Short-cut procedure for error estimate in laboratory studies of synergism in insecticides


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Short-cut procedure for error estimate in laboratory studies of synergism in insecticides
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Wadley, F. M ( Francis Marion ), 1892-
United States -- Bureau of Entomology and Plant Quarantine
U.S. Department of Agriculture, Bureau of Entomology and Plant Quarantine ( Washington, D.C )
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aleph - 30361996
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Full Text

August 1949 E T-275

United States Department of Agriculture
Agricultural Research Administration
Bureau of Entomology and Plant Quarantine


By F. M. Wadley

A circular has been published (3) giving a short graphic method for
the study of synergism in insecticides. It involves the use of log
probability plotting paper. Work based on the procedure described has
led to various inquiries; and a supplement to this circular, carrying
evaluations further, seems desirable.

For the further steps in evaluation proposed, it is advisable to trans-
form percentages of mortality to probits, and concentrations to logarithms.
These are plotted on ordinary cross-section paper. If concentrations, of
the mixture are reduced to the equivalents in terms of the principal in-
secticide and plotted, they can quickly be compared with results for the
principal insecticide alone. Eye-fitted lines can be drawn, as in the
circular cited. The horizontal distance between these lines is a measure
of log difference of expected and actual curves (which is the logarithm of
the ratio of concentrations needed for the same effect).

An estimate of standard error of this quantity is needed for satis-
factory evaluation. Formulae for the calculation of the log ratio and its
standard error are available (1). The formulae are very complex and
require laborious calculations. However, it is found that the standard-
error formula depends on several factors, which tend to vary but little
in ordinary toxicological work. Thus a possibility exists of using a
standardized estimate for quick preliminary evaluation.

Finney's formula (Eq. 8.13, p. 127) is formidable looking; it includes
number of insects, weights, ratio of adjunct to principal toxicant, equiv-
alence, regression coefficient, average kill, and sum of squares of
deviations of log concentrations as its main factors. These factors are
almost standardized in many laboratory tests. Concentrations are often
spaced evenly on a log scale to give a series of mortalities centering
around 50 percent. Number of insects used is determined by number of
concentrations (often 3 or 4), and number of insects treated with each
concentration. Weights vary with variation of mortalities around 50


percent. Error often does not exceed the theoretical value embodied in
weights. Regression slopes are similar with toxicants of similar action.
The curves should be parallel, or nearly so, for the evaluation to have
fullest validity; and all the conditions named should hold approximately.

Basis for Error Estimates

Experiments lately discussed with Dr. J. J. Willaman (2) of the
Department of Agriculture will illustrate the point. In nine of these tests
there were usually four concentrations with about 30 insects per con-
centration for each material; mortalities centered about 50 percent, and
regression coefficients ranged from about 3 to 6. Adjuncts as a rule had
some toxicity, but not so much as the principal insecticide; ratios of
ingredients were usually 50-50. Results from all these tests were sub-
jected to the full analysis. The standard error of the log ratio varied
somewhat, partly in response to small variations in conditions named,
but averaged a little below 0.06. Trials showed that use of this value
as standard was satisfactory in drawing preliminary conclusions. The
average total number of insects per material was 118; the average
regression coefficient about 4.5. Some material cited by Finney agrees
with this error estimate fairly well, considering difference in numbers

Table 1 shows expected standard errors of log ratio under the
general conditions described, with allowance for varying numbers and
regression slopes. They are based on standard errors derived by the
Finney formula from the actual cases mentioned-

Table l.--Tentative standard errors for log ratio.

Regression Total number of insects used per material
60 12 150 200 2501 300 1000

2 0.20 0.17 0.15 0.14 0.13 0.11 0.10 0.09 0.05
3 .13 .11 .10 .09 .08 .07 .07 .06 .03
41 .09 .08 .07 .06 .06 .05 .04 .04 .02
6 .07 .06 .06 .04 .04 .04 .03 .03 .02
8 .05 .04 .03 .03 .03 .03 .03 .02 .01
10 .04 .03 .03 .03 .03 .02 .02 .02 .01


Use of Standard Errors

It should be kept in mind that the standard errors in table 1 are
approximate; also that even with exact determinations the fiducial
limits may be uneven (1). Therefore a larger allowance than usual
should be made. If an actual curve for a mixture is 3 standard errors
or more from its expected value, to the side of lower concentration,
there is strong evidence of synergism. Results showing much promise
will probably be analyzed by the more detailed process, but the above
approach will make possible quick preliminary evaluations. A graphic
estimate cf regression is satisfactory in such tests.

