This document discusses correlation analysis techniques. It defines correlation as a statistical tool used to study the relationship between two variables. There are different types of correlation including positive, negative, simple, partial and multiple correlations. Methods for studying correlation include scatter diagrams, graphs, and calculating the correlation coefficient. The correlation coefficient quantifies the degree of correlation between -1 and 1. Significance tests can determine if a correlation coefficient is significantly different from zero.

2.  Introduction
 History
 Contents of correlation
 Correlation analysis
 Correlation and causation
 Types of correlation:
1.Positive or Negative Correlation
2.Simple, Partial or Multiple Correlation
3.Linear or Non –Linear Correlation
 Types of studying method of correlation
(I) Scatter diagram method
(II) Graphic method
(III) Correlation coefficient
 Degree of Correlation
 Significance test of correlation coefficient
 Conclusion
 Reference

3.  The “Correlation techniques’’ help in
measuring the independence and relationship
between Bivariate data ,and predict the value of
one variable for the given value of the other
variable.
 Correlation analysis is helpful in ascertaining
the strength of relationship the two variable .

4.  The correlation technique was first investigated
graphically by Sir Francis Galton .
 Karl Pearson (1857 – 1936) introduced a method of
assessing correlation by means of coefficient of
correlation.

5. CORRELATION ANALYSIS :-
 The statistical tool with the help of which the
relationship between two variable is studied, is called
Correlation.
 According to W.I. King “ Correlation means that
between two series or groups of data there exists some
casual connection”.
 Croxton and Cowden stated that “ When the
relationship is of quantitative nature , the appropriate
statistical tool for discovering and measuring the
relationship and expressing it in a brief formula is
known as correlation ”.

6. A. THE CORRELATION MAY BE DUE TO PURE CHANCE
Ex- The production of corn, availability of dairy products
,chlorophyll content and plant height .These variable
have no relationship .However ,if a relationship is
formed ,it may be only a chance or coincidence.
B . INFLUENCE OF SOME FACTORS ON TWO VARIABLES
Ex-A high degree of correlation may exist between
yield per acre in maize due to the effect on rainfall and
other factors like fertilizers and the favourable
weather conditions.

7. C.INFLUENCE OF TWO VARIABLES ON EACH OTHER OR
MUTUAL INFLUENCE
EX- Breakage of rice grains in milling and temperature of
unhusked rice, mutually interact. Both the variable effect
each other, but it is difficult to explain which is the cause
and which is the effect.
D. INFLUENCE OF ONE VARIABLE UPON THE OTHER
EX- One variable is truely independent and free from external
force and influences the other truely dependent variable. In
a correlation between rainfall and agricultural production ,
rainfall is the cause for agricultural production to grow well
and it is not the production that causes favourable rainfall.

8. POSITIVE OR
NEGATIVE
CORRELATION
SIMPLE, PARTIAL
OR MULTIPLE
CORRELATION
LINEAR OR NON-
LINEAR
CORRELATION

9. POSITIVE
CORRELATION
NEGATIVE
CORRELATION
Both variables
increase
Both variables
decrease
One variable
increases , other
decreases
One variable
decreases ,other
increases
X Y X Y X Y X Y
55 21 35 47 40
30
60 45
62 27 30 44 45
25
55 50
67 30 25
42
52
21
51 52
72 35 21
37
60
15
45 57
77 42 15 65 40 62

10. SIMPLE CORRELATION
PARTIAL CORRELATION
MULTIPLE CORRELATION

11.  Simple correlation
when study of only two variables ,the relationship is
described as simple correlation. Ex. Yield of wheat
and use of fertilizers.
 Partial correlation
The study of two variables excluding some other
variables is called partial correlation. Ex. Yield of
maize and fertilizers excluding, effect of pesticides &
manure.
 Multiple correlation
Three or more variables are studied simultaneously. Ex.
Relation between agricultural production, rainfall,
fertilizers used.

