Introductory Medical Statistics, 3rd edition

Richard F. Mould

• Publisher: CRC Press
• Year: 1998
• eBook ISBN: 9781000765076
• Topic: Mathematics
• Subtopic: Probability & Statistics
• Index: Mathematics

Introductory Medical Statistics, now in its third edition, is an introductory textbook on basic statistical techniques. It is written for physicians, surgeons, radiation oncologists, medical physicists, radiographers, hospital administrators, medical statisticians in training, biochemists, and other professionals allied to medicine. It is suitable

Chapter 1

Data Presentation

1.1 INTRODUCTION

Data presentation is an essential but sometimes neglected topic for any introduction to statistics. Lack of a proper understanding of the various possibilities of data presentation can lead to confusion for those who are expected to interpret statistical results. Even if the results are correct, they will not be of much use if nobody can understand them. A useful adage is that simplicity of presentation should be a priority.

The following diagrams, charts and graphs are only a few examples but they clearly show the range of possible presentations. Real data has been used, including some examples referring to the problems of cancer of the cervix in developing countries¹.

With the graphics capabilities of computer software, three-dimensional data presentations, such as isometric charts, are also readily available. These are charts or graphs that portray three dimensions on a plane surface.

1.2 BAR CHART

A bar chart, bar diagram or bar graph, is a series of horizontal or vertical bars of equal width for a two-dimensional chart, or equal cross-section for a three-dimensional chart as in Figures 1.1 and 1.2. The width or cross-section does not have any significance for a bar chart; only the height presents the data of interest.

1.3 PIE CHART

Figure 1.3 is a pie chart or pie diagram and is a circle which is divided into segmental areas representing proportions. Since a circle consists of 360°, the segments are calculated by dividing these 360° in the relevant proportions. Thus for three segments of 10, 30 and 60%, the segmental angles are 36°, 108° and 216°, respectively.

Figure 1.1. Bar chart of the world population². Three-dimensional vertical blocks are used in this chart and they are an example of how to present data for two populations (less and more developed regions of the world) in a single diagram. The world’s largest countries in 1996, ranked in order 1–10, are as follows. (Courtesy: United Nations.)

Rank	Country	Population (millions)	Percentage of world population
1	China	1232	21.4
2	India	945	16.4
3	USA	269	4.7
4	Indonesia	200	3.5
5	Brazil	161	2.8
6	Russia	148	2.6
7	Pakistan	140	2.4
8	Japan	125	2.2
9	Bangladesh	120	2.1
10	Nigeria	115	2.0

Figure 1.2. Bar chart of the average annual changes in the world population². This is an example where the vertical scale can be negative to show a decrease. (Courtesy: United Nations.)

1.4 HISTOGRAM

In a histogram, the height of each vertical block does not always represent the value of the variable of interest (unless the width of the block is unity), as is the case of a bar in a bar chart. Also, in a histogram, the horizontal scale is continuous and not, like the bar charts, discrete. Also, unlike a bar chart width, a histogram block width does have a meaning. Histogram blocks are usually of a constant width, indicating equal intervals on the horizontal scale, although this is not absolutely necessary, since it is the area of each histogram block which is important, in that it is this which represents the value of the variable of interest. Figure 1.4(a) is a histogram of the distribution of ages of 667 cancer of the cervix patients treated in Algeria, and the constant intervals on the horizontal scale are 5 year age ranges. The vertical scale indicates the observed frequency, which is the number of patients in a given 5 year age group. The dimensions of these particular histogram blocks are ‘patient numbers ×5 years of age’ and thus the first two blocks have values of 3 × 5 and 10 × 5 in these dimensions, totalling 65. If, alternatively, the first histogram block is to be made with a width of 10 years, from 20–29 years, then the height to signify 13 patients must be $\frac{1}{2}\times 13=6.5$ since the area of this single histogram block must equal that ...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Table of Contents
• Preface
• 1 Data Presentation
• 2 Describing Curves and Distributions
• 3 The Normal Distribution Curve
• 4 Introduction to Sampling, Errors, Accuracy and Precision
• 5 Introduction to Probability
• 6 Binomial Probabilities
• 7 Poisson Probabilities
• 8 Introduction to Statistical Significance
• 9 The Chi-squared Test
• 10 The Fisher Exact Probability Test
• 11 The t-test
• 12 Difference Between Proportions for Independent and for Non-independent (McNemar’s Test for Paired Proportions) Samples
• 13 Wilcoxon, Mann-Whitney and Sign Tests
• 14 Survival Rate Calculations
• 15 The Logrank and Mantel-Haenszel Tests
• 16 Regression and Correlation
• 17 Analysis of Variance
• 18 Multivariate Analysis: The Cox Proportional Hazards Model
• 19 Sensitivity and Specificity
• 20 Clinical Trials
• 21 Cancer Treatment Success, Cure and Quality of Life
• 22 Risk Specification with Emphasis on Ionising Radiation
• 23 Types of Epidemiological Study: Case-control, Cohort and Cross-sectional
• Glossary of Rates and Ratios: Terminology in Vital Statistics
• References
• Index