Practical Statistics for Nursing and Health Care

Jim Fowler, former Principal Lecturer, Department of Biological Sciences, De Montfort University, Leicester, UK.

Philip Jarvis, Statistician, Novartis Pharma AG, Basel, Switzerland.

Mel Chevannes, Emeritus Professor of Nursing, University of Wolverhampton, Wolverhampton, UK.

PREFACE xi


FOREWORD TO STUDENTS xv


1 INTRODUCTION 1


1.1 What do we mean by statistics? 1


1.2 Why is statistics necessary? 1


1.3 The limitations of statistics 2


1.4 Performing statistical calculations 2


1.5 The purpose of this text 3


2 HEALTH CARE INVESTIGATIONS: MEASUREMENT AND SAMPLING CONCEPTS 5


2.1 Introduction 5


2.2 Populations, samples and observations 5


2.3 Counting things - the sampling unit 6


2.4 Sampling strategy 7


2.5 Target and study populations 8


2.6 Sample designs 8


2.7 Simple random sampling 9


2.8 Systematic sampling 9


2.9 Stratified sampling 10


2.10 Quota sampling 11


2.11 Cluster sampling 12


2.12 Sampling designs - summary 12


2.13 Statistics and parameters 13


2.14 Descriptive and inferential statistics 13


2.15 Parametric and non-parametric statistics 14


3 PROCESSING DATA 15


3.1 Scales of measurement 15


3.2 The nominal scale 15


3.3 The ordinal scale 16


3.4 The interval scale 17


3.5 The ratio scale 17


3.6 Conversion of interval observations to an ordinal scale 17


3.7 Derived variables 19


3.8 Logarithms 20


3.9 The precision of observations 21


3.10 How precise should we be? 22


3.11 The frequency table 22


3.12 Aggregating frequency classes 24


3.13 Frequency distribution of count observations 26


3.14 Bivariate data 27


4 PRESENTING DATA 29


4.1 Introduction 29


4.2 Dot plot or line plot 29


4.3 Bar graph 30


4.4 Histogram 32


4.5 Frequency polygon and frequency curve 33


4.5 Centiles and growth charts 35


4.7 Scattergram 35


4.8 Circle or pie graph 35


5 CLINICAL TRIALS 39


5.1 Introduction 39


5.2 The nature of clinical trials 39


5.3 Clinical trial designs 40


5.4 Psychological effects and blind trials 41


5.5 Historical controls 42


5.6 Ethical issues 43


5.7 Case study: Leicestershire Electroconvulsive Therapy (ECT) study 43


5.8 Summary 45


6 INTRODUCTION TO EPIDEMIOLOGY 47


6.1 Introduction 47


6.2 Measuring disease 48


6.3 Study designs - cohort studies 50


6.4 Study designs - case-control studies 51


6.5 Cohort or case-control study? 53


6.6 Choice of comparison group 54


6.7 Confounding 55


6.8 Summary 56


7 MEASURING THE AVERAGE 57


7.1 What is an average? 57


7.2 The mean 57


7.3 Calculating the mean of grouped data 59


7.4 The median - a resistant statistic 60


7.5 The median of a frequency distribution 61


7.6 The mode 62


7.7 Relationship between mean, median and mode 64


8 MEASURING VARIABILITY 65


8.1 Variability 65


8.2 The range 65


8.3 The standard deviation 66


8.4 Calculating the standard deviation 67


8.5 Calculating the standard deviation from grouped data 68


8.6 Variance 69


8.7 An alternative formula for calculating the variance and standard deviation 70


8.8 Degrees of freedom 71


8.9 The Coefficient of Variation (CV) 72


9 PROBABILITY AND THE NORMAL CURVE 75


9.1 The meaning of probability 75


9.2 Compound probabilities 76


9.3 Critical probability 78


9.4 Probability distribution 79


9.5 The normal curve 81


9.6 Some properties of the normal curve 82


9.7 Standardizing the normal curve 83


9.8 Two-tailed or one-tailed? 84


9.9 Small samples: the t-distribution 86


9.10 Are our data normally distributed? 88


9.11 Dealing with 'non-normal' data 91


10 HOW GOOD ARE OUR ESTIMATES? 95


10.1 Sampling error 95


10.2 The distribution of a sample mean 95


