Birthweights

Example 6.2.3 Lamb Birthweights

Graphical Presentation of the SE and the SD

Example 6.2.4 MAO and Schizophrenia

Exercises 6.2.1–6.2.9

6.3 Confidence Interval for μ

Confidence Interval for μ: Basic Idea

Confidence Interval for μ: Mathematics

Student’s t Distribution

Confidence Interval for μ: Method

Example 6.3.1 Butterfly Wings

Example 6.3.2 Butterfly Wings

Remark

Confidence Intervals and Randomness

Example 6.3.3 Blue Jay Bill Length

Interpretation of a Confidence Interval

Example 6.3.4 Bone Mineral Density

Example 6.3.5 Seeds per Fruit

Relationship to Sampling Distribution of y¯

One-Sided Confidence Intervals

Example 6.3.6 Seeds per Fruit—One-Sided, 90%

Example 6.3.7 Seeds per Fruit—One-Sided, 95%

Exercises 6.3.1–6.3.22

6.4 Planning a Study to Estimate μ

Example 6.4.1 Butterfly Wings

Exercises 6.4.1–6.4.6

6.5 Conditions for Validity of Estimation Methods

Conditions for Validity of the SE Formula

Example 6.5.1 Marijuana and Intelligence

Example 6.5.2 Canine Anatomy

Example 6.5.3 Germination of Spores

Conditions for Validity of a Confidence Interval for μ

Summary of Conditions

Verification of Conditions

Example 6.5.4 Sediment Yield

Exercises 6.5.1–6.5.8

6.6 Comparing Two Means

Notation

Standard Error of (γ1¯−γ¯2)

Basic Ideas

Example 6.6.1 Vital Capacity

Example 6.6.2 Vital Capacity

Example 6.6.3 Tonsillectomy

The Pooled Standard Error (Optional)

Example 6.6.4 Vital Capacity

Exercises 6.6.1–6.6.9

6.7 Confidence Interval for (μ1 − μ2)

Example 6.7.1 Fast Plants

Example 6.7.2 Fast Plants

Example 6.7.3 Thorax Weight

6.8 Perspective and Summary

Sampling Distributions and Data Analysis

Choice of Confidence Level

Characteristics of Other Measures

Summary of Estimation Methods

Supplementary Exercises 6.S.1–6.S.23

Chapter 7 Comparison of Two Independent Samples

Objectives

7.1 Hypothesis Testing: The Randomization Test

Example 7.1.1 Flexibility

Example 7.1.2 Flexibility

Larger Samples

Example 7.1.3 Leaf Area

Exercises 7.1.1–7.1.5

Preview of the t Test (Section 7.2)

7.2 Hypothesis Testing: The t Test

The Null and Alternative Hypotheses

Example 7.2.1 Toluene and the Brain

The t Statistic

Example 7.2.2 Toluene and the Brain

The P-Value

Example 7.2.3 Toluene and the Brain

Drawing Conclusions from a t Test

Example 7.2.4 Toluene and the Brain

Example 7.2.5 Fast Plants

Using Tables versus Using Technology

Example 7.2.6 Fast Plants

Reporting the Results of a t Test

Exercises 7.2.1–7.2.18

7.3 Further Discussion of the t Test

Relationship Between Test and Confidence Interval

Example 7.3.1 Crawfish Lengths

Interpretation of α

Example 7.3.2 Music and Marigolds*

Significance Level versus P-Value

Type I and Type II Errors

Example 7.3.3 Marijuana and the Pituitary

Example 7.3.4 Immunotherapy

Power

Exercises 7.3.1–7.3.11

7.4 Association and Causation

Example 7.4.1 Mosquito Weight

Example 7.4.2 Exercise During Pregnancy

Observational versus Experimental Studies

Example 7.4.3 Cigarette Smoking

More on Observational Studies

Example 7.4.4 Race and Brain Size

Confounding

Example 7.4.5 Smoking and Birthweight

Example 7.4.6 Smoking and Birthweight

Spurious Association

Example 7.4.7 Ultrasound

More on Experiments

Example 7.4.8 Headache Pain

Randomization Distributions

Only Statistical?

