BASIC Microcomputing and Biostatistics: How to Program and Use Your Microcomputer for Data Analysis in the Physical and Life Science Including Medicine

280 Pages·1984·11.628 MB·English

by  Donald W. Rogers (auth.)

BASIC Microcomputing
and Biostatistics
BASIC Microcomputing
and Biostatistics
How to Program and Use
Your Microcomputer for Data Analysis
in the Physical and Life Sciences,
Including Medicine
WITH A PERMANENT liBRARY OF MANY HELPFUL PROGRAMS,
CHALLENGING PROBLEMS, AND WORKED EXERCISES
by
Donald W. Rogers
Humana Press Inc • Clifton, New Jersey
To
Doris M. Rogers
With other men, perhaps, such things would not have been induce
ments; but as for me, I am tormented with an everlasting itch for things
remote. I love to sail forbidden seas, and land on barbarous coasts.
-Melville
Library of Congress Cataloging in Publication Data
Rogers, Donald, 1932-
Basic microcomputing and biostatistics.
(Contemporary instrumentation and analysis)
Includes bibliographies and index.
1. Life sciences-Data processing. I. Title.
II. Series.
QH324.2.R63 574' .028'54 81-85465
AACR2
TSBN-13: 978-1-4612-9776-5 e-TSBN-13: 978-1-4612-5300-6
DOT: 10.1007/978-1-4612-5300-6
© 1983 the HUMANA Press Inc.
Crescent Manor
P.O. Box 2148
Clifton, NJ 07015
All rights reserved
No part of this book may be reproduced, stored in a retrieval system,
or transmitted, in any form of by any means, electronic, mechanical, photo
copying, microfilming, recording, or otherwise without written
permission from the Publisher.
iv
Preface
BASIC Microcomputing and Biostatistics is designed as the first practical
"how to" guide to both computer programming in BASIC and the statis
tical data processing techniques needed to analyze experimental, clinical,
and other numerical data. It provides a small vocabulary of essential com
puter statements and shows how they are used to solve problems in the bio
logical, physical, and medical sciences. No mathematical background be
yond algebra and an inkling of the principles of calculus is assumed. All
more advanced mathematical techniques are developed from "scratch"
before they are used. The computing language is BASIC, a high-level lan
guage that is easy to learn and widely available using time-sharing com
puter systems and personal microcomputers.
The strategy of the book is to present computer programming at the
outset and to use it throughout. BASIC is developed in a way reminiscent
of graded readers used in human languages; the first programs are so sim
ple that they can be read almost without an introduction to the language.
Each program thereafter contains new vocabulary and one or more con
cepts, explained in the text, not used in the previous ones. By gradual
stages, the reader can progress from programs that do nothing more than
count from one to ten to sophisticated programs for nonlinear curve fitting,
matrix algebra, and multiple regression. There are 33 working programs
and, except for the introductory ones, each performs a useful function in
everyday data processing problems encountered by the experimentalist in
many diverse fields.
BASIC Microcomputing and Biostatistics arose as the result of a two
fold need perceived by the author almost a decade ago. Students of statis
tics were overwhelmed by masses of trivial calculations that were meant to
illustrate statistical principles, but obscured them instead. Even routine
techniques, such as constructing simple and cumulative frequency distri
butions, were made complicated by the need to sort many numbers into
arbitrarily sized' 'bins" while wondering what to do with the data that fall
on the border separating one bin from its neighbor. On the other hand, in
computer programming courses, then rare, now ubiquitous, programming
principles were taught using exercises that illustrated them more or less
well, depending on the textbook, but solved no problem anyone needed or
wanted to solve.
v
vi Preface
Statistics courses needed a means of handling routine number
crunching so that the student might see the conceptual forest for the trees
and neophyte computer programmers needed meaningful problems to
solve with their newfound programming skills. Why not combine statistics
and programming and teach two courses in one? I tried it; it worked. The
course outline became the framework for this book and it has been filled in
and modified from then until now.
