Two Computer Programs for Probit Analysis1
By R.
J.
DAUM,2
and W.
A statistical technique called "probit analysis" to aid in
the interpretation of dose-mortality data has become common practice, not only among entomologists but also
among other biologists conducting tests that involve dose
and response when the response is quanta!. An adequate
summarization of dose-mortality data consists of the LD60,
its confidence (fiducial) limits, and the slope of the probit
regression line or that dose which will cause 50% of the
population to respond (die) and the standard deviate of
the distribution of tolerances (reciprocal of the slope).
However, in practice, the tedious, extensive, and often
baffling calculations associated with probit analysis have
deterred many biologists from obtaining an adequate summarization of dose-mortality data. The increasing number
and availability .of electronic computers and their ability to
process routinely large volumes of calculations present the
biologist with the opportunity of obtaining a much more
adequate summary of his dose-mortality data.
KILLCREAS3
listed dose. If SENSESWITCH I is on, an intermediate output is obtained after each cycle of iteration. This output
consists of the slope, the sum of squares and cross products of the probit-response and log-dose, and the sum of
squares attributable to regression. If SENSE SWITCH 1 is
off, the intermediate output is bypassed, and no output is
obtained until the last and the next-to-Iast slope values
agree within ±0.00005 or until 30 cycles of iteration have
been completed. After convergence or 30 cycles of iteration, the computer prints the results in an analysis of
linear regression format which includes the degrees of
freedom, the sum of squares, the mean squares, and the
critical values of Fooand Chi square (all at the 5% probability level). It then prints out the number of iterations
required for convergence, the slope of the regression line,
the sum of the weighting coefficients, and the means of
the probit-response and log-dose. The next line presents
the critical value of too used in setting the confidence
limits (too = 1.96 if homogeneous; if hetergeneous, too
Student's "t" with K-2 degrees of freedom, where K is
the number of doses) ; G, the precision in estimating the
slope of the regression line or the ratio of the F values;
the sum of squares and the cross products of the log-dose
and probit-response;
and the standard error and the
standard error of the slope. If the data are homogeneous
(i.e., if the sum of squares of deviations from regression
is less than Chi square with K-2 degrees of freedom). the
standard error is set equal to 1.00; otherwise, the standard error is taken as the square root of the deviations
from the regression mean square.
=
To assist researchers who would like to use probit
analysis of dose-mortality data, the authors have written
2 programs for use on an IBM 1620 electronic computer.
The 1st fits a single log-probit regression line and is an
c.'Ctensive revision of a previous program (Daum et al.
1961) that was designed for a small memory computer
(IBM 1620 MocIel I, 20K) and has been used extensively
throughout the United States and in other countries for
over 5 years. Criticism and comments received since construction of this program were considered in making revisions and in writing the 2nd program (Potency Probit
Analysis). Both programs are written in FORTRANII language and obtain the weighted linear regression of pro bits
on log-dose by employing the maximum likelihood procedure described by Finney (1%2). This article has been
prepared in response to the many requests for and inquiries about these 2 programs.
The program then tests for significance of regression.
If the regression is not significant, the computer prints
NONSIGNIFICANTREGRESSIONand proceeds to read the
parameter card for the next set of data. A nonsignificant
regression indicates that the relationship between log-dose
and probit-response is not defined by the data. If the
regression is significant, the computer calculates and
presents the LD.o. 50. 70, and 00 and their 95% confidence
(fiducial) limits before proceeding to the next set of data.
An unlimited number of sets of data may follow the 1st
and will be processed without operator intervention.
A
completed example of probit analysis is presented in
Table 1.
PROBIT ANALYSIs.-The 1st program fits a single logprobit regression line that contains from 3-25 doses for
as many as 999,999 animals/dose.
Input consists of a
parameter card followed by 3-25 data cards. The parameter card instructs the computer ()f the number of data
cards comprising the regression line, the number of animals that were observed and that responded in the control (check), the identification numbers, and whether
individual controls are associated with each dose. The
data cards contain the identification number (two 4-digit
numbers), the dose administered, the number of animals
observed and the number that responded, and if individual
checks were used, the number of animals observed and
the number that responded in the check associated with
the listed dose.
Output consists of the identification numbers listed on
the data cards, the dose administered, the percentage of
animals responding adjusted for response in the control,
the perccntage rcsponse in the control, the number of
animals observed, and the number that responded to the
1 In cooperation with the Mississippi Agricultural
Experiment
Station.
