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- Herausgeber: John Wiley & Sons
- Kategorie: Wissenschaft und neue Technologien
- Sprache: Englisch
Nursing is a growing area of higher education, in which anintroduction to statistics is an essential component. There iscurrently a gap in the market for a 'user-friendly' book which iscontextulised and targeted for nursing. Practical Statistics forNursing and Health Care introduces statistical techniques in such away that readers will easily grasp the fundamentals to enable themto gain the confidence and understanding to perform their ownanalysis. It also provides sufficient advice in areas such asclinical trials and epidemiology to enable the reader to criticallyappraise work published in journals such as the Lancet and BritishMedical Journal.
* Covers all basic statistical concepts and tests
* Is user-friendly - avoids excessive jargon
* Includes relevant examples for nurses, including case studies anddata sets
* Provides information on further reading
* Starts from first principles and progresses step by step
* Includes 'advice on' sections for all of the tests described
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Seitenzahl: 259
Veröffentlichungsjahr: 2013
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CONTENTS
PREFACE
FOREWORD TO STUDENTS
1 INTRODUCTION
1.1 What do we mean by statistics?
1.2 Why is statistics necessary?
1.3 The limitations of statistics
1.4 Calculators and computers in statistics
1.5 The purpose of this text
2 HEALTH CARE INVESTIGATIONS: MEASUREMENT AND SAMPLING CONCEPTS
2.1 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
3 PROCESSING DATA
3.1 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
4 PRESENTING DATA
4.1 Introduction
4.2 Dot plot or line plot
4.3 Bar graph
4.4 Histogram
4.5 Frequency polygon and frequency curve
4.6 Scattergram
4.7 Circle or pie graph
5 CLINICAL TRIALS
5.1 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 (ECT) study
5.8 Summary
6 INTRODUCTION TO EPIDEMIOLOGY
6.1 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
7 MEASURING THE AVERAGE
7.1 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
8 MEASURING VARIABILITY
8.1 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 Obtaining the standard deviation and sum of squares from a calculator
8.9 Degrees of freedom
8.10 The Coefficient of Variation (CV)
9 PROBABILITY AND THE NORMAL CURVE
9.1 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 ‘normal’?
9.11 Dealing with ‘non-normal’ data
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
11 THE BASIS OF STATISTICAL TESTING
11.1 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
12 ANALYSING FREQUENCIES
12.1 The chi-squared 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
13 MEASURING CORRELATIONS
13.1 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 r2
13.6 The Spearman Rank Correlation Coefficient rs
13.7 Advice on measuring correlations
14 REGRESSION ANALYSIS
14.1 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 we can ‘straighten up’ curved relationships?
14.12 Advice on using regression analysis
15 COMPARING AVERAGES
15.1 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–Wallace test
15.6 Advice on using the Kruskal–Wallace 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
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
APPENDICES
Appendix 1: Table of random numbers
Appendix 2: t-distribution
Appendix 3: χ2 -distribution
Appendix 4: Critical values of Spearman’s Rank Correlation Coefficient
Appendix 5: Critical values of the product moment correlation coefficient
Appendix 6: Mann–Whitney U-test values (two-tailed test)
Appendix 7: Critical values of T in the Wilcoxon test for matched pairs
Appendix 8: F-distribution
Appendix 9: Tukey test
Appendix 10: Symbols
Appendix 11: Leicestershire ECT study data
Appendix 12: How large should our samples be?
BIBLIOGRAPHY
INDEX
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PREFACE
Background
Over the past few years, substantial changes have taken place in the education, training and practice of nursing and midwifery. All pre-registration education and training is now provided at a minimum of Diploma of Higher Education, and much is at degree level. Pre-registration education and training incorporates an equality of hours between knowledge (2300 hours) and clinical/practice skills (2300 hours). Knowledge includes the application and use of scientific skills (ENB 1999; DoH 1993; 1999)*. Additionally, there are many continuing professional development and post-graduate training opportunities designed to enable practitioners to maintain their knowledge and skills.
More recently, the UKCC (1999) emphasized the effects of health service changes on the work of nurses and midwives:
‘…future of the health services raised a number of paradoxes likely to affect the role of nurses and midwives; in particular the greater demands upon nurses and midwives for technical competence and scientific rationality’.
