probit analysis in estimation of LC50

3. INTRODUCTION
HISTORY
APPLICATIONS
DETERMINATION OF LC50 0
CASE STUDY
CONCLUSION
REFERENCES

4. Probit Analysis is a specialized regression model of
binomial response variables.
Remember that regression is a method of fitting a line to
the data to compare the relationship of the response variable
(Y) to the independent variable (X).
Y = a + b X + e
Where ,
a = intercept
b = the slope of the line
e = error term

5. Binomial response variable refers to a
response variable with only two outcomes.
For example:
• Flipping a coin: Heads or tails
• Testing beauty products: Rash/no rash
• The effectiveness or toxicity of pesticides:
Death/no death.

6. Probit analysis can be conducted by one
of three techniques:
• Using tables to estimate the probits and
fitting the relationship by eye,
• Hand calculating the probits, regression
coefficient, and confidence intervals,
• Using statistical packages such as
SPSS,SAS, etc..

7. The idea of probit analysis was
originally published in Science by
Chester Ittner Bliss in 1934. He worked as an
entomologist for the Connecticut agricultural
experiment station and was primarily concerned
with finding an effective pesticide to control insects
that feed on grape leaves (Greenberg 1980).
By plotting the response of the insects to
various concentrations of pesticides, he could
visually see that each pesticide affected the insects
at different concentrations, i.e. one was more
effective than the other. However, he didn’t have a
statistically sound method to compare this
difference

8. • The most logical approach would be to fit a
regression of the response versus the
concentration, or dose and compare between
the different pesticides. Yet, the relationship
of response to dose was sigmoid in nature and
at the time regression was only used on linear
data.
• Therefore, Bliss developed the idea of
transforming the sigmoid dose-response curve
to a straight line.

9. • In 1952, a professor of statistics at the
University of Edinburgh by the name of David
Finney took Bliss’ idea and wrote a book
called Probit Analysis (Finney 1952).
• Today, probit analysis is still the preferred
statistical method in understanding dose-
response relationships.

10. • Probit analysis is used to analyze many kinds of dose-
response or binomial response experiments in a variety of
fields.
• Probit Analysis is commonly used in toxicology to
determine the relative toxicity of chemicals to living
organisms.
• Probit analysis acts as a transformation from sigmoid to
linear and then runs a regression on the relationship.
• Once a regression is run, the researcher can use the output
of the probit analysis to compare the amount of chemical
required to create the same response in each of the various
chemicals. There are many endpoints used to compare the
differing toxicities of chemicals, but the LC 50 (liquids) or
LD 50 (solids) are the most widely used outcomes of the
modern dose-response experiments.

11. Bioassay is the combination of two words:
Bios-life : Assay-determination.
It is defined as estimation or determination
of concentration or potency of a physical,
chemical or biological substance (agent)
by means of measuring and comparing the
magnitude of the response of the test with that of
standard over a suitable biological system under
standard set of conditions.

12. Bioassay stands for determination of
relative toxicity of insecticides by studying and
examining their effects on living organisms.
In broad sense, the term “bioassay” or
“biological assay” refers to the procedures for
the determination of relation between a
physiologically active agent and the effect
which it produces in the living organism.

13. In bio-analysis the response produced by the
test compound is compared with that of standard
sample the way similar to other analytical methods
but here the biological system is involved in the
determination.
In the usual experiments, the magnitude of
effects of different treatments are compared
whereas in bio-assays the potencies of treatments
are compared.

14. Principle of bioassay
The bioassay compares the test sample with a
same Internationally applicable standard
substance. It determines the quantity of test
sample required to produce an equivalent
biological response to that of standard substance.
In the field of agriculture, practically all
chemical programmes involving response of an
organism to a chemical fall in the realm of bio-
assay.

15. Bioassay in the field of agriculture
In Entomology
In the determination of potency of new
chemicals.
To measure the level of resistance to insecticides
in chemicals.
Bio-assay may be used in place of chemical
methods or supplement chemical methods in
analysing insecticides.
It is a simple and easily adopted technique to the
assay of new insecticides.

