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1. ASSOCIATION ANALYSIS / CORRELATION
GPB 621 – PRINCIPLES OF QUANTITATIVE GENETICS
Class - 8
Dr. K. SARAVANAN
Professor
Department of Genetics and Plant Breeding
Faculty of Agriculture
Annamalai University

2. Dr. K. Saravanan, GPB, AU
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3. Dr. K. Saravanan, GPB, AU
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4. Dr. K. Saravanan, GPB, AU
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5. Dr. K. Saravanan, GPB, AU
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6. Dr. K. Saravanan, GPB, AU
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7. Dr. K. Saravanan, GPB, AU
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8. Dr. K. Saravanan, GPB, AU
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9. Dr. K. Saravanan, GPB, AU
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10. Dr. K. Saravanan, GPB, AU
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11. Dr. K. Saravanan, GPB, AU
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12. Dr. K. Saravanan, GPB, AU
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ESTIMATION OF CORRELATION COEFFICIENT – IN PLANT BREEDING
• Correlation coefficients are of three types
• Simple or total correlation
• Partial correlation
• Multiple correlations
• All the three types of correlations can be estimated form both non-replicated and
replicated data.
• But phenotypic , Genotypic and Environmental correlation can be estimated from
replicated data only

13. Dr. K. Saravanan, GPB, AU
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Simple or Total correlation
• The association between any two variables, regardless of (ignoring) the
influence of other related characters is termed as simple or total correlations
or zero order correlations.
• Calculation of simple correlation from non-replicated data requires sum of
squares of two variables and sum of products of all the observations on both
the variables.
• Where, N is the number of observations on the variable x and y.
N
y
y
N
x
x
N
y
x
xy
rxy 2
2
2
2 )
(
.
)
(
)
.
(

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

14. Dr. K. Saravanan, GPB, AU
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Simple or Total correlation - From replicated data :
• Using the variances and covariances between two traits.
• Where σp(x.y), σg(x.y) and σe(x.y) are phenotypic, genotypic and
environmental covariances respectively between the variables x and y.
• σ2
p, σ2
g, σ2
e are Phenotypic, genotypic and environmental variances
respectively.
2
2
.
)
.
(
py
px
p
p
y
x
r




Phenotypic correlation Genotypic correlation Environmental correlation
2
2
.
)
.
(
gy
gx
g
g
y
x
r

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 2
2
.
)
.
(
ey
ex
e
e
y
x
r

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


15. Dr. K. Saravanan, GPB, AU
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Test of significance
• The calculated r can be tested for its significance (i.e. whether greater
than O) by comparing it with the table value or r-table at N-2 degrees
of freedom.
• In the absence of r-table values, the test of significance is
accomplished by t-test as under
Where,
r
SE
r
t 
2
1 2



N
r
SEr

16. Dr. K. Saravanan, GPB, AU
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Partial correlation
• It is a study of relationship between one dependent variable and one
independent variable by keeping the other independent variables
constant.
• In fact, the degree of actual correlation between two characters,
eliminating the effect of third and /or fourth is the partial correlation.
• It is estimated from the estimates of simple correlation coefficients.
• Types
• First order partial correlation
• Second order partial correlation

17. Dr. K. Saravanan, GPB, AU
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First order partial correlation :
• Eliminating the effect of (keeping constant) other characters, one at a
time
• where, r12.3 is the partial correlation coefficient between the variables 1 and 2
by eliminating the effect of variable 3.
• r12, r13 and r23 are simple correlation coefficients between the respective
variables.
• where, r12.4 is the first order partial correlation coefficient between the variable
1 and 2 by eliminating the effect of variable 4.
)
1
)(
1
(
.
2
24
2
14
24
14
12
4
.
12
r
r
r
r
r
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)
1
)(
1
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.
2
23
2
13
23
13
12
3
.
12
r
r
r
r
r
r
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