"Entomologist. Entomology Research Division, Agr. Res.
Sen'., USDA, State College, Mississippi.
3 Programmer', Computing Center, Mississippi
State Univer·
sity, State College, Mississippi.
POTENCY PROBIT ANALYSls.-The
2nd program fits
from 2 to 10 parallel log-probit regression lines, each line
containing from 2 to 20 doses and as many as 999,999
animals/ dose. Input consists of a main parameter card
which instructs the computer in the number of log-probit
regression lines comprising the set of data and of 2-10
subsets of data each of which is preceded by a subparameter card which instructs the computer in the number of
doses comprising the probit-regression
line. The subparameter cards are identical to the parameter cards used
in fitting a single probit regression line, and the data
cards are completely compatible with either program. The
subparameter cards contain the number of animals that
were observed and that responded in the control or
whether individual controls were used with each dose.
365
Output consists of the identification numbers listed on
the cards, the doses administered, the percentage of animals that responded adj usted for the control, the [Jercent-
Table I.-Example
of computer output: fitting a single line of dose-mortality
data (SENSE SWITCH 1 off).
=====================================~--*~~.=
PROBITANALYSIS]\IAXIMUMLIKEUHOOD
DOSE
IDE
III
.050000
90
.075000
90
.100000
90
.250000
90
90
.500000
ANALYSISOFLINEARREGRESSION
SOURCEOF VARIATIONOF
TOTAL
4
REGRESSION
1
DEVREGRESSION
3
ITERATIONS
3
IDE
1
IDE
1
LD-30
LD-30
LD-70
LD-90
NETRESPONSE
54.612546
70.436066
90.103794
98.401658
99.999993
SUJ\lOFSQUARES
273.974930
259.344680
14.630250
SLOPE
3.198934
T05
3.182000
STANDARD
ERROR
2.208336
CHECK
0.000000
1.000000
2.000000
3.000000
4.000000
OBSERVED
542.
492.
464.
516.
486.
...
~--:--:-=_~--
RESPONDED
296.
348.
419.
508.
486.
MEANSQUARE
10.130000
53.179818
2.810000
259.344680
4.876750
SUMOFNW
842.758970
MEANDOSE
-1.142691
ssxx
25.343498
G
.190394
F05
FCAL
CHI SQUARE
MEANRESPONSE
5.607664
SSXY
81.072200
STDERROR
SLOPE
.438663
UPPERLlJ\UT
.042524
.056907
.081360
.181477
LD
.031872
.046488
.067807
.116945
LOWERLlMIT
.016283
.030916
.054941
.094674
age response in the control, and the number of animals
set of data. If the lines are parallel, the computer comobserved that responded to each dose. If SENSE SWITCH putes and prints the potencies (obtained by dividing the
1 is on, an intermediate output is obtained after each
LD"" of the 1st line by the LD50 of the 2nd and each succycle of iteration. This output consists of the number of ceeding line) and their 950/0 confidence limits before proiterations, the slope, the sum of squares and cross prodceeding to read the main parameter card for the next set
ucts of the log-dose and probit-response, and the sum of of data.
the weighting coefficients. If SENSE SWITCH 1 is off, the
CHECK, ZEROS, AND ONE HUNDREDs.-In both prointermediate output is bypassed, and no output is obtained
grams, automatic provision has been made to handle Oro
until the last and next-to-Iast slope values agree within
and 100% responses to a dose by substituting 0.0001 or
±0.00005, or until 40 cycles of iteration have been com0.9999, respectively, after adj ustment for the check has
pleted. After convergence or 40 cycles of iteration, the
been made in the Oth cycle of iteration. Thereafter, the
sum of squares, the cross products, and the slope of each
observed responses (P) and the percentage response corlog-probit line is printed and is immediately followed by
responding to the computed line (p) are used (see equathe pooled values for each of these sums of squares and
tions below) so that the sums of squares for deviations
the common slope.
from regression are:::; nw (P -p) '.
