Jim Fowler - Practical Statistics for Nursing and Health Care

1 Cover

2 Title Page

3 Copyright Page

4 PrefaceBackground Changes in the Context of Health Care Technological Imperatives Team Working Modern Ways of Working to Make a Difference

5 Foreword to Students

6 1 Introduction1.1 What Do we Mean by Statistics? 1.2 Why Is Statistics Necessary? 1.3 The Limitations of Statistics 1.4 Performing Statistical Calculations The Purpose of this Text

7 2 Health Care Investigations2.1 Introduction 2.2 Populations, Samples and Observations 2.3 Counting Things – The Sampling Unit 2.4 Sampling Strategy 2.5 Target and Study Populations 2.6 Sample Designs 2.7 Simple Random Sampling 2.8 Systematic Sampling 2.9 Stratified Sampling 2.10 Quota Sampling 2.11 Cluster Sampling 2.12 Sampling Designs – Summary 2.13 Statistics and Parameters 2.14 Descriptive and Inferential Statistics 2.15 Parametric and Non‐Parametric Statistics

8 3 Processing Data3.1 Scales of Measurement 3.2 The Nominal Scale 3.3 The Ordinal Scale 3.4 The Interval Scale 3.5 The Ratio Scale 3.6 Conversion of Interval Observations to an Ordinal Scale 3.7 Derived Variables 3.8 Logarithms 3.9 The Precision of Observations 3.10 How Precise Should We Be? 3.11 The Frequency Table 3.12 Aggregating Frequency Classes 3.13 Frequency Distribution of Count Observations 3.14 Bivariate Data

9 4 Presenting Data4.1 Introduction 4.2 Dot Plot or Line Plot 4.3 Bar Graph 4.4 Histogram 4.5 Frequency Polygon and Frequency Curve 4.6 Centiles and Growth Charts 4.7 Scattergram 4.8 Circle or Pie Graph

10 5 Clinical Trials5.1 Introduction 5.2 The Nature of Clinical Trials 5.3 Clinical Trial Designs 5.4 Psychological Effects and Blind Trials 5.5 Historical Controls 5.6 Ethical Issues 5.7 Case Study: Leicestershire Electroconvulsive Therapy Study 5.8 Summary

11 6 Introduction to Epidemiology6.1 Introduction 6.2 Measuring Disease 6.3 Study Designs – Cohort Studies 6.4 Study Designs – Case‐Control Studies 6.5 Cohort or Case‐Control Study? 6.6 Choice of Comparison Group 6.7 Confounding 6.8 Summary

12 7 Measuring the Average7.1 What Is an Average? 7.2 The Mean 7.3 Calculating the Mean of Grouped Data 7.4 The Median – A Resistant Statistic 7.5 The Median of a Frequency Distribution 7.6 The Mode 7.7 Relationship between Mean, Median and Mode

13 8 Measuring Variability8.1 Variability 8.2 The Range 8.3 The Standard Deviation 8.4 Calculating the Standard Deviation 8.5 Calculating the Standard Deviation from Grouped Data 8.6 Variance 8.7 An Alternative Formula for Calculating the Variance and Standard Deviation 8.8 Degrees of Freedom 8.9 The Coefficient of Variation

14 9 Probability and the Normal Curve9.1 The Meaning of Probability 9.2 Compound Probabilities 9.3 Critical Probability 9.4 Probability Distribution 9.5 The Normal Curve 9.6 Some Properties of the Normal Curve 9.7 Standardizing the Normal Curve 9.8 Two‐Tailed or One‐Tailed? 9.9 Small Samples: The t ‐Distribution 9.10 Are our Data Normally Distributed? 9.11 Dealing with ‘Non‐normal’ Data

15 10 How Good Are our Estimates? 10.1 Sampling Error 10.2 The Distribution of a Sample Mean 10.3 The Confidence Interval of a Mean of a Large Sample 10.4 The Confidence Interval of a Mean of a Small Sample 10.5 The Difference between the Means of Two Large Samples 10.6 The Difference between the Means of Two Small Samples 10.7 Estimating a Proportion 10.8 The Finite Population Correction

16 11 The Basis of Statistical Testing11.1 Introduction 11.2 The Experimental Hypothesis 11.3 The Statistical Hypothesis 11.4 Test Statistics 11.5 One‐Tailed and Two‐Tailed Tests 11.6 Hypothesis Testing and the Normal Curve 11.7 Type 1 and Type 2 Errors 11.8 Parametric and Non‐parametric Statistics: Some Further Observations 11.9 The Power of a Test

