THIRD INTERNATIONAL BIOMETRIC CONFERENCE, 1-5 SEP 53, AT BELLAGIO, ITALY.

• Document Type: CREST
• Collection: General CIA Records
• Document Number (FOIA) /ESDN (CREST): CIA-RDP80-00809A000500400179-7
• Release Decision: RIPPUB
• Original Classification: C
• Document Page Count: 89
• Document Creation Date: December 15, 2016
• Document Release Date: April 22, 1999
• Sequence Number: 179
• Publication Date: March 15, 1954
• Content Type: REPORT

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CENTRAL INTELLIGENCE AGENCY
INFORMATION REPORT
Third International Biometric Conference, 1-5 Sep 53,
at Bellagio, Italy.
DATE DISTR.
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NO. OF PAGES I 2
NO. OF ENCLS.
'TMI% OOCUYfMT COM AIM[ IM"ATION A/1[CTIMO TN[ MA TIOM AI D[I[M[[
01 Vol UMIT[0 [TAT[[. 71 TMIM TM[ N[ANIMD10/ TITi.[ IA. [[CTIOM[ T[[
THIS Is UNEVALUATED INFORMATION
25X1
25X1 1.
The Biometric Conference was
informal
25X1
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SUPP. TO
REPORT NO.
relatively small and
11 1
2- T1bD 1L t of >mowbors _J booklet containing this list a~ abstracts of papers pre-
sented is available Rat the end of this re ort
contains 95 names on the main ?. "
25X1
CONFIDENTIAL
DtSTRISUTIOM STATE ARMY' U N/,vY r'T AIR ',~fQ'!Q,0 pOt
This report la for the use within the USA of the Intelligence components of the partments or
Agencies indgca;..rd s` . it Is not to be tranilmitted ovorseae without the cdneurronce o e
origi'rrwrtirEg opppsgfrFt$f 11~~904~1?. 14F~P~t>1~t1~91~1?00010>4~1b31 IA!
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III INTERNATIONAL BIOMETRIC CONFERENCE
Bellagio, 1-5 Sept 1953
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I.,1S7 OF NIEM13EIIS
Mr, M.W. BVNTZON
Dr. C. BIAGINI
Mr. R. E. BLACKITII
Statistic:^1 i.:l;,r.itorv
St.. Andrews Ili i1
CAMBRIDGE (England)
Viale S, I, avagnini, 28
FIRENZE (Italia)
Istituto di Genetica
Via Celnria, 10
MILANO (Italia)
15 Edwards Place
PRINCETON N.J. (U.S.A.)
Dept, of Mathematics
The University
MANCHESTER 13 (England)
Berberisvaenget 3:3
LINGBY (Danmark)
Via B, Latina, 122
FIRENZE (Italia)
Imperial College of Science
and Technology
Field Station, Ashurst Lodge
SUNNINGIIILL, Berkshire (Engleaci)
P.O. Box 1106 - The Biometric Society
NEW HAVEN 4, Conn. (U.S.A.)
Inst, of Mathematical Statistics
Norrtullsgatan 16
STOCKHOLM Va. (Sweden)
Piazza Repubhlica, 23
MILANO (Italia)
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Dr. M KEULS
Mr, E.III van der LAAN
London School of Hygiene
and Tropical Medicine
Keppel St.
LONDON W-C,1 (England)
Zederstrasse 4
ZUERICII 7/32 (Suisse)
Committee on Mathematical
Biology - (University of Chicago)
5741 Drexel Ave
CHICAGO 37, 111, (U S A
Institut voor de Veredeling
van Tuinboowgowassen
Ileerenstraat 25
WAG6:NINGEN (The Netherlands)
Ministry of Agriculture
Room 3L5
THE 11AGUE (The Netherlands)
M. me
51. J.
LAURENT-DUHAMEL
8 Square Vauban
VIROF'LAY Seine et Oise (Prance)
Mr.
F.111.
LEECH
Statistics Department
Rothamsted Experimental Station
HARPENDEN, Ilerts (England)
Mr.
J.M.
LEGAY
Station de Recherches Sdricicoles
ALES (GARD) _ (France)
Dr.
A .I LENGER
37 Rue Colonel Chaltin. Uccle
BRUXELLES (Belgique)
Prof. !I.M. LERNER
Istituto di Genetica
Piazza Botta
PAVIA (Italia)
24, Avenue de Champel
GENEVE (Suisse)
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Dr. ('', LUKACS 3727 Van Ness Street. N W
WASHINGTON 16, D C. (U S A
Prof. J L. LUSH Animal Husbandry Dept. I S C
AMES Iowa (U S A )
Dr. G', MAGNI Istituto di Genetica
Piazza Hotta
PAVIA (Italia)
Dr., L. MARTIN 104 Avenue Albert
BRUXELLES (Belgique)
Prof MATHER
Genetics Department
The University Edgbastou
BIRMINGHA51,15 (England)
Istituto di Genetica
Via Vezzocannone 8
NAPOLI (Italia)
Directeur Ecole d'Application
Institut do Statistique
I Rue do la Banque
PARIS (Prance)
Nederlands Instituiit voor
Praeventieve Genceskunde
Wassenaarse Weg. 56
LEIDEN (The Netherlands)
National Vegetable Research
Station
WELLESBOURNE: Warwick (England)
The Agricultural College of Norway
VOLLEBEKK (Norway)
Prof, P, OTTESTAD The Agricultural College of Norway
VOLLEBEKK (Norway)
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Dept, of Genetics
44 Storeys Way
CAMBRIDGE (England)
Dr. A.F. PARKER-RHODES 20 Desley-Taylor Rd.
CAMBRIDGE (England)
Dr. P. PELEGRIN
Mr. S. PETO
Dr. A. PREVITERA
East Mulling Research Station
EAST MALLING, MAIDSTONE, Kent
(England)
Institut des Pruits et Agrumes
Colon Iaux
G rue du General Clergerie
PARIS XVI (Prance)
Ministry of Supply,
Microb. Res. Dept,
PORTON nr. SALISBURY. Wilts.
(England'',
Lab. Provinciale Igione e
Profilassi
Via Matteotti
MASSA-APUANIA (Italia)
Prof. R, PRIGGE Paul-Ehrlich, Strasse 44
FRANKFURT a/M (Germany)
Statistical Laboratory
Presidency College
CALCUTTA (India)
Prof. G. RASCHI Skovmindeves 14
IIOLTE (Danmark)
Distiller's Co, Ltd.
Great Burgh
EPSOM, Surrey (England)
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Tobacco Research Board,
P 0. Box 1909
SALISBURY(Southern Rhodesia)
(Africa)
M.R. SAMPFORD
Dr. It. SCOSSIROLI
Dr. F. SELLA
Dr. L.G. SILVESTRI
Dr. G.A.R. SMITH
C. Dk. Bobillo; 17
MADRID (Espana)
Avenue Elisabeth 5
MERELBEKE (Belgique)
177, Godston Road; Wolvercote
OXFORD (England)
Seita, 2 Avenue d? Orsay
PARIS VII (Prance)
Istituto di Genetica
Piazza Botta
PAVIA (Italia)
Istituto Sieroterapico Milanese
Via Darwin, 20
MILANO (Italia)
Istituto Superiore di Sanit&
Viale Regina Margherita 299
ROMA 735 (Italia)
The Calton Laboratory
University College, Gower St.
LONDON W.C.1 (England)
c/o PAo
Viale delle terme di Caracalla
ROMA (Italia)
Institut National d'Etudes
Ddmographiques
23 Avenue V. Roosevelt
PARIS VIII (Prance)
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Dr. J.M, TANNER Sherrington School of
Physiology
St. Thomas? s Hospital
LONDON SE I (England)
Istituto
PALLANZA
Itaiiano Idrohiologia
(Italia)
r, Viriato. 5
LISRONNEI(Portugal)
Prof. L.A, VESSEREAU 41 Rue Boulard
PARIS 14?! (Prance)
Mr. D R. W'CSTGARTII
Prof. J. WISIIART
Prof. 11. WOLD
Dr. R. YArES
The Rubber Research ins
P.O. Box 1150
KUALA LAMPUR Malaya)
Statistical Laboratory
St. Andrei57 s Hill
CAMBRIDGE (England)
Statistics !Institute
Skolgatan 1
UPPSALA ;Sweden)
Rothamsted Experimental Station
HARPENDEN, Ilerts (England)
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ABSTRACTS OF PAPERS
Aiiscombe (lI nti.stica] Laboratory - University of
Cambridge )
FIXED- S MPLE-SIZE ANALYSIS OF SEQUENTIAL OBSERVATIONS
Most methods
are hap'ed on th
vance before th
size is!, often or
not connected wi
m
observ rtions thi1Pnselves. Very often there is little
using 1'axerl-samt X I-size methods of analysis in such
supposing that ttie, eventual sample size was chosen Ir
typicalexamples Ial'e given.
or, no error in
cases i e, in
advance Some
It is possiblI,? however to devise sequential sampiIina rules which
completely invulildLte certain fixed sample size methods of analysis,
Por oxalIlfhple ttec1re is a sequential sampling rule by which one may
prove Cat any pr1enssigood level of significance] tihat a coin is
biased: and also ai rule by which one may prove that ttie Poi n is not
biased: both r?ul~s apply equally well whether or not the
coin is in
fact biased
~in common use for the statistical analysis of data
a
I
e{assumption that the sample size was chosen in ad o observations were taken. In practice, the sample
t
fixed in advance but depends on fortuitous events
tmh~the observations or it may someti
es depend on the
The fixed sumJe-slzo methods of analysis which may possibly be
incorrect when aip1Ied to observations obtained wits
nsequential
sam
lina
l
p
ru
e all
tement about the
some function of
probability distr
have the common feature, that they inviolve some sta-
probability distribution of the ohseryatiens (or of
the observations) but do not introduce any prior
birtion. for example a
i
e
s
gnificance t
st based on a
critical region. )r a confidence interval, or an unbiased mate. point-esti^
On th`e other 0n. any method of analysis which uses the oLserva
Lions on,t.y in their1likelihood function (such as a minimum risk deci-
sion pracedure or a statement of posterior prnbahi.liti?s based on a
prior probability distribution) is independent of the ampling rule
*cllowed~,and it is always legitimate to treat the ohse vations as if
the sample size had been chosen in advance.
I
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G Barbensi (Firenze)
L'INSEGNAMENTO DELLA BIOMETRIA
I)efinita in biometr'ia in base al concetti oggi generalmente accet-
tati considerato it coriltributo the al suo sviluppo viene port:ato dai
bic,togi. dei matematici le dagli atat.istjcl .9i considerano In varie
tasr the quellolsvilupplI ha avuto in Italia per concludere con tin
quadro (lei !a situazione!attuale soprat:tntto per quanta riguarda
1 insegnamento di quellal matorict net nn.,tri Istituti universitari
Considerate I'inadeguatezzu di. noes to insegnamento se no anali.z-
zano In cause le qua.lil menLre in parte sono da ricercarsi neli:c
deticienza di plovvedimenIti di l.cgge per I. isLl.tuzione (it ,nsegnamen
ti adeguati alle necessitn in part:e ciipendono Belle difficoit;c Cho
gli studenti. lncontrano iel seguirIi diff;coita chr_ son r, - ssenzIaI
manta des attribuirsi al la rnancanza dei necesse:cri fondamenti mat.emati
ci
Vi.ene posto in evidenza I into rosse dimostraIo alai bionntt.ri .ita
1in ni sla nellit pr ima R1ittiione Italians del la 13iometrIc Socie1,y a Mi
lano net 1951 s'i.a uellalltiunrnne a Firenze di quest.'anno nella qua-
1e :it procedett.e al la cos ti t.uzlone. de llit Reg ione ILit] in na dolls Rio
noire Society per Iinsegnamer,Lo delta biomel,ria interesve the si
enncr eta noun firmulaaione di due inviti al Ministrn del la Pubblica
ISt.ruzione perche attuas5ia i richiesLi Insegnamenti.
