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→Mathematical definition: ''This section goes beyond high school math and can be skipped by most readers.''
'''Correlation''' refers to how a characteristic is common to a group, as in the '''correlation''' between hard work and success. The correlation is usually not 100%, as a few people may succeed without hard work, and a few people may fail with hard work. But there is a correlation if typically hard work does result in success, and without hard work there is often a lack of success.
'''Correlation''' refers to how a characteristic is common to a group, as in the '''correlation''' between hard work and success. The correlation is usually not 100%, as a few people may succeed without hard work, and a few people may fail with hard work. But there is a correlation if typically hard work does result in success, and without hard work there is often a lack of success.
== Mathematical definition ==
== Formal definition ==
''This section goes beyond high school math and can be skipped by most readers.''
The '''correlation coefficient''', also known as '''Pearson's r''', is a statistical measure of association between two ratio variables. It is defined as:
The '''correlation coefficient''', also known as '''Pearson's r''', is a statistical measure of association between two ratio variables. It is defined as:
It is important to note that the correlation coefficient should not be calculated when either of the variables are non-ratio. That is, when they do not vary continuously and have a meaningful zero. As such, correlating a dichotomous variable (e.g. sex) with a ratio variable (e.g. IQ) is inappropriate and will return uninterpretable results.
It is important to note that the correlation coefficient should not be calculated when either of the variables are non-ratio. That is, when they do not vary continuously and have a meaningful zero. As such, correlating a dichotomous variable (e.g. sex) with a ratio variable (e.g. IQ) is inappropriate and will return uninterpretable results.
Additionally, correlation estimates a linear relationship between X and Y. Thus, an increase in variable X is assumed to exert the same influence on Y across all values of X and Y.
Additionally, correlation estimates a linear relationship between X and Y. Thus, an increase in variable X is assumed to exert the same influence on Y across all values of X and Y.
==Correlation and Causation==
==Correlation and Causation==