| |

| |

Preface | |

| |

| |

Foreword to Students | |

| |

| |

| |

Introduction | |

| |

| |

| |

What do we mean by statistics? | |

| |

| |

| |

Why is statistics necessary? | |

| |

| |

| |

The limitations of statistics | |

| |

| |

| |

Calculators and computers in statistics | |

| |

| |

| |

The purpose of this text | |

| |

| |

| |

Health Care Investigations: Measurement and Sampling Concepts | |

| |

| |

| |

Introduction | |

| |

| |

| |

Populations, samples and observations | |

| |

| |

| |

Counting things--the sampling unit | |

| |

| |

| |

Sampling strategy | |

| |

| |

| |

Target and study populations | |

| |

| |

| |

Sample designs | |

| |

| |

| |

Simple random sampling | |

| |

| |

| |

Systematic sampling | |

| |

| |

| |

Stratified sampling | |

| |

| |

| |

Quota sampling | |

| |

| |

| |

Cluster sampling | |

| |

| |

| |

Sampling designs--summary | |

| |

| |

| |

Statistics and parameters | |

| |

| |

| |

Descriptive and inferential statistics | |

| |

| |

| |

Parametric and non-parametric statistics | |

| |

| |

| |

Processing Data | |

| |

| |

| |

Scales of measurement | |

| |

| |

| |

The nominal scale | |

| |

| |

| |

The ordinal scale | |

| |

| |

| |

The interval scale | |

| |

| |

| |

The ratio scale | |

| |

| |

| |

Conversion of interval observations to an ordinal scale | |

| |

| |

| |

Derived variables | |

| |

| |

| |

Logarithms | |

| |

| |

| |

The precision of observations | |

| |

| |

| |

How precise should we be? | |

| |

| |

| |

The frequency table | |

| |

| |

| |

Aggregating frequency classes | |

| |

| |

| |

Frequency distribution of count observations | |

| |

| |

| |

Bivariate data | |

| |

| |

| |

Presenting Data | |

| |

| |

| |

Introduction | |

| |

| |

| |

Dot plot or line plot | |

| |

| |

| |

Bar graph | |

| |

| |

| |

Histogram | |

| |

| |

| |

Frequency polygon and frequency curve | |

| |

| |

| |

Scattergram | |

| |

| |

| |

Circle or pie graph | |

| |

| |

| |

Clinical Trials | |

| |

| |

| |

Introduction | |

| |

| |

| |

The nature of clinical trials | |

| |

| |

| |

Clinical trial designs | |

| |

| |

| |

Psychological effects and blind trials | |

| |

| |

| |

Historical controls | |

| |

| |

| |

Ethical issues | |

| |

| |

| |

Case study: Leicestershire Electroconvulsive Therapy (ECT) study | |

| |

| |

| |

Summary | |

| |

| |

| |

Introduction to Epidemiology | |

| |

| |

| |

Introduction | |

| |

| |

| |

Measuring disease | |

| |

| |

| |

Study designs--cohort studies | |

| |

| |

| |

Study designs--case-control studies | |

| |

| |

| |

Cohort or case-control study? | |

| |

| |

| |

Choice of comparison group | |

| |

| |

| |

Confounding | |

| |

| |

| |

Summary | |

| |

| |

| |

Measuring the Average | |

| |

| |

| |

What is an average? | |

| |

| |

| |

The mean | |

| |

| |

| |

Calculating the mean of grouped data | |

| |

| |

| |

The median--a resistant statistic | |

| |

| |

| |

The median of a frequency distribution | |

| |

| |

| |

The mode | |

| |

| |

| |

Relationship between mean, median and mode | |

| |

| |

| |

Measuring Variability | |

| |

| |

| |

Variability | |

| |

| |

| |

The range | |

| |

| |

| |

The standard deviation | |

| |

| |

| |

Calculating the standard deviation | |

| |

| |

| |

Calculating the standard deviation from grouped data | |

| |

| |

| |

Variance | |

| |

| |

| |

An alternative formula for calculating the variance and standard deviation | |

| |

| |

| |

Obtaining the standard deviation and sum of squares from a calculator | |

| |

| |

| |

Degrees of freedom | |

| |

| |

| |

The Coefficient of Variation (CV) | |

| |

| |

| |

Probability and the Normal Curve | |

| |

| |

| |

The meaning of probability | |

| |

| |

| |

Compound probabilities | |

| |

| |

| |

Critical probability | |

| |

| |

| |

Probability distribution | |

| |

| |

| |

The normal curve | |

| |

| |

| |

Some properties of the normal curve | |

| |

| |

| |

Standardizing the normal curve | |

| |

| |

| |

Two-tailed or one-tailed? | |

| |

| |

| |

Small samples: the t-distribution | |

| |

| |

| |

Are our data 'normal'? | |

| |

| |

| |

Dealing with 'non-normal' data | |

| |

| |

| |

How Good are Our Estimates? | |

| |

| |

| |

Sampling error | |

