This documents entails a detailed comparison of Pearson's and Spearman's correlation. It also explains different tests for normality. How to analyze and discuss scatterplots is explained.
Correlation is the degree to which two variables are linearly related. This is used for
bi-variate data analysis. A correlation is any statistical relationship between two
random variables. Correlation doesn’t imply causation.
Example: The consumption of ice-cream increased during the summer months.
There is a strong correlation. Here, we see there is a casual relationship between
extreme summer conditions and the sale of ice creams.
Example: Ice-cream sales also have a strong correlation with shark attacks. Now, it’s
very clear that shark attacks are definitely not caused due to ice-cream. So there is
no causation here.
Correlation coefficient is the statistical measure of the strength of the relationship
between two variables. The values range between -1.0 and 1.0. A correlation of -1.0
shows a perfect negative correlation, while a correlation of 1.0 shows a perfect
positive correlation. A correlation of 0.0 shows no linear relationship between two
variables.
Pearson Correlation Coefficient – Measures linear correlation between two
variables (a relationship is linear only when a change in one variable is
associated with a proportional change in the other variable)
, Below is an example of how the Pearson correlation coefficient (r) varies with
the strength and the direction of the relationship between the two
variables. Note that when no linear relationship could be established (refer to
graphs in the third column), the Pearson coefficient yields a value of zero.
Spearman’s Coefficient Correlation - is a nonparametric measure of rank
correlation (statistical dependence between the rankings of two variables). It
assesses how well the relationship between two variables can be described
using a monotonic function. The Spearman correlation can evaluate a
monotonic relationship between two variables — Continuous or Ordinal and it
is based on the ranked values for each variable rather than the raw data.
A monotonic relationship is a relationship that does one of the following:
(1) as the value of one variable increases, so does the value of the other variable,
OR,
(2) as the value of one variable increases, the other variable value decreases.
BUT, not exactly at a constant rate whereas in a linear relationship the rate of
increase/decrease is constant.
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