Exercises 7.4.1–7.4.10

7.5 One-Tailed t Tests

Directional Alternative Hypotheses

Example 7.5.1 Niacin Supplementation

The One-Tailed Test Procedure

Example 7.5.2 Niacin Supplementation

Directional versus Nondirectional Alternatives

Example 7.5.3 Niacin Supplementation

Choosing the Form of HA

Example 7.5.4 Music and Marigolds

Exercises 7.5.1–7.5.16

7.6 More on Interpretation of Statistical Significance

Significant Difference versus Important Difference

Example 7.6.1 Serum LD

Example 7.6.2 Body Weight

Effect Size

Example 7.6.3 Serum LD

Example 7.6.4 Body Weight

Confidence Intervals to Assess Importance

Example 7.6.5 Serum LD

Example 7.6.6 Body Weight

Example 7.6.7 Yield of Tomatoes

Example 7.6.8 Yield of Tomatoes

Exercises 7.6.1–7.6.11

7.7 Planning for Adequate Power (Optional)

Dependence of Power on α

Dependence on σ

Dependence on n

Dependence on (μ1−μ2)

Example 7.7.1 Heights of People

Planning a Study

Example 7.7.2 Heights of People

Example 7.7.3 Postpartum Weight Loss

Exercises 7.7.1–7.7.12

7.8 Student’s t: Conditions and Summary

Conditions

Verification of Conditions

Consequences of Inappropriate Use of Student’s t

Other Approaches

Example 7.8.1 Tissue Inflammation

Summary of t Test Mechanics

Exercises 7.8.1–7.8.3

7.9 More on Principles of Testing Hypotheses

A General View of Hypothesis Tests

How are H0 and HA Chosen?

Another Look at P-Value

Interpretation of Error Probabilities

Example 7.9.1 Medical Testing

An Implicit Assumption

Perspective

Exercise 7.9.1

7.10 The Wilcoxon-Mann-Whitney Test

Statement of H0 and HA

Example 7.10.1 Soil Respiration

Applicability of the Wilcoxon-Mann-Whitney Test

Method

Example 7.10.2 Soil Respiration

Directionality

Directional Alternative

Example 7.10.3 Directional HA

Rationale

Conditions for Use of the Wilcoxon-Mann-Whitney Test

The Wilcoxon-Mann-Whitney Test versus the t Test and the Randomization Test

Exercises 7.10.1–7.10.10

Supplementary Exercises 7.S.1–7.S.35

Chapter 8 Comparison of Paired Samples

Objectives

8.1 Introduction

Example 8.1.1 Hunger Rating

Example 8.1.2 Hunger Rating Randomization Test

Exercise 8.1.1

8.2 The Paired-Sample t Test and Confidence Interval

Analyzing Differences

Example 8.2.1 Hunger Rating

Confidence Interval and Test of Hypothesis

Example 8.2.2 Hunger Rating

Example 8.2.3 Hunger Rating

Result of Ignoring Pairing

Example 8.2.4 Cheese Gumminess

Conditions for Validity of Student’s t Analysis

Example 8.2.5 Squirrels

Summary of Formulas

Exercises 8.2.1–8.2.11

8.3 The Paired Design

Examples of Paired Designs

Experiments with Pairs of Units

Example 8.3.1 Fertilizers for Eggplants

Observational Studies

Example 8.3.2 Smoking and Lung Cancer

Repeated Measurements

Example 8.3.3 Working Memory

Pairing by Time

Example 8.3.4 Stream Coliform Contamination

Purposes of Pairing

Randomized Pairs Design Versus Completely Randomized Design

Example 8.3.5 Fertilizers for Eggplants

Choice of Analysis

Exercises 8.3.1–8.3.5

8.4 The Sign Test

Method

Example 8.4.1 Skin Grafts

Example 8.4.2 Stream Coliform Contamination

Bracketing the P-Value

Directional Alternative

Caution

Treatment of Zeros

Example 8.4.3 Null Distribution

How Table 7 Is Calculated

Example 8.4.4

Applicability of the Sign Test

Example 8.4.5 THC and Chemotherapy

Exercises 8.4.1–8.4.11

8.5 The Wilcoxon Signed-Rank Test

Method

Example 8.5.1 Nerve Cell Density

Bracketing the P-Value

Directional Alternative

Treatment of Zeros

Treatment of Ties

Applicability of the Wilcoxon Signed-Rank Test

Exercises 8.5.1–8.5.7

8.6 Perspective

Before–After Studies

Example 8.6.1 Wrist Fracture and Pain

Limitation of D¯

Example 8.6.2 Measuring Serum Cholesterol

Limitation of the Aggregate Viewpoint

Example 8.6.3 Treatment of Acne

Reporting of Data

Exercises 8.6.1–8.6.5

Supplementary Exercises 8.S.1–8.S.23

Unit II Highlights and Study (Reflections on Chapters 6, 7, and 8)