The computer then presents the weighted means of the
Occasionally, the e.,xperimenter has valid independent
log-dose and probit-response, the sum of the weighting
checks for each dose. Provision is made in both programs
coefficients, and the intercept for each regression line. for handling this situation, and it is initiated by punching
Then the analysis is summarized in an analysis of linear
0.9 in the parameter card in the field that is set aside for
regression format, which includes the degrees of freedom,
entering the number of animals that responded in the conthe sum of squares, the critical values of F05, and Chi
trol. The control values (numbers) for each dose are
square for parallelism and homogeneity (all at the 5ro then entered on each data card.
probability level); the computer presents the number of
\%en responses less than 0% or greater than 100% are
iterations completed, the value of t"" [= Student's "t"
obtained after adjustment for the control, the computer
with :::;(K-I) -1 degrees of freedom if heterogeneous or
continues to read the remaining data cards and to print
1.96 if homogeneous], the standard error, and the standthe adj usted responses before branching to the next set of
ard error of the slope, and finally the LD30,s. 50'S, 70'S. and
data. A negative response after adjustment for the conOO's for each line before
testing for significance of regrestrol indicates that: (1) an error was made in punch ing
sion. If the regression is not significant the computer
the data, (2) the check was overestimated, or (3) the
prints NONSIGNIFICANTREGRESSIONand proceeds to read
response to a dose was underestimated. If (2) or (3) has
the main parameter card for the next set of data. Again,
occurred, the e.,xperimenter, in consultation with a bioa nonsignificant regression indicates the relationship between the log-dose and probit-response is not defined by metrician, must decide what to do with the data. Correction for the check by use of Abbott's formula assumes
the data. If the regression is significant, the computer
that
the check is known without error.
tests for parallelism of the regression lines. If the lines
are not parallel, the computer prints LINES NOT PARALLEL
A zero response or absence of a control is also autoand proceeds to read the main parameter card of the next
matically provided for regardless of whether the control
366
aPllcars with each dose or a single control has been used
for carh line.
of critical values of to., F ••, and Chi square (5% probability level) with automatic look-up (based on the degrees of freedom which are computed from a card count).
This latter feature eliminates the need to search 3 separate tables for critical values and to enter them on the
parameter cards. If 1 or more doses or 1 or more lines
are to be deleted, only the parameter card needs to be
repunched, and only 1 number on this card needs to be
changed.
PR"crsION OF PROGRA~I.-Empirical probits are computed by using a polynomial approximation
(Hastings
1955) with 0.0001 and 0.9999 substituted for 0% and
100'70 responses, respectively, after adjustment for the
control by Abbott's formulae. The weighting coefficients
are obtained from:
NZ'
NW=
Q(P
+
Cfl-C)
COMPUTINGTIME.-Computing
time for either program
depends on the number of doses and the number of iterations required for convergence. Problems containing 0%
and 100'10 responses usually take longer (because they
require additional iterations) than those that do not. The
computing time required to fit a single line of 5 doses is
usually less than 1 min with 3-4 cycles of iteration on an
IBM 1620 Model 2 equipped with a 1443 series on-line
printer. Running time for the example (Table 1) was
12.5 sec with SENSE SWITCH Ion. Proportionally greater
computing time should be anticipated for larger problems
or for a greater number of cycles of iteration. In contrast, a person familiar with the calculations will need
from 4 to 8 hr to properly complete a probit analysis for
a single line with 5 points on a desk calculator, and then
his results will only approximate the values that can be
obtained by the computer in 4 cycles of iteration. An
estimated 24 man hours would be required with a desk
calculator to approximate the values obtained in the 2nd
example (Table 2); with the computer, the completed
analysis was obtained in 1 min, 20 sec with SENSESWITCH
Ion.
(1)
where N is the number of animals that received a particular dose, P = 1-Q is the proportion that responded, C is
the proportion that responded in the control, and
,
Z
1
= vi:;
exp
(
-
(YP;- 5)" )
(2)
where YP is the provisional probit obtained from the
weighted provisional probit regression line, that is, YP =
A
BX, where X is the logarithm of the dose that produced the predicted response, and A and B are the intercept and slope of the weighted probit regression line.
+
The 1st set of provisional probits is obtained from a
weighted linear regression of empirical probits on logdose. The Z's used in the weighting of empirical probits
are obtained by substituting empirical probits for provisional probits in (2).
From these provisional probits the 1st set of working
probits is computed as follows:
YW
=
p-P
YP
+-Z
(3)
where p is the proportion corresponding to the provisional
probit (YP) and P is the observed proportion that responded. These provisional probits are in turn regressed
on the log-dose to obtain the 2nd set of provisional
probits. This recycling (iterating)
continues until the
difference between the last and ne..'Ct-to-last slope values,
B, is less than 0.00005. The proportion p is obtained by
using a polynomial approximation where accuracy is ±
1XlO-u within the limits of 0.000,001>p<0.999,999.