V,.ene espostcll un programtna di studi per studenti del to h'aco1ta
biologlche (Scienze NaturI?ali Scienze biologiche Scienze agrarie
Medicina Aledi.clin. veterinaria, Farmacia, tencendo conto dal diverso
grail,, di cultures matematica propedeutica e at considers 1 opportunitd
elm i torsi sano fondamelntali (obbligutorio) o complementari (facol-
tativi) a seconds del cas'i.
Viene quindi esarninata I 1opportunitd di rendere obbligatorlo it
Corso di biometria per alcune categorle di laureati perfezionandi oil
assistenti. Si esamina illlproblema Bella creuzione di docenti in nu-
mern udegusto per conclude re che. messi suila via della realizzuzio-
ne unche la nostra Istrulzione Superiore potra annoverare la biome..
trill come mnteriu di inseglnamento nelle Facolti hiologiche, con quel-
la estensione e gviltippo Inerenti ally importanza da essa acquistata
nello studio deiproblemiliiologic1.
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111Y. Bentzon (Statens SeruminstItut Copenhagen)
ON THE STATISTICAL EVALUATION OF DOSE RESPONSE CURVES
IN CASE THE DOSE INTERVALS ARE LARGE
Two different situations are considered
1 ? Dose response curves with quantal response and 2 Dose response
curves with quantitative response. The mean value and the variance of
various estimates of the median effective dose are cpnsidered as
functions of the true median effective dose the slope o the respon-?
Sc curve and the logarithmic close interval. (The latter Iare taken to
be equal over the whole dose range)., When the dose intervals are
small the ordinary estimates of the median effective dose esuaily is
unbiased and the variance depends upon the slope x interval product
only. This rule however breaks clown as the intervals are increased
the estimates and the variances becoming dependent upon the location
of thr true :.._.linn effective dose within a dose interval. This effect
is investigated in some cases of practical interest,
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Experience gained in teaching biometry at Yale University to
graduate students majoring in Jifferent branches of biology is re-
viewed. Originally two courses were offered in alternate years or
terms, differing partly in statistical content and approach but pri-
marily in illustrative examples; one for pharmacologists and bacte-
riologist and the other for botanists and zoologists. Later these
were combined into a single class with the addition of a large pro-
portion of forestry majors. The class has averaged about nine stu?.
dents, consisted of two or three one-hour lectures a week for one or
two semesters and required from 12 to 15 laboratory hours per week in
the solution of numerical examples. The course is introductory; in-
volves a minimum of mathematics, and considers the logic of experi??
mental design and statistical analysis with the objective of enabling
potential biological investigators to design and evaluate their own
research more effectively and intelligently. A detailed outline has
been developed through the years and serves as the main text material
How well the course has accomplished its aims and how it might be
improved are considered in the light of a poll of all students who
have taken the course.
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N. t?lomgvist (Institute of mathematical Statistics Stockholm)
RANK ANALYSIS OF INCOMPLETE BLOCK DESIGNS
Suppose that t treatments shall be compared in an experiment where
the number of experimental units It that are available in a block is
less than t. This situation naturally leads into an incomplete block
design. Led b be the number of blocks used.
in order to test the observed differences between the treatment
effects we rank the observations in each block from 1 to it according
to their order of magnitude and compute the rank sum Si for each
treatment Since each treatment occurs equally often (r times where
r.t h.I() the expected value of S1 under the null hypothesis (no
treatment effects) is 1?. Icl ? A natural test statistic is then
t kr1 2
is r. -
.i-1 d )y
the distribution of which can he computed. It can be proved that the
limiting distribution of
]
12(t-1)
t
1+1
_
(S
r
---
-?
4
9
Ic' -]c
)
.
1=1
2
is a x2 - distribution with t-1 d.f.
as b
m
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W.G. Cochran (.Johns Hopkins University ?? Baltimore, Aid,)
THE COMBINATION OF ESTIMATES FROM DIFFERENT EXPERIMENTS
In a series of experiments, each designed to estimate the same
quantity p., the ith experiment provides an estimate xi of 14 and an
estimate si of the variance of xi, based on ni degrees of freedom.
The experiments may be, for instance, determinations of a physical
constant by different scientists. or bioassays conducted in different
laboratories, or agricultural field experiments carried out in dif-
ferent parts of a region.
This paper discusses the problem of making a combined estimate of
I.L. The best combined estimate depends on the nature of the data. The
first step in the analysis is to determine whether the xi agree with
each other within the limits of their experimental errors si, In
practice, owing to differences in experimental techniques, presence
of biases., or a real variation in 1j. from one experiment to another,
the x1 frequently do not agree. Various implications of this situa-
tion are discussed: the recommended estimates of IL are either the
unweighted mean x or a semiwefghted mean
i
where s2 is an estimate of the variation in I,, from experiment to
experiment.
If there is no real variation In the xi from one experiment to
another, the recommended estimates are the unweighted mean, or the
xw
or a partially-weighted mean. Specific recommendations are given
about the use of each type of mean with illustrations for actual da.
t a.
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FUNCTIONAL RELATIONSHIPS IN EXPERIMENTATION
(Their Role in the Design and Analysis of Experiments!
Agricultural and biological experiments may be divided into throe
categories in respect of the extent to which functional relationships
are important'
1) Experiments in which such relationships are irrelevant or even
non- existent.
2) Experiments for Which an underlying structure of functional re
lationshipa between the effects of different treatments is ap
parent but only certain characteristics are directly of inte
rest and other details of the relationship matter little,
3) Experiments whutio primary object is the study of a functional
relationship.
This classificati.n is an operational convenience rather than it
clear-cut
:;epurut i..n.
Examples of experiments falling into these categories will be pre-
sented. Category ii rlearly contains little of interest for the pre-
sent purpose and ai occurs relatively infrequently Evidence will he
presented that for category 2) in a well-designed experiment cha-,
racteristies of the functional relationship other than those under
study often do not materially affect the validity of estimation for
example the position and magnitude of a maximum on a curve may be
estimated fairly satisfactorily without knowledge of the precise form
of the curve provided that observations have been made on points
well-distributed about the maximum. Nevertheless careful utilization
of all existing information on a functional relationship at the time
of planning a new experiment may help greatly in the obtaining of
high precision for new estimates.
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Appro
Sir Ronald Fisher (University of Cambridge)
sequence that the amount of heterogenic m varies g eatly from
one individual to another, though obtained by the same procedure.
More exact knowledge of the nature and extent of this v ritttion is
obtainable by two paths: 1,. by the calculation of theI'pptimbers of
junctions formed by recomhinatihn nt ,ai ffr,,... .? 1I . .
geneity is. however, affected by chance lat each stage, wil h the con-
AFTER A GIVEN AMOUNT OF INBREEDING
Elementary inbreeding theory gives the expected pro
which that part of the germ plasm init ally heterogeneIc
reduced by a given procedure of inbreeding, The progress It
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THE VARIABILITY IN THE LENGTH OF GERI PLASM STILL HETEROGENEOUS
Using these two methods together the variance may be calgal~ated, and
the parts ascribed to variation in the lengths of bete ogeneon,
tracts, and in their numbers can be distinguished,
--- Sc, 111
plasm at two different loci ceases to be simultani!ously he erogeneous
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portion in
us will he
oward homo??
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D W Goodall (University College of the Gold Coast, Achimota
Gold Coast)
The methods of factor analysis developed first for the purposes of
psychology: and subsequently used in a wide variety of fields are
also sui able for studying the Joint distribution in the field of
different' species of plants, some measure of the quantity of each
species of plant present in sample areas providing one variable for
the anal l
ysis. The results of a set of observations on an area of
desert scrub in south-eastern Australia are analysed for purposes of
illustratlion by methods based on those of flotelling, data for four-
teen species being used. Some difficulties likely to arise in the
appllcution of factor analysis to problens of plant sociology are
discussed
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1 - Once properly understood "experimental design" in the statisti-
cal sense does mean a minor revolution in our concepts of tech-
nological experimentation,
2 That only a very small fraction of this revolution has so far
been realized is due to the fact that the design of experiment
is usually presented via the analysis of variance, a method of
presentation exclusively directed towards the mathematical in-
terpretatlon of the data. Thereby the technological meaning of
the analysis is largely lost.
3 - It is possible to present the analysis in a very simple way from
which the connection of the various components with the corre-
sponding technological influences can easily be grasped. Such an
analysis makes sense oven without applying test of significance
and probability theory. These statistical techniques should only
be brought, into play as a final cheek but should not be seen as
the principal aim. Statistical jargon should he carefully avoided.
The analysis should he represented in terms of averages and stan-
dard-deviations, instead of sums of rows and coltims and mean
squares.
Whenever possible the result of an analysis should he presen-
ted in graphical form. A graph is much more easily understood and
remembered than a mean square with double asterisk.
4 - The only way in which the technique can he mastered is by using
.it. Bence design of experiment should be taught by showing nume-
rous examples of one design and by demonstrating how technologi-
cal conclusions can he drawn from the analysis. Most textbooks
give only one example and then expatiate largely on the mathema-
tical aspects.
5 - The common use of the terms "interaction" and "residue" is confu-
sing and there is a lack of precise definition, We analyse the
data into components of the zeroth; first second etc. order
while-each component may in its turn be composed of (i) systema-
tic effects and (2) random fluctuations. Experimentally these can
be separated by repetition of the experiment.
6 - In agriculture and biology it is usually only possible to carry
out one experiment in a year. llence there is a need for involved
designs in order to get the maximum information out of one expe-
riment. Except with life tests, industrial conditions are es-
sentially different in that experiments can be repeated at will.
Hence industry does not require too Involved designs, but has it
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need for wide-scale application of the simpler designs.
7 Application c,f statistical techniques to industrial problems is
heavily impeded by an exaggerated drive after exactness.
If in industry we assume a significance level of 5% it is perfec
tly satisfactory when the actual level lies say between 3% and
7%. Without statistical techniques people are generally inclined
grossly to overestimate the value of their observations and the
useful function of statistics is to prevent these gross errors in
judgment.
Industrial conditions are perfectly insensitive however
against variations in the significance level as indicated above.
By purposely disregarding variations of this order we can tremen
dously simplify statistical techniques and this is of the utmost
importance to an effective introduction into industry.
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When in agriculture or technology a new treatment or process is
suggested, the difference in output per unit I1 between old and new
processes can be estimated by the mean y of the results of n expert
ments. The net gain associated with the new treatment may be taken to
be a linear function of T1_ say
I = k' (I - C)
where k' is a positive factor depending on the scale of application
and c is a constant which depends on the difference in cost of the
old and new treatments and the capital cost of the change. The new
treatment will be adopted if y - c is positive. We wish to arrive at
the number of experiments which is economically justifiable allowing
for the losses due to possible wrong decisions which in the long run
will he added to the cost of experimentation. If. therefore the cost
per unit of experimentation is It and P denotes the probability of
getting y - c ;. 0, we wish to minimize the difference
R kn - P?
tin - It' I' (11 - c).
This expression is the risk function measured from the status quo,
The present note deals with the case analogous to the double sam-
pling procedure of Dodge and Romig in which n has to be decided
after a single experiment (or unit. of experimentation) has been
carried out, For simplicity we assume that the errors in all experi
nients are independent normal deviates with known standard deviation o'.
The probability P is new calculated allowing for the known result yl
of the first experiment. Moreover, the risk depends on the unknown n
which must be eliminated' this has been done by averaging R over the
fiducial distribution of r (a normal distribution with mean yl and
standard deviation c). Minimisation of the resulting function R pro
vides an intuitively reasonable determination of n, and it has been
shown that no other rule can have a uniformly better performance,
one notable result brought out by the theory is that it is seldom
economic to do a very small amount of additional experimentation. The
reason for this is the disproportionate smallness of the chance of
altering the decision indicated by the preliminary experimentation,
When k, k', a and yl c are given the ratios (k a/k and (y1 - c)/o
suffice to determine n, and a nomogram for doing this rapidly has
been prepared.
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The pert-rmance of the suggested rule has been evaluated for a
series of parameter values, A comparison has been made with the
results of an alternative rule in which n is chosen so as to maxi -
mize the gain per unit outlay, Some work has also been clone on an
analogous sequential sampling scheme.
