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Michael Nelson. Statistics in Nutrition and Dietetics
Table of Contents
List of Tables
List of Illustrations
Guide
Pages
Statistics in Nutrition and Dietetics
About the Author
Preface. WHY IS THIS BOOK NEEDED?
WHO IS THIS BOOK FOR?
LEVEL AND PRE‐REQUISITE
AIMS AND SCOPE
Scope
Unique features
CONTENTS
Part 1: Setting the statistical scene
Part 2: Statistical tests
Part 3: Doing research
Part 4: Solutions to exercises
ONLINE
TEACHING TOOLS. Teaching notes
PowerPoint slide sets
SPSS data, syntax, and output files
Learning resources
Note
Acknowledgements
About the Companion Website
PART 1 SETTING THE STATISTICAL SCENE. Learning Objectives
Approaching the Statistician
Using Computers
CHAPTER 1 The Scientific Method. Learning Objectives
1.1 KNOWING THINGS
1.2 LOGIC
1.2.1 Inductive Logic
Examples of Research Designs that Depend on Inductive Logic
1.2.2 Deductive Logic
Examples of Research Designs that Depend on Deductive Logic
1.3 EXPERIMENTATION AND RESEARCH DESIGN
1.3.1 A Children’s Story
1.4 THE BASICS OF RESEARCH DESIGN
1.4.1 Developing the Hypothesis
BOX 1.1 The four key elements of research
TIP
1.4.2 Developing the ‘Null’ Hypothesis
BOX 1.2 Testing the hypothesis
1.4.3 Hypothesis Generating Versus Hypothesis Testing
1.4.4 Design
1.4.5 Statistics
1.4.6 Interpretation
1.5 NEXT STEPS
1.6 RESEARCH DESIGN
1.6.1 Project Aims
BOX 1.3 Steps in undertaking research
1.6.2 Demonstrating Causality
BOX 1.4 Bradford Hill hierarchy of causality
1.6.3 Types of Study Design
Observational Studies
Experimental and Intervention Studies
1.6.4 Epidemiological Studies
Descriptive Studies
Analytical Studies
Experimental Studies
Confounding and Bias
1.7 DATA, RESULTS, AND PRESENTATION
1.7.1 Data Are What You Collect, Results Are What You Report
TIP
1.7.2 Never Present Endless Detailed Tables Containing Raw Data
1.7.3 Significant Digits and Rounding
TIP
1.8 READING
1.9 EXERCISES
REFERENCES
Notes
CHAPTER 2. Populations and Samples. Learning Objectives
2.1 DEFINING POPULATIONS AND SAMPLES
2.1.1 Population
2.1.2 Samples and Sampling Frames
2.1.3 Inclusion and Exclusion Criteria
2.1.4 Sampling Techniques. Simple Random Sampling
EPSEM and Non‐EPSEM Simple Random Sampling
Systematic Sampling
Stratified Sampling
Staged or Cluster Sample
Quota Sampling
A Final Word About Sampling
Box 2.1 The danger of selection bias
2.2 MEASURES OF CENTRAL TENDENCY
2.2.1 The Mean
Variables
Back to the Calculation of the Mean
2.2.2 The Median
2.2.3 The mode
2.2.4 The Geometric Mean
TIP: showing multiplication in a formula
2.3 WEIGHTING AND WEIGHTED AVERAGES
2.4 MEASURES OF VARIATION: RANGE, QUANTILES, AND THE STANDARD DEVIATION
2.4.1 Range
2.4.2 Quantiles
2.4.3 The Standard Deviation
TIP
TIP
2.5 THE RELATIONSHIP BETWEEN SAMPLES AND POPULATIONS
2.5.1 Relating the Sample to the Population
Box 2.2 The definition of s. Important‼
2.5.2 Calculating the Values for s and σ
Box 2.3 The difference between ‘the sum of x‐squared’ and ‘the sum of x all squared’ Understanding the user‐friendly expression for the sum of squares
Box 2.4 Calculating ‘the sum of x‐squared’ and ‘the sum of x all squared’
2.5.3 Variance
2.5.4 Coefficient of Variation
2.6 BE PATIENT AND DON’T GIVE UP
2.7 GLOSSARY
Summary of terms, definitions, and formulae relating to populations and samples
2.8 EXERCISES
Notes
CHAPTER 3 Principles of Measurement. Learning Objectives
3.1 INTRODUCTION
3.2 TYPES OF RESEARCH
3.3 TYPES OF MEASUREMENT
3.4 MEASUREMENT SCALES
3.4.1 Nominal Scales
3.4.2 Ordinal Scales
3.4.3 Interval Scales
3.4.4 Ratio Scales
3.4.5 Discrete Versus Continuous Scales
3.4.6 Parametric Versus Nonparametric Distributions
3.5 RELIABILITY, VALIDITY, AND ERROR
BOX 3.1 ‘Truth’
BOX 3.2 Reliability is not the same as validity
3.5.1 The Statistical Concept of ‘Error’
3.5.2 Random and Nonrandom Error
3.5.3 Precision and Accuracy
3.5.4 Measuring Reliability
