Spearman Correlation Coefficient

Background

ρ was developed by Charles Edward Spearman, a professor of psychology who was known for his application of statistical concepts to the study of psychology. He is most famous for his developmental work in factor analysis and for his development of the Spearman ρ.

Because the Spearman ρ is a correlation statistic, it measures the strength of an association between two variables. Correlation statistics provide 4 items of information: First, they answer the question, “Do these two variables covary?” That is, does one variable change when the other changes? Second, when two variables do covary, these statistics describe the direction of the association, which can be positive or negative. A positive correlation means as one variable increases the other also increases. A negative correlation means that as one variable increases the other decreases. Third, correlations describe the strength of the association. Strength in this context means how closely do the two variables change together? In a perfect correlation, for every one level of rise in one variable, the other variable would change exactly one level; it would either rise (positive correlation) or fall (negative correlation) that one level. The ρ value can range from −1.0 to + 1.0. Fourth, the significance of the obtained value can be determined using a significance table (if the statistic is hand calculated), and the statistical programs that produce the ρ provide a significance level as part of the output.

Assumptions

The ρ, like virtually all inferential statistics not specifically designed to test matched pairs or other related measures, assumes that the sample was randomly selected from a defined population. It assumes subjects were independently sampled from the population. That is, selection of one subject is unrelated to selection of any other subject. It is not appropriate for use with paired or otherwise related samples.

The relationship between the two variables must be generally linear. That is, for the ρ to be useful, there must be a single direction of the correlation (Figure 1). Specifically, as one variable increases, the other variable either increases (positive correlation) or decreases (negative correlation). If the relationship has one or several distinct curves (Figure 2), the ρ is not an appropriate statistic and may find little or no association because it cannot test curvilinear associations.

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