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T,N, Iloblyn and S C Pearce (East %falling Research Station Kent,
SOME CONSIDERATIONS Itl THE DESIGN OF SUCCESSIVE EXPERIMENTS
ON FRUIT PLANTATIONS
Some points needing consideration in designing trials with long Ii
ved plants, especially trees, are:
1 The initial trial.
Reliance has usually to be placed on a single trial and conse-
quently it is necessary for the questions under investigation to he
posed clearly from the beginning.
Trees are large and there is often only one to a plot. The perfor
nonce of a single tree is not determiner) solely by positional effects
but is a complex of its history and environment consequently ad
,l ustment. by covariance on to past performance is often an advantage
2 Subs,?r/uent trials.
Plants often outlast the experiment for which they were initially
intended and it is then necessary to provide for the application of
further treatments when the first set me no longer of interest
Where there is lll.1.le likelihood of the new and original LiuuL-
ments interacting the new treatments may be applied orthogonally to
the blocks or original treatments, or they may be balanced ether
totally or partially, or they may he supplemented, in this last de
vice one treatment, USu:rll.y the control occurs a different number of
times from the rest, which are balanced among themselves. From a
consideration of available useful design, it is concluded (hat trials
in which a further set of treatments is likely to he cal led for are
best designed, if in randomized blocks. with the number of blocks and
of original treatments either equal or differing only by one. In the
latter case repeated changes become possible as the residual effects
of former treatments disappear,
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J..W. Hopkins (National Research Council of Canada)
SOME NEEDED TESTS OF SIGNIFICANCE
Requirements for test of significance of the following are illu
strated by experimental data. (i) Inconstancy of the negative Uino
mial parameter k characterizing each of inn samples of 2: needed to
validate analyses of blood counts before and after imposition of m
treatments on groups of n animals assuming that random manipulative
and secular discrepancies result in successive counts on the same
individual being negati'iely binomially distributed with a k common to
all mn individuals, iii> Tnconstancy of the analogous hypergeometric
variance parameter in m samples needed to validate simple criteria
for 2-stage acceptance sampling by attributes of large consignments
of packaged items (e, g, boxed fruit) when defectives are contagiously
distributed between packages. (iii) Departures from goodness of fit
of linear regression formulae when both variables are subject to
error, needed to demonstrate inconsistencies in measurements by two
procedures e.g. standard and accelerated methods for moisture in
grain, (iv) Inequality of means of in binomial variates of Poisson-
needed to demonstrate differences in mean acuity of in groups of
subjects in a taste experiment,
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J. ipsen (Institute of Laboratories ? Boston - Mass,)
FACTORS OF DOSAGE AND HOST. DETERMINING ANTIBODY RESPONSE
TO SECONDARY ANTIGEN STIMULUS
A secondary stimulus is an injection of antigen in individuals who
have previously been exposed to the same antigen.
The antibody concentration in the serum after a secondary stimulus
is dependent on
(1) The immunity status when the secondary stimulus is given.
(2) The antigenic potency of the secondary stimulus,
(3) A negative interaction between the factors of l and 2,,
The immunity status is in pract.rce estimated in twri ways One is
the anti]lod,y concentration which can only be used as a comparable
function Hof the immunity status of different. individuals i t compa -
rable t.i r'e intervals have clapsed since primary exposure has occurred
and if the antibody concentration is above the measurable leveI,iri
the major'it:y of the individuals The second estimate can be obtained
if the potency of the primary chase is known and the individuals have
comparable iuununi?sabiiit.y inunuu r.icbiliL.v is an inherent host charac-
toristic `vhic determines t:he -salons, to primary sbimuias it can be
measured by the dose of antigen which ir; necessary to confer a given
primary immune status,
1mmunivaLion of 128 iuinates of a ,school fin I' tnont.ally retarded
individuals was performed with two injections of tet.uruts toxoid 28
clays apart. Eight different doses were given in each injection acCor-
ding to a'ilatin square design for the first: and second Injections.
Antibody Niters were only mintsurrible in 50 individuals prior to the
second injjection,. The antitoxin titers 14 clays after the second sti-
mulus was 'fitted to the following expectancy formula
Y= a l b x b x ' b X x
r r ti I 2
there Y i s ! log antitoxin L i t e r and x and x is the log potency of
the first and second close, respect.ivetry,
A satisfactory fit could only be obtained if the individuals were
divided into three groups according to certain somatic criteria. and
a parameter,' c was introduced being constant for each group
Y (xi , ci , b x - h x ? (x ' c)
The variable c is interpreted as the primary immunizabiiity
inherent with the somatic characteristic of the individual,
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Karreman (Committee on Mathematical Biolog
University of Chicago)
~9A000500400179-7
THE MATHEMATICAL BIOLOGY OF T~RESH',LD
or iepoproteinate) which is in equilibrium !ionization pro-?
ducts (including calcium),. In an electrical ftyy~ill
je'',I;dF:_the calcium ions
of one or two molecular layers of a calcium co ours .e. 1;, proteinate
model of membrnne permeability, The membrane islsu posed to consist
The existence of a threshold is proved fc}r,,at`physico?chemical
AND RELATED PHENOMENA IN EXCTATIPL . N
'l f
is given of the diffusion of the potassium throIij h he membrane the
t~ ~V! U r'i'meubi.Lit.y of which to potassium is determine, the eguilihri um
state of the above mentioned reactions It is iolwq that: the system
possesses an unstable equilibrium. Prom this tr'ders of magni?
and its ionization products. The electrical 'rote t'.ial across the
layer(s) is supposed to he the superposition afr~the~;{ 1iffusion poten?
lode are derived for the chemical and electiic?lal;hreshoids the
II
))
G:xeitability curves are derived from the model
good ngt?eement with experimental evidence
several predictions are made suggesting new
slight modification of the model repetitive disc
The order of magnitude of the potential changes
right as well as that of their duration.
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tic ion potential,
experiments [iments From a
IT' 4 ICI are oht ained.
I x?i ed from them is
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E. A. G. Knowles DepL. of Engineering Production,
University of Birmingham)
EXPERIMENTAL DESIGNS IN INDUSTRY
N.th particular reference to production investigations
1 Pilot experiments and their in terpi-e tat toll
Consideration of a variety of different possible interpretations
and representations as an aid to obtaining the best guide for the
planning of the final investigation appears desirable. The variety of
interpretations would often be greater than that which might he
thought sufficient from the point of view of the pure statistician
because the purpose of the pilot experiment is not only that of
giving the best consideration to the particular objectively known
scientific and technical conditions of the materials and processes.
but in audition that of enlisting the cooperation of all human
personalities involved in every aspect of the work together with
their knowledge and experience.
Final investigations, thetr form and interpretation.
At this stage it, is desirable to have the mode of interpretation
and the methods of representation agreed beforehand and strictly
adhered to as is usually recommended so that the validity of the
statistical significance tests is not threatened by preferred choices.
However, renewed experiments with analysis and representation become
desirable as soon as the results of the investigation lead to the
consideration of further investigations
3 - Practical illustration from an investigation connected with tool
manufacture.
The above considerations will be illustrated by means of results
obtained in a recent industrial investigation in which the writer has
cooperated; the subject being that of hardness variations of standard
drills in relation to the various assignable causes given by the raw
materials and the methods of production and test.
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D. C? Lowry (University of California Berkeley Cali
VARIANCE COMPONENTS WITH REFERENCE
TO GENETIC POPULATION PARAMETERS
One of the important problems both of applied and of Lheoretteal
genetics is the determination of the comparative effects of the
various factors which affect, the inheritance of quantitative charac-
ters, These characters may be controlled by the action of a large
number of gene pairs. by environment and possibly by the inf.eracLion
of genotype and environment, in analyzing their inheritance Fisher
Wright and others have found the analysis of variance a powerful tool
in identifying these effects and in characterizing the multigenic
system according to additive genetic effects. dominance deviations
from the additive scheme and non-allelic gene interaction. Their
analyses have been based on models of Mendelian horedit.v which invol-?
ve some restrictive assumptions.
The detection and interpretation of components of variance in the
study of quantitative Lraits involve statistical problems of two kinds
first, the con.;I:ruct.ion of models and of experimental designs based
upon these models, containing fewer restrictive assumptions and
second, the consideration of the purely statistical aspects of the
functions of components of variance used as estimates of population
parameters.
This paper is intended as it review of what has been accomplished
in these two phases of study, particularly the latter
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site do Bruxelles).
SUGGESTIONS POUR LA COLL9CTION ET L"ANALYSE
DE DONNEES LONGITUDINAL SEN GERONTOLOGIE
Supposons qu'un medecin trnuve quo e cholesterol est normal (1,8
gr/1) chez tin patient A et trop e'leve (2,8 gr/1.) chez patient. B gLii
manifesto des signer cliniques d'artetioclerose. Ces deux patients
sent de mente age, 60 ens par exemple. 0 peat supposer qu' it 40 ans le
cholesterol sanguin dtait normal dons 1~es 2 cas, Si oui. it partir de
quel age le patient B est-i.l devenu "hors contrale"? Si Von pout
determiner cet instant, in methode de la mddecine preventive aura one
bonne chance de reussir, car les lesions au sons large du root soot
peut-etre encore reversibles. On propo a de determiner les limiter
fiduciaires pour is moyenne et Line observation isolee a Lin age donne
en ajustant des polynomes orthogonaux individuals a des donneos re-
cueillies sur tin echantillon de patients suivis d'annee en anode des
1'dge de to ans. L Importance de cot echantillon ainsl quo son mode
de prelevement dependront des facilites techniques. Une telle methode
u etd discutee avec le Prof. W.G. Cochran et appliquee Bans le as du
devoloppernent de P activate histaminoly ique chez 18 femmes suivies
pendant los 9 mois tie is grossesse. Rdferonce est fa.ite a tine sugge.
st:ion de Sjogen et tine autre de Tanner. Cc dernier etudie duns lc cas
de In croissance des enfants,les tndrites respectifs de V information,
tired de donneos tranversales (it temps fixe on longitudinales
(me"me
individu suivi a des moments successifs).
L'auteur fait tine suggestion de collection de donneos a one echelle
collaborative intra-et inter pays civili.5es,
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 II
n
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lines of Mendelian genetics. Finally we shall require a theory of
variability interpretable in terms of mendelisn theory but differing
in structure from it, and the recognition of effective units of inhe-
ritance whose relation to the genes of Mendelian genetics will re.
quire close consideration.
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pp 11 q
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fl. Alorice (Inst:itut National de la Statistique et des Etudes
Economiques, Paris)
A STATISTICAL STUDY OF THE PHENOMENONS OF HUMAN GROWTH (Exhibit)
The inquiry held in the United States in 1936 contains a great
number of documents on the measurements of the numerous elements of
the human body in children - boys and girls from 4 to 17 years of
age - as well as on the correlations between these measurements at
various ages.
The comparison of these various measurements with the height for
instance,enables us to determine the relations in allometry (relative
growth) of a general form y - K x'', One notices that the hypothesis
a. -- constant is confirmed only exceptionally for some dimensions. In
general from 4 to 16:
a) for vertical dimensions, u, at first superior to I diminishes to
become approximately I or inferior to I
h) for herls'.ontal dimensions and perimeters, as well as for the
ceight, the variations of o. arc, in general, in the inverse order
of the preceding ones and more accentuated.
On the other hand, the correlations between the various measure-
ments - studied for seven of them - Show important variations with
the age, variations of different types
a) according to the sex
b) according to the nature of the variables placed in correlation.
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J;. Neym-n (University of California)
The original problem formulated by Ra.gnar Frisch in 1936 is con
eerned with two not directly observable random variables and
n]', = u lid where cc and (i are unknown constants. Instead of observing
the values of S and il we observe those of X = E '1 U and of Y :1 V
where U and V are random errors of measurlement assumed independent of
{?'l and 71 and independent of each other. Frisch s question say uhal
must be the distribution of e. U and V so that. irrespective of the
values of o. and p, the regression of Y on X and of X on Y be i inear,
The purpose of the present paper is to report on the results related
t;o this problem that were obtained by njembers of the staff of the
Statistical Laboratory, University of California Evelyn Fla 1'. F'er
uson, Terry A, Jeeves.. E, 1, Scott and the present. author.