12. LINEAR
CORRELATION
NON-LINEAR
CORRELATION

13. FERTILIZERS USED (IN
K.g.) PER ACRE
WHEAT PRODUCTION
(PER ACRE)
10 10
20 20
30 30
40 40
50 50

14. 0
10
20
30
40
50
60
0 10 20 30 40 50 60
wheat production
fertilizeruses

15. FERTILIZERS USED (IN K.
g.) PER ACRE
WHEAT PRODUCTION
PER ACRE
100 10
200 20
300 30
400 40
500 50

17. Scatter
diagram
method
Graphic
method
Coefficient
of
correlation

18. S.N. PLANT
HEIGHT
(CMS.)
No. OF
FLOWER
S
S.N. PLANT
HEIGHT
(CMS)
No. OF
FLOWER
S
1 18 20 11 37 43
2 25 25 12 40 42
3 25 33 13 20 23
4 32 35 14 25 28
5 35 40 15 27 33
6 20 26 16 40 45
7 30 30 17 15 20
8 13 15 18 23 20
9 30 25 19 35 33
10 30 37 20 23 30

21. 0
20
40
60
80
100
120
0 20 40 60 80 100 120 140
Dissolvedoxygen
Temperature
Dissolved oxygen

24.  Merits
(1)Scatter diagram method is a simple device to find out the
nature of correlation between the two variables.
(2)we can have a rough idea of the correlation ,whether it is a
positive or negative.
 Demerits
we can not get the exact degree of correlation ,between the
two variables ,as it is possible only by the coefficient of
correlation.

25. Variables Jan. Mar. May. July. Sept. Nov. Jan.
Variable1 4.00 6.01 8.02 5.98 7.00 6.13 5.00
Variable2 4.11 6.89 7.00 6.65 8.00 6.00 4.21

27.  The degree of relationship can be established by
calculating a coefficient called the correlation coefficient
which always gives a quantitative measure of the degree of
closeness between the two attributes .
 Karl Pearson’s measure of correlation is based on
arithmetic mean and standard deviation .The Pearsonian
coefficient of correlation is denoted by “r” and determined
by using the following formula:
r =

28. r
then simplification of the components of the formula ;
∑ xy-∑
∑
∑
-

29. r =
DEGREE OF CORRELATION
Degree of correlation Positive Negative
Perfect correlation +1 -1
Very high degree of
correlation
+0.9 or more -0.9 or more
Sufficiently high degree
of correlation
From+0.75to+0.95 From -0.75 to -0.95
Moderate degree of
correlation
From+0.6to+0.75 From-0.6 to-0.75
Only the possibility of
correlation
From+0.3to+0.6 From-0.3 to-0.6
Possibly no correlation Less than +0.3 Less then -0.3
Absence of correlation 0 0

30. Height
(inches)
x
Weight
(pounds)
y
x2 y2 x y
65 128 4225 16384 8320
68 140 4624 19600 9520
62 120 3844 14400 7440
70 152 4900 23104 10640
65 138 4225 19044 8970
72 160 5184 25600 11520
67 135 4489 18225 9045
66 130 4356 16900 8580
68 125 4624 15625 8500
70 165 4900 27225 11550
∑=673 ∑=1393 ∑=45371 ∑=196107 ∑xy=94085

31. r =0.837
r =
r =

32.  The correlation coefficient like the mean value and the
standard deviation is a numerical character of the population,
and is estimated from a sample of the Bivariate population .
 In order to test the significance of deviation of the estimate of
correlation coefficient(r )from zero ,one may apply the ‘t’ test
with n-2 degree of freedom .The formula of ‘t’ test is as
follows:
t =
t =
t = 4.3264
Calculated value Tabulated ‘t’values Degrees of Freedom
r=0.837 t at5%=2.31 n-2=10-2=8
t =4.3264 at1%=3.36

33.  By correlation technique we can easily
estimate the degree of relationship between
two variables .It is very simple method for
studying in Bivariate calculation problem .so
the technique help in measuring the
independence or relationship between
bivariate data.

34.  FUNDAMENTALS OF BIOSTATISTICS –
Khan and Khanum - UKAAJ PUBLICATIONS
– third revised edition .

35. Presented
by;-