Pre-registration education and training and continuing professional development are required to prepare nurses and midwives with technical and scientific skills to work competently in the NHS today and in the future. These skills demand an understanding of the principles underlying statistics, and using them appropriately in the daily practice of nursing and midwifery.
Changes in the context of health care
The context of health care is changing, most notably between primary care/home/community-based services and those provided in acute hospitals. Public expectation of wellness and patterns of disease have also changed (DoH 1999). At the same time, opportunities created by the development in pharmaceutical services and technological advances combine to amplify the dynamic context of health care where nurses, midwives and other health professionals work. All these changes point to a need for nurses and midwives to be prepared to respond in knowledgeable and practical ways, and to do so competently every time.
Technological imperatives
Telemedicine and telecare will make screening for diseases, diagnosis and monitoring quicker and more accurate. Patients and other users are likely to benefit from an improvement in the methods by which diagnoses are made, and as a result, care and treatment will be more effective (DoH 1999). Nurses and midwives need to know and understand the data they see, the most appropriate analysis to make, and how to use the information in the patient’s care and treatment plan.
Team working
Organizational changes in the way nurses work make it imperative to do so in a team and to provide an integrated planning pathway of care for patients. A Plan of Care, for example for patients with diabetes, may include evaluating response to medication – insulin or tablets – by age, gender and ethnicity, or undertaking a comparable analysis of the stabilization of diabetes among a group of patients by insulin injection.
Nurses working in specialist areas such as heart, thoracic surgery, intensive care, renal, endosocopy clinics, and cancer centres/units use skills of a highly technical and statistical nature. Students and qualified nurses in these settings should be enabled to access and manage health information, including the accurate recording of clinical changes in individual patients’ conditions (ENB 1999). Analysis of clinical variations by drawing on basic statistical principles enable health care professionals to decide on appropriate treatment and predict recovery.
In relation to midwifery, the Institute of Manpower Studies (1993) found that over 40 percent of maternity services had recently introduced ‘team midwifery’. The practice of team midwifery requires all midwives to use scientific evidence to under-pin the care they provide to women and babies. For example, an understanding of the AGPAR score of the baby at birth and in the immediate post-delivery period is important to a team of midwives operating in the delivery room, and the post-natal area. A baby’s APGAR score at birth, and in particular when there is delay, with the maximum score of 10 being achieved postnatally may indicate the need for accurate monitoring of heart, pulse and breathing rates.
Modern ways of working to make a difference
The new education and training of nurses and midwives spelt out in Making a Difference (DoH 1999) emphasizes modern roles in acute, community and primary care. Nurses, midwives and health visitors working in the community and in primary care are expected to provide accurate and reliable health information to patients about health risks and patterns of disease. As public health workers, health visitors undertake community profiling, health needs assessment, and provide advice about a range of topics, including the control of communicable diseases.
Requirement of health visitors to prescribe drugs (from the Nurses’ Prescribing Formulary for patients) places additional demands for good statistical understanding and skills in order to prescribe accurately, appropriately and safely. As this role expands in the future, and for nurses to administer a range of medicines with direct referral to a doctor (DoH 2001), the need for the use of quantitative methods in nursing will increase.
In the context of care for young children, health visitors and paediat-ric nurses know that mothers are likely to be anxious about whether the weight of their child is high, low or just within the expected range. The ability of these health professionals to understand the principles underlying weight calculations, analysis and predictions place them in a good position to accurately explain and reassure mothers.
This book on practical statistics for nurse and other health care professionals is an introductory text produced to assist with the growing demand for user-friendly worked examples which are clear and easily understood, not only by students, but also by busy practitioners. We aim to provide an introduction to the statistical techniques that are most commonly used that also provides a sound foundation for those who choose to expand their careers into research.
Jim Fowler
Philjarvis
Mel Chevannes
*Details of references cited throughout this book are listed in the bibilography in Appendix 13.
FOREWORD TO STUDENTS
It is possible that you have recently enrolled on a nursing, midwifery or other health care course. It is likely that you did so with high ideals and a motivation to help humankind in the relief of suffering. It is also possible that you did not enjoy handling ‘numbers’ at school, and you have sought to escape from them. And now you have in your hands a textbook that might, at first sight, look terrifying.
