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Scion Publishing Ltd.
Medical Statistics Made Easy, third edition / Edition 3

Medical Statistics Made Easy, third edition / Edition 3

by Michael Harris, Jacquelyn Taylor
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Product Details

ISBN-13: 9781907904035
Publisher: Scion Publishing Ltd.
Publication date: 06/18/2014
Edition description: 3rd Edition
Pages: 128
Sales rank: 475,593
Product dimensions: 6.30(w) x 9.10(h) x 0.40(d)
Age Range: 3 Months to 18 Years

Read an Excerpt

Medical Statistics Made Easy

By Michael Harris, Gordon Taylor

Scion Publishing Limited

Copyright © 2014 Scion Publishing Ltd
All rights reserved.
ISBN: 978-1-907904-45-5



You can use this book in a number of ways.

If you want a statistics course

• Work through from start to finish for a complete course in commonly used medical statistics.

If you are in a hurry

• Choose the sections with the most stars to learn about the commonest statistical methods and terms.

• You may wish to start with these 5-star sections: percentages (Chapter 3), mean (Chapter 4), standard deviation (Chapter 7), confidence intervals (Chapter 8) and P values (Chapter 9).

If you are daunted by statistics

• If you are bewildered every time someone tries to explain a statistical method, then pick out the sections with the most thumbs up symbols to find the easiest and most basic concepts.

• You may want to start with percentages (Chapter 3), mean (Chapter 4), median (Chapter 5) and mode (Chapter 6), then move on to risk ratio (Chapter 13), incidence and prevalence (in Chapter 22).

If you are taking an exam


• The "Exam Tips" give you pointers to the topics which examiners like to ask about.

• You will find these in the following sections: mean (Chapter 4), standard deviation (Chapter 7), confidence intervals (Chapter 8), P values (Chapter 9), risk reduction and NNT (Chapter 15), sensitivity, specificity and predictive value (Chapter 20), incidence and prevalence (in Chapter 22).

Test your understanding

• See how statistical methods are used in five extracts from real-life papers in the "Statistics at work" section (Chapters 23—28).

• Work out which statistical methods have been used, why, and what the results mean. Then check your understanding in our commentaries.


• Use the Glossary as a quick reference for statistical words or phrases that you do not know.

Study advice

• Go through difficult sections when you are fresh and try not to cover too much at once.

• You may need to read some sections a couple of times before the meaning sinks in. You will find that the examples help you to understand the principles.

• We have tried to cut down the jargon as much as possible. If there is a word that you do not understand, check it out in the Glossary.



Every section uses the same series of headings to help you understand the concepts.

"How important is it?"

We noted how often statistical terms were used in 200 quantitative papers in mainstream medical journals. All the papers selected for this survey were published during the last year in the British Medical Journal, The Lancet, BJU International, the New England Journal of Medicine and the Journal of the American Medical Association.

We grouped the terms into concepts and graded them by how often they were used. This helped us to develop a star system for importance. We also took into account usefulness to readers. For example, "numbers needed to treat" are not often quoted but are fairly easy to calculate and useful in making treatment decisions.

***** Concepts which are used in the majority of medical papers.

**** Important concepts which are used in at least a third of papers.

*** Less frequently used, but still of value in decision-making.

** Found in at least 1 in 10 papers.

* Rarely used in medical journals.

How easy is it to understand?

We have found that the ability of health care professionals to understand statistical concepts varies more widely than their ability to understand anything else related to medicine. This ranges from those that have no difficulty learning how to understand regression to those that struggle with percentages.

One of the authors (not the statistician!) fell into the latter category. He graded each section by how easy it is to understand the concept.

***** Even the most statistic-phobic will have little difficulty in understanding these sections.

**** With a little concentration, most readers should be able to follow these concepts.

*** Some readers will have difficulty following these. You may need to go over these sections a few times to be able to take them in.

** Quite difficult to understand. Only tackle these sections when you are fresh.

* Statistical concepts that are very difficult to grasp.

When is it used?

One thing you need to do if critically appraising a paper is check that the right statistical technique has been used. This part explains which statistical method should be used for what scenario.

What does it mean?

This explains the bottom line – what the results mean and what to look out for to help you interpret them.


Sometimes the best way to understand a statistical technique is to work through an example. Simple, fictitious examples are given to illustrate the principles and how to interpret them.

Watch out for ...

This includes more detailed explanation, tips and common pitfalls.

Exam tips

Some topics are particularly popular with examiners because they test understanding and involve simple calculations. We have given tips on how to approach these concepts.



How important are they?

***** An understanding of percentages is probably the first and most important concept to understand in statistics!

How easy are they to understand?

***** Percentages are easy to understand.

When are they used?

Percentages are mainly used in the tabulation of data in order to give the reader a scale on which to assess or compare the data.

