Why is the semi-partial correlation sometimes called the "part correlation"?

Question

I understand the difference between partial correlation and semi-partial and zero-order correlation. This terminology makes sense to me in that the partial correlation of X and Y partials out the effect of one or more variables from both X and Y, and semi-partial correlation only partials out the effect of one or more variables on either X or Y (i.e., it only partially partials; i.e., it semi-partials).

For example, SPSS labels the semi-partial correlation as part correlation. This is the source of some confusion to students encountering this output for the first time.

• Why is the semi-partial correlation sometimes called the "part correlation"?
• What is the etymology of the term "part correlation"?

Answer 1

I'm afraid that my attempt at an answer is hardly more satisfying than gung's. Snedecor and Cochran's book discuss this briefly. That was an old statistics text, based out of a lot of agricultural work (and so much of the early work was) and in any case, takes us back, I think, to early work by Mordecai Ezekiel and Bradford Smith around the 1920s or 1930s. At that point, the linear model was already established, and that a correlation, assuming bivariate normality, could be extended to the multivariate normal case and regression. However, considerable effort was placed on formulae and shortcuts that made by hand calculations easier.

My belief is that the part correlation, was an early derivation that actually pre-dated what we now call partial correlations, and in the absence of partial correlations, referring to it as part correlation makes sense. I think the reference you might want is Correlation Theory and Method Applied to Agricultural Research, but alas I do not have easy access to it to see if all is explained.

Answer 2

I have no idea (and if you object, I can delete this answer), but I can tell you how I've tried to explain it to people so that they can get it.

Namely, the word "part" goes only half way through the word "partial". In the same sense, the part correlation partials the variable out of only one of X or Y, so it only goes half way though a partial correlation. I acknowledge that this is an arbitrary mnemonic, but it does help people remember it.

Answer 3

According to Howell (2012, in the partial and semi-partial correlation), "part correlation" is due to McNemar (1969) Psychological statistics, Wiley. If someone can get a copy, maybe we could get further.