We wish to offer a word of reassurance. Modern health care is a ‘science’, and as such, involvement with numbers is inescapable. It was, after all, Florence Nightingale herself who recognized the importance of maintaining accurate numerical records. However, it might not be as bad as you fear. This book seeks to guide you through the subject ‘from scratch’, and we make no assumptions about your previous learning. The chapters develop in difficulty progressively through the book, and the material is extensively cross-referenced. If you wish to ‘dip in’ to the text, you will find guidance on where to look back for under-pinning explanations.
It is very unlikely that you will ever need to know all that is contained in this book. In the first instance, it may be simply a supporting text to help you through a statistical element of your course. Later, you may be involved in a project of some kind, when this book can help you plan correctly the gathering, presentation and analysis of your data. Some of you may then venture into an area of research, in which case the more advanced chapters in this book will give you a sound foundation in the quantitative techniques that are required.
We plead with you not to feel intimidated by the formulae that you see by flicking through these pages. How they are used is carefully described in each case. By persisting with the book from ‘square one’, reworking some of our own examples to make sure that you get the same answer, you will rapidly become sufficiently confident to apply them to your own data. And, who knows, you may even come to enjoy statistics!
1
INTRODUCTION
1.1 What do we mean by statistics?
Statistics are a familiar and accepted part of the modern world, and already intrude into the life of every nurse and health care worker. We have statistics in the form of patients registered at a GP practice or outpatient clinic; hospital measurements and records of temperature, blood pressure and pulse rate; data collected from various surveys, censuses and clinical trials, to name but a few. It is impossible to imagine life without some form of statistical information being readily at hand.
The word statistics is used in two senses. It refers to collections of quantitative information, and methods of handling that sort of data. A hospital’s database listing the names, addresses and medical history records of all its registered patients, is an example of the first sense in which the word is used. Statistics also refers to the drawing of inferences about large groups on the basis of observations made on smaller ones. Estimating the relationship between smoking and the incidence of lung cancer illustrates the second sense in which the word is used.
Statistics looks at ways of organizing, summarizing and describing quantifiable data, and methods of drawing inferences and generalizing upon them.
1.2 Why is statistics necessary?
A second reason why statistical literacy is important to health care workers is if they are going to undertake an investigation that involves the collection, processing and analysis of data on their own account. If the results are to be presented in a form that will be authoritative, then a grasp of statistical principles and methods is essential. Indeed, a programme of work should be planned anticipating the statistical methods that are appropriate to the eventual analysis of the data. Attaching some statistical treatment as an afterthought to make a survey seem more ‘respectable’ is unlikely to be convincing.
1.3 The limitations of statistics
Statistics can help an investigator describe data, design experiments, and test hunches about relationships among things or events of interest. Statistics is a tool that helps acceptance or rejection of the hunches within recognized degrees of confidence. They help to answer questions like, ‘If my assertion is challenged, can I offer a reasonable defence?’
It should be noted that statistics never prove anything. Rather, they indicate the likelihood of the results of an investigation being the product of chance.
1.4 Calculators and computers in statistics
A hand calculator that has the capacity to calculate a mean and standard deviation (typically referred to as a ‘scientific’ calculator) from a single input of a set of data is indispensable. All the calculations and worked examples in this book were first worked out using such a calculator. Because different makes of calculator operate somewhat differently, we have not attempted to offer guidance about the use of individual calculators: we suggest that you study the instruction booklet that comes with your calculator.
In a modern world, computer packages are readily available and easy to use. However, we suggest caution against jumping straight into computer packages without first understanding the underlying background and principles of a particular statistical technique. Computers undertake any analysis that you ask of it, but can not provide the intelligent reasoning about whether the test is appropriate for the kind of data you are using. Moreover, a ‘print-out’ of the analysis can be ambiguous and confusing if you do not understand the underlying principles. We feel this is best achieved by first familiarizing yourself with the techniques ‘long hand’, working through our own examples and applying them to your own data. In due course, support from a computer package will become a natural extension of your analysis.