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V.G- Panse (Indian Council of Ag icultural Research -New Delhi-India
PRINCIPLES OF THE SURV Y METHOD OF EXPERIMENTATION
The urgent need of increasinE agricultural production by passing
on to farmers the results of ag icultural research has led to a ra
pidly growing emphasis in India curing the last few years of what may
be termed the survey method of a perimentation, as against the clas-
sical type of experiments at agrIllcultural experiment stations The
results from the latter, valuabl as they are, cannot he recommended
directly for large scale use and r actual farming conditions, because
the number of experiment station. is small and cannot be regarded as
fully representative of the tract;I served by them, Experiments on a
representative sample of the cullivtted area therefore become neces
nary, before recommending a technique to farmer Such a sample can be
secured only by selecting field for experiments randomly out of
fields on which it particular crop is grown in the tract
The aim of the experiments is generally to estimate with a reaso.
noble degree of precision the ave age response to treatments over the
tract, detect any interaction of h'ese responses with variation among
agriculturally homogeneous sub-division into which tract may be
divided and estimate the responstslin the individual sub-divisions
The precision of the estimates is based on the random variation among
fields selected for experiments or rather on the interaction of
treatment responses with this variation Consequently, the importance
of the experimental error, as calculated in the classical replicated
experiment recedes to the backgiound and replication in the same
field- which is essential for est mating the latter, may be sacrifi-
ced altogether in order to secure more information on the variation
among fields Replication in the sense of the number of repetitionsof
the experiment in different fields is, of course, important, but
randomization of treatments in a ch field has not the same role in
securing the unbiased comparison between the treatments as in the
classical experiment. It is, howe er, safe to adhere to it in order
to avoid possible biases arising from border and competition effects
peculiar to any fixed arranganent of experimental plots In a field
The third principle of replicated experiments, namely, local control
involving a compact arrangement oflplots and attention to size and
shape of plots and blocks Is also of little importance, since the
variation between fields is far greater than variation between plots
In a field which local control is intended to minimise. This allows
the latitude needed for fitting the ,experiment in the farmer's sche-
dule of operations with the least possible disturbance of the latter,
which is an essential organisation 1! consideration,
39
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Two sets of projects on the survey type of experiment have been
undertaken in India recently In one scheme following the recommenda-
tions made by Dr. A.B. Stewart in his report on Soil Fertility In
vestigations in India, two or three treatments with the local prac-
tice as control are tried in each field selected randomly in the
tract. The treatments are those which State Departments of Agricultu-
re consider as likely to increase the yield on the basis of the past
results at experiment stations. A more ambitious programme of experi.
ments has been commenced this season in several areas under the ferti
livers research project sponsored jointly by the Government of India
and the T.C A,.; with the object of acquiring information on the
response of certain important food crops to different nitrogeneous
and phosphatic fertilizers
A somewhat different type of experiment is represented by the
assessment surveys, conducted by the Indian Council of Agricultural.
Research in different States in order to estimate the additional
yield resulting from various Grow More Food schemes such as distri
bution of improved seed and fertilizers provision of new sources of
irrigation. tractor ploughing; weed infested land etc. Comparison is
made between the yield in the area which has received one or more o1'
these aids and an appropriate control The experiment is not a stric
tly controlled one in that the treated areas are not selected random-
ly vis-n?vis the control and the comparison may therefore he open to
bias. These surveys form an example of operational research in agri
culture and have yielded much valuable data.
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ESTIMATING POPULATIONS OF IRREGULARLY OBSERVABLE ORGANISM
The problem treated is that of estimating the total population of
an organism in a given area when we cannot assume that all me,~)bers of
the population are ever observable simultaneously. There alr1Ie many
examples of such cases; my own work concerns the higher Basl'diomy-?
cetes, whose mycelia do not fructify every year and cannot be iden-
tified unless they do so.
It is assumed that a permanently and constant population exists in
the given area; cases where the population changes appreciably during
the period of observation, and where the lifetime of an individual is
comparable to the phenological periodicity, are excluded, I
The principle of estimation is this. If we have a number' N of
consecutively numbered counters, known to be less than N but 1other-
wise indeterminate, and sample 1 of them t times with repiacpment,
the highest ordinal borne by any of the counters taken, n; will1 have
a determinul.e probability distribution depending on t, N, and N
Thus,given t, 11, and N, we can estimate N and obtain fiducial llimits.
1
1
t (n
t
)-2
/N
(
]
-
N
-t
I
1
nt 1 1 19 %t
P-5% [N] _
(N~ 20 20
t . 1
N
19 1 1=t
20 20
If the frequency distribution of the fraction of the population
observable over all the occasions when observations are made should
be rectangular, the problem of estimating the total populatioI is
formally identical with the above, provided we know the upper Limit
N. But if the actual frequency distribution is f(x), it can be shown
that n(x) = f f(x)dx is a rectangular variate over the same filEld,
provided that Lt n(x) is finite; if this condition fails there is no
In general the form of f cannot be foreseen; in the case of mylda-
ta on basidiomycetes it can be shown to be at least approximately
41
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1 ~I
f (x) , x". r
In general, one of the limitations of the method will he that
there may be no way of discovering f On integration. this value of f
gives an incomplete gamma function
n(x) _ u! log )x~
1
Of the two parameters 3 can be expressed in terms of c and the
Only weighted) mean of the observed numbers of fructifications x
The parameter a requires great lubou r for its rigorous estimation.
but for the purposes of this method which is necessarily rather
crude, graphical methods are sufficient.
For each series of observations to be analysed, we first estimate
,7. and thence compute a series of n values corresponding to the raw
x s From the highest of these we can Cat cu late by the formulae given
figures for F [NJ. If (NJ, and F (N1 We can then employ the
inverse function to n in order to estimate from these the expec?
tatlon and fiducial 11.nits ul' the unknown population X
These estimates are of course nut. strictly correct since in
general f (E[NJ )7t' F [ 1'(N) ( but the error involved is relative ly
trivial,. The expectation distribution is extremely skew, so !hat
upper fiducial limits are often meaningl^ss and represent Impossibly
large populations. But the estimates of population which the method
gives can he generally be relied upon to within 50n either way This
may not sound very good, hut most of the error is inherent In the
nuLure of the prohlem, and more rigorous methods would not usefully
reduce it,
Particular examples of the kind of fiducial limits one gets may
be cited from my work on Skokholm Island,
%ales, which I estimate to
have the following total populations of
certain basidiomycetes.
lower
fiducial
limit
Estimate
upper
fiducial
limit
5%
5 %
Naucoria nana
5,000
7,000
50000
Panaeolus pupilionaceus
1,000
2,000
10,000
Clitocybe fragrans
500
1.400
17;000
Panaeolus campanulatus
150
250
000
(these fiducial limits include also errors of sampling in the raw
data),
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S C- Pearce and G?II Freeman (East Mailing Research Station, East Mailing
Maidstone. Kent)
REPEATED CHANGING OF TREATMENTS IN TRIALS WITH LONG LIVED SPECIES
(Exhibit)
111th long- Ii.ved species it is a good plan to arrange that a fresh
set of treatments can he imposed on the experiment after it has
served its original purpose. It is a useful extension to provide for
a third set. of treatments. The design shown here makes this possible
when there are no longer any residual effects of the first set, and
indeed permits the introduction of an In 2) th net when there are
no residual effect:; remaining from any of the first n sets thus
permitting indefinite use of the original experimental material
The lop diagram represenLa it design with seven treatments the two
below it show the addition of a second set, either of four or of
seven treatments. In the bottom diagrams it: Is assumed that the ori -
ginal t reatments no longer have an.v residual effects, and a third
set. wither of four or of coven treatments, is added to each of the
middle diagrams
This property is possessed by many experiments designed initially,
like this one in balanced incomplete blocks At any stage., an anaiy
sis of variance on the data can be carried out readily by solution
of the parametric equations.
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S, Pete (Microbiological Research Department Ministry cf Supply
Porton; wilts)
A DOSE-RESPONSE EQUATION FOR THE INVASION OF MICRO-ORGANISMS
If several hatches of test animals are exposed to invading mi -
crn -organisms, linearity between log (proportion surviving) and dose
is theoretically established. assuming that
(i) the test animals are homogeneous
(ii) the probability of one organism killing its
host is constant and small
tiii) the organisms act independently of each other.
The relevant maximun likelihood solution is given and gables
recommended to help computation.
When doses are expressed in terms of the, ED.30 a fixed regression
Jine emerges from the underlying hypothesis. Illustrative examples
taken from practice are quoted. Comparison with probit analysis is
discussed The problem of economical use of test animals is treated
The method can be applied to dilution series Bacteriological Re
search in general might be stimulated and itntnunologieal phenomena in
particular elucidated if the mode of action of pathogenic organisms
is explained by the hypothesis expressed in this paper lantern
slides are used to illustrate essential points
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Im I and II.Abschnitt wird die F rage behandelt,welche Rueckschlus
se aus den an einer Stichprobe gewonnenen Ergebnissen eines Immu_
nisierungsversuches auf die Zusammensetzung der Gesamtpopulation
gezogen werden durfen der (lie Stichprobe antnommen ist?Die verschie-
denen Verfahren werden hest)rochen, um den "blutungsbereich" zu er--
mitteln, innerhalb dessen der unbelcannte wahre Anteil der immunisier-?
ten Tiere erwartet werden dart. Es werden Angaben iiher die Wahrschein
lichkeit der so gewonnenen Aussagen gemacht. Im III.. Abschnitt wird
ein Naherungsverfahren erortert, dessen Resultate mit den nach den
exakten Methoden gewonnenen Ergehnissen gut iihereinstimmen and des
die Rechenarbeit erheblich reduziert.
Der IV. Abschnitt diskutiert die treffertheoretische and die vu--
riationsstatistische Deutung von Immunisierungskurven and zeigt die
Moglichkeit, wit Hilfe der Mutungsbereiche zu einer Entscheidung zwi-
schen beiden Erlclnrungsversuchen zu kommen.
Im V. Abschnitt wird (lie Verwendung der Mutungsberelche zur Er?-
rnittlung des Il'irksamheitsverhaltnisses zweier Inrpfstoffe behandelt
Im VI Abschnitt ward die Anwendharlceit der Naherungslasung nu. dr.a
Geblet der seltenen Ereignisse nachgewiesen and ihre Verwendung zur
fiestimmung des ICeimgehaltes von Flussiglcelten besprochen.
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C. Itadhalcrishna Rao (Indian Statistical Institute - Calcutta,
A GENERAL THEORY OF DISCRIMINATION
WHEN THE INFORMATION ABOUT ALTERNATIVE POPULATION
DISTRIBUTIONS IS BASED OH SAMPLES
The problem may be stated as follows
Two samples of sizes n1 and n2 are available from two Populations
PI (x 1 01) and P2 (x 02) where x stands for all the measurements and
8 for all the parameters. An individual with given measurements y has
to be assigned as a member of one of the two groups basing the deci
sion on the observed values only, the parameters occurring in the
alternative distributions being unknown. In this paper an attempt Is
being made to Jay down a decision rule independent of the unknown
parameters.
If the measurements are p in number we have a total of (nl:n2,i)P
observations which can be represented by a point in a Euclidean
space The decision rule requires the division of the space into two
regions R1 and R2 such that when the point of observations falls in
RI the individual is assigned to the t';rst group and otherwise to the
second Whatever may he the set of regions, it should have the pro
perty that errors of classification when the alternative populations
are different must he smaller than those when the populations are the
same, This criterion leads to the restriction that the size of each
region should be the same whenever the two probability densities PI
and P2 are identical irrespective of what the actual values of the
common parameters are
We have now to fix the size of the regions RI and R2 when PI and
P2 are identical. When the population distributions are identical-
the decision may be equivalent to that of tossing an unbiassed coin
so that it is reasonable to take each size as 50 percent The special
case of fixing the size at the 5% level leads to a test of the null
hypothesis that the individual belongs to the first group at level
5%. the alternative being the second group.