16. • The bioassay involves a stimulus applied to a
subject and the response of the subject to the
stimulus.
• The stimulus may be a pesticide, a fungicide, a
vitamin. The intensity of the stimulus may be
varied so as to vary the dose given to the
subject. The dose can be measured as a
weight, a volume or a concentration.
• The subject may be an insect, a plant, a
bacterial culture.
Concept of bioassay

17. Conti…
.• When a stimulus is applied to a subject there
may be a change in some characteristics of the
subject. For example, weight of the whole
subject or of some particular organ may
change, an analytical value may change or the
subjects may die. Such changes in the subject
are known as responses.
• Response may be quantitative as in the case
of weight or qualitative as in the case of
mortality.

18. Types of bio-assay
Direct assay
Indirect assays based upon quantitative
responses
Indirect assays based upon quantal
responses.

19. –The assays in which the responses are
qualitative are called as quantal response
assays.
• In most of the biological assays, the responses are
qualitative in nature.
• For example, in the assay of insecticides the
response is mortality of insects.
• Quantal response assays are closely related to direct
assays.

20. • In quantal response assay, the strength of a
preparation is characterized by the median
tolerance or the dose that induces 50%
responses.
• If the response is mortality it is called median
lethal dose and is denoted by LD 50.
• If the response is not mortality, it may be
called median effective dose (ED 50), median
knock down dose (KD 50), median anti-feeding
dose ( AD 50) and etc…
• Most commonly used measurement is LD 50.

21. • Here the dose levels are chosen first.
• The dose levels should range between a
lowest range, to which virtually no subjects
will respond, and a highest dose, to which
virtually all subjects will respond.
• The proportion of subjects responding to each
dose is observed.
• The LD 50 is then determined by using
appropriate methods.

22. • LD 50 - This value represents the lethal dose of the
poison per unit weight which will kill 50 per cent
population of test animals or organisms. It is
expressed as milligrams per kilogram of body
weight.
• LC 50 - The lethal concentration of toxic compound
mixed in external medium i.e. water that kills half
of the population of test animals is used.
• Toxicity – Ability of a chemical to bring about
changes in the biological system of the target
organism.

23. Methods of finding LD50
• Dragstedet-Behren’s method
• Spearman-karber method
• Probit analysis

24. • The most common way of estimation of LD50
is from the regression line relating the log-
dose to a transformed percentage response.
• There are many transformations, in those
probit transformation is one of the most
common method.

25. • Probit is the short form of probability + unit.
• The probability is the value of the normal
equivalent deviation. Since it (Z) may be
positive or negative , a constant or unity is
added to make it positive. The constant is
taken as 5.

26. How to calculate LC50 using probit
analysis??

27. Procedure
• Before proceeding to estimate LC50, it has to be
seen whether natural mortality is anticipated.
when natural mortality is anticipated, the
mortality rates should be corrected using Abbot’s
formula. It is given by
• corrected mortality, P* = p – c
1-c
Where, p= proportion of mortality for a given dose,
c= proportion of mortality for a zero dose( natural
mortality).

28. • In the process of estimating the LD50, we use
empirical probits, expected probits and
working probits.
• The empirical probits are read directly from
the tables.
• Using the relation between log-dose and
empirical probits, the expected probits are
obtained.
• Using the expected probits and mortality rates
the working probits are determined.

29. 1. Complete the column upto 5.
• Column 1- Dose(D)
• Column 2- no. of insects(n)
• Column 3- no.of insects killed(r)
• Column 4- log(10D) (x)
• Column 5- proportion killed(p)
2. Obtain the empirical probits(ye) corresponding to p
values. Enter them in column 6.
Steps

30. Source ; manual for testing insecticides on rice

31. 3. Fit a regression line using empirical probits
and log-dose. From this line estimate the
expected probits(Yp). Enter these Yp in column 7.
Here we will have a regression equation like
Yp = a + bx
4. For each Yp value , find out the weighting
coefficients ,w. The values of w can be obtained
from the tables.
5. Multiply each w by the corresponding n to get
nw. enter nw values in column 9.