For tests replicated on each of several days, as is desirable in more
critical work, several courses may be followed. If the data are fairly
homogeneous, they may be put together as if they were repeated determi-
nations on the same day. The significance may be determined by con-
sistency in separate evaluations from day to day. Some intermediate
method of analysis, such as outlined in Finney's tables 27 and 28, may
be brought in. In such replicated experiments it is desirable to have
a complete set of tests on each day.

Numerical Example

Table 2.-- Dos age- mortality data with principal insecticide,!/ adjunct,
and a mixture.

Number Concentration, mg/cc Log of Percent, Probit
Material insects Insecti- Insecticidelconcen- mortal-: for
used cide Adjunctequivalent tration ity mortality

Insecticide 23 4.7 0.67 35 4.61
23 6.0 .78 78 5.77
22 7.5 .88 82 5.92
Adjunct 22 6.7 .83 27 4.39
21 10.4 1.02 83 5.95
24 11.7 1.07 71 5.55
plus Adjunct 24 2.3 .4 2.54 .40 29 4.45
24 2.8 .5 3.10 .49 46 4.90
24 3.4 .6 3.76 .57 67 5.44

1/ The principal insecticide here was nicotine, the adjunct was
phthalonitrile, the insects were larvae of the diamondback moth.


From the graphic procedure outlined in ET 223 (3), it is found that
the adjunct shows an insecticide equivalence of about 0.6. The insecti-
cide equivalent of the mixtures is then calculated; for example, the
calculation of the lowest concentration shows this equivalent as
2.30+(0.4 x 0.6), or 2.54. Logs of these equivalents are shown in the
sixth column of the table.

The values for the insecticide and for the mixture are plotted in
figure 1. The expected line for the mixture is that of the insecticide,
since it has been put in terms of the insecticide. The actual line is that
given by the logs and probits from the last three lines of the table. Eye-
fitted lines are drawn. They do not fall so much in the same range as
could be desired; but in the region of overlapping the mixture line is
about 0.22 log units to the left of its expected value. The average re-
gression coefficient estimated graphically is about 6, since the probit
goes up about 0.6 with an increase of 0.1 in the log; the number of in-
sects per material is about 70. By interpolation with these figures in
table 1, a standard error of about 0.065 is inferred. The log ratio is
about three times the standard error. The evidence for synergism is
strong. The materials used have shown evidence of synergism in several

6 /
Probit of0

4 0 Insecticide
X Mixture

0 0.20 O. 4o 0.60 0.90 1.00
Log Concentration, Insecticide Equivalent

Figure 1. Graphic estimation of synergism, from data in table 2.
(In!ectii.i e line is expected line for mixture; mixture line
giv a tuol result.)


Logarithms can be secured from many sources; any book of
mathematical tables will include them. Probit tables are also widely
available, and probits may, in fact, be read from any table of areas of
the normal frequency curves. However, for the convenience of some
workers, an abridged table of probits is appended for the range most
used (table 3).

Table 3.--Probit values for percentages of mortality. (Add values at
left and at top forpercentage.)

0 1 2 3 4 5 6 7 8 9

0 3.36 3.45 3.52 3.59 3.66
10 3.72 3.77 3.82 3.87 3.92 3.96 4.01 4.05 4.08 4.12
20 4.16 4.19 4.23 4.26 4.29 4.33 4.36 4.39 4.42 4.45
30 4.48 4.50 4.53 4.56 4.59 4.61 4.64 4.67 4.69 4.72
40 4.75 4.77 4.80 4.82 4.85 4.87 4.90 4.92 4.95 4.97
50 5.00 5.03 5.05 5.08 5.10 5.13 5.15 5.18 5.20 5.23
60 5.25 5.28 5.31 5.33 5.36 5.39 5.41 5.44 5.47 5.50
70 5.52 5.55 5.58 5.61 5.64 5.67 5.71 5.74 5.77 5.81
80 5.84 5.88 5.92 5.95 5.99 6.04 6.08 6.13 6.18 6.23
90 3.28 6.34 6.41 6.48 6.55 6.64 6.75 6.88 7.05 7.33

Literature Cited

(1) Finney, D. J.
1947. Probit analysis. 256 pp. Cambridge.

(2) Mayer, E., McGovran, E. R., Talley, F. B., and Willaman, J. J.
1949. Results of tests with a number of insecticides and adjuncts,
on several insect species] Jour. Econ. Ent. 'n press7

(3) Wadley, F. M.
1945. The evidence required to show synergistic action of insecti-
cides and a short cut in analysis. U. S Bur. Ent. and
Plant Quar. ET 223. 6 pp.



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