Simple Bivariate Correlation

Directional Relationship

Knowing the relationship between two variables does not do very much good without at least knowing the direction of the association. Correlations between variables can be positive, negative, curvilinear, or nonexistent. A positive relationship between variables is illustrated when both increase together. For instance, in the above-mentioned example, a positive correlation between class attendance (X) and final exam scores (Y) exists when higher class attendance relates to better final exam scores. If a negative correlation is present, the observations of one variable increase as the observations of the other decrease. Higher class attendance relating to lower final exam scores would reflect a negative correlation between the two variables. Curvilinear relationships are a bit more complicated than typical positive or negative correlations, in that both positive and negative relationships are present in this type of correlation. Higher class attendance would be related to final exam scores up to a point, at which a negative relationship starts to show higher class attendance associated with lower final exam scores. If no relationship is present between the variables then they are said to be uncorrelated or nonexistent.

Pearson Product-Moment

The Pearson product-moment correlation (i.e., r) is the most common statistic used to measure the relationship between two variables in social and behavioral research. The statistic provides the direction of the relationship between variables (expressed as positive and negative numbers), as well as the strength (i.e., 0 is weak, 1 is perfect correlation). For example, if variables X and Y were found to have r = .7, then the positive number reflects a positive relationship, and the .7 out of a possible 1 represents a moderately strong correlation. The coefficient (i.e., r) is understood as an absolute value, and the positive or negative delineation refers to the direction of the relationship. For example, r = .5 is a weaker correlation than r = –.65 because 1 or –1 represents perfect correlation. Larger correlations between variables imply stronger relationships, and a higher likelihood of predicting the presence of either variable with the known value of at least one of them.

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