The problem is now to determine such similar divisions RI R2
covering the entire space which have fixed values when the two disLr.
buttons are identical and for which the errors of classification is a
minimum The problem of minimising the errors reduces to dividing the
region common to the surfaces of sufficient statistics as in the
general problem of testing composite hypothesis.
Again, in all cases no uniformly best division is possible on the
surfaces of sufficient statistics We may then determine regions for
which the errors of classification is least locally, I. e, for small
departures from the equality of populations.
The theory is general and can he applied even when the alternative
distributions are more than two.
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 n
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D.R. Read (Research & Development Dept., The Distillers Co, Ltd.,
Great Burgh - Epsom - Surrey)
The main features that are more or less peculiar to chemical (as
contrasted with biological) experimentation are briefly set out, and
attention is subsequently confined to the following case which often
arises: experimental error small and a prior estimate available, no
need for local control, sequential procedure and quantitative fac-?
tors: the object of the investigation being to estimate a set of op-
timum conditions for a chemical reaction process, e.g ? conditions
giving maximum yield or minimum impurity,
A short account is given of the methods already developed by Bo
& Wilson, which consist essentially in carrying out experiments in a
sequence of small groups, estimating first- or second-degree regres-
sions that give approximate local. fits to the reaction surface, and
using the estimated regression from each group as a guide to the most
effective disposition of experimental points in the next group, These
methods are then illustrated by an example of their use in a typical
problem of chemical development.
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 F
Approved For
I
G.L. Scottl (University of can
I : CIA-RDP80-00809A000500400179-7
Pornia)
BIVARIATE CONTAGIOUS DISTRIBUTIONS
The observed distributions pf counts of certain larva' in experi-
mental plots exhibit marks of 4ontagion: if one plot contains a larva
then somew ere in the viclnit- there was a batch of eggs and this
implies an increase in the pro ability of there being more larvae in
the same acd neighboring plots This machinery underlies the single
variate contagious distributioglls'deduced by Neyman and later genera..
lized by Beall. The present p!per gives formulae for the analogous
bivariate istrihution that ma be useful in closer studies of the
behavior of larvae, r'I I
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 F
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C ? B Smith the Gal ton Laboratory University Colegs Londonl
THE CALCULATION OF CORRELATION BETWEEN OUSINS
For any given character it is possible to find he cousin cousin
correlation by plotting all points x y) in a correliation diagram in
the usual way where x y are the measured values in a pair of cousins.
However if two sibs have large numbers of childre1 every child of
one will he a cousin of every child of the other. his will produce
a very large number of points in the diagram whilRh may swamp the
contribution of the other cousin pairs. It is bette to use a three
stage analysis of variance, giving sums of squares i) between indi-
viduals within sibships (ii) between sibships, within cousinsh+.ps
tiii> between consinships. By the use of suitable formulae both the
sib-sib and cousin-cousin correlations can then be fi`tund.
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J .11 Tanner (Sherrington School of Physiology St. Thomas s Hospital.
London)
SIZE SHAPE.- AND REGIONAL DIFFERENCES IN THE VERTEBRAL COLUMNS OF
INBRED STRAINS OF RABBITS STUDIED BY ANALYSIS OF VARIANCE
(11xhibit)
The lengths and breadths of the bodies of vertebrae numbers 2-29
were measured in two of Dr. P.B. Sawins strains of inbred rabbits at
the Jackson laboratory Bar Harbor, Maine. The rabbits were of various
ages from 75 to 1440 days, not all being quite full-grown. The problem
was to describe the inter-strain differences in the vertebral columns
as succintly as possible, as a basis for genetical experiments on
body build in the rabbit
Analysis of variance was used, with a three-way classification by
vertebral number (28 classes) race (2 classes) and age (4 classes),
The data provided considerable replication within each cell hc,wever,
an average of 8 rabbits having been measured within each age group of
each race The mean values for each cell were the figures analysed
with an estimate of the variance of these cell means used as the
error mean square.
The triple interaction term and the other interactions have then
all clear biological interpretations The conclusion from their
significance tests is that one strain differs from the other in (i)
general size of all vertebrae (ii) shape of the vertebral column as a
whole one strain being slenderer. and ;iii) shape of vertebrae in
particular and circumscribed regions of the column
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A- Vessereau clistitut de Statistique Universite de Paris)
ENSEIGNEMENT DES METHODES STATISTIQUES APPLIQUEES A LA BIOMETRIE
Ce n est qu apres In derniere guerre qu one action coordonnee a
etc entreprise pour;diffuser of appliquer Ins methodes statistiques
clans differents domaines reconverts par 1e terme general de "Biome-
trio".
Un enseignement de ces methodes a etc cr6e en 1946 a I'Institut de
Statistique de 1 Universite de Paris it a etc suivi des le debut et
continue h titre suivi par les etudiants qui se destinent h in re-
cherche agronomiqucidens les territoires de In France d Outre?lter
ainsi quo par des chercheurs deja nffectes fl des Centres do Recher-
ches. Quelques annees plus tard 1 Institut do Statistiqu'? a egale-
ment cree tin enseignement de "(3enetique des populations".
11 y u quelques annees 1' Institut National Agronomique a inscrit
1 enseignement des methodes statistiques all programme de sit troisieme
annec d etude (dli:ves se destinant a des carribres de recherches
gendticloon pedologties; etc . ) des complements de mathematique et
en particulier des notions de calcul des probabilitts preparatoires n
cot enseignement. soot!donnes an Coors des deux premieres annees d c?
tilde
Pans le cadre de la Paculte des Sciences, les etudiants qui pre-
parent, le certificat de "genetique" regoivent les notions Ile stati-?
stique indispensahleson cette maticre. Les etudiants en psychologie
applique" (Institut de psychol.ogie de 1 Universite de Paris) reaoi-
vent egalement on ensedgnement stntistique de base et on enseignement
specialise,
Si. dons le- sect ours "biologic" et "agronomic"; 1 enseignement
des methodes statistiques se trouve organise de facon d pen pros
coherente.par centre, clans 1e secteur "medical"; i1 n`y a out jusqu?i-?
ci clue des tentatives fragntentaires (quelques series de conferences)
insuffisamment ceordonnees~ des progrbs importants restent a faire
daps tie domaine.
Une des principalesdiificultes rencontrdes dons 1- enseignement;
des m?t.hodes statistiques reside daps 1 insuffisance de formation
mathematique do Iu pluparte des e16ves (lours etudes anterieures out
etc orienties surtout,vers les sciences naturelles) et clans la
nottvoaute clue prdsente jour eux 1e mode de raisonnement probabiliste.
Cette situation pourr a t titre ameliorie Si one initiation statistique
et probabiliste 6tait donnee au cours des etudes secondaires, et si
certaines niodificationsetaient apportees an programme des connais
sauces exigees des candidats aux carrieres biologiclues et medicales.
lI
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 Approved For Relo
Dans 1 enseig{'ment dispense a des etudlants de formation muthdmu
tique parfois pr caLre it est souvent prdfdrable de ren^r,cer all
exposes rigoureuI% et de faire appel a des raisonnoments approches out
intuitifs sans J,4 ufois masquer les difficultes In strict dumaine
d'application methodes dolt d autre part. tie bien precisd
I1 a etd recop'nu,que, sans sacrifier le notions thooriques essen
tielles, 1 enseillnement dolt rester aussi concret quo possible. Les
exercices prattgpp~as',sont indispensables et peuvent prendre plusieurs
e
e
formes
tablissgm
nt on verification de loss statistiques et, pru
prietes des echu~Iltlllons_ a partir de Iirnges de boules jeux de des
on de cartes pet s
parties theoriqulees
execution complq:e
problemes destines n facilttcr I assimilation des
de 1'enseignement applications numeriques avec
des calculs et emploi de machines a cnlculer.
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 F
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Dept. of Public Health
1800 West Fillmore St.
CHICAGO. 12 (U S A,)
Chalmers University of Technology
Dept. of Appl. Mathematics
GOTEBORG (Sweden)
Prof. J.
BERKSON
Mayo Clinic
ROCHESTER. Minn.
Dr. B.B.
DAY
3136 Dumbarton Ave N.W,
WASHINGTON 7 D,C ;U.S.A. )
Prof. M,
FRECHET
2, Rue Emi lie Paguet, 14e
PARIS (France)
Dr.
11, C.
HADIAKER
Philips Research Laboratories
EINDHOVEN (The Netherlands)
Dr.
L, B.
DOLT
The Wright Fleming Institute
St. Marys Hospital
Paddington, LONDON W.2 (England)
Eeonesserweg 89
BEARN (The Netherlands;
26 Westfield Rd.
Edgb as ton
BIRMINGHAM 15 (Englund)
2310 Baldwin St.
HOUSTON 6 Texas (U,S,A
Statistical Laboratory
University of California
BERKELEY 4 California (u
Mullerstr. 59
INNSBRUCK iAUstria)
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 r
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Dr. II, PROBSTEL
Dr. W. RODDEWIG
Dr. E.L. SCOTT
Indian Council
of Agricultural Research
NEW DELHI (India)
Eberstudterstr. 13
PFUNGSTADT/IIESSEN (Germany)
W'alluferstrasse 4
ELTVILLE/RHEIN (Germany)
Statistical Laboratory
University of California
BERKELEY 4 California (U.S.A.)
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I
 Approved Fpr'I Release 2004/02/11 : CIA-RDP80-00809A000500400179-7
J, Qerksoii (Division of Biometry 'Ind Medical Statistics Mayo Clinic,
Rochester. Minnesota, U- S A
MAXIMUM LIKELIHOOD AND MINIMUM CHI-SQUARE
ESTIMATES OF REGRESSION COEFFICIENTS
Several f unctions will be briefly discussed, but chiefly attention
will be given to the logistic function, P = 1/1-e-(a + fix) with the
observatipn on P assumed to be a random binomially distributed va-
riable, as in the model for bioassay with quantal response. Three
estimators are investigated: (1) Maximum likelihood; (2) Minimum X2
(Pearson); and (3) Minimum lugit x2 (Berkson J. J. Am. Statist, A.
39 [ 1944] 357).
are considered, (1) j3 known, a to be estimated, and (2)
a and pi both' to be estimated. In the example dealt with there are
three equilly spaced values of x ("doses" in bioassay) with N = 10
at each. The dose arrangements are for P = 0.3, 0.5
0. 7, correspon-
ding respectively to the three consecutive doses, and for other sets
of three doses each, in which the value of P corresponding to the
central dose' is 0.6, 0. 7, 0.8, 0.85.
In the dase with P known, a to be estimated, the results are based
on calculations of the total sampling population; in the case with
both a and l to be estimated, they are based on a sample of 2;000
with each dose arrangement.
For central dosage P = 0.5 each of the three estimators is un-
biased: for other dosage arrangements each is biased, the maximum
likelihood estimate positively, each of the x2 estimates negatively,
The mean square error and variance about the mean are largest for the
maximum likbliihood estimate, smaller for the minimum Pearson x2 esti-
mate, and smallest for the minimum logit X2 estimate.
The estimates are considered in relation to the Cramer-Rao lower
bound for to mean square error. The bound value itself is highest
for the maxmum likelihood estimate, lower for the minimum x2 esti-
mate. and lgwel st for the minimum logit X2 estimate, but the m. s, e, of
all three e.timates is higher than their respective lower bound va-
lue.
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Two cases
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Each of the estimators is sufficient. Blackwell's theorem (Ann.
Math. Statis. 1)3 [1947] 105), may therefore appropriately be applied,
The "Blackellized" value of the estimate (conditional expectation of
estimate for fixed value of sufficient statistic) is the same for the
maximum likelihood estimate as before Blackwellization, but with the
minimum logit X2 estimate, the mean square error is diminished by
Blackwellization to its lower bound value.
