This is an electronic version of the print textbook. Due to electronic rights restrictions, some third party content may be suppressed. Editorial review has deemed. Page 1. Introduction to Biostatistics. Larry Winner. Department of Statistics. University of Florida. July 8, Page 2. 2. Page 3. Contents. 1 Introduction. 7. Introduction to Biostatistics / Robert R. Sokal and F. James Rohlf. Dovcr cd. . is little in it that needs changing for an introductory textbook of biostatistics for an.
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PDF | This text emphasizes the relationships among probability, probability distributions and hypothesis testing. The expected value of various. PDF | Preface to Third Edition Biostatistical aspects are receiving increased To enhance focus, this book is titled Medical Biostatistics. helping authors and publishers reach new audiences. You can search through the full text of this book on the web at medical-site.info
W h y h a s there been such a m a r k e d increase in the use of statistics in biology? Apparently, because biologists h a v e f o u n d t h a t the interplay of biological causal a n d response variables d o e s n o t fit the classic m o l d of n i n e t e e n t h - c e n t u r y physical science. In so doing, they helped create the impression t h a t the experim e n t a l m e t h o d s a n d n a t u r a l philosophy t h a t h a d led to such d r a m a t i c p r o g r e s s in the physical sciences should be imitated fully in biology.
M a n y biologists, even to this day, have retained the tradition of strictly mechanistic a n d deterministic concepts of t h i n k i n g while physicists, interestingly e n o u g h , as their science has b e c o m e m o r e refined, have begun t o resort t o statistical approaches. In biology, most p h e n o m e n a are affected by m a n y causal factors, u n c o n t r o l l a b l e in their variation a n d often unidentifiable. A m i s u n d e r s t a n d i n g of these principles and relationships h a s given rise t o the a t t i t u d e of some biologists t h a t if differences induced by an experiment, or observed by nature, are not clear on plain inspection and therefore a r e in need of statistical analysis , they arc not w o r t h investigating.
There are few legitimate fields of inquiry, however, in which, f r o m the n a t u r e of the p h e n o m e n a studied, statistical investigation is unnecessary. Statistical thinking is not really different f r o m o r d i n a r y disciplined scientific thinking, in which wc try to q u a n t i f y o u r observations.
In statistics we express o u r degree of belief or disbelief as a p r o b a b i l i t y rather than as a vague, general s t a t e m e n t. In m a n y ways the h u m a n mind is a r e m a r k a b l e statistical machine, a b s o r b ing m a n y facts f r o m the outside world, digesting these, a n d regurgitating them in simple s u m m a r y form.
F r o m o u r experience we k n o w certain events to o c c u r frequently, o t h e r s rarely.
All these facts have been processed by that r e m a r k a b l e c o m p u t e r , t h e h u m a n brain, which furnishes an abstract. A l t h o u g h statistics arose t o satisfy the needs of scientific research, the develo p m e n t of its m e t h o d o l o g y in t u r n affected the sciences in which statistics is applied.
T h u s , t h r o u g h positive feedback, statistics, created t o serve the needs of n a t u r a l science, h a s itself affected the c o n t e n t a n d m e t h o d s of t h e biological sciences.
T o cite a n example: Analysis of variance has h a d a t r e m e n d o u s effect in influencing the types of experiments researchers carry out.
Then, in Section 2. In Section 2. We shall then be ready to consider in Section 2.
T h e data in biostatistics are generally based on individual observations. T h e y are observations or measurements taken on the smallest sampling unit.
These smallest s a m p l i n g units frequently, b u t not necessarily, are also individuals in the o r d i n a r y biological sense. If we m e a s u r e weight in rats, then the weight of each rat is an individual observation; t h e h u n d r e d rat weights together represent the sample of observations, defined as a collection of individual observations selected by a specified procedure.
In this instance, one individual o b s e r v a t i o n an item is based on o n e individual in a biological s e n s e — t h a t is, o n e rat. However, if we h a d studied weight in a single rat over a period of time, the s a m p l e of individual o b s e r v a t i o n s w o u l d be the weights recorded on one rat at successive times.
W e have carefully avoided so far specifying what particular variable was being studied, because the terms "individual o b s e r v a t i o n " a n d " s a m p l e of observations" as used a b o v e define only the s t r u c t u r e but not the n a t u r e of the d a t a in a study.
T h e actual property m e a s u r e d by the individual o b s e r v a t i o n s is the character, or variable. T h e m o r e c o m m o n term employed in general statistics is "variable. M o r e t h a n one variable can be measured on each smallest sampling unit.
Next we define population. T h e biological definition of this term is well k n o w n. It refers to all the individuals of a given species p e r h a p s of a given life-history stage or sex f o u n d in a circumscribed area at a given time. In statistics, p o p u l a t i o n always m e a n s the totality of individual observations about which inferences are to he made, existing anywhere in the world or at least within a definitely specified sampling area limited in space and time.