Hypothesis Testing

Type I and Type II Errors

Effect Size and Confidence Intervals

Nonsignificant Findings

Requirements

Outliers

Unit II Summary Exercises

Background for II.15–II.19

Unit III Inference for Categorical Data

Chapter 9 Categorical Data: One-Sample Distributions

Objectives

9.1 Dichotomous Observations

The Wilson-Adjusted Sample Proportion, p˜

Example 9.1.1 Contaminated Soda

Example 9.1.2 Contaminated Soda

The Sampling Distribution of p˜

Example 9.1.3 Contaminated Soda

Example 9.1.4 Contaminated Soda and a Larger Sample

Relationship to Statistical Inference

Example 9.1.5 Contaminated Soda

Dependence on Sample Size

Example 9.1.6 Contaminated Soda

Exercises 9.1.1–9.1.10

9.2 Confidence Interval for a Population Proportion

Standard Error of p˜

Example 9.2.1 Smoking During Pregnancy

95% Confidence Interval for p

Example 9.2.2 Breast Cancer

Example 9.2.3 Breast Cancer

Example 9.2.4 ECMO

Conditions for Use of the Wilson 95% Confidence Interval for p

One-Sided Confidence Intervals

Example 9.2.5 ECMO—One-Sided

Planning a Study to Estimate p

Example 9.2.6 Vegetarians

Planning in Ignorance

Example 9.2.7 Vegetarians

Exercises 9.2.1–9.2.17

9.3 Other Confidence Levels (Optional)

Example 9.3.1 Vegetarians

Exercises 9.3.1–9.3.4

9.4 Inference for Proportions: The Chi-Square Goodness-of-Fit Test

Example 9.4.1 Deer Habitat and Fire

Example 9.4.2 Deer Habitat and Fire

The Chi-Square Statistic

Example 9.4.3 Deer Habitat and Fire

Example 9.4.4 Deer Habitat and Fire

The x2 Distribution

The Goodness-of-Fit Test

Example 9.4.5 Deer Habitat and Fire

Example 9.4.6 Flax Seeds

Compound Hypotheses and Directionality

Example 9.4.7 Deer Habitat and Fire

Dichotomous Variables

Directional Conclusion

Example 9.4.8 Deer Habitat, Fire, and Two Regions

Directional Alternative

Example 9.4.9 Harvest Moon Festival

Exercises 9.4.1–9.4.13

9.5 Perspective and Summary

Supplementary Exercises 9.S.1–9.S.22

Chapter 10 Categorical Data: Relationships

Objectives

10.1 Introduction

Example 10.1.1 Migraine Headache

Example 10.1.2 HIV Testing

Conditional Probability

Example 10.1.3 Migraine Headache

A Randomization Test

Example 10.1.4 ECMO

10.2 The Chi-Square Test for the 2 × 2 Contingency Table

Example 10.2.1 Migraine Headache

The Chi-Square Statistic

Example 10.2.2 Migraine Headache

Example 10.2.3 Migraine Headache

The Test Procedure

Example 10.2.4 Migraine Headache

Computational Notes

Illustration of the Null Hypothesis

Example 10.2.5 Fictitious Migraine Study

Example 10.2.6 HIV Testing

Exercises 10.2.1–10.2.15

10.3 Independence and Association in the 2 × 2 Contingency Table

Two Contexts for Contingency Tables

Independence and Association

Example 10.3.1 Hair Color and Eye Color

Example 10.3.2 Hair Color and Eye Color

Example 10.3.3 Plant Height and Disease Resistance

Facts About Rows and Columns

Fact 10.3.1

Fact 10.3.2

Verbal Description of Association

Example 10.3.4 Plant Height and Disease Resistance

Example 10.3.5 Hair Color and Eye Color

Exercises 10.3.1–10.3.12

10.4 Fisher’s Exact Test (Optional)

Example 10.4.1 ECMO

Combinations

Example 10.4.2 ECMO

Example 10.4.3 ECMO

