Summary of Correlation

• To measure the strength of relationship between two variables, it would be best to use a correlation
• A correlation can only be between -1 and +1.
• The closer the correlation coefficient is to 1 (either + or -), the stronger the relationship.
• The sign indicates the direction of relationship.
• The coefficient of determination is calculated by squaring r. The coefficient of determination shows how much area the two variables share; the percentage of variance explained (accounted for).
• The coefficient of nondetermination is calculated by subtracting the coefficient of determination from 1. The coefficient of nondetermination shows how much the two variables don’t share; the percentage of unexplained variance.
• To calculate the correlation between two continuous variables, the Person product-moment coefficient is used. To calculate the correlation between two discrete variables, the phi coefficient is used. To calculate the correlation between one discrete and one continuous variable, the point biserial coefficient is used.
• Correlations are primarily a measure of consistency, reliability, and repeatability.
• Correlations are based on two paired-observations of the same subjects.
• A cause-effect relationships has a strong correlation but a strong correlation doesn’t guarantee a cause-effect relationship. In a correlation, A can cause B or B can cause A or both A and B can be caused by another variable. Inferences of cause-effect based on correlations are dangerous. A correlation shows that a relationship is not likely to be due to chance but it cannot indicate which variable was cause and which effect.
• Test-retest coefficients are correlations.
• In order to make good predictions between two variables, a strong correlation is necessary.

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