32. Table
Dose No. of
insects
No.of
insects
killed
Log(10D) Proportion
killed
Empirical
probits
Expected
probits
D n r x p ye yp
Weighing
coefficients
nw Working
probits
Estimated
probits
w nw y 𝑦

33. Source ; manual for testing insecticides on rice

34. 6. For each p and Yp determine the working
probits (y) as explained below,
y = y0 + pA
Where, y0 = minimum working probit,
p = proportion of mortality
A = range
When p is close to 1,
y = y1 - qA
where, y1 = maximum working probit
q = 1-p
And these y values are entered in column10.

35. Source ; manual for testing insecticides on rice

36. 7. Enter in column 12 to 16 the product of
computed values from respective columns as
indicated below
Column 12- nwx
Column 13-nwy
Column 14 nwx 2
Column 15- nwxy
Column 16-nwy 2
And find the summations of these columns.

37. ) )((

40. • Step 13 : Using Feller’s theorem compute the
confidence limits for m.
mL, mU= 𝑚 + (
𝑔
1−𝑔
)(𝑚 − 𝑥
_
) ± tSE(m)
Where
𝑔 =
𝑡2.𝑉(𝑏)
𝑏²
SE(m)=
1
𝑏(1−𝑔)
√ 1 − 𝑔 𝑉( 𝑦
−
) + (𝑚 − 𝑥
−
)2
𝑉(𝑏)
𝑉( 𝑦
_
) =
1
∑𝑛𝑤
𝑉(𝑏)=
1
𝑆𝑆(𝑥)

41. 14.In original units ,
LD50=
𝑎𝑛𝑡𝑖𝑙𝑜𝑔(𝑚)
10
lower limit =
𝑎𝑛𝑡𝑖𝑙𝑜𝑔(𝑚𝐿)
10
Upper limit=
𝑎𝑛𝑡𝑖𝑙𝑜𝑔(𝑚𝑈)
10

42. Calculation of LD50 through SPSS
42

43. •Probit Analysis is a type of regression used with
binomial response variables. It is very similar to logit, but
is preferred when data are normally distributed.
•Most common outcome of a dose-response experiment
in which probit analysis is used is the LC50/LD50.
•Probit analysis can be done by eye, through hand
calculations, or by using a statistical program.

44. Case study - 1
TOXICITY OF INSECTICIDES AGAINST Sitophilus zeamais and
Sitophilus oryzae
B.S. Srinivasacharayulu and T.D.Yadav

45. • Location – IARI farm
• Insecticides like deltamethrin, etrimofos,
chlorpyriphos-methtyl, fluvalinite and malathion
were tested against the adults of the s. zeamais
and s. oryzae.
• S. zeamais- maize
• S. oryzae- wheat
• The mortality was observed and moribund insects
were also counted as dead.
• The percent mortality was calculated and data
was subjected to probit analysis to workout LC50
and LC95 values.

46. Results

47. Toxicity of insecticides against S.zeamais and S. oryzae
Insecticide Heteroge
neity*
Regression
equation
LC50 LC95 Standard
error
Fiducial limits
LC50
S.zeamais
Deltamethrin 4.614 Y=2.32X+2.13 0.1738 0.8877 0.0548 0.1375-0.2225
Fluvalinate 6.588 Y=2.73X+1.15 2.5719 10.3431 0.0405 2.1409-3.0859
Chlorypriphos
methyl
2.934 Y=2.50X+1.50 2.5119 11.4815 0.0412 2.0857-3.0252
Etrimfos 3.604 Y=2.34X+1.74 0.2473 1.2540 0.0436 0.2016-3.0252
Malathion 4.814 Y=1.74X+2.28 3.6578 32.4709 0.0574 2.8022-4.7044
S.oryzae
Deltamethrin 3.9767 Y=2.49X+1.54 0.2452 1.1277 0.0412 0.2038-0.2989
Fluvalinate 2.4180 Y=2.89X+0.44 3.7832 14.0860 0.0374 3.2114-4.5009
Chlorypriphos
methyl
2.5250 Y=2.44X+1.84 1.9728 9.3608 0.0490 1.5631-2.4324
Etrimfos 2.2864 Y=3.93X-1.19 0.3759 0.9884 0.0265 0.3374-0.4285
Malathion 1.3280 Y=2.37X+1.50 3.0199 14.8935 0.0424 2.4940-3.6568
*= significant at 0.05percent
Y=probit kill
X =log( concentration*100)

48. The lowest LC50 value of 0.1738 ppm was obtained against
s.zeamais with deltamethrin.
At LC95 level deltamethrin remained most toxic followed by
etimfos, fluvalinite, chlorpyriphos-methtyl, and malathion.
In case of S.oryzae, deltamethrin proved most toxic with
LC50 value of 0.2452 ppm.
But at LC95 value, etrimofos was found most toxic with the
value of 0.9884 ppm followed by deltamethrin(1.1277ppm).