| |

| |

| |

The distribution of a sample mean | |

| |

| |

| |

The confidence interval of a mean of a large sample | |

| |

| |

| |

The confidence interval of a mean of a small sample | |

| |

| |

| |

The difference between the means of two large samples | |

| |

| |

| |

The difference between the means of two small samples | |

| |

| |

| |

Estimating a proportion | |

| |

| |

| |

The finite population correction | |

| |

| |

| |

The Basis of Statistical Testing | |

| |

| |

| |

Introduction | |

| |

| |

| |

The experimental hypothesis | |

| |

| |

| |

The statistical hypothesis | |

| |

| |

| |

Test statistics | |

| |

| |

| |

One-tailed and two-tailed tests | |

| |

| |

| |

Hypothesis testing and the normal curve | |

| |

| |

| |

Type 1 and type 2 errors | |

| |

| |

| |

Parametric and non-parametric statistics: some further observations | |

| |

| |

| |

The power of a test | |

| |

| |

| |

Analysing Frequencies | |

| |

| |

| |

The chi-squared test | |

| |

| |

| |

Calculating the test statistic | |

| |

| |

| |

A practical example of a test for homogeneous frequencies | |

| |

| |

| |

One degree of freedom--Yates' correction | |

| |

| |

| |

Goodness of fit tests | |

| |

| |

| |

The contingency table--tests for association | |

| |

| |

| |

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

| |

| |

| |

Larger contingency tables | |

| |

| |

| |

Advice on analysing frequencies | |

| |

| |

| |

Measuring Correlations | |

| |

| |

| |

The meaning of correlation | |

| |

| |

| |

Investigating correlation | |

| |

| |

| |

The strength and significance of a correlation | |

| |

| |

| |

The Product Moment Correlation Coefficient | |

| |

| |

| |

The coefficient of determination r[superscript 2] | |

| |

| |

| |

The Spearman Rank Correlation Coefficient r[subscript s] | |

| |

| |

| |

Advice on measuring correlations | |

| |

| |

| |

Regression Analysis | |

| |

| |

| |

Introduction | |

| |

| |

| |

Gradients and triangles | |

| |

| |

| |

Dependent and independent variables | |

| |

| |

| |

A perfect rectilinear relationship | |

| |

| |

| |

The line of least squares | |

| |

| |

| |

Simple linear regression | |

| |

| |

| |

Fitting the regression line to the scattergram | |

| |

| |

| |

Regression for estimation | |

| |

| |

| |

The coefficient of determination in regression | |

| |

| |

| |

Dealing with curved relationships | |

| |

| |

| |

How we can 'straighten up' curved relationships? | |

| |

| |

| |

Advice on using regression analysis | |

| |

| |

| |

Comparing Averages | |

| |

| |

| |

Introduction | |

| |

| |

| |

Matched and unmatched observations | |

| |

| |

| |

The Mann--Whitney U-test for unmatched samples | |

| |

| |

| |

Advice on using the Mann--Whitney U-test | |

| |

| |

| |

More than two samples--the Kruskal--Wallace test | |

| |

| |

| |

Advice on using the Kruskal--Wallace test | |

| |

| |

| |

The Wilcoxon test for matched pairs | |

| |

| |

| |

Advice on using the Wilcoxon test for matched pairs | |

| |

| |

| |

Comparing means--parametric tests | |

| |

| |

| |

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

| |

| |

| |

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

| |

| |

| |

The t-test for matched pairs | |

| |

| |

| |

Advice on comparing means | |

| |

| |

| |

Analysis of Variance--Anova | |

| |

| |

| |

Why do we need ANOVA? | |

| |

| |

| |

How ANOVA works | |

| |

| |

| |

Procedure for computing ANOVA | |

| |

| |

| |

The Tukey test | |

| |

| |

| |

Further applications of ANOVA | |

| |

| |

| |

Advice on using ANOVA | |

| |

| |

Appendices | |

| |

| |

| |

Table of random numbers | |

| |

| |

| |

t-distribution | |

| |

| |

| |

x[superscript 2]-distribution | |

| |

| |

| |

Critical values of Spearman's Rank Correlation Coefficient | |

| |

| |

| |

Critical values of the product moment correlation coefficient | |

| |

| |

| |

Mann--Whitney U-test values (two-tailed test) | |

| |

| |

| |

Critical values of T in the Wilcoxon test for matched pairs | |

| |

| |

| |

F-distribution | |

| |

| |

| |

Tukey test | |

| |

| |

| |

Symbols | |

| |

| |

| |

Leicestershire ECT study data | |

| |

| |

| |

How large should our samples be? | |

| |

| |

Bibliography | |

| |

| |

Index | |