Comparison to the Chi-Square Test

Example 10.4.4 ECMO

Nondirectional Alternatives and the Exact Test

Example 10.4.5 Flu Shots

Exercises 10.4.1–10.4.9

10.5 The r × k Contingency Table

Example 10.5.1 Plover Nesting

The Chi-Square Test for the r × k Table

Example 10.5.2 Plover Nesting

Two Contexts for r × k Contingency Tables

Example 10.5.3 Hair Color and Eye Color

Exercises 10.5.1–10.5.11

10.6 Applicability of Methods

Conditions for Validity

Verification of Design Conditions

Example 10.6.1 Food Choice by Insect Larvae

Example 10.6.2 Pollination of Flowers

Power Considerations

Example 10.6.3 Physiotherapy

Exercises 10.6.1–10.6.3

10.7 Confidence Interval for Difference Between Probabilities

Example 10.7.1 Migraine Headache

10.8 Paired Data and 2 × 2 Tables (Optional)

Example 10.8.1 HIV Transmission to Children

McNemar’s Test

Example 10.8.2 HIV Transmission to Children

Exercises 10.8.1–10.8.4

10.9 Relative Risk and the Odds Ratio (Optional)

Relative Risk

Example 10.9.1 Smoking and Lung Cancer

The Odds Ratio

Example 10.9.2 Smoking and Lung Cancer

Odds Ratio and Relative Risk

Example 10.9.3 Smoking and Lung Cancer

Advantage of the Odds Ratio

Example 10.9.4 Smoking and Lung Cancer

Example 10.9.5 Smoking and Lung Cancer

Example 10.9.6 Smoking and Lung Cancer

Example 10.9.7 Smoking and Lung Cancer

Confidence Interval for the Odds Ratio

Example 10.9.8 Smoking and Lung Cancer

Example 10.9.9 Heart Attacks and Aspirin

Exercises 10.9.1–10.9.9

10.10 Summary of Chi-Square Test

Supplementary Exercises 10.S.1–10.S.21

Unit III Highlights and Study (Reflections on Chapters 9 and 10)

Chi-Square Test of Independence

Drawing Conclusions Based on the Study Design

Chi-Square Goodness-of-Fit Test

Wilson Adjusted Confidence Interval for a Proportion

Unit III Summary Exercises

Background for III.6–III.9

Unit IV Modeling Relationships

Chapter 11 Comparing the Means of Many Independent Samples

Objectives

11.1 Introduction

Example 11.1.1 Sweet Corn

A Randomization Test

Example 11.1.2 Sweet Corn

Why Not Repeated t Tests?

A Graphical Perspective on ANOVA

A Look Ahead

11.2 The Basic One-Way Analysis of Variance

Notation

Example 11.2.1 Weight Gain of Lambs

Measuring Variation Within Groups

Example 11.2.2 Weight Gain of Lambs

ANOVA Notation

Example 11.2.3 Weight Gain of Lambs

Variation Between Groups

Example 11.2.4 Weight Gain of Lambs

A Fundamental Relationship of ANOVA

Example 11.2.5 Weight Gain of Lambs

The ANOVA Table

Example 11.2.6 Weight Gain of Lambs

Comment on Terminology

Summary of Formulas

Exercises 11.2.1–11.2.7

11.3 The Analysis of Variance Model

Example 11.3.1 Weight Gain of Lambs

11.4 The Global F Test

The F Distributions

The F Test

Example 11.4.1 Weight Gain of Lambs

Relationship between F Test and t Test

Exercises 11.4.1–11.4.9

11.5 Applicability of Methods

Standard Conditions

Verification of Conditions

Example 11.5.1 Weight Gain of Lambs

Example 11.5.2 Sweet Corn

Example 11.5.3 Sweet Corn

Further Analysis

Exercises 11.5.1–11.5.4

11.6 One-Way Randomized Blocks Design

Example 11.6.1 Alfalfa and Acid Rain

Example 11.6.2 Blocking by Litter

Example 11.6.3 Within-Subject Blocking (Pairing)