49. Case study - 2
BIOEFFICACY AND PERSISTANCE OF INSECTICIDES
AGAINST Sitophilus oryzae(L.), Callosobruches chinensis(L.), and C.
maculatus(F.) ON WHEAT AND COWPEA.
RAJANI B. RAJPUT

50. • Objective – to evaluate bioefficacy of insecticides
against sitophilus oryzae(l.), callosobruches
chinensis(l.), and c. maculatus(f.) on wheat and
cowpea.
• Location – laboratory, Dept. of Agricultural
Entomolgy, UAS.Dharwad.
• Insecicides used – cypermethrin, deltamethrin,
fenvelerate, dichlovaras, malathion and spinosad.
• Concentrations = 5 + 1
• The mortality was observed and moribund insects
were also counted as dead.
• The percent mortality was calculated and data was
subjected to probit analysis to workout LC50 and
LC95 values.

51. Results

52. Toxicity of insecticides on mortality of insects
Insecticide
Regression
equation
Chi
square LC50
Fiducial limits
LC90
Fiducial limits
LL UL LL UL
S. oryzae
Fluvalinate Y=0.04X-0.30 0.63 29.52 13.40 51.07 181.77 123.83 643.21
Malathion Y=0.03X-0.26 0.39 12.64 8.97 28.12 83.87 62.36 187.09
Deltamethrin Y=1.21X-0.68 0.40 0.66 0.35 1.11 1.61 1.20 2.69
Spinosad Y=1.55X-0.004 0.46 0.08 0.77 0.36 0.83 0.77 1.62
Cypermethrin Y=0.10X-0.18 1.89 3.10 1.53 7.54 24.92 18.35 57.97
Dichlorvos Y=0.02X-0.23 0.30 13.60 8.80 30.53 97.34 72.32 212.70
C.chinensis
Fluvalinate Y=0.017X-0.27 0.32 23.87 7.57 36.64 154.03 109.62 403.20
Malathion Y=0.03X-0.73 0.76 23.13 3.94 34.29 82.20 63.38 149.72
Deltamethrin Y=1.04X-0.59 1.23 0.96 0.18 1.16 1.79 1.38 2.90
Spinosad Y=1.60X-1.00 0.26 0.24 0.20 0.49 0.96 0.70 1.62
Cypermethrin Y=0.11X-0.46 1.16 5.25 4.65 8.18 24.80 18.91 46.57
Dichlorvos Y=0.03X-0.60 1.63 23.67 16.28 43.86 95.80 73.65 172.86
*= significant at 0.05percent
Y=probit kill
X =logconcentration

53. Insecticide
Regression
equation
Chi
square LC50
Fiducial limits
LC90
Fiducial limits
LL UL LL UL
C.maculatus
Fluvalinate Y=0.03X-0.58 0.54 20.74 13.22 33.08 84.93 64.91 160.9
8
Malathion Y=0.03X-0.91 1.11 34.33 14.66 45.90 120.25 85.09 382.0
6
Deltamethrin Y=1.26X-0.83 0.58 0.76 0.32 1.15 1.67 1.31 2.66
Spinosad Y=1.02X+0.22 0.80 0.05 0.01 0.33 1.04 0.67 2.18
Cypermethrin Y=0.10X-0.15 1.08 2.64 16.95 55.85 23.07 16.95 55.85
Dichlorvos Y=0.01X+0.03 1.00 4.96 1.37 29.03 107.00 84.62 170.4
5
*= significant at 0.05percent
Y=probit kill
X =logconcentration

54. The lowest LC50 value of 0.08 ppm was obtained against S.oryzae with
spinosad. Hence spinosad was found to be more toxic against S.oryzae.
In case of C.maculatus , spinosad proved to be most toxic with LC50
value of 0.05 ppm followed by deltamethrin.
In case of C.chinensis , spinosad proved most toxic with LC50 value of
0.2452 ppm.
Even at LC90 value for all insects, spinosad remains more toxic than all
other insecticides.

