Two Meanings of "Rho"
Unfortunately, the term "rho" has two different meanings in the field of statistics. Because this situation can lead to confusion, perhaps it would be helpful if I (1) clarified what these two meanings are and (2) indicated which of the two rhos you're more likely to come across as you read or hear summaries of research investigations.
If a researcher computes Spearman's rank-order correlation, he/she may refer to this procedure, or the correlation coefficient that's computed, as "Spearman's rho." Some researchers drop Spearman's name and refer to this correlational procedure (or it's resulting coefficient) as "rho." A few refer to Spearman's rho via the Greek letter r. When used in this way, rho belongs under the umbrella of descriptive statistics.
If a researcher takes his/her data and computes Pearson's product-moment correlation, he/she will likely refer to the resulting correlation coefficient as the "product-moment correlation," "Pearson's r," or simply "r."
If the researcher who computes Pearson's r is interested only in describing the relationship between scores on the two variables of interest, then r would fall under the umbrella of desriptive statistics, just like the rho I talked about two paragraphs ago.
However, many researchers compute r on data that have come from a sample, and their intent is to make a correlational inference from the sample to the appropriate population. In other words, in this kind of situation, r is being used for the purpose of making an educated guess as to the value of the product-moment correlation in the population. Using more formal, statistical language, the computed r is the "statistic" while the unknown value of the product-moment correlation in the population is the "parameter."
Normally, lower-case Greek letters are used to represent population parameters. The letter mu, m, stands for the population mean, while the letter sigma, s, stands for the population standard deviation. The letter that represents the population product-moment correlation is r. This letter, of course, is rho.
Thus, the word "rho," when you see or hear it in a research summary, might be referring to Spearman's rank-order correlation or it might be referring to the parameter value of Pearson product-moment correlation. Usually, the written or spoken use of the word "rho" carries the first of these two meanings. That's because most researchers don't very often think about or refer to the population parameters toward which their inferential procedures are directed. Sadly, they get so caught up with their sample data that they fail to discuss population parameters. For this reason, any use of the term "rho" is probably descriptive in nature, and that means the referent is Spearman's rank-order correlation rather than the parameter value of Pearson's correlation.
I hope this clarification helps you avoid some potential confusion when you next come across the term "rho."
Copyright © 2012
Schuyler W. Huck