What do they mean?

"Per cent" means per hundred, so a percentage describes a proportion of 100. For example 50% is 50 out of 100, or as a fraction ½. Other common percentages are 25% (25 out of 100 or ¼) and 75% (75 out of 100 or ¾).

To calculate a percentage, divide the number of items or patients in the category by the total number in the group and multiply by 100.

Watch out for ...

Some papers refer to "proportions" rather than percentages. A proportion is the number of items or patients in the category divided by the total number in the group, but unlike a percentage it is not then multiplied by 100.

Authors can use percentages to hide the true size of the data. To say that 50% of a sample has a certain condition when there are only four people in the sample is clearly not providing the same level of information as 50% of a sample based on 400 people. So, percentages should be used as an additional help for the reader rather than replacing the actual data.



Otherwise known as an "arithmetic mean" or "average".

How important is it?

***** A mean appeared in 70% of papers surveyed, so it is important to have an understanding of how it is calculated.

How easy is it to understand?

***** One of the simplest statistical concepts to grasp. However, in most groups that we have taught there has been at least one person who admits not knowing how to calculate the mean, so we do not apologize for including it here.

When is it used?

It is used when the spread of the data is fairly similar on each side of the mid point, for example when the data are "normally distributed".

The "normal distribution" (sometimes called the "Gaussian distribution") is referred to a lot in statistics. It's the symmetrical, bell-shaped distribution of data shown in Fig. 1.

What does it mean?

The mean is the sum of all the values, divided by the number of values.

Watch out for ...

If a value (or a number of values) is a lot smaller or larger than the others, "skewing" the data, the mean will then not give a good picture of the typical value.

For example, if there is a sixth patient aged 92 in the study then the mean age would be 62, even though only one woman is over 60 years old. In this case, the "median" may be a more suitable mid-point to use (see Chapter 5).

A common multiple choice question is to ask the difference between mean, median (see Chapter 5) and mode (see Chapter 6) – make sure that you do not get confused between them.



Sometimes known as the "midpoint".

How important is it?

**** It is given in almost half of mainstream papers.

How easy is it to understand?

Even easier than the mean!

When is it used?

It is used to represent the average when the data are not symmetrical, for instance the "skewed" distribution in Fig. 2. Compare the shape of the graph with the normal distribution shown in Fig. 1.

What does it mean?

It is the point which has half the values above, and half below.

Watch out for ...

The median may be given with its inter-quartile range (IQR). The 1st quartile point has the 1/4 of the data below it, the 3rd quartile point has the 3/4 of the sample below it, so the IQR contains the middle 1/2 of the sample. This can be shown in a "box and whisker" plot.



How important is it?

* Rarely quoted in papers and of limited value.

How easy is it to understand?

***** An easy concept.

When is it used?

It is used when we need a label for the most frequently occurring event.

What does it mean?

The mode is the most common of a set of events.

You may see reference to a "bi-modal distribution". Generally when this is mentioned in papers it is as a concept rather than from calculating the actual values, e.g. "The data appear to follow a bi-modal distribution". See Fig. 5 for an example of where there are two "peaks" to the data, i.e. a bi-modal distribution.

The arrows point to the modes at ages 10–19 and 60–69.

Bi-modal data may suggest that two populations are present that are mixed together, so an average is not a suitable measure for the distribution.



How important is it?

***** Quoted in two-thirds of papers, it is used as the basis of a number of statistical calculations.

How easy is it to understand?

*** It is not an intuitive concept.

When is it used?

Standard deviation (SD) is used for data which are "normally distributed" (see Chapter 4), to provide information on how much the data vary around their mean.

What does it mean?

SD indicates how much a set of values is spread around the average.

A range of one SD above and below the mean (abbreviated to ± 1 SD) includes 68.2% of the values.

± 2 SD includes 95.4% of the data.

± 3 SD includes 99.7%.

Watch out for ...

SD should only be used when the data have a normal distribution. However, means and SDs are often wrongly used for data which are not normally distributed.

A simple check for a normal distribution is to see if 2 SDs away from the mean are still within the possible range for the variable. For example, if we have some length of hospital stay data with a mean stay of 10 days and a SD of 8 days then:

mean - (2 × SD) = 10 - (2 × 8) = 10 - 16 = -6 days.

This is clearly an impossible value for length of stay, so the data cannot be normally distributed. The mean and SDs are therefore not appropriate measures to use.

Good news – it is not necessary to know how to calculate the SD.

It is worth learning the figures above off by heart, so a reminder –

± 1 SD includes 68.2% of the data

± 2 SD includes 95.4%,

± 3 SD includes 99.7%.

Keeping the "normal distribution" curve in Fig. 6 in mind may help.