10.3 The confidence interval of a mean of a large sample 98


10.4 The confidence interval of a mean of a small sample 99


10.5 The difference between the means of two large samples 100


10.6 The difference between the means of two small samples 102


10.7 Estimating a proportion 103


10.8 The finite population correction 105


11 THE BASIS OF STATISTICAL TESTING 107


11.1 Introduction 107


11.2 The experimental hypothesis 107


11.3 The statistical hypothesis 108


11.4 Test statistics 110


11.5 One-tailed and two-tailed tests 110


11.6 Hypothesis testing and the normal curve 111


11.7 Type 1 and type 2 errors 113


11.8 Parametric and non-parametric statistics: some further observations 113


11.9 The power of a test 114


12 ANALYSING FREQUENCIES 115


12.1 The chi-squared test 115


12.2 Calculating the test statistic 115


12.3 A practical example of a test for homogeneous frequencies 118


12.4 One degree of freedom - Yates' correction 119


12.5 Goodness of fit tests 120


12.6 The contingency table - tests for association 121


12.7 The 'rows by columns' (r x c) contingency table 125


12.8 Larger contingency tables 127


12.9 Advice on analysing frequencies 129


13 MEASURING CORRELATIONS 131


13.1 The meaning of correlation 131


13.2 Investigating correlation 131


13.3 The strength and significance of a correlation 133


13.4 The Product Moment Correlation Coefficient 134


13.5 The coefficient of determination r2 136


13.6 The Spearman Rank Correlation Coefficient rs 137


13.7 Advice on measuring correlations 139


14 REGRESSION ANALYSIS 141


14.1 Introduction 141


14.2 Gradients and triangles 142


14.3 Dependent and independent variables 143


14.4 A perfect rectilinear relationship 144


14.5 The line of least squares 146


14.6 Simple linear regression 147


14.7 Fitting the regression line to the scattergram 150


14.8 Regression for estimation 150


14.9 The coefficient of determination in regression 151


14.10 Dealing with curved relationships 152


14.11 How we can 'straighten up' curved relationships? 155


14.12 Advice on using regression analysis 155


15 COMPARING AVERAGES 157


15.1 Introduction 157


15.2 Matched and unmatched observations 158


15.3 The Mann-Whitney U-test for unmatched samples 158


15.4 Advice on using the Mann-Whitney U-test 160


15.5 More than two samples - the Kruskal-Wallace test 161


15.6 Advice on using the Kruskal-Wallace test 163


15.7 The Wilcoxon test for matched pairs 164


15.8 Advice on using the Wilcoxon test for matched pairs 167


15.9 Comparing means - parametric tests 168


15.10 The z-test for comparing the means of two large samples 168


15.11 The t-test for comparing the means of two small samples 170


15.12 The t-test for matched pairs 171


15.13 Advice on comparing means 173


16 ANALYSIS OF VARIANCE -ANOVA 175


16.1 Why do we need ANOVA? 175


16.2 How ANOVA works 176


16.3 Procedure for computing ANOVA 178


16.4 The Tukey test 181


16.5 Further applications of ANOVA 183


16.6 Advice on using ANOVA 185


APPENDICES 187


Appendix 1: Table of random numbers 187


Appendix 2: t-distribution 188


Appendix 3: 2-distribution 189


Appendix 4: Critical values of Spearman's Rank Correlation Coefficient 190


Appendix 5: Critical values of the product moment correlation coefficient 191


Appendix 6: Mann-Whitney U-test values (two-tailed test) 192


Appendix 7: Critical values of T in the Wilcoxon test for matched pairs 193


Appendix 8: F-distribution 194


Appendix 9: Tukey test 198


Appendix 10: Symbols 200


Appendix 11: Leicestershire ECT study data 201


Appendix 12: How large should our samples be? 203


BIBLIOGRAPHY 209


INDEX 211