17 12 Analysing Frequencies12.1 The Chi‐Square Test 12.2 Calculating the Test Statistic 12.3 A Practical Example of a Test for Homogeneous Frequencies 12.4 One Degree of Freedom – Yates' Correction 12.5 Goodness of Fit Tests 12.6 The Contingency Table – Tests for Association 12.7 The ‘Rows by Columns’ (r × c ) Contingency Table 12.8 Larger Contingency Tables 12.9 Advice on Analysing Frequencies

18 13 Measuring Correlations13.1 The Meaning of Correlation 13.2 Investigating Correlation 13.3 The Strength and Significance of a Correlation 13.4 The Product Moment Correlation Coefficient 13.5 The Coefficient of Determination r 2 13.6 The Spearman Rank Correlation Coefficient r s 13.7 Advice on Measuring Correlations

19 14 Regression Analysis14.1 Introduction 14.2 Gradients and Triangles 14.3 Dependent and Independent Variables 14.4 A Perfect Rectilinear Relationship 14.5 The Line of Least Squares 14.6 Simple Linear Regression 14.7 Fitting the Regression Line to the Scattergram 14.8 Regression for Estimation 14.9 The Coefficient of Determination in Regression 14.10 Dealing with Curved Relationships 14.11 How Can We ‘Straighten Up’ Curved Relationships? 14.12 Advice on Using Regression Analysis

20 15 Comparing Averages15.1 Introduction 15.2 Matched and Unmatched Observations 15.3 The Mann–Whitney U ‐Test for Unmatched Samples 15.4 Advice on Using the Mann–Whitney U ‐Test 15.5 More than Two Samples – The Kruskal–Wallis Test 15.6 Advice on Using the Kruskal–Wallis Test 15.7 The Wilcoxon Test for Matched Pairs 15.8 Advice on Using the Wilcoxon Test for Matched Pairs 15.9 Comparing Means – Parametric Tests 15.10 The z ‐Test for Comparing the Means of Two Large Samples 15.11 The t ‐Test for Comparing the Means of Two Small Samples 15.12 The t ‐Test for Matched Pairs 15.13 Advice on Comparing Means

21 16 Analysis of Variance – ANOVA 16.1 Why Do We Need ANOVA? 16.2 How ANOVA Works 16.3 Procedure for Computing ANOVA 16.4 The Tukey Test 16.5 Further Applications of ANOVA 16.6 Advice on Using ANOVA

22 Appendix A: Table of Random Numbers

23 Appendix B: t ‐Distribution

24 Appendix C: χ 2‐Distribution

25 Appendix D: Critical Values of Spearman's Rank Correlation Coefficient

26 Appendix E: Critical Values of the Product Moment Correlation Coefficient

27 Appendix F: Mann–Whitney U ‐test Values (Two‐Tailed Test) P = 0.05

28 Appendix G: Critical Values of T in the Wilcoxon Test for Matched Pairs

29 Appendix H: F ‐Distribution

30 Appendix I: Tukey Test

31 Appendix J: Symbols

32 Appendix K: Leicestershire ECT Study Data: Subgroup with Depressive Illness

33 Appendix L: How Large Should Our Samples Be?L.1 Introduction L.2 Proportions L.3 Calculating Sample Size for a Quantitative Measure

34 Bibliography

35 Index

36 End User License Agreement

1 Chapter 3 Table 3.1 Weights of 100 babies (kg).Table 3.2 Grouped new‐born baby weights.Table 3.3 Systolic blood pressure of 50 males after myocardial infarct.Table 3.4 A grouped frequency table.

2 Chapter 4Table 4.1 Boys weight‐for‐age percentiles from birth to 24 months.Table 4.2 Gender differences in locations of accidents (percentages in bracke...

3 Chapter 5Table 5.1 Features of clinical trial designs.Table 5.2 Two treatments, two treatment periods (2 × 2) cross‐over design.Table 5.3 1981/2 Leicestershire electroconvulsive therapy study.

4 Chapter 6Table 6.1 Relationship between breast cancer and oral contraceptive usage.Table 6.2 Mortality from coronary disease among smokers and non‐smokers.Table 6.3 Advantages and disadvantages of cohort and case‐control studies.Table 6.4 Choice of comparison group for cohort and case‐control studies.

5 Chapter 8Table 8.1 Calculating a standard deviation from grouped data.

6 Chapter 10Table 10.1 Weights of 100 babies (kg).