Taught in its entirety, this book is intended as a text for a one
semester course in biostatistics, biomedical statistics, or related fields such
as quantitative courses in agriculture, agronomy, ecology, botany, experi
mental psychology, indeed any field in which masses of numerical data are
treated. Students have finished one semester of this combined course with
an understanding of statistics roughly equivalent to the level attained in the
traditional one-semester statistics course, and they have mastered the fun
damentals of computer programming in BASIC at about the level achieved
by students in the usual one-semester course in that subject. Not the fine
points, mind you, but enough to make the machine work for them, solving
the quantitative problems that life scientists encounter in the laboratory or
in the field.
Although complete coverage of this book is at the advanced
undergraduate-beginning graduate level, experience has shown that, by
selective deletion, it can be modified for use in quite a broad spectrum of
programming courses. By cutting out all the calculus (presenting the inte
gral as merely an area and giving several equations ex cathedra) I have
used the manuscript as a basis for a crash review of high-level
programming for juniors who are about to embark on an assembly
language course, a one-week short course for junior biologists entering an
NIH research program, the computer component of an honors course in
introductory chemistry, and a similar honors course for beginning biolo
gists. By deleting almost all of the theory and concentrating on games and
graphics, I have had considerable success using programs in this book in a
two-and-a-half week orientation course. for entering freshmen at L.I. U. in
the summer of 1982. All the programs in this book have been run on a DEC
20-60 time-sharing system. With a very few modifications, discussed in
the text, they have also been run on a home microcomputer. These short,
simple programs are ideally suited to bring the microcomputer into playas
a powerful laboratory research tool.
Table of Contents
Preface.................................... v
Chapter 1. Introduction to the Computer. . . . . . . . . 1
Computer Memory. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
Data Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
Control. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
Kinds of Computers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
Batch Processing and Time Sharing. . . . . . . . . . . . . . . . . . . . . 10
When Not to Use the Computer. . . . . . . . . . . . . . . . . . . . . . . . 11
Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
Problems. . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
Bibliography. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
Chapter 2. Understanding Experimental Error
and Averages. . . . . . . . . . . . . . . . . . . . .. 19
Significant Figures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
Sources of Errors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
Truncation Errors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
Propagation of Errors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
Euler's Theorem and Variations. . . . . . . . . . . . . . . . . . . . . . . . 27
Geometrical Interpretation of Euler's Theorem. . . . . . . . . . . . 28
Measures of Central Tendency. . . . . . . . . . . . . . . . . . . . . . . . . 30
The Means of Means. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
Problems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
Bibliography. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
vii
viii Contents
Chapter 3. Understanding Experimental Data
Dispersion. . . . . . . . . . . . . . . . . . . . . . .. 47
The Average Deviation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
The Mean Deviation Independent of the Sign. . . . . . . . . . . . . 48
Population Parameters and Sample Statistics. . . . . . . . . . . . . . 49
The Standard Deviation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
Relative Standard Deviation . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
Grouped Data and Frequency Distributions. . . . . . . . . . . . . . . 52
Cumulative Frequency Distributions. . . . . . . . . . . . . . . . . . . . . 58
Application: Dose-Response Curve . . . . . . . . . . . . . . . . . . . . . 61
Frequency Grouping and Pictorial Representation of
Continuous Data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
Quartiles and Percentiles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
Skewness and Kurtosis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
Problems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
Bibliography. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
Chapter 4. Understanding Probability . . . . . . . . . .. 71
Simultaneous and Equally Acceptable Probabilities . . . . . . . . 72
Application: Heredity ................................ 76
The Urn Problem: Dependent Probabilities. . . . . . . . . . . . . . . 77
Conditional Probabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
Bayes' Theorem. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
Application of Bayes' Theorem: Diagnosis. . . . . . . . . . . . . . . 82
Permutations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
Combinations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
The Binomial Coefficient. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
Problems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
Bibliography. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
Chapter 5. Determining Probability Distributions.. 91
Tree Diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
Application: Heredity ................................ 97
Modal and Mean Scores ............................ " 103
The Binomial Distribution ........................... " 107
Effect of p on the Binomial Distribution ............... " 111
Mean Occurrences for Data Groups of N ............... " 112
Application: Evaluation of a New Treatment. ........... " 114
Contents ix
Glossary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 114
Problems ........................................... 115
Bibliography. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 116
Chapter 6. Using the Poisson Distribution ....... 117
Application: Disintegration of Radioactive Nuclei ......... 120
Mean, Variance, and Standard Deviation for the Poisson
Distribution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 121
Computer Graphics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 123
Glossary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 129
Problems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 129
Bibliography. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 130
Chapter 7. Using the Normal Distribution ........ 131
Relative Areas by Computer Graphics ................. " 134
Normalization of the Gaussian Distribution ............. " 136
The Mean, Variance, and Standard Deviation of the Gaussian
Distribution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 138
The Standard Normal Deviate, 139
Z . . . . • . • . . • . • . • . . . . • . • ..