Example 11.6.4 Blocking in an Agricultural Field Study

Creating the Blocks

Example 11.6.5 Agricultural Field Study

The Randomization Procedure

Example 11.6.6 Agricultural Field Study

Analyzing Data from a Randomized Block Experiment

Example 11.6.7 Alfalfa and Acid Rain

Visualizing the Block Effects

The One-Way Randomized Complete Block F Test

Example 11.6.8 Alfalfa and Acid Rain

Example 11.6.9 Alfalfa and Acid Rain

Exercises 11.6.1–11.6.12

11.7 Two-Way ANOVA

Factorial ANOVA

Example 11.7.1 Growth of Soybeans

Example 11.7.2 Growth of Soybeans

Example 11.7.3 Iron Supplements in Milk-Based Fruit Beverages

Example 11.7.4 Iron Supplements in Milk-Based Fruit Beverages

Example 11.7.5 Growth of Soybeans

Example 11.7.6 Toads

Exercises 11.7.1–11.7.9

11.8 Linear Combinations of Means (Optional)

Linear Combinations for Adjustment

Example 11.8.1 Forced Vital Capacity

Contrasts

Example 11.8.2 Growth of Soybeans

Standard Error of a Linear Combination

Example 11.8.3 Forced Vital Capacity

Example 11.8.4 Growth of Soybeans

Confidence Intervals

Example 11.8.5 Growth of Soybeans

t Tests

Contrasts to Assess Interaction

Example 11.8.6 Growth of Soybeans

Example 11.8.7 Chromosomal Aberrations

Exercises 11.8.1–11.8.10

11.9 Multiple Comparisons (Optional)

Experimentwise Versus Comparisonwise Error

Fisher’s Least Significant Difference

Example 11.9.1 Oysters and Seagrass

How does Fisher’s LSD control the experimentwise Type I error rate?

Displaying Results

Example 11.9.2 Oysters and Seagrass

The Bonferroni Method

Example 11.9.3 Oysters and Seagrass

Tukey’s Honest Significant Difference

Conditions for Validity

Exercises 11.9.1–11.9.8

11.10 Perspective

Advantages of Global Approach

Other Experimental Designs

Nonparametric Approaches

Supplementary Exercises 11.S.1–11.S.20

Chapter 12 Linear Regression and Correlation

Objectives

12.1 Introduction

Examples

Example 12.1.1 Amphetamine and Food Consumption

Example 12.1.2 Dissolved Oxygen

12.2 The Correlation Coefficient

Example 12.2.1 Length and Weight of Snakes

Measuring Strength of Linear Association

Interpreting the Correlation Coefficient

Example 12.2.2 Length and Weight of Snakes

Inference Concerning Correlation

R Testing the Hypothesis H0:ρ=0

A randomization test

Example 12.2.3 Blood Pressure and Platelet Calcium

A t Test

Example 12.2.4 Blood Pressure and Platelet Calcium

Why n − 2?

Confidence Interval for ρ (Optional)

