Definition
A coefficient of
correlation is a single number that tells us to what extent two things are
related, to what extent variation in one go with variations in the other.
The
coefficient of correlation is the ratio which expresses the extent to which changes
in one variable are accompanied by-or dependent upon-changes in second variable.
Introduction
The association or
relationship between two variables or phenomena. Simple correlation means linear
correlation between two variables. It explains how one thing varies with
another. It’s a single number that paints a picture of relationship between
variables. It explains a kind of interdependency among variables. Correlation
attempts to draw a line of best fit through the data of two variables, and the
value of the Pearson correlation coefficient, r, indicates how far away all these
data points are to this line of best fit. Also known as bivariate correlation.
Most Common Types of Correlation
(i) Pearson Product-Moment Method (r)
(ii) Spearman Rank Difference Method (ρ)
(i) Pearson Product-Moment Method (r) - The Pearson's correlation coefficient
(r) is the covariance (the covariance is
defined as the expected value (or mean) of the product of their deviations from
their individual expected values) of the two variables divided by the product
of their standard deviations. Also known as product-moment method and used for
data that meets the assumptions of normal distribution (Parametric statistics
tool).
The Pearson’s
correlation coefficient (r) is used to determine the strength and the direction
of the relationship between X and Y variables. The variable should have
measured at interval level.
Where, 𝒓_𝒙𝒚 = Correlation between X and Y X
= X score
Y
= Y scores
𝑵 = Sample size
(ii) Spearman Rank Difference Method (ρ)
The Spearman Rank
Difference correlation is non-parametric statistical tool used where data is
measured in ordinal form and does not meet the assumptions of normal
distribution.
Salient Features
of Correlation
(i) It is the important tool of scientific prediction.
(ii) It explains causal relationships.
(iii) It varies from -1 to 1.
(iv) Correlation [Coefficient] is a directional
(Positive or Negative) index.
(v) It can be linear as well as curvilinear.
Some Traditions
1. For to compute correlation coefficient the cases should not be
less than 25.
2. Broad and tentative classification of coefficient of
correlation.
|
Values
of r |
Interpretation |
|
.00
to ± .20 |
Indifferent
or Negligible Correlation |
|
± .20 to ± .40 |
Low Correlation |
|
±
.40 to ± .70 |
Substantial
or marked Correlation |
|
± .70 to ± 1.00 |
High or Very High |
Context for Decision Making in
Regard to Coefficient of Correlation
(i) The nature of selected variables.
(ii) The significance of the coefficient.
(iii) The variability of the group.
(iv) The reliability coefficient of the tests used.
(v) The purpose for which r is computed.
References:
1. https://stattrek.com/probability-distributions/poisson.aspx.
2. https://www.itl.nist.gov/div898/handbook/eda/section3/eda366j.htm
3. https://brilliant.org/wiki/poisson-distribution/
4. https://www.statisticshowto.com/poisson-distribution/
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