Correlation- If two variables are so inter-related in such a manner that change in one variable brings about change in the other variable, then this type of relation of variable is known as correlation. Types of Correlation. 1.Based on the direction of change of variables a. Positive correlation b. Negative correlation 2. Based upon the number of variables studied a. Simple correlation b. Partial correlation c. Multiple correlation 3. Based upon the constancy of the ratio of change between the variables a. Linear correlation b. Non-linear correlation METHODS OF STUDYING CORRELATION 1) GRAPHIC METHODS A) SCATTER DIAGRAM B) CORRELATION GRAPH 2). ALGEBRIC METHOD A) KARL PEARSON COEFFICIENT OF CORRELATION B) RANK CORRELATION METHOD C) CONCURRENT DEVIATION METHOD Uses of Correlation. Merits of Correlation. Demerits of Correlation.

1. BIOSTATISTICS AND RESEARCH METHODOLOGY
Unit-1: CORRELATION
PRESENTED BY
Gokara Madhuri
B. Pharmacy IV Year
UNDER THE GUIDANCE OF
Gangu Sreelatha M.Pharm., (Ph.D)
Assistant Professor
CMR College of Pharmacy, Hyderabad.
email: sreelatha1801@gmail.com

2. CORRELATION
• If two variables are so inter-related in such a manner that change in one
variable brings about change in the other variable, then this type of relation of
variables is known as correlation.
• If we change the value of one variable that will make corresponding change
in the value of other variable on an average, then we can say that the two
variables are in correlation. The value of correlation coefficient will vary from
-1 to +1.
• According to Croxton and Cowden, “When the relationship is of a
quantitative nature, the appropriate statistical tool for discovering and
measuring the relationship and expressing it in brief formula is known as
correlation.”
• According to E. Davenport “It refer to that interrelation between separate
characters by which they tend to move together at least in some degree”.

3. I. TYPES OF CORRELATION
Types of correlation
Based upon the direction of
change of variables
Positive
correlation
Negative
correlation
Based upon the number of
variables studied
Simple
correlation
Partial
correlation
Multiple
correlation
Based upon the constancy of the ratio
of change between the variables
Linear
correlation
Non-linear
correlation

4. A. POSITIVE, NEGATIVE AND CORRELATION
Example:
• Example of negative correlation
X 1 2 3 4 5 6
Y 70 60 50 40 30 20
• Example of positive correlation
X 1 2 3 4 5 6
Y 10 20 30 40 50 60

5. B. SIMPLE, PARTIALAND MULTIPLE
CORRELATION
simple correlation
partial correlation
multiple correlation
• Note

6. C. LINEAR AND NON – LINEAR CORRELATION
• Example:
x 1 2 3 4 5 6
y 0.8 1.5 3.8 4.4 4.5 6
NON- LINEAR CORRELATION
• The correlation is said to be non-linear if the value in one variable does not
make a constant ratio with change in the value of other variable.
• Example: In scatter diagram, all the points does not lies in a straight line.
x 10 20 30 40 50 60
y 1 1 5 2 3 1

7. II. METHODS OF STUDYING
CORRELATION
METHODS OF
STUDYING
CORRELATION
GRAPHIC
METHODS
SCATTER
DIAGRAM
CORRELATION
GRAPH
ALGEBRAIC
METHOD
KARL PEARSON
COEFFICIENT
OF
CORRELATION
SPEARSON’S
RANK
CORRELATION
METHOD
CONCURRENT
DEVIATION
METHOD

8. a) SCATTERED DIAGRAM
• Perfect positive correlation
• Highly positive
• Positive correlation: I
• Perfect negative: I
• Highly negative

9. • Negative:
• Zero correlation
b) KARL PEARSON’S COEFFICIENT OF CORRELATION
𝑟 =
𝑋𝑌
𝑁𝜎𝑥𝜎𝑦
r =
𝑋𝑌
√ 𝑋2 𝑌2
𝑂𝑅 𝑟 =
Cov.(𝑋𝑌)
𝑆.𝐷. 𝑥 ×𝑆.𝐷.(𝑦)

10. a) DIRECT METHOD
ρ X, Y =
dxdy
dx2 × dy2
rxy =
𝑑𝑥𝑑𝑦
𝑛𝜎𝑥×𝜎𝑦
i X, Y =
dxdy − (
dx dy
n
)
dx2 −
(dx)2
n
× dy2 −
(dy)2
n

11. Working Rule
𝑟 =
𝑑𝑥𝑑𝑦
𝑑𝑥2× 𝑑𝑦2
or 𝑟 =
dxdy
𝑛𝜎𝑥×𝜎𝑦

12. • Example:
• Solution:
Weight of
tablets in
grams (x)
65 66 67 68 69 70 71
Weight of
capsules
(y)
67 68 66 69 72 72 69

13. dx= (x –
68)
dx2=(x –
68)2
y dy=(y – 68) dy2=(y-68)2 dxdy
65 -3 9 67 -2 4 6
66 -2 4 68 -1 1 2
67 -1 1 66 -3 9 3
68 0 0 69 0 0 0
69 1 1 72 3 9 3
70 2 4 72 3 9 6
71 3
𝑑𝑥 =
0
9
𝑑𝑥2 =
28
69 0
𝑑𝑦 = 0
0
𝑑𝑦2 = 32
0
𝑑𝑥𝑑𝑦 =
20

14. b) SHORT – CUT METHOD
rxy =
𝑑𝑥𝑑𝑦 −(
𝑑𝑥 𝑑𝑦
𝑛
)
𝑑𝑥2 −
( 𝑑𝑥)2
𝑛
× 𝑑𝑦2 −
( 𝑑𝑦)2
𝑛
• Working Formula:
rxy =
𝑑𝑥𝑑𝑦 −(
𝑑𝑥 𝑑𝑦
𝑛
)
𝑑𝑥2 −
( 𝑑𝑥)2
𝑛
× 𝑑𝑦2 −
( 𝑑𝑦)2
𝑛

15. Example:
Solution:
x y dx dy dx2 dy2
dxdy
1 2 -4 -12 16 144 48
3 6 -2 -8 4 64 16
4 8 -1 -6 1 36 6
5 10 0 -4 0 16 0
7 14 2 0 4 0 0
8 16 3 2 9 4 6
10 20 5 6 25 36 30
n=7 n=7
𝑑𝑥 = 3 𝑑𝑦 = 22 𝑑𝑥2 = 59 𝑑𝑦2 = 300 𝑑𝑥𝑑𝑦 = 106
X: 1 3 4 5 7 8 10
Y: 2 6 8 10 14 16 20

16. rxy =
dxdy −(
dx dy
n
)
dx2 −
( dx)2
n
× dy2 −
( dy)2
n
=
106+
66
7
59 −
9
7
× 300−
484
7
=
808
404× 1616
=
808
808
= 1

17. USES OF CORRELATION
Example:

18. MERITS AND DEMERITS OF KARL’S PEARSONS
COEFFICIENT METHOD
MERITS:
DEMERITS: