# More on Correlation Coefficients

### Correlation coefficients are a numerical indicator of the strength of a relationship between two variables.  Correlations also tell us the direction of the relationship.  By direction we mean whether both variables go up or down together (a positive or direct relationship) or whether one goes up when the other goes down (a negative or inverse relationship).

The most widely used correlation coefficient is the Pearson r.  Note that Pearson’s r is a bivariate correlation technique.  The term bivariate means that two variables are represented by the correlation.  (We will discuss correlation techniques that consider the relationship between more than two variables in the later section on Multiple Correlations).

The highest possible value of r is 1.00, which represents a perfect correlation.  A perfect negative correlation is indicated by a value of -1.00.  A value of zero (0.00) indicates that there is no relationship between the two variables.  The closer the value of r is to |1.00|, the stronger the relationship.  Thus, the magnitude of the value of indicates the strength of the relationship, and the sign shows the direction of the relationship.

To determine the strength (magnitude) of a correlation, we look at the absolute value of the coefficient.  For example, a correlation of 0.90 between two variables would indicate a very strong positive relationship, whereas a correlation of 0.20 would indicate a weak (but positive) relationship.  A correlation of –0.8 would indicate a very strong negative relationship.  A correlation of –0.30 would designate a weak negative relationship. A correlation of 0.00 would show that two variables are independent (that is, unrelated).

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