18. Dr. K. Saravanan, GPB, AU
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Second order partial correlation
• By eliminating the effect of (keeping constant) other characters, the
correlation between two characters at a time is called second order
partial correlation.
where, r12.34 is the second order partial correlation coefficient between the variables 1 and 2 by
eliminating the effect of variables 3 and 4.
)
1
)(
1
(
.
2
3
.
24
2
3
.
14
3
.
24
3
.
14
3
.
12
34
.
12
r
r
r
r
r
r

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

19. Dr. K. Saravanan, GPB, AU
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Multiple Correlation
• The effect of all the independent variables is studied on a dependent
variable.
• The estimate of joint influence of two or more independent variables
on a dependent variable is called multiple correlation coefficient.
• It helps in understanding the dependence of one variable on a set of
independent variables.
• It is a non-negative estimate and it can never be negative.
• Hence, its value ranges from 0 – 1.
• Multiple correlation coefficients are calculated from the estimates of
simple correlation coefficients

20. Dr. K. Saravanan, GPB, AU
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• Multiple Correlation coefficient
Where R1.23 is the multiple correlation coefficient between the dependent
variable 1 and the independent variables 2 and 3.
2
23
23
13
12
2
13
2
12
23
.
1
1
.
.
2
r
r
r
r
r
r
R





21. Dr. K. Saravanan, GPB, AU
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Problem -1.
In an experiment, 12 cotton genotypes were evaluated in a RBD with three replications. The mean values of
number of symbodia/plant (x1), number of bolls per plant (x2), boll weight (x3) and seed cotton yield per plant
(y) were given below. Estimate phenotypic, genotypic and environmental correlation and comment on the
results.
Genotype R1 R2 R3
1 10.68 11.37 11.16
2 13.46 17.13 18.22
3 16.64 15.30 14.26
4 15.20 13.68 15.52
5 12.64 14.12 14.64
6 11.98 14.38 12.64
7 13.28 14.64 11.47
8 13.30 11.80 11.50
9 18.43 16.23 18.74
10 12.46 15.20 12.93
11 11.64 15.27 14.28
12 13.46 12.85 10.68
X1
Genotype R1 R2 R3
1 46.80 38.62 38.78
2 32.48 36.00 36.73
3 23.68 18.00 22.73
4 21.92 26.43 23.86
5 35.40 35.42 31.78
6 33.84 33.42 29.34
7 33.28 29.64 27.89
8 27.86 26.38 25.17
9 36.78 37.19 32.62
10 33.84 29.73 31.23
11 26.38 29.56 29.47
12 19.68 22.74 19.77
X2
Genotype R1 R2 R3
1 2.83 3.13 3.13
2 3.20 3.86 3.26
3 3.02 3.69 3.13
4 3.82 3.19 4.12
5 3.32 3.63 3.76
6 3.62 3.14 3.71
7 3.92 4.08 3.64
8 3.24 2.86 3.08
9 3.62 3.28 3.54
10 3.41 3.68 3.77
11 3.94 3.28 4.15
12 2.86 3.10 3.10
Genotyp
e
R1 R2 R3
1 113.86 108.53 98.40
2 62.10 71.04 69.87
3 72.37 70.21 74.68
4 49.91 54.68 57.32
5 89.46 94.28 89.26
6 89.83 85.28 87.48
7 82.78 80.85 76.43
8 73.28 68.89 68.43
9 89.28 85.46 85.45
10 96.78 101.38 102.80
11 53.86 51.38 53.61
12 57.22 55.09 51.43
X3 Y

22. Dr. K. Saravanan, GPB, AU
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• Analysis of Variance for four characters
• Analysis of Covariance for combination of characters
Source df X1 X2 X3 Y
Replication 2 1.68 10.78 0.07 5.52
Genotypes 11 10.59 114.50 0.26 986.18
Error 22 2.07 6.15 0.09 14.10
MEAN SQUARES
Source df X1 X2 X1 X3 X1Y X2X3 X2Y X3Y
Replication 2 -0.84 -0.04 -0.09 -0.79 7.60 -0.59
Genotypes 11 0.21 0.57 -18.40 0.29 248.76 -1.61
Error 22 0.45 0.09 1.69 -0.23 4.74 0.29
MEAN PRODUCTS

