Facts from Figures

481 Pages·1956·10.31 MB·English

by  M. J. Moroney

FACTS
FROM FIGURES
M. J. MORONEY
PENGUIN BOOKS
PELICAN BO,?K
A236
FACTS
M. J. MORONI!~
C. fl. Bu/mall
M. J. Moroney, a graduate of London University,
Fellow of the Association of Incorporated Statis
ticians and of the RoyaJ Statistical Society, is in
charge of a team of statisticians in the Organization
Division of Unilever Ltd.
His inten~~t in statistical methods developed in
the laboratories of Standard Telephone and Cables,
Ltd. Later, he joined the s'taff of the Leicester
College 'of Technology' and Commerce, where, as
Senior Lecturer in the Depart'tnentof Mathematics,
be was responsible for the' Service to Industry
section developed at that time. In 1950, he lost his
deposit' after a worthwhile fight' as Liberal can
didate for Leicester N.B.
He is married and has two daughters and a son.
Cover design by La~ry Carter
For a complete list of books available
please write to Ptmgllill Books
whose address call be/oulld 011 the
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Penllllin Book~ Ltd, Harmondsworth, Middlese.
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AUSTRALtA, Penguin Book. Pty Ltd, 762 Whitehorse Road,
Mitcham, Victoria
First published 195 I
Second and revised edition 1953; reprinted 1954
Third and revised edition 1956; reprinted 1957, 1958, 1960, 1962 (twice)
Made and printed in Great Britain
William Clowe. and Sons, Limited
London and Beccle.
Set in Monotype Times
TO
MY WIFE
This book is sold subject to the condition
that it ,hall not, by way of trade, be lent,
re .. sold, hired out. or otherwise disposed
of without. the publisher's consent,
in any form of bindinll or cover
other than that in which
it i. publisbed
Contents
Acknowledgements vi
Preface vii
Preface to the Second Edition viii
1. Statistics Undesirable
2. The Laws of Chance 4
. 3. The Magic Lantern Technique 19
4. On the Average 34
5. Scatter 56 '
6. Speeding up Calculations 66
7. Fault-Finding - The Binomial Distribution 82
8. Goals, Floods, and Horse-kicks - The Pois-
son Distribution 96
9. The Nonnal Distribution 108
10. What Happens when we take Samples 120
11. Control Charts 141
12. Safety in Sampling 173
13. How to be a Good Judge - Tests of Signifi-
cance 216
14. How to be Precise though Vague - Estima-
tion and Confidence Limits 238
15. Association, Contingency, ~d Goodness of
Fit - The x2 Distribution 246
16. Correlation, Cause and Effect 271
17. Time Series and Fortune Telling 321
18. Ranking Methods 334
19. The Analysis of Variation and Co-Variation 371
20. Statistics Desirable 458
Bibliography 464
AnsweB 468
Index 470
Acknowledgements
I am indebted to many people directly and indirectly. Many
of them will be found mentioned in the -bibliography. My
recommendation is my thanks. If I have inadvertently adopted
or adapted where I should have sought permission, I hope it
will be excused as oversight or ignorance. In particular, I have
to acknowledge my indebtedness to the following;
Professor Sir Ronald Fisher, Cambridge, Dr. Frank Yates,
Rothamsted, and Messrs. Oliver & Boyd, Ltd, Edinburgh, for
permission to reprint abridged tables of the Ordinate and Area
of the Normal-Curve (page 116), the graph of Student's t (Fig.
81), abridged tables of the Variance Ratio (pages 234 and 235),
.and the graph of X2 (Fig. 82), all based on their book Statistical
Tables/or Biological, Agricultural and Medical Research.
Professor E. S. Pearson and Mr. L. H. C. Tippett, for material
utilized in the chapter on Control Charts.
Professor M. G. Kendall, some of whose tables for significance
in ranking tests I have compressed into approximate formulae
which are adequate for the purposes of a book such as this yet
not suitable for those who might later wish to use the techniques
described in serious work.
Messrs H. F. Dodge and H. G. Romig, from whose extensive
and valuable Sampling Tables I have given a simplified extract
to supplement my description of the tables.
Dr J. Wishart for persuading me to stress Hotelling's T2 test
rather than the discriminant function and for suggesting better
figures for the numerical example.
Her Majesty's Stationery Office, by whose permission Figures
2, 3, 4 and 6 (a) are reproduced from Survey '49 and Fig1:lJ'C 10
from The Budget and Your Pocket.
Mrs C. N. McCaig, for her skill and diligence in translating
my rough sketches into drawings for the blockmaker.
My publishers, especially for their great care during production
and for the many things they have helped me with when, alone,
1 would haye floundered. ,
Those who have been kind enough to point out errors in the
earlier printings.
Preface
This book attempts to take the reader on a con
ducted tour of the statistician's workshop. The
reader is shown many tools and machines, given
a quick explanation of their purpose and method
of operation, and then encouraged, after watching
the craftsman for a while, to try for himself. It
does not claim to do everything. It does not claim
to be exhaustive Oil what it does attempt. But it
does aim at giving enough information to satisfy
a man on a conducted tour and to let him see
enough of the game as he goes around to really
learn something. If the reader finishes up with a
smattering of the workshop jargon, a rough idea
of the jobs tackled and of the tools required to do
them, I shall be more than satisfied. Moreover, I
believe he will, too.
There are many to whom a conducted tour of
this sort should appeal: not only students, but
those whose work calls for a general knowledge