3.5.5 Measuring Validity
3.6 BIAS AND GENERALIZABILITY
3.6.1 Protecting Validity
3.7 RELIABILITY AND VALIDITY IN QUALITATIVE RESEARCH
3.7.1 Reliability in Qualitative Research
3.7.2 Validity in Qualitative Research
3.8 CONCLUSION
3.9 EXERCISES
REFERENCES
Notes
CHAPTER 4 Probability and Types of Distribution. Learning Objectives
4.1 INTRODUCTION
BOX 4.1 Definitions in statistics of terms that express the chance of something happening
4.2 TYPES OF PROBABILITY DISTRIBUTION
BOX 4.2 The sum of probabilities for all observations of a given variable x
4.2.1 Uniform Distribution
4.2.2 Binomial Distribution
4.2.3 Poisson Distribution
4.2.4 Normal (or Gaussian) Distribution: The Bell‐Shaped Curve
The Area under the Normal Curve
Calculation of Areas under the Normal Curve
Areas in the Tail of the Normal Distribution
4.3 SAMPLING ERROR
4.3.1 The Distribution of the Values of Sample Means x
BOX 4.3 A key characteristic of the Standard Error
4.4 TRANSFORMATIONS
4.5 EXERCISES
REFERENCES
Notes
CHAPTER 5 Confidence Intervals and Significance Testing. Learning Objectives
5.1 INTRODUCTION
5.2 CONFIDENCE INTERVALS AND CONFIDENCE LIMITS
5.2.1 Specifying a Confidence Interval based on μ and σ
5.2.2 The 95% Confidence Interval (x̅ around μ)
5.2.3 More than One Way to Define a Confidence Interval
BOX 5.1 The relationship between x̅ and μ
99% and 99.9% Confidence Intervals
5.2.4 Deriving the Confidence Interval based on and s
Degrees of Freedom
5.2.5 Calculating the Confidence Interval based on and s, using t
BOX 5.2 General definitions of Confidence Interval and Confidence Limits
5.3 LEVELS OF SIGNIFICANCE
5.4 A TEST STATISTIC
5.4.1 Using u as a Test Statistic
5.4.2 Using t as A Test Statistic
5.5 EXERCISES
REFERENCE
Notes
PART 2. STATISTICAL TESTS. Introduction
Creating a Model
Using Statistical Tests
Notes
CHAPTER 6 Two Sample Comparisons for Normal Distributions: The t‐test. Learning Objectives
6.1 INTRODUCTION
6.2 PAIRED t‐TEST
Fundamental principles
Assumptions
BOX 6.1 The steps to carry out a statistical test
BOX 6.2 Assumptions for the paired t‐test
Example 6.1 Paired t‐test
Model
BOX 6.3 Model for the paired t‐test
Test procedure: paired t‐test7
BOX 6.4 Test procedure for the paired t‐test
Decision and interpretation
Two‐tailed or one‐tailed test
Conclusion
6.3 UNPAIRED t‐TEST
Fundamental principle
Assumptions
BOX 6.5 Assumptions for the unpaired t‐test
Example 6.2 Unpaired t‐test
Model
BOX 6.6 Model for the unpaired t‐test
Test procedure: unpaired t‐test
BOX 6.7 Test procedure for the unpaired t‐test
Decision and interpretation
Conclusion
The unequal variances assumption
6.4 EXERCISES
Notes
CHAPTER 7 Nonparametric Two‐Sample Tests. Learning Objectives
7.1 INTRODUCTION
7.2 UNPAIRED NONNORMAL DATA: THE MANN–WHITNEY TEST
Assumptions
Example
BOX 7.1 The steps to carry out a statistical test
BOX 7.2 Assumptions for the Mann–Whitney test
Model
Test procedure
BOX 7.3 Model for the Mann–Whitney test
BOX 7.4 Test procedure for the Mann–Whitney test
Decision and interpretation
Conclusion
7.3 WILCOXON SIGNED‐RANK TEST
Assumptions
Example
Model
Test procedure
BOX 7.5 Assumptions for the Wilcoxon signed‐rank test
BOX 7.6 Model for the Wilcoxon signed‐rank test
BOX 7.7 Test procedure for the Wilcoxon signed‐rank test
Decision and interpretation
Conclusion
7.4 WILCOXON SIGN TEST
Assumptions
Model
BOX 7.8 Assumptions for the Wilcoxon sign test
BOX 7.9 Model for the Wilcoxon sign test
Conclusion
7.5 SPSS
7.6 EXERCISES
REFERENCE
Notes
CHAPTER 8 Contingency Tables, Chi‐Squared Test, and Fisher's Exact Test. Learning Objectives
8.1 INTRODUCTION
8.2 THE FOUR‐FOLD OR 2 × 2 CONTINGENCY TABLE. Fundamental principles
BOX 8.1 Assumptions for a 2 × 2 contingency table
Assumptions for the 2 × 2 table
Fundamental principle
Model
BOX 8.2 Model for a 2 × 2 contingency table 6
Test procedure
Decision and interpretation
Conclusion
8.2.1 Standardized Residual
8.3 p × q TABLES