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 Apprfoved For Release 2004/02/11 : CIA-RDP80-00809A000500400179-7
An attempt has been made to characterise the antigenicity of any
dipl;theria prophylactic in mathematical terms (responses to a single
inoc
U
elation).
ke is made of the observation that the responses among a group of
simi,ar subjects, identically treated, is ing. normally distributed;
as w 11 as the observation that when the results of a dose-response
expeiiment are plotted as probit y% against log, dose administered a
stra
It
re du i
the S
respe
some
the s
ght line is obtained - the probit regression line.
,was found that three variables are involved, namely d. the dose
red to produce some arbitrary reference point of response, b.
lope of the probit regression line, which gives information in
t of the percentage increase of subjects attaining or exceeding
rbitrary level of response with increase of dose, and aIog
andard deviation of logs of titres. These three variables are
incor'orated into one general equation:
Log G.M. (dose D. log. G. M. (dose if. ulogs, h. (log.cldoossee d D,
) ) ,
ThG'product of ologs. and h. for any one set of data is it constant
(N.) -,hick is numerically equal to the slope of the dose-response
curve
T lie
in chi
about
guinea
log. G.M. /log. dose.
value of K. for the diphtheria prophylactic P. T. A. P. measured
ldrer was found to be approximately 0. 86 and in guinea pig.
G; and the olog. of titres 0.65 for children and 0.51 for
Ppigs.
Evidence is offered to show a marked dissimilarity in the con-
stain tsfor other prophylactics measured in children and in guinea
pigs; sometimes the guinea pig will underrate a prophylactic in terms
of children, and overrate it for another hind of prophylactic.
The mportance of the laboratory use of appropriate "Standard An-
tigens" that have been calibrated in the field is stressed.
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The problem: in applying an analysis of variance, after having
concluded from an F-test at a significance level 0,05 that the null-
hypothesis 1LI = {L2 = !Lm has to be rejected, so that at least some of
the ?i are different, most research workers feel the lack of'a con-
venient statistical procedure stating what differences should be con-
sidered real. In general we may be interested in the question what
contrasts within a previously chosen subset of the set of all con-
trasts }, ai I`i (1 ai = o) should be considered different fro,n null.
A procedure in general use is the least significant difference
test (l.s.d.-test), consisting of applying an ordinary t-test to each
difference or contrast seperately, then and only then, if the IF-test
rejects the null-hypothesis. This procedure has been denounced by
most writers to-day, as it highly exaggerates the significance of the
conclusions.
Several alternative procedures which fall into two classes have
been suggested. The oldest are the multilayer significance (tests
(Newman, Duncan, Tukey, Keuls). Although these tests implicate
nominal significance level, the real significance levels arel
blematic. The other class contains procedures of multiple confi
some
pro-
dence
statements (Tukey, Scheffe, Roy, Bose and Roy and others). Here no-
minal and real significance levels are identical. The procedures are
simple and will be clear also to non-statistically trained rend Irs of
the records.
In discussing old and new procedures, the following points are of
interest:
1. There may be defined different significance levels or according to
prof. Tukey "error rates".
2. There may he a choice between a significance level procedure and a
n
3. A point that has been insufficiently stressed by writer on co
fi-
dence procedures, is to indicate, before choosing a procedure,
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Analytical genetics is a suitable term to describe that kind of
genetical research where, by controlled breeding of organisms, we
follow the assortment and recombination of sets of discrete Mendelian
factors. The analysis and interpretation of the data which arise
involve a coherent system of statistical methods, exhibiting points
both of analogy and contrast with those so well-known in the realm of
agricultural experimentation.
In analytical genetics we are concerned fundamentally with the
estimation of certain pure numbers such as segregation ratios or re-
Combination fractions; i.e. those parameters which enable the breed-
ing behaviour of organisms to be predicted. in agriculture we tend to
stress the detection of differences between stocks of treatments.
This however is clearly a question of estimation and the difference
is only one of ernphnsis.
In agricultural statistics almost everything involves normally
distributed variates, and the prime tool is the analysis of variance,
with the principle of orthogonality as guiding consideration allowing
individual effects to be distinguished. In genetics the variates are
always whole numbers being multinomial class frequencies. Tatting
estimation as the basic problem, complete coherence of method is
acheived by proceeding from the maximum likelhood theory, using the
technique of scores, a mude of presentation whose power is not yet
always fully appreciated.
Scores are linear functions of the class frequencies, and they
lead directly to the analysis of Chi-Squared which is our prime tool
and the counterpart of the analysis of variance. The analysis of
Chi-squared can be arranged to exhibit such features as orthogonality,
component effects, interaction and error terms.
Both discriminant functions for grouping and the normal theory of
curvilinear regression have their Chi-squared analogues in this field.
The Latin Square occurs inevitably and essentially in the design
of multiple point linkage tests, when we wish to separate Mendelian
ratios from viability effects, but it is used in a way peculiar to
the subject. For instance the feature of randomisation is absent.
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DESIGN AND IMPLEMENTATION OF A SAMPLE ON MILK PRODUCTION IN AGRICUL-
TURAL AND FOREST FARMS OF BAVARIA IN THE AGRICULTURAL YEAR 1951/1952
In the compass of a research commission the Bavarian Statistical
Office implemented it sample on milli production in the agricultural
and forest farms of Bavaria from 0.5 ha of agricultural area and more
for the agricultural year 1951/52.
The inquiry was designed as a stratified sample with "cow-keeping
agricultural farm" as unit of selection. For an efficient stratifica-
tion the following three main strata were considered:
a) farms from 0 to less than 50 ha of agricultural area (sampling
ratio 2 per cent)
b) farms from 50 to less than 150 ha of agricultural area (sam-
pling ratio 10 percent)
c) farms comprising 150 and more ha of agricultural area (complete
enumeration).
On the whole, about 9, 100 cow-keeping agricultural farms in Bava-
ria (2.15 per cent of the totul) were covered.
The cow keepers selected had to report the cow's milk produced on
their farms on it fixed day every month on a report form. The collabo-
ration of the cow-keeping farms included at random in the sample was
voluntary. Therefore only about half the cow keepers selected had
filled in their report forms. As is well known, the disregard of such
cases may bias the estimates of the sample to an unknown extent. For
this reason detailed investigations on the problem of non-response its
defined by K. Hansen and W. liurwutz were made: the population of the
respondents may be divided into two groups:
those who
completed
are readu to
report form.
In selecting
the respondents, the contingency must
respondent can be found who responds.
complete
be given
it probability measuring this contingency.
As estimate for the milli production x'
X, _ N (m xl + S
it is
ux, h2 1)n 2 -N $2 (Ic - 1) ub
S-1
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 Approved For Release 2004/02/11
Here are:
N = number of cow-keeping farms
n = number of farms selected
m = number of answers received
: CIA-RDP80-60809A000500400179-7
s - n - m = number of non-respondent
S _ total number of cow-keeping farms unwilling to answer
r number of cow keepers selected from the s cow keepers for another
requiry
it = s
r
a2 dispersion of the N cow keepers
a2 dispersion of non-respondent cow keepers
a'i = average milk production from thel m answering covy keepers
z2'-- average milk production from the r cow keepers covered in adds--
tion
The result was that the sample was not biased by non-response.
The mean square deviation of the NON-RESPONSE problem was for x',
0.8 per cent- the mean square deviation for V without taking into
account the non-responding cow keeperry, 1.0 per cent.l
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I= 9 t-d(i--lo-ks.)
K 1 M
a 1 4(.4
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 Approved For Release 2004/02/11 : CIA-RDP80-00809A000500400179-7
1 lli),;1;-1 i;1PO\~P: 1;;Q1?A'I'1O\ FOR 'I'IIE I ' V.A.SION
M1CI;t)-O1t(t:~ I '.IS
S. P1, ro
1/irrubl / /itvtl tic arc/ 1)eparhnetrl, .tiIll ?rr _i Suppl/l, 11'i/!s.
The' ProIfrut
A series of k ofosus (n, , It, , ... 11, micro-organisms) is :ulminist,ered
tom, , nl, , ... lit, test animals respellively, allot Ilse cor.?cspnnding
survivors :t re ohsct.i?ved to number r, r- .. , r, . ('I'll(! Ierms "sttr~?iv-
ul:s" artd "killed" whenever Iltev 01(11? subsequelt.ly, :trc meant. In cover
also Iha rase when( "lint: inf(cted" :u?( (ontl,lretl Willt "infected"). This
paper derites a dose-reSI)MIsc rel:tliun from n ItypoIIWSis based on the
hit( of art ion of the milro-nrganisllts against t:hcir host ti1:st suggested
by 11.A. I)ru( 11 (2).
Assuming Ilint
(i) the l'sl :initials are honu,geu(ous,
(ii) the probes )ilily of one organism killing its hurt is p (slui.ll),
(iii) the org:tttisms act, Ildep(nde111y- of CM-11 other,
then if it is the number of org:otisnts administered Io (1011 subject., the
ospe(-tetl proporl,iurt surviving is given I)y
The sl l l ist iral problem is I() (st int:,(( the single p:o?wueter p from a
scrips of observations of corresponding valves of the :tot tat proportions
surviving r In :utd the numbers oI attacking I rganisnls it. I m at inn (I)
may be Writ ten
In .' = -pn, (:la);
lot ''' I1 r`' In ' `=
"In, Ill, ' llt,.
against; It, , lt, , ? I' , 11,:urtl fit :t sIlitigltl, lily to Ill(! reso!Iittg peills, the
neg:tlive slulw of this line will represlnL p, Ill(-' prof hilit_: ol? :11IV one
orgalistn killing nk: animal.
It follow:; lhaI. (Iu);e-response r(la1 0nsltips for all kinds of organisms
and test':oiim:tls shoulti be represented b, :t single line of? 101st:o1t slope
Whell the doses ire expressed is multiples of the . For taking c
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organisms to he the eijual ion (la) I,ocOtn,s
In (1.5 = -!x
and pulling n = fc we oht:,ia
In ,ti = f In0.5 (2)
The l1ua?i7,r+rar Li/n/ihnarl ,1u/rrdia,r
Let tl,e prolrrhilit.y that one part,i(.al:u? aninu,l survives he
then the prohahilit,l` of r surviving out of in :tnint:ch :It, risk will he
/'rjrstlrt'. of lilt = I nr I/,'(I - P) = rrrrlr
and the logarithm of the likelihood is
L = -p e r, -L On, - r,) In (I - r?.. n) -1- coast..
Hence
Ills -,,,,~
I )r,~
(nr, - r,) 1 (:3)
1 ,.
- !7_ (nt; - r,)(n,p) r,.? (?I)
Suhstitnting,+r/) = a? crlnation (3) t:tlccs Ilse follott?ing form for L
0
and using the s:uuc subslit,litior' for ctpLttion (.1) the variation of 1) is
giver, by
Val. (p) = -7,1 = -- ~'
Equal inn (5) call he readily solwe,l to any (legron of acela?any with the
help of the Table A :unl tshc application of Newton's \lutlurl ol':y,pt osi-
Approved For Release j2004/02/11 : CIA-RDP80-00809A000500400179-7
 Approved For Release 2004/02/11 : CIA-RDP80-00809A000500400179-7
I
r111fion; 'I':t)11e li et;tlnates ospression (ti) iu or(ier to 01,11(11( litluci:tl
limils to /).
7'hc? gooilttess of fit (-lilt he I(:Sled a'ifh x'.:11(11 II,It(1(Ietlee filtuLS c:ut
he nssign(?tl :it am' tlesirotl i ' ) of (lase or response.
1 _ ,lilt?crirn! 1:'a nra plr
This tle11:11?I111enl (11,1:tille(I the I'ollo\)?ing titl:t (tint 1 columns of
'1'ahic I) !'runt ouc of :t series of e\perinu'rtis in which B. (ta1/11?ar?i.s spores
were alio',vt'ti to t?nlor guino:t pig., l1(? Ow Itspiratot,l' lottf.e (:3).
'1'Itr 1(o(?(:,s:u.\? steps to coot tit It '1'a.hlo I ant[ to nht,ain (he required
r?esulis :11v :is iollott:
(I) :Mier itt ing t'itIorc l I.III \?allll?s r 1(1 in the appropri;t.II! column,
11( 1? 111 is plotted against It (I;referahly on log paper) :unI :t lino
through the origin is III lid ITV y(.; :alt eslirnale /1,(().1)1!11 of the
slope p is thus ohl:tined (set fig. I ).