of the capabilities of this subject in the industrial
and research world. They must be the judges of
whether the book serves a useful purpose. And
those critics whose excellent books I have not
been able to write and whose pet theories I have
not hesitated to ignore or make fun of will per
haps treat me lightly when they realize that I am
not trying to do more than I have here said.
M. J. M.
Preface to. the Second Edition
It is fair to .judge from the rapid sale and many
.. kind· letters: trom readers that this little book
·does ~rve· a useful purpose. I am particularly
indebted to those who sent in details of errata,
the elimination of which should increase the
usefulness of the book.
The contents remain almost unchanged, except
for the latter part of Chapter IJ which J have
revised to include a new approach to modified
limit control charts.
I am sorry still to remain persona non grata to
the index number men and the fortune tellers,
but there it is. I give way to none in my admiration
for the theory (may its shadow never be less I),
but when it comes to a great deal of the practice
I simply cannot help chuckling.
M. J. M.
There is more than a germ of truth in the suggestion that, in a
society where statisticians thrive, liberty and individuality are
likely to be emasculated. Historically, Statistics is no more than
State Arithmetic, a system of computation by which differences
between individuals are eliminated by the taking of an average. It
has been used - indeed, still is used - to enable rulers to know just
how far they may safely go in picking the pockets of their sub
jects. A king going to war wishes to know what reserves of man
power and money he can call on. How many men need be put in
the field to defeat the enemy? How many guns and shirts, how
much food, will they need? How much will all this cost? Have the
citizens the necessary money to pay for the king's war? Taxation
and military service were the earliest fields for the use of Statistics.
For this reason was Domesday Book compiled.
We are reminded of the ancient statisticians every Christmas
when we read that ~aesar Augustus decreed that the whole world
should be enrolled, each man returning to his own city for regis
tration. Had it not been for the statisticians Christ would have
been born in the modest comfort of a cottage in Nazareth instead
of in a stable at Bethlehem. The story is a symbol of the blindness
of the planners of all ages to the comforts of the individual. They
just didn't think of the overcrowding there would be in a little
place like Bethlehem.
But Statistics suffers from other drawbacks in the public eye.
No one who has lived through recent years can have failed to
notice the uses to which statistics are put in times of economic
desperation. John Citizen is assumed to develop a sudden and re
markable aptitude for contemplating thousands of millions of
pounds. He is supposed to brush up his knowledge of index num
bers and respond with enthusiasm to the tables and charts flung at
his head by benevolent authority. He is even expected to pay his
sixpences to see exactly what his elected representatives are doing
2 FACTS FROM FIGURES
with £3,778 million in the brief space of 52 weeks. The people who
issue these things would get a shock if they knew the proportion
of the adult population that does not even know its multiplication
table. Having looked at the charts, John Citizen feels less able
than ever to put his resentment into words. He feels a fool, blinded
by science, and he resents the clever statisticians who have made
him feel so inferior.
Statistics has other claims to unpopularity. It lends itself only
too easily to the pinchbeck taradiddle to which advertising is by
nature prone. The public is told that' nine people out of ten' in a
certain class for whom the reader will have the greatest admira
tion use a certain excellent product. No doubt this is plain truth.
But we must be forgiven for suspecting that it is obviously artful.
Were the ten people specially chosen so as to include one who was
less wise than the nine knowing virgins who had the gumption to
agree with the advertiser? There is undoubted cozenage in saying
'nine out of ten ' in the confident hope that the reader will unsus
pectingly lend at least partial credence to the idea that' nine out
of every ten' of the excellent people in question do what the
reader is urged to do.
What we have already said is amply sufficient to make clear the
origin of the popular mistrust in statistics and to show that it bas
very real justification. But the worst has not yet been said. There
still remains the sorry spectacle of opposing factions in politics
and medicine (to mention only two of the most obvious cases)
who bolster up their respective cases by statistics in tbe confident
hope that 'figures cannot lie' or, as they often hope, that 'you
can't dispute the figures'. All this is very sad indeed, for these
ardent computers are usually truly sincere in their convictions,
even where they are rash with their statistical deductions. The
cynic sums it up in the old tag: 'There are lies, damned lies, and
statistics.'
!fno more were to be said about Statistics, this book would end
here. But it is just about to begin. It is true that it is extremely dif
ficult to interpret figures when they relate to some concrete prob
lem. It is equ!'lIy true that it is extremely easy to do arithmetic.
Herein lies the real difficulty. Averages can be calculated to nine
teen places of decimals with astonishing ease. When the job is