1.5 The purpose of this text
The objectives of this text stem from the points made in Section 1.2. First, the text aims to provide nurses and health care workers with sufficient grounding in statistical principles and methods to enable them to read survey reports, journals and other literature. Secondly, the text aims to present them with a variety of the most appropriate statistical tests for their problems. Thirdly, guidance is offered on ways of presenting the statistical analyses, once completed.
Full details of references and other material that we suggest for further reading are listed in full in the Bibliography in Appendix 13. For assistance in cross-referencing, we classify items according to chapter. Thus, Section 9.1, Figure 9.1, Table 9.1 and Example 9.1 are all to be found in Chapter 9.
2
HEALTH CARE INVESTIGATIONS: MEASUREMENT AND SAMPLING CONCEPTS
2.1 Introduction
A health care investigation is typically a five-stage process: identifying objectives; planning; data collection; analysis; and, finally, reporting. The methodologies frequently used are sample surveys, clinical trials and epidemiological studies that are the subject of this and subsequent chapters. However, we must first be clear about the definitions of some basic terms. Many of the terms used in statistics also have usage in daily life, where the meaning might be quite different. The word ‘population’ may conjure images of ‘people’, whilst ‘sample’ might mean a ‘free sample’ of cream offered by a pharmaceutical company, or a ‘sample’ requested by a doctor for urine analysis. In statistics, however, these words have much more precise meanings.
2.2 Populations, samples and observations
In statistics, the term ‘population’ is extended to mean any collection of individual items or units that are the subject of investigation. Characteristics of a population that differ from individual to individual are called variables. Length, age, weight, temperature, number of heart beats, to name but a few, are examples of variables to which numbers or values can be assigned. Once numbers or values have been assigned to the variables, they can be measured.
Because it is rarely practicable to obtain measures of a particular variable from all the units in a population, the investigator has to collect information from a smaller group or sub-set that represents the group as a whole. This sub-set is called a sample. Each unit in the sample provides a record, such as a measurement, which is called an observation. The relationship between the terms we have introduced is summarized below:
Observation:
3.62 kg
Variable:
weight
Sample unit (item):
a new-born male baby
Sample:
those new-born male babies that are weighed
Statistical population:
all new-born male babies that are available for
weighing.
Note that the biological or demographic population would include babies of both sexes, and indeed, all individuals of whatever age or sex in a particular community.
2.3 Counting things – the sampling unit
We sometimes wish to count the number of items or objects in a group or collection. If the number is to be meaningful, the dimensions of the collection have to be specified.
For example ‘the number of patients admitted to an accident and emergency department’ has little meaning unless we know the time scale over which the count was made. A collection with specified dimensions is called a sampling unit. An observation is, of course, the number of objects or items counted in a sampling unit. Thus, if 52 patients are admitted to a particular A & E department in a 24 hr period, the sampling unit is ‘one A. & E. 24-hour period’ and the observation is 52. The sample is the number of such 24-hour periods that were included in the survey. However, the definition of the ‘population’ requires care. It might be tempting to think that the population under investigation is something to do with patients, but this is not the case when they are being counted. The statistical population comprises the same ‘thing’ as the sample units that comprise the sample. In this case, the statistical population is a rather abstract concept, and represents all possible ‘A & E department 24 hour periods’ that could have been included in the survey.
It is very important to be able to identify correctly the population under investigation, because this is essential in formulating a ‘null hypothesis’ when undertaking statistical tests. This is the subject of Chapter 11.
2.4 Sampling strategy
As we said above, it is not always possible or practicable to sample every single individual or unit in a particular population either due to its size, or constraints on available resources (for example, cost, time, manpower). The solution is to take a sample from the population of interest and use the sample information to make inferences about the population.
A common, but misguided, approach to sampling is to first decide what data to collect, then undertake the survey, and finally, decide what analyses should be done. However, without initial thought being given to the aims of the survey, the information or data may not be appropriate (e.g. wrong data collected, or data collected on wrong subjects, or insufficient data collected). As a result, the desired analysis may not be possible or effective.
The key to good sampling is to:
The crucial point relates to the sequence. For example, if the aim of a study is to identify the effectiveness of asthmatic care within a single GP practice, suitable measures of effectiveness need to be defined. One measure could be based on the number of acute asthma exacerbations (deteriorations) in the preceding 12 months, and this number could be compared with that for the previous 12 months. Other measures might assess the number of patients who have had their inhaler technique checked or are using peak flow meters at home. Most of this information can be obtained from practice records, although crosschecking with hospital records may be required to validate the assessment based on acute exacerbations.