Assumptions
BOX 8.4 Assumptions for a p × q contingency table
A note on small values for E
Labelling the cells in a p × q table
Model
Test procedure
BOX 8.5 Model for a p × q contingency table
BOX 8.6 Test procedure for a p × q contingency table
Decision and interpretation
Conclusion
8.4 SMALL SAMPLE SIZE
BOX 8.7 Model for a 2 × 2 contingency table with small sample
Model
8.4.1 Yates’ Correction for Continuity
8.5 FISHER’S EXACT TEST
8.6 USING ALL YOUR DATA
BOX 8.8 Model for a 6 × 4 contingency table with small sample
BOX 8.9
BOX 8.10
8.7 SPSS
8.8 EXERCISES
REFERENCES
Notes
CHAPTER 9 McNemar’s Test. Learning Objectives
9.1 INTRODUCTION
9.2 THE BASICS. Fundamental principle
Assumptions
BOX 9.1 Assumptions underpinning McNemar’s test
Example 1: before and after an intervention
Fundamental principle
Model
Test procedure
BOX 9.2 Model for McNemar’s test: status in individuals before and after an intervention
Decision and interpretation
Example 2: repeat observations (outcomes) within each subject on each of two treatments
Fundamental principle
Model
BOX 9.3 Model for McNemar’s test: status in individuals before and after an intervention
Test procedure
Decision and interpretation
Example 3: exposed/not exposed status in matched cases and controls
Fundamental principle
Model
Test procedure
BOX 9.4 Model for McNemar’s test: status in individuals in a matched case‐control study
Decision and interpretation
9.3 SPSS
9.3.1 Legacy Dialogue
9.3.2 New Commands
9.4 EXERCISES
REFERENCES
Notes
CHAPTER 10 Association: Correlation and Regression. Learning Objectives
10.1 INTRODUCTION
10.2 THE CORRELATION COEFFICIENT
10.2.1 The Pearson Product‐Moment Correlation Coefficient
Fundamental principle
Assumptions
BOX 10.1 Assumptions underpinning the Pearson product‐moment correlation coefficient r
Model
Test procedure
BOX 10.3 Calculation and test procedure for the Pearson product‐moment correlation coefficient r
Decision and interpretation
Conclusion
10.2.2 The Spearman Rank Correlation Coefficient
Fundamental principle
Assumptions
Model
BOX 10.4 Assumptions underpinning the Spearman correlation coefficient ρ or rS
BOX 10.5 The model for the Spearman correlation coefficient ρ or rS
Test procedure
BOX 10.6 Test procedure for the Spearman correlation coefficient ρ or rS
Decision and interpretation
10.2.3 Kendall’s Tau
10.3 REGRESSION
Fundamental principle
Assumptions
BOX 10.7 Assumptions underpinning regression analysis
Test procedure
Decision and interpretation
Conclusion
10.4 SPSS
10.5 EXERCISES
REFERENCES
Notes
CHAPTER 11 Analysis of Variance. Learning Objectives
11.1 INTRODUCTION
11.2 ONE‐WAY ANALYSIS OF VARIANCE
Assumptions
BOX 11.1 Assumptions underpinning one‐way analysis of variance
An explication of the new symbols in Table 11.1
The fundamentals
BOX 11.2 Fundamental equation for one‐way analysis of variance
An example
Fundamental principle
The model
BOX 11.3 Model for one‐way analysis of variance
Test procedure
Decision and interpretation
11.3 SPSS
Comparing groups
BOX 11.4 Why making multiple comparisons between groups can be problematic
Normality and equal variances
Testing for normality
Testing for equal variances
11.4 TWO‐WAY ANALYSIS OF VARIANCE
Assumptions
Test procedure
11.5 N‐WAY ANALYSIS OF VARIANCE AND BEYOND
A warning!
11.6 NONPARAMETRIC ANALYSIS OF VARIANCE
11.7 EXERCISES
REFERENCES
Notes
PART 3 DOING RESEARCH. Introduction
CHAPTER 12 Design, Sample Size, and Power. Learning Objectives
12.1 RANDOMIZATION OF PROCEDURES
12.1.1 Randomized Block Design
12.1.2 Latin Square Design
12.1.3 A Thing Not to Do
12.1.4 Factorial Design
12.2 SAMPLE SIZE
12.2.1 Obtain a Standard Error of a Given Size
12.2.2 Given Difference Between Sample Means to be Significant
12.2.3 Given Power Against Specified Difference Between Population Means
12.2.4 Calculating Sample Size using P and Power
12.2.5 More Variations
REFERENCE
Annex – why is β one‐tailed?