The
precision of estimating a proportion corresponding to a
provisional probit is important in computing weighting
coefficients as well as working probits and thus in the
overall precision of the analysis. The precision of this
program is far superior to that obtainable by using existing tables and greatly exceeds the precision of most bioassays.
OUTSTANDINGFEATURESOF PROGRAlI1s.-The outstanding features of these programs are (I) a neatly labeled
and well-organized output that contains sufficient information to permit checking of the input data, to permit
plotting the original data and the computed dose-mortality
lines, and to allow spotting those data which cause invalidity and rejection of data if such occurs; (2) the inclusion of numerous checks which permit the analyses to
be completed only when the data are statistically valid;
(3) prucedures and checks which permit handling almost
any set of data without operator intervention;
(4) complete compatibility of parameter and data cards with
either program, which permits the fitting of individual
lines when nonparallel ism occurs without the necessity of
repunching a single card, and (5) the inclusion of tables
\'\Then the response to 3 doses falls into certain patterns
(0%, P%, P%; P%, P%, 100%; 0%, P%, 100%; 0%,
0%, P%; or P%, 100%, 100%), convergence may be
slow or may not occur at all. Then the program permits
as many as 30 cycles of iteration before attempting to
complete the remaining calculations. A response of 20%,
50%, 70% to equally spaced doses (on the logarithmetic
scale) requires only a single iteration, and occasionally
0%, 50%, 100% responses will fall into this same category
and require only 1 cycle of iteration (1st cycle is not
counted because empirical probits rather than provisional
pro bits are regressed on the log-dose). With the probit
analysis program for fitting a single dose-response line,
the number of floating point digits carried in the computer is usually sufficient so that no reduction in the
number of cycles of iteration occurs when additional
digits are used. However, with the potency probit analysis program, a reduction in the number of cycles of
iteration (computing time) may result when a large number of floating point digits are used with large sets of
data. For small problems (i.e., few lines and few doses),
a reduction in computing time will probably not occur
when an increased number of digits is used. Additional
time will be required with either program if the intermediate output is obtained after each cycle of iteration.
This intermediate output is useful in deducing the cause
of rejection of the data, especially when regression is nonsignificant, or in discovering which line or lines are not
parallel; the biologist, in consultation with the biometrician, may then decide to omit the nonparallel line or to
fit each line individually.
ApPLICATIONOF BIOASSAy,-The usefulness of a simple
bioassay is limited to the determination of the LDr.o •• and
their confidence limits. The application of a computer
program for summarization of such data is obvious. The
367
Table
2.-Example
of computer
output:
fittmg 4 parallel
lines of dose-mortality
-. -- --= .•.'--=......-:--:-=---
POTENCY PROBITANALYSIS MAXIMUM LIKELIHOOD
LINE
ID
NET RESPONSE
DOSE
3
1
.064260
22.413793
1
.073440
49.999999
3
1
.082620
3
99.999999
data.
--
CHECK
3.333333
3.333333
3.333333
OBSERVED
60.
60 .
60.
RESPONDED
15.
31.
60.
3
3
3
2
2
2
.082620
.091800
.101000
16.666666
60.344827
92.857142
0.000000
3.333333
6.666666
60.
60.
60.
10.
37 .
56.
3
3
3
3
3
3
.101900
.109800
.117600
3.333333
21.666666
48.333333
0.000000
0.000000
0.000000
60 .
60 .
60.
2.
13.
29.
3
3
3
4
4
4
.235200
.313600
.392000
3.773584
48.076923
99.999999
11.666666
13.333333
15.000000
60 .
60.
60.
9.
33.
60.
IDENT
3
3
3
3
IT
2"
3
4
5
6
7
3
3
SLOPE
26.23435
26.46940
26.48641
26.48746
26.48752
26.48753
LINE NO.
1
2
3
4
TOTAL
DOSES
3
3
3
3
LINE NO.
