Introducing Statistics: A Graphic Guide

250 Pages·2005·26.2 MB·English

by  Eileen Magnello

Published by Icon Books Ltd., Omnibus Business Centre, 39–41 North Road, London N7 9DP
email: [email protected]
www.introducingbooks.com
ISBN: 978-184831-773-4
Text copyright © 2009 Eileen Magnello
Illustrations copyright © 2009 Icon Books Ltd The author and artist have asserted their moral rights.
Originating editor: Duncan Heath No part of this book may be reproduced in any form, or by any means,
without prior permission in writing from the publisher.
Contents
Cover
Title Page
Copyright
Drowning by Numbers
Averages or Variation?
Why Study Statistics?
What are Statistics?
What Does Statistics Mean?
Vital Statistics vs. Mathematical Statistics
The Philosophy of Statistics
Darwin and Statistical Populations
Victorian Values
Where Did it All Begin?
Parish Registers
The London Bills of Mortality
Halley’s Mortality Tables
Malthusian Populations
Demography – the Science of Populations
The Statistical Society of London
Edwin Chadwick and Sanitary Reforms
William Farr and Vital Statistics
Florence Nightingale: the Passionate Statistician
The Statistics of the Crimean War
Mortality Statistics in the Crimea
Polar Area Graphs
Probability
Variables
Games of Chance
De Moivre and Gambling in Soho
The Mathematical Theory of Probability
Relative Frequency
The Bayesian Approach
Probability Distributions
The Poisson Distribution
The Normal Distribution
Astronomical Observations
The Central Limit Theorem
The Gaussian Curve and the Principle of Least Squares
What’s Normal?
The Naming of the Normal
So What is the Normal Distribution?
Quetelismus
Galton’s Pantograph
How to Summarise the Data?
Quetelet and the Arithmetical Mean
The Mean
The Median
How to Locate or Calculate the Median
Does it Matter Which Statistical Average is Used?
Misleading With Statistics
Data Management Procedures
Standardized Frequency Distributions
Samples vs. Populations
The Histogram
Frequency Distributions
The Method of Moments
Natural Selection: the Changing Shapes of Darwinian Distributions
The Peppered Moth
The Pearsonian Family of Curves
The Interquartile Range
The Standard Deviation
Coefficient of Variation
Comparing Variation of Variables
Practical Applications
Pearson’s Scales of Measurement
Nominal and Ordinal Variables
Ratio and Interval
Early Uses of Correlation
Causation and Spurious Correlation
Path Analysis and Causation
Scatter Diagrams
Weldon and Negative Correlation
Curvilinear Relationships
Galton and Biological Regression
Regression to the Mean
Galton’s Two Regression Lines
George Udny Yule and the Method of Least Squares
Correlation vs. Regression
Galton’s Dilemma
Pearson’s Product-Moment Correlation
Simple Correlation and Multiple Correlation
Statistical Control
Discrete 2 × 2 Relationships
Biserial Correlations
Egon Pearson and Polychoric Correlations
Factor Analysis
Maurice Kendall’s Tau Coefficient
Correlation vs. Association
Curve-Fitting for Asymmetrical Distributions
Interpreting Results with Degrees of Freedom
The Chi-Square Probability Table
A Statistical Test for the Guinness Brewery
Quantifying Brewery Material
Agricultural Variation
Small Samples vs. Large Samples
Testing Statistical Differences Between Two Means
Statistical Results for Guinness
Student’s t-test
A New Statistical Era: Rothamsted’s Broadbalk Agricultural Data
Fisher’s Statistical Analysis of Variance
The Analysis of Agricultural Variation
The Analysis of Variance and Small Samples
Inferential Statistics
The Sampling Distribution
Conclusion
Bibliography
About the Author
Index
Drowning by Numbers
We are drowning in statistics. And they are not just numbers. For the media,
statistics are routinely “damning”, “horrifying”, “deadly”, “troublesome” – or,
on occasion, “encouraging”. The press constantly suggest that statistical
information about crime, disease, poverty and transport delays is not only the
source of the problem, but that it represents real entities or real people instead of
one point on a graph.
This tendency to assign meaning to a single essence or example by looking at one point on a statistical distribution creates unnecessary confusion and fear.
Averages or Variation?
Much of the shock-horror statistical information used by the media is based on
statistical averages. Despite the often misleading preoccupation with averages,
the most important statistical concept neglected by journalists and news reporters
is variation. This concept is essential to modern mathematical statistics and
plays a pivotal role in biological, medical, educational and industrial statistics.
Variation measures individual differences, while averages are concerned with summarising this information into one exemplar.
So why is variation important?
Variation can be quite easily seen in multicultural Britain, and especially
London, which now consists of more than 300 sub-cultures with as many
languages spoken (from Acholi to Zulu) and thirteen different faiths. For some,
multiculturalism is about valuing everybody and not making everyone the same
(or not reducing this ethnically diverse group of individuals to one representative
person).
There are so many individual differences across the British population that it is now practically meaningless to talk about the ‘average’ British person, as one might have done before 1950.
These multifarious individual differences embody the statistical variation that is
the crux of modern mathematical statistics.