Notes
CHAPTER 13 Describing Statistical Models and Selecting Appropriate Tests. Learning Objectives
13.1 DESCRIBING STATISTICAL MODELS
BOX 13.1 Questions about your data set to be answered when seeking the best statistical test
13.2 CHOOSING STATISTICAL TESTS
BOX 13.2 Do not go fishing to find statistically significant values of P
13.3 SOLUTIONS
Note
CHAPTER 14 Designing a Research Protocol. Learning Objectives
14.1 INTRODUCTION
14.2 THE RESEARCH PROTOCOL
14.3 STAGES OF DEVELOPMENT
14.4 STAGE 1: INITIATION3
BOX 14.1 Less haste, more speed
14.4.1 Choosing a Research Topic
14.4.2 Limitations to the Research
14.4.3 Developing a Hypothesis
14.4.4 Write Your Hypothesis
14.4.5 Developing the Study Design, Aims and Objectives
14.5 RESPONSES TO STAGE 1 PROTOCOL DEVELOPMENT
14.5.1 Feedback to Stage 1
14.6 STAGE 2: DEVELOPMENT
14.6.1 Choosing and Describing the Methods
14.6.2 The Next Draft of Your Proposal
14.7 STAGE 3: FULL PROTOCOL
14.7.1 Consider the Following Outline for this Exercise:
14.8 COMMENTS ON PREVIOUS SUBMISSIONS AT STAGE 3. PLEASE READ THESE CAREFULLY BEFORE COMPLETING STAGE 3
14.9 PRESENTATION OF PROTOCOLS
14.9.1 Grading Scheme
14.9.2 Breakdown of Mark Allocation
Notes
CHAPTER 15 Presenting Results to Different Audiences. Learning Objectives
15.1 INTRODUCTION
15.2 MY ELDER SON’S GROWTH – A SIMPLE TIME TREND ANALYSIS
15.3 DISTRIBUTION OF CHILDREN’S AGES ACCORDING TO HOUSEHOLD INCOME – CONTINGENCY TABLES, PIE CHARTS, BAR CHARTS, AND HISTOGRAMS
15.4 MORE EXAMPLES
15.4.1 The Eatwell Guide – Changes Over Time and Stacked Column Bar Charts
15.4.2 Room Service in a Public Hospital – Comparing Means in a Table
15.4.3 Impact of Feeding Support on Dysphagic Patients ‐ Comparing Means in a Table with 95% Confidence Intervals
15.4.4 Probiotics and Immune Response; Gene‐nutrient Interaction and Metabolic Disease – Statistical Findings Shown in a Bar Chart
15.4.5 Fat Versus Carbohydrate Restriction in Type 2 Diabetes Mellitus – Correlation, Individual Change Plots, and Box‐and‐Whisker Plots
15.4.6 Chronic Inflammation, Diet Quality Score, and Morbidity and Mortality – Analysis of Variance and Risk
15.5 CONCLUSION
REFERENCES
Notes
PART 4 SOLUTIONS TO EXERCISES. Learning Objectives
Introduction
Chapter 1 The Scientific Method
Chapter 2 Populations and Samples
Chapter 3 Principles of Measurement
Chapter 4 Probability and Types of Distribution
Chapter 5 Confidence Intervals and Significance Testing
Chapter 6 Two Sample Comparisons for Normal Distributions: The t‐test
Chapter 7 Nonparametric Two‐sample Tests
Chapter 8 Contingency Tables, Chi‐squared, and Fisher's Exact Test
Chapter 9 McNemar's Test
Chapter 10 Association: Correlation and Regression
Chapter 11 Analysis of Variance
REFERENCE
Notes
APPENDIX A1 Probabilities (P) of the Binomial Distribution for n, r, and p (Based on Sample Proportions) or π (Proportion in the Population)
APPENDIX A2 Areas in the Tail of the Normal Distribution
APPENDIX A3 Areas in the Tail of the t Distribution
APPENDIX A4 Wilcoxon U Statistic(Mann–Whitney Test)
APPENDIX A5. Wilcoxon T Statistic
APPENDIX A6. Sign Test Statistic R
APPENDIX A7. Percentages in the Tail of the Chi‐Squared Distribution
APPENDIX A8 Quantiles of the Spearman Rank Correlation Coefficient
APPENDIX A9 Percentages in the Tail of the F Distribution
APPENDIX A10 Flow Chart for Selecting Statistical Tests
Index
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
Y
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