Michael Nelson - Statistics in Nutrition and Dietetics

7 PART 2: STATISTICAL TESTS CHAPTER 6: Two Sample Comparisons for Normal Distributions: The t ‐test 6.1 INTRODUCTION 6.2 PAIRED t ‐TEST 6.3 UNPAIRED t ‐TEST 6.4 EXERCISES CHAPTER 7: Nonparametric Two‐Sample Tests 7.1 INTRODUCTION 7.2 UNPAIRED NONNORMAL DATA: THE MANN–WHITNEY TEST 7.3 WILCOXON SIGNED‐RANK TEST 7.4 WILCOXON SIGN TEST 7.5 SPSS 7.6 EXERCISES REFERENCE CHAPTER 8: Contingency Tables, Chi‐Squared Test, and Fisher's Exact Test 8.1 INTRODUCTION 8.2 THE FOUR‐FOLD OR 2 × 2 CONTINGENCY TABLE 8.3 p × q TABLES 8.4 SMALL SAMPLE SIZE 8.5 FISHER’S EXACT TEST 8.6 USING ALL YOUR DATA 8.7 SPSS 8.8 EXERCISES REFERENCES CHAPTER 9: McNemar’s Test 9.1 INTRODUCTION 9.2 THE BASICS 9.3 SPSS 9.4 EXERCISES REFERENCES CHAPTER 10: Association 10.1 INTRODUCTION 10.2 THE CORRELATION COEFFICIENT 10.3 REGRESSION 10.4 SPSS 10.5 EXERCISES REFERENCES CHAPTER 11: Analysis of Variance 11.1 INTRODUCTION 11.2 ONE‐WAY ANALYSIS OF VARIANCE 11.3 SPSS 11.4 TWO‐WAY ANALYSIS OF VARIANCE 11.5 N‐WAY ANALYSIS OF VARIANCE AND BEYOND 11.6 NONPARAMETRIC ANALYSIS OF VARIANCE 11.7 EXERCISES REFERENCES

8 PART 3: DOING RESEARCH CHAPTER 12: Design, Sample Size, and Power 12.1 RANDOMIZATION OF PROCEDURES 12.2 SAMPLE SIZE REFERENCE CHAPTER 13: Describing Statistical Models and Selecting Appropriate Tests 13.1 DESCRIBING STATISTICAL MODELS 13.2 CHOOSING STATISTICAL TESTS 13.3 SOLUTIONS CHAPTER 14: Designing a Research Protocol 14.1 INTRODUCTION 14.2 THE RESEARCH PROTOCOL 14.3 STAGES OF DEVELOPMENT 14.4 STAGE 1: INITIATION 3 14.5 RESPONSES TO STAGE 1 PROTOCOL DEVELOPMENT 14.6 STAGE 2: DEVELOPMENT 14.7 STAGE 3: FULL PROTOCOL 14.8 COMMENTS ON PREVIOUS SUBMISSIONS AT STAGE 3. PLEASE READ THESE CAREFULLY BEFORE COMPLETING STAGE 3. 14.9 PRESENTATION OF PROTOCOLS CHAPTER 15: Presenting Results to Different Audiences 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 15.5 CONCLUSION REFERENCES

9 PART 4: SOLUTIONS TO EXERCISES 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

10 Index

11 End User License Agreement

1 Chapter 1 TABLE 1.1 Height of Five Students (cm) TABLE 1.2 Rules for Rounding TABLE 1.3 Impact of Rounding Styles on Mean Value TABLE 1.4 Impact of Screening for Breast Cancer on 5‐year Mortality in 62 000...

2 Chapter 2 TABLE 2.1 Numbers of Subjects Recruited and Serum Vitamin C Levels, According to... TABLE 2.2 Tertiles, Quartiles, Range, and Limits of the Range for the Distributi... TABLE 2.3 Dietary Fibre Intakes (g/d) in Seven Subjects, and the Differences Bet... TABLE 2.4 Dietary Fibre Intakes (g/d) in Seven Subjects, the Differences Between...TABLE 2.5 Dietary Fibre Intakes (g/d) in Seven Subjects, the Differences Between...TABLE 2.6 Income (£/yr) by Social Class in a Town with Population = 100 000TABLE 2.7 Starting the TallyTABLE 2.8 The Completed TallyTABLE 2.9 Calcium Intake (mg/d) in 100 Cambridge Women 18–53

3 Chapter 3TABLE 3.1 Exercise on Measurement Scales

4 Chapter 4TABLE 4.1 Probabilities of ‘Success’ in Samples Where n = 10 and π = 0.6,...TABLE 4.2 Areas Under the Curve Based on the Standard Normal Deviate, u TABLE 4.3 Transformations of Variable x TABLE 4.4 Coefficients of Variation of x and Transformed Variables

5 Chapter 5TABLE 5.1 Values for the Upper and Lower Limits of the Confidence Interval fo...TABLE 5.2 Values for the Standard Normal Deviate Corresponding to Values for ½ ...