1
2
3
4
DOSES
3
3
3
3
SSYY
195.45051
181.38863
179.20471
179.04758
179.03798
179.03741
SSyy
61.17713
66.75816
31.55786
19.54424
179.03741
XBAR
-1.141577
-1.043086
- .950319
- .496542
ANALYSIS OF LINEAR REGRESSION
SOURCEVARIATION
DF
TOTAL
8
REGRESSION
1
DEV REGRESSION
4
PARALLELISM
3
IT
7
G
.146940
IDENT
3
3
3
3
LINE
1
2
3
4
IDENT
3
3
3
LINE
2
3
4
• SENSE SWITCH
1 turned
SSREG
49.46914
66.71966
31.35372
18.88712
166.42964
ST.OPF.
23.78048
27.70875
27.81115
30.20917
26.48753
INTERCE.PT
35.~26587
32.750389
29.578746
18.319947
SNW
63.934992
83.347917
80.314669
32.486764
7.710
52.444
9.490
2.810
165.301334
3.151940
.376105
T05
2.776000
POTENCY
1.261932
1.662559
4.424228
UPPER LIMIT
1.364538
1.828685
4.890829
LD90
.079372
.100163
.131961
.351163
LD70
.074316
.093782
.123555
.328792
LD50
.071004
.089602
.118049
.314140
---------
-
~
-._._----~-
F05
FCAL
CHI SQ
CHI SQ
SLOPE
26.487530
STDEB
3.657567
STDE
1.775370
Oth and 1st cycle of iteration
SSNW
271.13021
261.50734
260.18477
260.09046
260.08469
260.08434
MS
SS
179.037411
165.301334
12.607761
1.128315
usefulness of a more complex bioassay in which
and their ratios are obtained from parallel probit
sion lines is not so obvious, probably because the
and tedious calculations
have prevented wider use
technique.
SSXX
.08747
.08689
.04053
.02069
.23560
SSXY
2.08024
2.40789
1.12737
.62521
6.24072
YBAR
5.189027
5.121613
4.407139
5.167763
LD30
.067840
.085610
.112788
.300141
on after
SSXX
.26612
.23955
.23588
.23562
.23561
.23560
SSXY
6.98169
6.34083
6.24778
6.24115
6.24074
6.24072
SSREG
184.13357
168.94090
166.60800
166.44048
166.43026
166.42964
~
LOWERLIMIT
1.169400
1.547336
4.004691
completed.
LD.., ••
regresdifficult
of this
Potency is the ratio of equally effective doses (LD.., ••,
for example)
and is most used in the bioassay of drugs
where a chemical method is normally not available, for
example, to determine whether various batches of vitamins are equally potent. Parallel probit-regression
lines
and the determination
of potency may also be useful to
368
measure the increase in resistance
(tolerance)
to an insecticide or the degrees of resistance
in various populations of an insect species. Parallel
line assays are also
useful in describing
the susceptibility
of an insect to a
single toxicant at different stadi or the influence of such
factors as light, temperature,
and nutrition on susceptibility to an insecticide.
Potency probit analysis may also
be used to measure the loss of an insecticide residue such
as occurs in DrosoPhila mclallogaster Meigen or brine
shrimp (Lippold 1965). In this latter application,
confidence limits can be placed around the residue value.
Potency,
however,
cannot be calculated
from probit-
simplest of situations is urged to consult with a biometrician for aid in planning such experiments.
rcgn'ssion lincs which arc not parallel (c.f. Finney 1966),
nor can complex experimental designs be used with paralIcl linc assays.
Cards containing the source statement for either or
both of these programs may be obtained by writing to
Richard ]. Daum, Boll \"1 eevil Research Laboratory,
P. O. Box 5367, State College, Mississippi 39762.
The c.."\':perimentercontemplating the use of more than
1 insecticide, true replications, and other such factors in
l'Ombination, is urged to consider a factorial set of treatments with the levels of the insecticide (say LD ••, LD ••,
LD,.) as 1 factor. The same dose need not be used for
each insecticide; instead the dose producing the same response should be selected. A preliminary experiment may
he necessary to determine these doses. The percentage
reSll0nse (mortality) may then be transformed to equivalent angles to eliminate unequal variances, and the transformcd data may then be subjected to an analysis of
variance. Lack of parallelism will be suggested (but not
proved or tested) by significance of the interaction of
doses with other factors in the experiment. In such experiments, care should be taken to assure the use (treatment) of the same numbers of insects. Thus the experimentl'r contemplating dose-mortality data for any but the
REFERENCES CITED
Daum, R. J., C. Givens, and G. Bearden.
