Journal of The Association of Physicians of India ■ Vol. 65 ■ March 2017
78
Principles of Correlation Analysis
NJ Gogtay, UM Thatte
Department of Clinical Pharmacology, Seth GS Medical College & KEM Hospital, Mumbai, Maharashtra
Received: 04.12.2016; Accepted: 10.12.2016
StatiSticS for reSearcherS
Introduction
The field of medicine often
requires drawing inferences
regarding the association or
relationship between two or more
variables. In an earlier article
on “Measures of Association”
we introduced the concept of
finding associations [relationships]
between two variables that
were binary and categorical in
nature.1 Therein, we explored
several possible relationships
between these binary variables
and understood metrics such as
absolute risk, relative risk and
odds ratio.
In the present article, we discuss
how to establish a relationship
or an association between two
quantitative variables, i.e.,
variables that can be “measured”.2
As an example, we could perhaps
ask the question “Is there a
relationship between the number
of hours of work put in by a sales
representative and the actual sales
of a product?” Or “Is there a
relationship between maternal age
[measured in years] and parity
[total number of pregnancies that
a woman has carried past 20 weeks
of pregnancy]? Correlation analysis
helps answer questions such as
these.
Definition of Correlation,
its Assumptions and the
Correlation Coefficient
Correlation, also called as
correlation analysis, is a term
used to denote the association
or relationship between two (or
more) quantitative variables. This
analysis is fundamentally based on
the assumption of a straight –line
with the construction of a scatter
plot or scatter diagram [a graphical
representation of the data] with one
variable on the X-axis and the other
on the Y-axis. Let us understand
this with an example.
We had carried out a study3
earlier that evaluated whether two
modalities of the informed consent
process – the written informed
consent process, and the audio
visual [AV] recording of this (in the
same clinical trial) were different
from each other in terms of the
extent of understanding of the
study by the participant using a
pre-validated questionnaire. This
questionnaire gave a “total score”
[a quantitative measure] at the end
of administration. One of the study
objectives was to see if there was a
relationship between the time (in
minutes) taken to administer the
consent in the two groups [again
a quantitative measure] and the
total score. Table 1 gives data on
individual participants in both
groups for time taken to consent
[measured in minutes] and the total
[linear] relationship between the
quantitative variables. Similar to
the measures of association for
binary variables, it measures the
“strength” or the “extent” of an
association between the variables
and also its direction.
The end result of a correlation
analysis is a Correlation coefficient
whose values range from -1 to
+1. A correlation coefficient of +1
indicates that the two variables
are perfectly related in a positive
[linear] manner, a correlation
coefficient of -1 indicates that two
variables are perfectly related
in a negative [linear] manner,
while a correlation coefficient
of zero indicates that there is no
linear relationship between the two
variables being studied. These are
depicted in Figures 1 and 2.
Eyeballing and Analyzing
the Data for Correlation -
Construction of the Scatter
Plot/Scatter Diagram
A correlation analysis begins
Fig. 1: Scatter Plot showing Correlation between two variables. Note: Fig. 1a
shows a weak positive correlation, Fig. 1b shows no correlation and Fig.
1c shows a weak negative correlation
(1a) (1b) (1c)
r = 0.4
Positive Correlation No correlation Negative
r = -0.4
r = 0