Example 12.2.5 Blood Pressure and Platelet Calcium

Correlation and Causation

Example 12.2.6 Reproduction of an Alga

Cautionary Notes

Exercises 12.2.1–12.2.12

12.3 The Fitted Regression Line

Example 12.3.1 Ocean Temperature

The SD Line

Example 12.3.2 Dissolved Oxygen

Example 12.3.3 Dissolved Oxygen

Equation of the Fitted Regression Line

Example 12.3.4 Dissolved Oxygen

Graph of Averages

Example 12.3.5 Amphetamine and Food Consumption

Example 12.3.6 Amphetamine and Food Consumption

The Residual Sum of Squares

Example 12.3.7 Dissolved Oxygen

The Least-Squares Criterion

The Residual Standard Deviation

Example 12.3.8 Dissolved Oxygen

Example 12.3.9 Dissolved Oxygen

The Coefficient of Determination

Example 12.3.10 Dissolved Oxygen

Example 12.3.11 Amphetamine and Food Consumption

Exercises 12.3.1–12.3.13

12.4 Parametric Interpretation of Regression: The Linear Model

Conditional Populations and Conditional Distributions

Example 12.4.1 Amphetamine and Food Consumption

Example 12.4.2 Height and Weight of Young Men

The Linear Model

Example 12.4.3 Amphetamine and Food Consumption

Example 12.4.4 Height and Weight of Young Men

Remark

Estimation in the Linear Model

Example 12.4.5 Length and Weight of Snakes

Interpolation in the Linear Model

Example 12.4.6 Dissolved Oxygen

Example 12.4.7 Amphetamine and Food Consumption

Prediction and the Linear Model

Exercises 12.4.1–12.4.9

12.5 Statistical Inference Concerning β1

The Standard Error of b1

Example 12.5.1 Length and Weight of Snakes

Structure of the SE

Implications for Design

Confidence Interval for β1

Example 12.5.2 Length and Weight of Snakes

Testing the Hypothesis H0:β1 = 0

Example 12.5.3 Blood Pressure and Platelet Calcium

A randomization test

Example 12.5.4 Blood Pressure and Platelet Calcium

Exercises 12.5.1–12.5.10

12.6 Guidelines for Interpreting Regression and Correlation

When Is Linear Regression Descriptively Inadequate?

Example 12.6.1 A Curvilinear Relationship with X

Conditions for Inference

Guidelines Concerning the Sampling Conditions

Example 12.6.2 Serum Cholesterol and Serum Glucose

Example 12.6.3 Growth of Beef Steers

Example 12.6.4

Labeling X and Y

Example 12.6.5 Height and Weight of Young Men

Guidelines Concerning the Linear Model and Normality Condition

Residual Plots

The Use of Transformations

Example 12.6.6 Growth of Soybeans

Exercises 12.6.1–12.6.9

12.7 Precision in Prediction (Optional)

Confidence and Prediction Intervals

Example 12.7.1 Dissolved Oxygen

Computing the Intervals

Exercises 12.7.1–12.7.4

12.8 Perspective

Regression and the t Test

Example 12.8.1 Toluene and the Brain

Example 12.8.2 Blood Pressure and Platelet Calcium

Extensions of Least Squares

Example 12.8.3 Serum Cholesterol and Blood Pressure

Nonparametric and Robust Regression and Correlation

Analysis of Covariance

Example 12.8.4 Caterpillar Head Size

Logistic Regression

Example 12.8.5 Esophageal Cancer

12.9 Summary of Formulas

Supplementary Exercises 12.S.1–12.S.30

Unit IV Highlights and Study (Reflections on Chapters 11 and 12)

Multiple Comparisons (Optional)

Checking ANOVA Requirements

Regression

Checking Regression Requirements

Unit IV Summary Exercises

Chapter 13 A Summary of Inference Methods

Objectives

13.1 Introduction

Exploratory Data Analysis

13.2 Data Analysis Examples

Example 13.2.1 Gibberellic Acid

Example 13.2.2 Whale Swimming Speed

Example 13.2.3 Progesterone Gel and Preemies

Example 13.2.4 Cystic Fibrosis

Example 13.2.5 Therapeutic Touch

Brief Examples

Example 13.2.6 Seastars

Example 13.2.7 Twins

Example 13.2.8 Soil Samples

Example 13.2.9 Vaccinations

Example 13.2.10 Estrogen and Steroids

Example 13.2.11 Damselflies

Example 13.2.12 Tobacco Use Prevention

Example 13.2.13 Reaction Times

Exercises 13.2.1–13.2.24

Chapter Appendices

Appendix

Appendix 3.1 More on the Binomial Distribution Formula

Appendix 3.2 Mean and Standard Deviation of the Binomial Distribution

Appendix 5.1 Relationship between Central Limit Theorem and Normal Approximation to Binomial Distribution

Appendix 7.1 How Power Is Calculated

Chapter Appendices

Appendix

Appendix 4.1 Areas of Indefinitely Extended Regions

Appendix 6.1 Significant Digits

Appendix 7.2 More on the Wilcoxon-Mann-Whitney Test

Appendix 9.1 More on Confidence Intervals for a Proportion

Appendix 12.1 Least-Squares Formulas

Appendix 12.2 Derivation of Fact 12.3.1

Chapter References

Chapter Notes

Answers to Selected Exercises

Statistical Tables

Credits

Chapter 1

Chapter 2

Chapter 6

Chapter 7

Unit III