(2) 'I'll(, lip, v:tluts :ore vonipnlyd :11(11 ottl,ere(l in the .r-voliltnn, IeaP-
ing room for corresponding \?:Ilttes of :t second'ycle
(:3) '1':thles :\ ;11(11 li give I he following? t?:tlnes:
0 '.x92
tl '.lti 1
u883
11 X1.1
I'hc 1 :duos .r (i r ') to.(' uutlliplietl in luru l)p S, IS, 2),
25(1!1 - rcnilunn) Ihesumot Ihescprntlnetsheint)33.21-1; the l
valet's (c' - 1 ) ' ' me Ire:Heil likewise vicl(ling U 1_311'. '!'hen
the residue of etfualioit (1(1 ?ll p,) = 80 :lilt[ V:o? (p) = 0.000D05 58
at?c tiltlaino(1 as st?I out in fill- bile(- p:u?t of '1':t11is 1.
(-I) :\ BoronO approxitnatinn p, Io p is t?umpulc(I I,}? apl)l\?ing N(-\\--
toll's \lctllo(l: = 1), -I- ?I(p,) A'0.(- (p) = 0.0191.
(;) In the .r-cnlnntti the nett plt values :uv? cttt(?retl in lhrackets
(11.:3:3 ? ? . 1.0:11, loin ?f(p.I =-- -{-3 is ,?1':citwie(I using '!'able A.
(?Iear)',? no closer apprnxitn:tlintt is rwltliretl 1111(1 in fact. \"?tr (p)
need ool he rerontpul '1I.
(li) The expec?Ietl ltulnhers of' surtiVot;s are calculatotl, amt twat to
ct?:tlualt' ,y- with degrees ?it* freotlonl one less 01:111 111c. litillillm. of
doses, siltc?e one p r:lIlleler has been estimate l from ill(! (i:tl:t.
Approved For Release 2004/02/11 : CIA-RDP80-00
 Approved For Release 2004/02/11: CIA-RDP80-00809A00050040
'I ll!).K .,
s ( I
0 111 II (I.3
9 (0) 907. 0OS
1 990
n9G~
1 (ilu
1111 1 .11'20 I .(123
Will 1 03.,
o11
if Ili
i ((31
1 gar
001
rnirI 4;2
j 1977
I ((02
I (11,7
1!1:)
I
11115
Ina
109
111-I
1111 I 127,
I I 130
i 1:15
III
I 147
I
1.32
1:17
1113
1.11,
1 .171 1 Inn
I 185
.1111
190
211_
1
.2115
1 2 1:1
1.210
1 2:411 I 2:411
_-12
2'11,
231
1 _:.!1
1
1.1,
1271
2..7
1 21)2
f .255 201
I :II III
:IIIO
I :112
11115
I
I
3::11
:{:pi
1 .3 1'2
11415 I I 4.1,1
I :tl if)
1 1400
1(72
11(7S
1
3SI
(III
1 11!17
1 .111:1
1.10!1 I I3
1 121
1.125
(III
I In
1411
1 45:)
1:1!1
.?111:7
1.(72 1475
1.153
1.(Ul
I '(1)7
301
1
.511)
I .GI7
,'23
1 .530
..5:411 .i 1:1
1 19
1 3:.11
;112
1 .7,11!1
1 .G.I2
1 301)
I .11112 I 1111!)
I:IG
1 .)12
1 (1211
035
^42
1 (III)
6.5 11
1 .1112
1 .110!1 1:711
I G s3
1 600
I (1117
1 70:1
710
717
I 721
1 .7:11
7!W
747,
7.1_
75!
I 766
I 77:1
I
7,111
1 757
1 7!)1
I .1111
110'
I 11 G
122
1 030
I 437
I 011
I
5.11
1555
I Slim-1
I .87:1
1550
IS7
1001
1102
110!1
1 !110
I
92 I
1 11.11
I II:lx
I ,0Ill
:.:4
9
I !hill
11(15
1902
1 !1!111
!)07
2 ((((7,
2 0)2
2.11211
1
_ .17
2 11
2 ((Iill
1 ((37
1 (((13
!
117_
2 11.411
2 IIS8
2 (195
2 1(1:4
10
2 (15
2.120
2 XI
2 111
2
1111
2 ISO
2 IIN
_.17
2 IS))
2 S7
11)5
2 2(1:1
2 III
2 21!)
/21;
2 231
212
.-,0
21111,
7:1
2.251
2 2.4!)
_ .1!17
2
:1111
2 .1)
2 :{1:)
2 :121
2.320
2 .:137
2 1
.
:
2 :13:1
2 :1(11
. 11)11)
2
355
2I
2 19:)
2 1111
2.1(11)
_..117
,
_
1
2 I:1:i
2 112
1:111
2
ilil;
2 171
2 142
. 1!11)
2 'I!1!1
:11(7
_ :.2:t
GIS
2.3
...57:1
2GS1
2 .14!1
2 (11111
2 (111
2 (12:4
2
'Cl)
2.1
2.656
_ 67:1
2 11!111
2 (1!10
2 7(17
71:1
21
732
2711
_ . 7 1 ! 1
_ 7.-.7
71111
2 771
7S3
_
2
5101
2 II
2.5011
2 ,1, 17
2,S26
2.5:11 113
,, l
2 Min
2 009
2 5N77
2
SSG
27
2 .097,
2 !10:4
!112
_.1120 11'91
2 !1:15
2 916
!11
2
1173
2.S
1! III
1 !1!11)
11!1'1
1111; .1
,
I
G
I 022.1
:I .(II I
:1 tl-13
1.(1:31
111111
2.11
:3 111:!)
:4075
I (150
'
,
,
:1.1)!)3 .1 11)1
:) 113
;1.111
:1 1:11
:1.13 I
IS
3.0
137
4 1)01
3.17-
I . I S) :I 111:2
1 2111
:i 211
! 219
:1 225
4
2:17
3 1
)
21)
2)11
:1.27:1 8 102
2!11
.:015
30!1
:1 )I.1,
327
0!
3 11
1 141:1
3 3.11
:4:1)1:4 :1 :172
:1 ISI
:1 :1!1()
:1 :{!1!)
:4 4115
:1
117
3 3
:) 21V
13.1
1.4(3
3.-II. 1 :I Ili:)
172
:I 151
:I I!19
:1 IUU
3
:1115
1
:1 17
_1
3 ..,36
:1 811:)
3..11_
1 -S1
3 7,91
1
)1)111
.5
3
({!I
:4 1114
1 (1'27
(.)1:17 :I 11, III
:I (0 1
(17:1
:I 115:1
:1
1,92
4
: .11
7111
71)1
:1.721)
(.72!I :I 7:15
1 717
7.17
1 7 n1i
1 775
1
755
.7
a . 79.1
a 553
1 x12
I. S22 :I 5:11
SIII
:1 Still
3 SG!)
:t 1)15
:1
S70
3.S
3.1,07
3 stir
3.0116
:1!)1:i !12
(:1 1
3.91:1
:1 9-7-2
:1 !Ili'
:1
!171
3,9
3! ISI
:1 1)1)1)
:1 .11911
1.1(01) I "IS
I ((2S
.11:17
4)Ili
1 .11:111
(110
0
I .117:1
(1.1,1
1 .110:1
-1 111:1 1 112
122
4.131
.1 'II
Ii.l)
NO
I I
1(11
17!1
-1 ..S
?1 (1)0 I 247
2 111
I
.221
1 2:4:1
245
1
231
2(11
4 27:)
12x:1
1 202 I 11(2
( 4(12
:1:11
4111
II))
i .8
.14:1!1
:1,:;0
'I .375
1 300 I (1 7
07
-II)!
'I (11;
1:411
d01
1.171
i .15:1 1 I9:1
.1113
1 .531
1 .5
I
4 .:151
R(ifl
1 .87)1
4.117!1 I 'IS!)
:1!1!1
lOIS
1 (1,)5
(127
I
IV:17
1.11
'I 11)7
113))
( lillli
1.)171' I 1155
'!I
1 . 7115
171.1
72.1
7:1:1
?i 7
1
.1 .713
1 7J3
'I 7,12
4 772 1712
791
I .0111
1111
15211
I
5:111
?1..1,
'I 040
I ti ill
1
I. SOa 1 571(
1505
!15
! (1)5
!117
!(27
?I U
1.!137
4 !111
1 .0511
.I 06,; I 976 1 ! IS1
!1!15
911:1
(111
3
II
:\Lri,I ,sI (r..m ''.\ 'I',Wr nJ ,Iu I+u url i.ln rt;~.r - (I - -rl 1.0,1 iln 0(191 iru(i.1nn 1)1 I'ruLlrlun
in Cnugnnw,l hu crl?sl" Ly .1. I" Sn11nnncu, SI:uudnl:l)i~d:.(klnnriutid.dc rif 1. (11:10; by kin, I.cr u. 1090,1)
of tlu? ti ur uu l If 4,uOl in) ur.n.
Approved For Release 2004/02/11: CIA-RDP80-00809A000500409179-7
41,
 Approved For Release 2004/02/11: CIA-RDP80-00809A00051,
7?:\ 111.1: It
T21.i0%(,-r - 1)2
2 I
2 :I
2 1
2 7
2x
23)
3 I
a 2
3 ?I
:1
:1 it
7
3 1
311
4
12
I . (11(1)
( 3)11
( 1117
:{
1(. 11.,7
!1_1
!1113;
(I 5x13
41 1,70
(1 1)111
0 .:;1))
( :i)1d
;III
(.1311
1 .11)111
1 3)311
(1.1)1(1)
11 113))
(1!17!)
(3 3)7(
1 !1,?11
I1 . (:11
11.1)1!)
0 .10:1
1 1,x(1
(1 ON
11 hill
((.Oa (I (1 (1 II') 3) (In
I (110) 1 .111111 1 .(1(111 1 111111 I 1)1(0
!(11!) . (.1!111 (.19,1, 1) !(I)', II !Il's
(1.!1!1(' 111!1!11) Il !115 11 1111., 11 !I!).1
1) (1. 0.!1!11 (1 3)3)3) II 1(!111 1) !13,!1
3) 3)5.) I) 913.) (1 !Ihl 11 111:1 1, II 13
!) 107, (1 977, (I 3)7))
11 !11111 (.33)11 u.(3(17
0 II:1)1 (.157. (1.16511
11 (II) 11 1)4.5 (1 1(.1:4
Il 1111{I (1.!1311
(1!11., I 0 91)) (.115
11 !(12 0.9011 11. NI5
.K 1.-, , 0 993 ' 0.1,1
11 507 0 930)5 (1 5O:1
11.1(1 II. H IIl 0114
11 121 0.926 0 .W2.3
11 1(7 1 11.10.; ! (1.8(1:{
0.711 0.7.1,2
11 7111 11.7(12 0.71)0
741 1). 710 0 7:68
1172( (.717 1) 715
(1 6117 1 .1)11 1) 602
II 671 11 671 (I 1)1)!1
II n.,I it lilt 0 Ii!
