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Common applications of the part correlation coefficient are in causal regression models and estimation of suppressor variable effects. However, there is no statistical test of the significance of the difference between a zero-order correlation and a part correlation, nor between a pair of part correlations. This note uses Hotelling's (1940) t for contrasting dependent rs for contrasting a zero-order and first order part correlation, and for contrasting first- order part correlations based on different predictors and different covariates, the same predictor but different covariates, and different predictors and the same covariate.
Robert G. Malgady (Tue,) studied this question.