2.5 Target and study populations
We have to distinguish between the target and study populations. The target population in the asthma example above is the number of patients registered with the GP practice who have asthma. The study population consists of all patients who could actually be selected to form the sample, i.e. those who are known to have asthma. For example, a proportion of the target population may not know they have asthma, will not therefore be registered, and thus will not form part of the study population. Ideally, the ‘target’ and ‘study’ populations coincide.
2.6 Sample designs
Once the study population has been defined, the next task is to decide which subjects from the population should form the sample. The following list is not exhaustive, but gives a selection of sample designs pertinent to audit:
simple random sampling
systematic sampling
stratified sampling
quota sampling
cluster sampling.
The first three designs can be applied to sampling from finite populations, i.e. situations where every member of the study population can be identified. Such is the case in our asthmatic care example (Section 2.4), where a list of all asthmatic patients registered with the GP practice is available or can easily be obtained prior to the study. Quota and cluster sampling are used when it is not possible or practicable to enumerate every member of the study population.
2.7 Simple random sampling
There are two usual ways of obtaining random numbers. First, many calculators and pocket computers have a facility for generating random numbers. These are often in the form of a fraction, e.g. 0.2771459. You may use this to provide a set of integers, 2, 7, 7, 1,…; or 27, 71, 45,…; or 277, 145; or 2.7, 7.1; and so on, according to your needs, keying in a new number when more digits are required.
Secondly, use may be made of random number tables. Appendix 1 is such a table. The numbers are arranged in groups of five in rows and columns, but this arrangement is arbitrary. Starting at the top left corner, you may read: 2, 3, 1, 5, 7, 5, 4…; or 23, 15, 75, 48,…; or 231, 575, 485…; or 23.1, 57.5, 48.5, 90.1,…; and so on, according to your needs. When you have obtained the numbers you need for your investigation, mark the place in pencil. Next time, carry on where you left off. It is possible that a random number will prescribe a subject (sampling unit) that has already been drawn. In this event, ignore the number and take the next random number. The purpose is to eliminate your prejudice as to which items should be selected for measurement. Unfortunately, observer bias, conscious or unconscious, is notoriously difficult to avoid when gathering data in support of a particular hunch!
Random sampling is the preferred approach to sampling. Although it does not guarantee that a representative sample is taken from the study population (due to sampling error, described in Section 10.1), it gives a better chance than any other method of achieving this.
2.8 Systematic sampling
Systematic sampling has similarities with simple random sampling, in that the first subject in the sample is chosen at random and then every subsequent tenth or twentieth patient (for example) is chosen to cover the entire range of the population.
Example 2.1
What interval is required to select a systematic sample of size 20 from a population of 800?
The required fixed interval is:
Therefore, the first patient (‘sampling unit’) is selected at random (as described in Section 2.8) from among patients numbered 1 to 40. Suppose number 23 is selected. The sample then comprises patients 23, 63, 103, 143,…., 783.
A disadvantage of systematic sampling occurs when the patients are listed in the population in some sort of periodic order, and thus we might inadvertently systematically exclude a subgroup of the population. For example, given a population of 800 patients listed by ‘first attendance’ at the clinic, and that over a 20 week period, 40 patients registered per week, 20 during the daytime and 20 during the evening surgeries. If these patients were listed in the following order: Week 1 daytime patients, Week 1 evening patients, Week 2 daytime patients,…., Week 10 evening patients, then selecting patients 23, 63,…., 783 would result in a sample of evening clinic patients, and exclude all the daytime patients. It is possible that this could generate a biased, or unrepresentative, sample.
An argument in favour of systematic sampling occurs when patients are listed in the population in chronological order, say, by date of first attendance at the GP practice. A systematic sample would yield units whose age distribution is more likely to perfectly represent the study population.
2.9 Stratified sampling
Stratified sampling is effective when the population comprises a number of subgroups (or ‘sub-populations’) that are thought to have an effect on the data being collected, such as male and female, different age groupings, or ethnic origin. These subgroups are called strata. A stratum