11 1)27 j 0.13213 11.1)23
.11117 II 1)1(1 11,1)11'2 11.1)111)
11 :11) II :111 II .13731 11.:;77
1111)1)1 11 1)13') 11 5131) 0 1)0.11:18 11 i,3) 11 511.1 II
fl 11111 (1 :11 i II 512 0 .509
0.411)
I) r5
(1 1113
0 11:(
1 11.1
0 33)3
(3.374
:(.;r
Il .3:11
11 218
0.27:1
II ..;1
(1 2.I I
1 Inv
(1.892
0171
(1.113:1
1.836
(1 .511)
() 71:1
(1. 77.1
7'11
(1 .72!1
11,7111)
011)
II .1)11(1
(1 1)37
1) 111
0 5!111
1) ;I)1
3) .315
0 1323
0 1)01
( 0400179-
(107
H(o
974
853
834
I3;91.1
1) 17)2
771
. 7-19
720
0I 3 0 170 0.111 0 1 rr, 1) 4)1,11 ' 11 11,2 1) 111 111 L;, 11
II l.2 0 IIt) 117 II 11.; I) I I.t ( III 1 1:1.1 (1 137 (I
0 I I I ! I I I 1, I I . I 0 . 3 2 13 ( 121 11 121 (I 111 1 .117 1)
U III 11 11') n ill 1 .105 1 111:3 1) MI II .{1'( II 11, 0
11 113(3 ! 11 (,0) I) 311 1111{11) 11 :111 II 141)'2 II {111 II 171 11
(1.:172 11 :171 11 '111!1 II :1), II 1111:, II 11)1'1 II :1111 11 ): 10 fl
((.3Li n sat II 3130 (I all 111 317 0 :115 0 34:1 i u 812 ll
II :(3') (:1:(-1 (:00) II 33) 11 (21) 0 :4213 11 :111) 1.391 11
tl 31!) II 117 11 311 ( 311 0 all 11 31 1 11 301) j )1 317 11
(.302
0 2x1
11 971
0 .2:11
n 211
n and j n 111 u 2!11 1 tun 0 19 131 it 111 u 211 n
lA.; U 111 ( 2._ 11 2I I 11 971 (1 2,7 11 271{
0 270 2)1, 0 267 0 2r:. 1 11)1 (1 Try I, 2)11 o
25: II 91.) II 2.S1 11.251 11 24!1 )1 91, II 2111 ' 11
II 211 11 131 11 2:1, I II-2:17 II 2:1.1 II 2.1) 11 1)33 11
-I (1 2:10 II 221 II 227 to 2211 11 II 21.1 II 2 2 ' II 221 11 2211 . 11
r, 0 217 (121( 11 215 1) 21:1 ' u 217 a'1I a 2(0 (2n, (1 2117 1)
7 ' (711)3 1 ( 203 II 202 I( 2111 200 11 II)'' r (117 n I10 0 115 '
1101 0 192 n I1U a 151) ( I8, II 97 11 1 ,1) n 11:1 0 11) 0
4 1 ((.111 ( 110 0 17!1 ( 171 0 177 II 3070 a C.; (1 171 ' II 173
11
:\I,ri,lu'?'I 1)11'0, ??? , ),11x1, t ':1,),. if 111,? I:I11.,1,111 1'11111'1 i"nr" 4' .I. 11,1.1.111,1111111,1 I(. 14. I':
'1'11,?.1110)10(01 ?f l'I,y'iiI'I'1 (111.111 i+1i;4, .101111 1912b. kin,) I,,,rn,i.v.+l?Il.,f I Ia. \\ I11,,,o 1?1 01 iIl.inn ('~~011~
1.1(0111 ( ra
l !IJ-I
II 1)2,
1)7 1
111(4
!13:3
11 !111
11.91:1. ( 111
(.117 (1 1!)13
11 1711 It 171
(I 11)1 (1.951
(1 112 0 530
(1 ..1,22 11 S20
0 1111 (I 7!I!1
II 7111 II 777
0 7:11 (1 7.1:1
11 7:1., 11 7:1:4
0.71:1 1 ( 710
(.li1.II) '11 1117
I) 111)7 I) GGI
11 011 11 till
II 1,211 11 (its
11 117 (1 IS
I III III (1.11!(!1
(.(Ills (.3)1)7
I) 1!(I (7.!)101
1) !(,!I (1.!111
(1 01,2 11,().,1
1) 1)111
11 1112
)1 !(:11)
1)15
11 III))
0111)
( 971
I) .4.1
(1 STS
(I SIN
0 7!17
7713
7:1:)
II 731
11 701
3.ti )
11 11'12
11:1!1
1111)
0 :197 11 19:1 1 11 )113
I) :,7) 11 II ,711
II :i.1 11 .i 10 n :1.17
0 i 21( 11 .527 11 52:,
0 507 0 505 (113(1(
Approved For Release 2004/02/11 : CIA-RDP80-00609A0005~0400179-1
 Approved For Release 2004/02/11 : CIA-RDP80-00809A000500400179-7
(',qup!rtativu, ice: i.!:c F;cti;
r ! nr - r r'rrt
No. of
i^ 100
:utimnl.<
ni
~urviv-
ing
11i.8
:32
2-1
31 7
32
11
1;1 G
32
11
100 5
32
4
211;.1;
128
53
using equ:;fiun (5):
Prop.
Filled Pure.
observed
8
0.;5
Is 0 -14
21 0 :;I
28 0 12.5
75
- Y uln = -211;.1; X 32 = -6931
1 a 133.21-1
P._ _ 1 - r_ 0.019
ffp,) =
In;S= -0.0191;
T110,1- I.
Do=e - In Prn; nrl;on viving Ilegre'- on E1ustion--- -__-
s 1 = rT. m:S r - :n.S (r - mS) HLS(1 - ,\'1
1.111. 1 Pun'. $urvivur:
expected espeeted
0 32 10 33; 0 72 23 0
oOf; ,0r,;, 05I 11; "1
1 23 1.251 0.20 9.3
1 91 1 !i.i; 0 1-1 -1.5
1.0 0 11;
-2 3 0 (;G
?1.7 0.1-1
-0.5 0.01;
x' = 1.32
0.000361
I) = O4.i(i = 0.(0)000558 (equation fi)
7011 p,=p,-E-((p)V:u' (p) =0.019 SOXti58X10-'=0.0191
+S0
P: = p, 1.9fi 1~ lar (p) = 0.02-10
P'=a~_-1.9r~~ aI(p)=0.0148
9a1";, Ed. Lt.
!15~o Intrer 1.im: In 0.5 (-p_) In 0.5 (-p11 95 % upper l.im: In 0. ri (_I,rrl
Approved For Release 2004/02/11 : CIA-RDP80-00809A000500400179-7
 Ap
proved For Release 2004/02/11 : CIA-RDP80-00809A000500400179-7
ls:rperit ewal Verification of the II!/poIIuai.s
The extent, to vshil I, the h:tsir Iivl,otlwsis fits the experirnel(lal farts
is shown hy Ilie figures in Tithle 11 which gives the pooled values of Y'
fur several experiments oft these difforcnt micro-ort;at(isms. The indi-
vidual responses are plut.fed in figs. 2a, I,, t ; t.lte doses have teen exln essed
as multiples of the J1).0's, and the lints have the theoretic:l slope of
11 10.5. It. should he noted shut in the ease of Ii, nll!ltrncix Lhe experiments
were not rep) ic:tiles since I lte purt.icle size ul? the cluti l was made to vary
cunsiderahlly from experiment to experiment, so that individual regres-
0.9
0.8
0 20 40 60 80 100
FIG. 1.
Rulntiunp(ip brt,crrn doso ,f It. tort nom. i.. ,purr.. nod lu pngn~rWm aurt?ivinrz of uniuru pig,, h me tog
n?gra.+ai,.u tier fitted by t i e).
ApIproved For Release 2004/02/11 : CIA-RDP80-00809A000500400179-7
 Approved For Release 2004/02/11 : CIA-RDP80-00809A000500400179-7
tiion lines were obtained in widely diffcreni. positions. 7`hc S esperiment.s
on !;. /f71lloslnll, vvt'rn pirlu?tI 11, random fl?olll 56 similar ones.
T\111.1: 11. \ \H1,11 Ithi.:\?1'IuNSIIIP.~ I[ITING ()X1,. I+1X19) :.)VF.
(h~>;anism
l:rutt?11^ nuiv (I)
li. itItIh?:IUii (3)
B. Iyphusun (I)
'1'ost :\niuutls
300 Cnlinrs pigs
'.190 Guinea pigs
lull) tlicc
Roult? of
Infrctina
I{OSitl I'1I t oIT
I?I-Spi IIIorv
II I t rnperi-
toucally
No. of
Expts.
3.2
25.0
o I 2 3 4 Dose
0.9
0.8
DhI.1.
of Jr.
fig. 2a
fig. 2!
!'IC). 2n.
Pine!re ceniun lino in colt urn i?tht?, ,i,lt of!oxirariuientn w'ithlrnurlla nui.; dn.ceno fthe nub Kruupn
ure ospreantci u tuult ipli?c f of tho 1i17an of ouch in lit?idunl on!n rimeut.
Approved For Release 2004/02/11: CIA-RDP8
 F
Approved For Release 2004/02/11 : CIA-RDP80-00809A000500400179-7
L'slimation of IL'rrlalive Potency
if different strains of the same pathogenic org:ulisnt are to he com-
pared as to their virulence with respect. to it host, one close-respousc line
is tit.ted for each strain and the ratio of the slopes estimates the relative
potency. For let p, and p? he the slopes of "standard" and "nnkuoct?n"
respectively and it, and n? he doses Producing it common response S; it,
follo\w?s from equation (I a) tiutt: n,p. = n? p? or
Relative Potency R P"
~x N.
0.9
0.8
0.7
ru:. SI,.
1 i:od rogruaninn lino in rou t?inn to Chu recd, of " o:porimunta with B.., nthra-,
Approved For Release 2004/02/11 : CIA-RDP80-00809A000500400179-7
 Approved For Rel
~IIIre Var ('p) an(I Var (p.l haV( been rrtmpttted a,lre;uly I ohether Wit It p,.
:uu1 //, , fiducial iiIII it.s h, le :1 re readily assigned as
",I - I ! V:u?
Where r/ = I Var /l,!p::utcl l is Llie normZII de~~iate f(n the level of pr(tl>-
a.hilily to he used (5).
Conl/uIrisoII Iail/t /Irn1il (utnlysi.S
'I'ltis llc.Ii:u Lmm~t: I srtl to) apply the met hods of prohii ; rutlysis to
III ill thiologieitl dose-response rehttionships (Ii). When for example ani-
1 2 3 4
0.9
0.6
0.7
0.6
Vi G.
Finn l n?R n?asiu^ lieu ~u n~Lrr ion to till, rr?nu ltn nt .s rgmrim rn t, rr i(6 !f. T1,10 u.m or.
10
r Approved For Release 2004/02/11 : CIA-RDP80-00809A000500400179-7
 Approved For Release 2004/02/11 : CIA-RDP80-00809A000500400179-7
tn:tls were, exposed to p;tfhngens, it (Ingtu dose) - (prnhi( killed) regrts-
Sinn (1111a1inn has fit t,?tl well rhu resillis in must vases. If, tits h) pnl lu?.;i5
expressed in tlti.s paltry holds good, i.e. if In S = -pit (etinafinit la)
:u funlly applits, :Ill Iht? ltt'uhit. lint:, enntlitrled so i tt olighl Insho\\' a.hout
the snow Slope within experinuenfal et'rnr (Examples are quoted in I;t?I'.
2). For log,,, dose - prohil. killed t rtsfor flis an ideal dose - Ill propot-
I.iGll stn'\'i\'iIIg ill Ion slight IV hell curve (see fig. 3) and it is easily proved
that, if' I' is the 1'rohil, the Slope r/} , (i log,,, It it, the El),,,, equals 2
(vet,y noat'ly)
ru:. 3
.\n ideal t o ? , - l u pr.q~i 11-^ -, vivita , vlaI ion. Lip pleaI., I to pr,Li I: n,;aiu I lot; ,1,11' '1'Lv nl
ut Ila? I?U,, ~~pc
i,1.
V '21r 1, c S (lit ttnd lu S
r1)' I-,)
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 Approved For Release 2004/02/11 : CIA-RDP80-00809A000500400179-7
(In
rl I"g.., ,1 = 11 log, 10
Substituting it) the prodart of (A) > (I3) X (C) for 1j :i, for S = 0.5
and for p11 = -h) 1).5 gives 1.0003.
It may he concluded Thal
(i) the I wvo nunlels differ only slightly find could not lu experiment-
ally distinguished without. forbidding expenditure ill lest ani-
mals,
(ii) that, the ralrulated 1?I),,,, should he on IIc w~hole lower when
prohif; analysis is used (see fable I[1),
(iii) the present nledio l eonrpare fay otn alll}