Computer Integration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 142
Tabulated Areas Under the Normal Curve. . . . . . . . . . . . . . .. 147
The Most Common Areas and Limits on 148
Z . • . . . . . . • • . • • ..
One- and Two-Tailed Tests. . . . . . . . . . . . . . . . . . . . . . . . . . .. 150
Glossary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 152
Problems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 152
Bibliography. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 153
Chapter 8. Determining Probabilities: How to Apply
the Chi Square Test and the Student's
t-Test . ........................... 155
Chi Square Detection of a Biased Coin. . . . . . . . . . . . . . . . .. 158
Degrees of Freedom. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 160
The Central Limit Theorem ............ . . . . . . . . . . . . . .. 160
Situations in Which the Population Mean Is Known But Not Its
Standard Deviation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 165
Determination of Confidence Limits When No Population
Parameters Are Known . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 168
Confidence Limits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 169
The Difference Between Means . . . . . . . . . . . . . . . . . . . . . . .. 170
x Contents
Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 172
Problems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 173
Bibliography. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 174
Chapter 9. Finding Linear Functions: The Principle
of Least Squares. . . . . . . . . . . . . . . . . .. 175
Linear Functions ............ . . . . . . . . . . . . . . . . . . . . . . .. 179
Least Squares Treatment of Linear Functions Passing Through
the Origin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 181
The Correlation Coefficient. . . . . . . . . . . . . . . . . . . . . . . . . . .. 185
Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 186
Least Squares with Two Minimization Parameters . . . . . . . .. 188
Simultaneous Equations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 194
Solution of Simultaneous Equations by Cramer's Rule. . . . .. 195
The Determinant of the Coefficients. . . . . . . . . . . . . . . . . . . .. 196
Cramer's Rule. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 199
Solution of the Normal Equations for Linear Curve Fitting by
Cramer's Rule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 200
Glossary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 201
Problems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 202
Bibliography. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 204
Chapter 10. Fitting Nonlinear Curves ........... 205
Boyle's Law. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 205
Exponential Decay. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 209
Second-Order Reaction Kinetics. . . . . . . . . . . . . . . . . . . . . . .. 214
Enzyme-Catalyzed Reactions. . . . . . . . . . . . . . . . . . . . . . . . .. 219
Unlimited Population Growth. . . . . . . . . . . . . . . . . . . . . . . . .. 224
Limited Population Growth. . . . . . . . . . . . . . . . . . . . . . . . . . .. 227
Nearly Linear Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 230
Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 235
Problems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 236
Bibliography. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 237
Chapter 11. Solving Simultaneous Equations ..... 239
Simultaneous Equations in Matrix Form ............... " 239
Matrix Algebra. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 241
Simultaneous Equations by Matrix Inversion. . . . . . . . . . . . .. 248
Simultaneous Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 250
Contents xi
Multiple Regression. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 253
Least Squares Treatment of Multiple Regression .......... 255
Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 261
Problems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 263
Bibliography. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 263
Answers to Problems . ........................ 265
Index . ..................................... 269