Page 171 - DMGT404 RESEARCH_METHODOLOGY

Unit 9: Correlation and Regression

Introduction Notes

Once best estimates are chosen, both from a statistical and epidemiologic perspective, hypotheses
about the estimated association between a single mean, proportion, or rate and a fixed value,
typically standard or goal, or about the estimated association between two or more means,
proportions, or rates can be tested.
The measures of association refer to a wide variety of coefficients that measure the strength of
the relationship that has been described in several ways. The word ‘association’ in measures of
association measures the strength of association in which there is at least one of the variables
that is dichotomous in nature, generally nominal or ordinal. The measures of association define
the strength of the linear relationship in terms of the degree of monotonicity. This degree of
monotonicity used by the measures of association is based on the counting of various types of
pairs in a relationship.

9.1 Correlation

Various experts have defined correlation in their own words and their definitions, broadly
speaking, imply that correlation is the degree of association between two or more variables.
Some important definitions of correlation are given below:
1. “If two or more quantities vary in sympathy so that movements in one tend to be
accompanied by corresponding movements in other(s) then they are said to be correlated.”
— L.R. Connor
2. “Correlation is an analysis of covariation between two or more variables.”
— A.M. Tuttle
3. “When the relationship is of a quantitative nature, the appropriate statistical tool for
discovering and measuring the relationship and expressing it in a brief formula is known
as correlation.”
— Croxton and Cowden
4. “Correlation analysis attempts to determine the ‘degree of relationship’ between variables”.
— Ya Lun Chou
Correlation Coefficient: It is a numerical measure of the degree of association between two or
more variables.

The Scope of Correlation Analysis

The existence of correlation between two (or more) variables only implies that these variables
(i) either tend to increase or decrease together or (ii) an increase (or decrease) in one is accompanied
by the corresponding decrease (or increase) in the other. The questions of the type, whether
changes in a variable are due to changes in the other, i.e., whether a cause and effect type
relationship exists between them, are not answered by the study of correlation analysis. If there
is a correlation between two variables, it may be due to any of the following situations:
1. One of the variable may be affecting the other: A correlation coefficient calculated from
the data on quantity demanded and corresponding price of tea would only reveal that the
degree of association between them is very high. It will not give us any idea about
whether price is affecting demand of tea or vice-versa. In order to know this, we need to

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