6 Chapter 6TABLE 6.1 Observations of Fasting Blood Glucose Levels in 10 Subjects at Base...TABLE 6.2 Observations of Fasting Blood Glucose Levels after Four Weeks of In...TABLE 6.3 Patients with Diabetes: Healthy Eating Knowledge Scores Before and ...TABLE 6.4 Patients with Diabetes: Healthy Eating Knowledge Scores Before and ...TABLE 6.5 Mortality Ratio (MR) in 13 Hospitals with or without Intensive Care...TABLE 6.6 Mortality Ratio (MR) in 13 Hospitals with or without Intensive Care...TABLE 6.7 Anxiety Scores of 10 Patients with Anorexia Given Drug or PlaceboTABLE 6.8 Knowledge Scores Related to the Hazards of SmokingTABLE 6.9 Weight Gain (g) between 4 and 12 Weeks in Breast‐fed or Bottle‐fed ...

7 Chapter 7TABLE 7.1 Overall Adverse Taste Impact Score Following Three Months of Chemot...TABLE 7.2 Overall Adverse Taste Impact Score Following Three Months of Chemot...TABLE 7.3 Yields of Two Strains of Wheat in a Randomized Block Design (Bushel...TABLE 7.4 Yields of Two Strains of Wheat in a Randomized Block Design (Bushel...TABLE 7.5 Scores for Pressure Scores in Two Groups of Hospital Patients Given...TABLE 7.6 Estimates of Child Height Using Two Different Assessment Methods

8 Chapter 8TABLE 8.1 General Layout of Data for a Four‐Fold aor 2 × 2 Contingency Table...TABLE 8.2 General Layout of Data for a Four‐Fold or 2 × 2 Table, with Statist...TABLE 8.3 Physical Activity Level versus Gender in Children Living in England...TABLE 8.4 Physical Activity Level versus Gender in Children Living in England...TABLE 8.5 Labelling of Data for a Table with Three Rows and Four ColumnsTABLE 8.6 Physical Activity Level versus Age Group in Children Living in Engl...TABLE 8.7 Physical Activity Level versus Age Group in Children Living in Engl...TABLE 8.8 Number of Children Aged 13–14 Years Whose Fruit and Vegetable Consu...TABLE 8.9 Number of Children Aged 13–14 Years Whose Fruit and Vegetable Consu...TABLE 8.10 The Probabilities Based on Fisher’s Exact Test of the Possible Tab...TABLE 8.11 Number (and Percentage) of Children Aged 5–15 Years Attending a Sm...TABLE 8.12 Number (Observed and Expected) of Children Aged 5–15 Years Attendi...TABLE 8.13 Number (Observed and Expected) of Children Aged 5–15 Years Attendi...TABLE 8.14 Number Observed and Percentage Within Age Group Consuming Specifie...TABLE 8.15 Numbers of Women and Men who Thought Changes in Dietary Habits Would ...TABLE 8.16 Number of Patients Who Had Nutritional Status Assessed Three Months P...TABLE 8.17 Presence of Anaemia in Adolescent Girls According to Menarchial Statu...

9 Chapter 9TABLE 9.1 Number of Medical Science Students who Found Statistics ‘Impossible...TABLE 9.2 Number of Women with or without Retinopathy during and After Pregna...TABLE 9.3 Numbers of Case‐Control Matched Pairs with or without Hyperthyroidi...TABLE 9.4 Number of Patients Classified by Walking Status (‘Moderate to no Restr...

10 Chapter 10TABLE 10.1 Death Rate from Cirrhosis and Alcoholism (per 100 000 Population) ...TABLE 10.2 Death Rate from Cirrhosis and Alcoholism (per 100 000 Population) ...TABLE 10.3 Unofficial Vocabulary for Describing the Strength of a Correlation...TABLE 10.4 Death Rate from Cirrhosis and Alcoholism (per 100 000 Population) ...TABLE 10.5 Typical Dietitian Salaries in the NHS in England, by Age (from Dietet...TABLE 10.6 Glucocorticoid Therapy (Months) and Bone‐Density ( T ‐Score) in 14 Wome...

11 Chapter 11TABLE 11.1 Symbols Used for Calculation of F Statistic in One‐Way Analysis of ...TABLE 11.2 Length of Hospital Stay versus Day of Initiation of Feeding Follow...TABLE 11.3 Length of Hospital Stay versus Day of Initiation of Feeding Follow...TABLE 11.4 Analysis of Variance Table for Data Comparing Length of Hospital S...TABLE 11.5 SPSS Output for One‐Way Analysis of Variance Based on Laparoscopic...TABLE 11.6 SPSS Output for Multiple Comparisons Based on Tukey (HSD) post hoc ...TABLE 11.7 SPSS Output for Homogeneous Subsets Based on Tukey (HSD) post hoc A...TABLE 11.8 SPSS Output for Tests of Normality Using the Present Data setTABLE 11.9 SPSS Output for Leven’s Statistic for Homogeneity of VariancesTABLE 11.10 Average Weight Loss after 10 Weeks in Men and Women on Three Diff...TABLE 11.11 Analysis of Weight Loss Data for NormalityTABLE 11.12 Levene's Test of Equality of Error VariancesTABLE 11.13 Two‐Way Analysis of Variance Table Showing the Impact of Gender, ...TABLE 11.14 Homogeneous Subsets Based on Tukey Analysis of the Impact of Diet...TABLE 11.15 Carbohydrate Intake (g/d) in Four Groups of Cyclists