If you take five men a n d study the n u m b e r of leucocytes in their peripheral blood and you are prepared to d r a w conclusions a b o u t all men from this s a m p l e of five, then the p o p u l a t i o n f r o m which the sample has been d r a w n represents the leucocyte c o u n t s of all extant males of the species Homo sapiens.
A report on the analysis of a s a m p l e f r o m a restricted p o p u l a t i o n should not imply that the results hold in general.
T h e p o p u l a t i o n in this statistical sense is sometimes referred t o as the universe. A p o p u l a t i o n m a y represent variables of a concrete collection of objects or creatures, such as the tail lengths of all the white mice in the world, the leucocyte c o u n t s of all the Chinese m e n in the world of age 20, or the D N A c o n t e n t of all the h a m s t e r sperm cells in existence: or it m a y represent the o u t c o m e s of experiments, such as all the h e a r t b e a t frequencies p r o d u c e d in guinea pigs by injections of adrenalin.
In cases of the first kind the p o p u l a t i o n is generally finite. A l t h o u g h in practice it would be impossible to collect, count, a n d e x a m i n e all h a m s t e r sperm cells, all Chinese men of age 20, or all white mice in the world, these p o p u l a t i o n s a r e in fact finite.
Certain smaller p o p u l a t i o n s , such as all the w h o o p i n g cranes in N o r t h America or all the recorded cases of a rare but easily d i a g n o s e d disease X, m a y well lie within reach of a total census.
By c o n t r a s t , an experiment can be repeated an infinite n u m b e r of times at least in theory. A given experiment, such as the a d m i n i s t r a t i o n of adrenalin t o guinea pigs, could be repealed as long as the e x p e r i m e n t e r could o b t a i n material a n d his or her health and patience held out.
However, t h o u g h p o p u l a t i o n s are theoretically finite in most applications in biology, they are generally so much larger than samples d r a w n from them that they can be c o n sidered de facto infinite-sized populations.
We have already referred to biological variables in a general way, but we have not yet defined them. We shall define a variable as a properly with respect to which individuals d i f f e r in some ascertainable If t h e property does not differ within a s a m p l e at h a n d or at least a m o n g the samples being studied, it c a n n o t be of statistical interest.
Length, height, weight, n u m b e r of teeth, vitamin ' c o n t e n t , and genotypes are examples of variables in o r d i n a r y , genetically and phcnotypically diverse g r o u p s of organisms.
We c a n divide variables as follows: Variables Measurement variables Continuous variables Discontinuous variables Ranked variables Attributes Measurement variables are those measurements and counts that are expressed numerically. T h e first kind consists of continuous variables, which at least theoretically can assume an infinite n u m b e r of values between a n y t w o fixed points.
Any given reading of a c o n t i n u o u s variable, such as a length of 1. M a n y of the variables studied in biology arc c o n t i n u o u s variables.
Examples are lengths, areas, volumes, weights, angles, temperatures, periods of time, percentages, c o n c e n t r a t i o n s , a n d rates. C o n t r a s t e d with c o n t i n u o u s variables are the discontinuous variables, also k n o w n as meristic or discrete variables. These are variables that have only certain fixed numerical values, with no intermediate values possible in between. T h u s , in an experiment one might record the rank o r d e r of emergence o f t e n p u p a e without specifying the exact time at which each p u p a emerged.
In such cases we code the d a t a as a ranked variable. I he o r d e r of emergence. Special m e t h o d s for dealing with such variables have been developed, and several arc furnished in this book. By expressing a variable as a series of ranks, such as 1,2, 3, 4.
Variables that c a n n o t be measured but must be expressed qualitatively are called attributes, or nominal variables. These are all properties, such as black or white, p r e g n a n t or not p r e g n a n t , d e a d or alive, male or female. W h e n such attributes are c o m b i n e d with frequencies, they can be treated statistically.
W h e n a t t r i b u t e s are c o m b i n e d with frequencies into tables suitable for statistical analysis, they are referred to as enumeration data. The main focus here is on ideas, rather than on methodological details.
Basic concepts are illustrated with representations from history, followed by technical discussions on what different statistical methods really mean.
Graphics are used extensively throughout the book in order to introduce mathematical formulae in an accessible way. This book will be useful for biostatisticians with little mathematical background as well as those who want to understand the connections in biostatistics and mathematical issues. Please check your email for instructions on resetting your password. If you do not receive an email within 10 minutes, your email address may not be registered, and you may need to create a new Wiley Online Library account.
If the address matches an existing account you will receive an email with instructions to retrieve your username. Skip to Main Content. Understanding Biostatistics Author s: First published: Print ISBN: About this book Understanding Biostatistics looks at the fundamentals of biostatistics, using elementary statistics to explore the nature of statistical tests. Key features: Discusses confidence intervals and p-values in terms of confidence functions.
Explains basic statistical methodology represented in terms of graphics rather than mathematical formulae, whilst highlighting the mathematical basis of biostatistics. Looks at problems of estimating parameters in statistical models and looks at the similarities between different models. Provides an extensive discussion on the position of statistics within the medical scientific process.