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Correlation, Spearman

Spearman’s rank-order correlation coefficient (ρ or rs) is a statistical measure of the strength of a relationship between two variables. Spearman’s correlation is a nonparametric variation of Pearson’s product-moment correlation, used most commonly for a relatively short series of measurements that do not follow a normal distribution pattern. Like other correlation coefficients, Spearman’s rank correlation describes a mathematic co-varying relationship between two datasets.

Spearman’s rank-order correlation is calculated from the equation:

ρ = 1–6d,2n(n2–1)

where di describes the difference between variable rankings and n is the number of cases.

Any statistical correlation coefficient is described using integers ranging from −1 to 1; with −1 indicating a perfect negative relationship (for every increase of 1 unit of variable X, there will be a −1 decrease of variable Y), 1 indicating a perfect positive relationship (1 unit increase of X is associated with 1 unit increase in variable Y), and 0 indicating no measurable relationship between the variables. Spearman’s correlation is not limited to variables with a linear relationship, although a monotonic relationship is assumed for both variables. The remainder of this entry reviews the history of Spearman’s rank-order correlation, discusses various applications of Spearman’s correlation in communication research, lists criteria that must be met in order to use Spearman’s correlation, fully details how to use the rank-order correlation, and then provides some of the benefits and limitations of its use.

History of the Spearman Rank-Order Method of Correlation

Spearman’s correlation is named after Charles Spearman (1863–1945), an English psychologist, statistician, and Royal Society Fellow. He first published the rank-order correlation method in 1904 in the paper, “The Proof and Measurement of Association Between Two Things,” which described several statistical methods of correlation and their utility at the time. The first of two papers in the series, Spearman’s work described what he saw to be a reluctance among psychology researchers to use statistical methods for measuring association between research variables. Spearman thus described several simple methods of correlation, including his novel rank-order method, as ways to describe association with use of fairly simple mathematical knowledge. It has been asserted that Spearman’s goal in this paper was to push his method of correlation, above and beyond the justification of other methods.

Spearman’s rank-order correlation coefficient was refined over the course of the 20th century and was not commonly used until well after his death in 1945. Spearman was better known for his efforts to establish a common metric of general intelligence, or g factor, within the field of psychology. Despite the relatively late adaptation of Spearman’s correlation, he is well recognized for his contributions toward establishing the use of statistics in psychology.

Applications in Communication Research

There are many possible applications for Spearman’s correlation in the discipline of communication studies. Continuous variables, which must be used in calculating Spearman’s correlation coefficient, are readily available within typical studies in communication. Ordinal variables (such as reported on a Likert scale), ratio variables (e.g., years of experience in a given subject), and interval variables (e.g., income brackets) are commonly used in surveys and can be derived from other datasets not normally recognized as sources of quantitative information (e.g., qualitative interviews, discourse analysis). Spearman’s correlation may also be more appropriate for convenience or limited samples that either make it difficult to meet the assumptions required for Pearson’s correlation, or simply do not require the same level of precision to successfully address the research question.

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