55. Case study - 3
RELATIVE TOXICITY OF PYRETHROID AND NON PYRETHROID
INSECTICIDES TO THE ADULTS OF GREY WEEVIL, MYLLOCERUS
UNDECIMPUSTULATUS MACULOSUS
D.S .SINGH and J.P.SINGH

56. • Location –Division of Entomology, IARI,New
Delhi.
• Insecicides used –labdacyhothrin, cypermethrin,
bifenthrin, decamethrin, fenvalerate, fluvalinate,
malathion, endosulfan.
• The mortality was observed and moribund insects
were also counted as dead.
• The percent mortality was calculated and data
was subjected to probit analysis to workout LC50
and LC95 values.

57. Results

58. Table.1.Toxicity of insecticides against adults of Grey Weevil
Insecticide Heterogen
eity*
Regression
equation
LC50 SEm Fiducial limits
labdacyhothrin 3=2.407 Y=2.625x-4.460 0.004018 0.0538 0.003159-
0.005122
cypermethrin 4=3.149 Y=1.868x-1.914 0.005023 0.0640 0.003763-
0.006705
bifenthrin 4=0.708 Y=2.783x-5.830 0.007780 0.0458 0.006327-
0.009568
decamethrin 4=6.978 Y=1.845x-2.292 0.008954 0.0574 0.006910-
0.011620
fenvalerate 3=1.732 Y=2.144x-4.591 0.029720 0.0583 0.022840-
0.038670
fluvalinate 3=1.796 Y=2.338x-6.050 0.053210 0.0510 0.042280-
0.066970
malathion 3=0.052 Y=1.884x-5.224 0.273500 0.0656 0.203400-
0.367800
endosulfan 4=2.546 Y=2.496x-9.878 0.914100 0.0412 0.759100-
1.104000

59. →RR
RS↓
Lambdacy
halotrin
cypermet
hrin
bifinthrin decamethrin fenvalerate fluvalinate
Lambdacyhal
otrin
1.00 1.25 1.94 2.23 7.40 13.24
cypermethrin 0.80 1.00 1.55 1.78 5.92 10.59
bifinthrin 0.52 0.64 1.00 1.15 3.82 6.84
decamethrin 0.45 0.56 0.87 1.00 3.22 5.94
Fenvalerate 0.13 0.17 0.26 0.30 1.00 1.79
Fluvalinate 0.07 0.09 0.15 0.17 0.56 1.00
Table.2.Relative susceptibility*and Relative resistance of myllocerus
undecimpustulatus maculosus to pyrethroids.

60. On the basis of LC50 value ( table 1) , lambdacyhalothrin was found to
be more toxic than all other insecticides.
Using table 2.Cypermethrin, bifenthrin, decamethrin, fenvalerate and
fluvalinite were 0.80, 0.52, 0.45, 0.13 and 0.07 times less toxic than
lambdacyhalothrin.
Similarly Cypermethrin, bifenthrin, decamethrin, fenvalerate and
fluvalinite were 1.25, 1.94, 2.33, 7.40, and 13.24 times respectvely
more tolerant than lambdachyhalothrin.

61. References
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Pickin,S., 1981, Manual For Testing Insecticides On Rice. International Rice
Research Institute., Philippines.
Lalmohan Bhar, Probit Analysis. Indian Agricultural Statistics Research Institute, New
Delhi.
Rajani B rajput.,2010, Bioefficacy and Persistence of Insecticides against Sitophilus
oryzae, Callosobruchus chinensis and C.maculatus on wheat and
cowpea.M.Sc(agri) Thesis,Univ.Agril.Sci.,Dharwad.
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insecticides to the adults of Grey Weevil, Myllocerus undecimpustulatus
maculosus. Indian J. Ent., 59(4) :354-358.

62. Srinivascharyulu, B.S. and Yadav,T.D.,1997,Toxicity of insecticides against Sitophilus
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