Examiners may ask what percentages of subjects are included in 1, 2 or 3 SDs from the mean. Again, try to memorize those percentages.



How important are they?

***** Important – given in four out of every five papers.

How easy are they to understand?

** A difficult concept, but one where a small amount of understanding will get you by without having to worry about the details.

When is it used?

Confidence intervals (CI) are typically used when, instead of simply wanting the mean value of a sample, we want a range that is likely to contain the true population value.

This "true value" is another tough concept – it is the mean value that we would get if we had data for the whole population.

What does it mean?

Statisticians can calculate a range (interval) in which we can be fairly sure (confident) that the "true value" lies.

For example, we may be interested in blood pressure (BP) reduction with antihypertensive treatment. From a sample of treated patients we can work out the mean change in BP.

However, this will only be the mean for our particular sample. If we took another group of patients we would not expect to get exactly the same value, because chance can also affect the change in BP.

The CI gives the range in which the true value (i.e. the mean change in BP if we treated an infinite number of patients) is likely to be.

Watch out for ...

The size of a CI is related to the size of the sample and the variability of the individual results. Larger studies usually have a narrower CI.

Where a few interventions, outcomes or studies are given it is difficult to visualize a long list of means and CIs. Some papers will show a chart to make it easier.

For example, "meta-analysis" is a technique for bringing together results from a number of similar studies to give one overall estimate of effect. Many meta-analyses compare the treatment effects from those studies by showing the mean changes and 95% CIs in a chart. An example is given in Fig. 8.

The long vertical line represents the point showing "no change" or "no effect".

The statistician has combined the results of all five studies and calculated that the overall mean reduction in BP is 14 mmHg, CI 12–16. This is shown by the "combined estimate" diamond and the dotted line. See how combining a number of studies reduces the CI, giving a more accurate estimate of the true treatment effect.

The chart shown in Fig. 8 is called a "Forest plot" or, more colloquially, a "blobbogram".

Standard deviation and confidence intervals – what is the difference? Standard deviation tells us about the variability (spread) in a sample.

The CI tells us the range in which the true value (the mean if the sample were infinitely large) is likely to be.

An exam question may give a chart similar to that in Fig. 8 and ask you to summarize the findings. Consider:

• Which study showed the greatest change?

• Did all the studies show change in favour of the intervention?

• Does the combined estimate exclude no difference between the treatments?

In the example above, study D showed the greatest change, with a mean BP drop of 25 mmHg.

Study C resulted in a mean increase in BP, though with a wider CI. This CI could be due to a low number of patients in the study. Note that the CI crosses the line of "no effect".

The combined estimate of the mean BP reduction is 14 mmHg, 95% CI 12–16. This tells us that the "true value" for the reduction in BP is likely to be between 12 and 16 mmHg, and this excludes "no difference" between the treatments.



How important is it?

***** A really important concept, P values are given in more than two-thirds of papers.

How easy is it to understand?

*** Not easy, but worth persevering as it is used so frequently.

It is not essential to know how the P value is derived – just to be able to interpret the result.

When is it used?

The P (probability) value is used when we wish to see how likely it is that a hypothesis is true. The hypothesis is usually that there is no difference between two treatments, known as the "null hypothesis".

What does it mean?

The P value gives the probability of any observed difference having happened by chance.

P = 0.5 means that the probability of a difference this large or larger having happened by chance is 0.5 in 1, or 50:50.

P = 0.05 means that the probability of a difference this large or larger having happened by chance is 0.05 in 1, i.e. 1 in 20.

It is the figure frequently quoted as being "statistically significant", i.e. unlikely to have happened by chance and therefore important. However, this is an arbitrary figure.

If we look at 20 studies, even if none of the treatments really work, one of the studies is likely to have a P value of 0.05 and so appear significant!


Excerpted from Medical Statistics Made Easy by Michael Harris, Gordon Taylor. Copyright © 2014 Scion Publishing Ltd. Excerpted by permission of Scion Publishing Limited.
All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher.
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Table of Contents

Statistics which describe data: Percentages; Mean; Median; Mode; Standard deviation
Statistics which test confidence: Confidence intervals; P values
Statistics which test differences: t tests and other parametric tests; Mann–Whitney and other non-parametric tests; Chi-squared
Statistics which compare risk: Risk ratio; Odds ratio; Risk reduction and numbers needed to treat
Statistics which analyze relationships: Correlation; Regression
Statistics which analyze survival: Survival analysis: life tables and Kaplan–Meier plots; The Cox regression model
Statistics which analyze clinical investigations and screening: Sensitivity, specificity and predictive value; Level of agreement
Other concepts
Statistics at work: Medians, interquartile ranges and odds ratios; Risk ratios and number needed to treat; Correlation and regression; Survival analysis; Sensitivity, specificity and predictive values

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