1961. Probit
Analysis. Biometrical Services, ARS, OA, Beltsville,
Maryland. (mimeo) (not available).
Finney, D. J. 1962. Probit Analysis. Cambridge Uni·
versity Press, 318 p.
1966. The meaning of bioassay. Biometrics 21 (4) :
785-98.
Hastings, Cecil, Jr. 1955. Approximation
for digital
computers. Princeton University Press, 201 p.
Lippold, P. C. 1965. Biological analysis of pesticide
residues. N. Y. State Agr. Exp. Sta. Farm Res.
31 (3) : 8-9.
A. I. B. S.-CAMPBELL AWARD FOR RESEARCH
RELATlNG TO VEGETABLE PRODUCfION
publication in a recognized scientific journal, 1tot
more than two years prior to the date of granting
the Award.
The American Institute of Biological Sciences and the
Campbell Soup Company are again sponsoring the annual
Camphl'll Award for outstanding research relating to
vegetable crop production. The following is the explanation and call for nominations for the A ward to be made
in the summer of 1967.
6. Nominations for the Award shall be by the colleagues of candidates or other appropriate persons
affiliated with established research organizations.
7. The Award Committee Chairman shall receive and
circulate manuscripts to all Committee members.
Selection of the annual winner shall be the sole
rcsponsibility of the Award Committee. Judgement
to be based on the potential or immediate importance
of the study for either economic or purely scientific
purposes.
1. The Award shall consist of a bronze medal, a cash
amount of $1,500, and travel expenses for the recipient to the annual AIBS meeting.
2. The Award is known as the AIBS-Campbell
Award
amI it will be presented at the general session of the
annual AIBS meeting. If the society to which the
recipient belongs meets with the AIBS, then both
the medal and check will be presented at the general session. If the society meets separately, then
the medal will be presented at the AIBS meeting
and the check at the meeting of the society.
8. Deadline: Nominations for the 1967 Award must be
in the hands of the Chairman of the AlBS-Campbell Award Committee, F. P. Cullinan, American
Institute of Biological Sciences, 3900 Wisconsin
Avenue, N.W., Washington, D. C. 20016, on or
before July 1. 1967.
3. The ArBS is sponsoring the Award for a period of
no less than 5 consecutive years, the first AIBSCampbell Award having been presented in August
1963.
4. The Award Committee consists of seven (7) membcrs. The AIBS selects the Chairman and each of
the following societies nominate one (1) representative to serve on the Committee:
American Phytopathological
Society
American Society for Horticultural
Science
Al11l'rican Society of Agronomy
Amcrican Society of Plant Physiologists
Entomological Society of America
Genetics Society of America
5. The basis of the Award shall be as follows: For an
outstanding single research contribution, of either
fundamental or practical significance relative to the
production of vegetable crops for processing purposes, in the fields of horticulture, genetics, soil science, plant physiology, entomology, plant pathology
or other appropriate scientific areas. Work in food
technology and food processing are /lot included;
the emphasis is on basic research and applications
thereof variously concerned with crop production
prior to crop utilization or crop processing. The
one or more papers reporting this single research to
have been published or the manuscript accepted for
NEW YORK ACADEMY OF SCIENCES
The New York Academy of Sciences will sponsor a
conference entitled, "B iological Effects of Pesticides" at
the Vhldorf Astoria Hotel in New York City on May
2-5, 1967. World authorities will be invited to discuss the
various facets of the conference. Address inquiries to the
Executive Director, the New York Academy of Sciences,
2 East 63rd Street, New York, N. Y. 10021.
INTERNATIONAL
CONGRESS OF ENTOMOLOGY
Reference to the International Congress of Entomology
in Moscow, Russia was made in the March and in the
June 1966 issues of the BULLETIN. The time was given
as August 1968. \Ve have now learned the exact dates.
These are August 23-30, 1968.
INTERNATIONAL
SCIENCE FAIR
The 18th International Science Fair will be held in San
Francisco, California on May 10-13, 1967. Each year the
Entomological Society of America presents a $100 U. S.
Savings Bond and a copy of the current issue of the
ANNUAL REVIEW OF ENTOMOLOGY
to the student who is
judged to have the best entomological exhibit. A judging
committee will be selected by the Chairman of the Society's Committee Oft Youth Activities. A visit to this Fair
is suggested to ESA members in the Bay area.
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