23. Dr. K. Saravanan, GPB, AU
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24. Dr. K. Saravanan, GPB, AU
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• Phenotypic correlation coefficient
X1 X2 X3 Y
VE 2.07 6.15 0.09 14.1
VG 2.84 36.1 0.06 324
VPH 4.91 42.3 0.15 338
X1 X2 X1 X3 X1Y X2X3 X2Y X3Y
VE 0.45 0.09 1.69 -0.23 4.74 0.29
VG -0.08 0.16 -6.7 0.17 81.3 -0.63
VPH 0.37 0.25 -5.01 -0.06 86.1 -0.34
03
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25. Dr. K. Saravanan, GPB, AU
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• Genotypic correlation coefficient
X1 X2 X3 Y
VE 2.07 6.15 0.09 14.1
VG 2.84 36.1 0.06 324
VPH 4.91 42.3 0.15 338
X1 X2 X1 X3 X1Y X2X3 X2Y X3Y
VE 0.45 0.09 1.69 -0.23 4.74 0.29
VG -0.08 0.16 -6.7 0.17 81.3 -0.63
VPH 0.37 0.25 -5.01 -0.06 86.1 -0.34
01
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r

26. Dr. K. Saravanan, GPB, AU
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• Environmental correlation coefficient
X1 X2 X3 Y
VE 2.07 6.15 0.09 14.1
VG 2.84 36.1 0.06 324
VPH 4.91 42.3 0.15 338
X1 X2 X1 X3 X1Y X2X3 X2Y X3Y
VE 0.45 0.09 1.69 -0.23 4.74 0.29
VG -0.08 0.16 -6.7 0.17 81.3 -0.63
VPH 0.37 0.25 -5.01 -0.06 86.1 -0.34
13
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27. Dr. K. Saravanan, GPB, AU
• Results
.
X1 X2 X3 Y
X1
Phenotypic Correlation 1.00 0.03 0.29 -0.12
Genotype Correlation 1.00 -0.01 0.40 -0.22
Environment Correlation 1.00 0.13 0.21 0.31
X2
Phenotypic Correlation 1.00 -0.02 0.72
Genotype Correlation 1.00 0.12 0.75
Environment Correlation 1.00 -0.31 0.51
X3
Phenotypic Correlation 1.00 -0.05
Genotype Correlation 1.00 -0.15
Environment Correlation 1.00 0.26

28. Dr. K. Saravanan, GPB, AU
Test of significant
• Correlation table N-2 df
• N=12
• r-table value 5% =0.576, 1 %=0.708
.
X1 X2 X3 Y
X1
Phenotypic Correlation 1.00 0.03 0.29 -0.12
Genotype Correlation 1.00 -0.01 0.40 -0.22
Environment Correlation 1.00 0.13 0.21 0.31
X2
Phenotypic Correlation 1.00 -0.02 0.72**
Genotype Correlation 1.00 0.12 0.75**
Environment Correlation 1.00 -0.31 0.51
X3
Phenotypic Correlation 1.00 -0.05
Genotype Correlation 1.00 -0.15
Environment Correlation 1.00 0.26
5 % level = 0.576 ≤ *
1 % level = 0.708 ≤ **

29. Dr. K. Saravanan, GPB, AU
Conclusion
• Among the component traits in both phenotypic
and genotypic level, X2 (number of bolls per plant)
alone had positively significant correlation with
seed cotton yield (Y)
• X1 (number of symbodials per plant) and X3 (boll
weight) had inter correlation among themselves.
• But X1 and X3 are negatively correlated with seed
cotton yield.
• Therefore, selection on number of bolls per plant
(X2) will be useful in increasing the seed cotton
yield per plant.
.
X1 X2 X3 Y
X1
P 1.00 0.03 0.29 -0.12
G 1.00 -0.01 0.40 -0.22
E 1.00 0.13 0.21 0.31
X2
P 1.00 -0.02 0.72**
G 1.00 0.12 0.75**
E 1.00 -0.31 0.51
X3
P 1.00 -0.05
G 1.00 -0.15
E 1.00 0.26

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37. Thank q
Dr. K. Saravanan, GPB, AU