Studying Conditional Relationships via Partial Rank Correlation

• Activity Number: 622
• Type: Contributed
• Date/Time: Thursday, August 4, 2011 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Calandra R. Tate Moore*+
• Companies: The City University of New York
• Keywords: Cross-classified Data ; Simulation ; Grouping Effects

Abstract

Suppose that X and Y are random variables whose relationship is of interest but may be quite different within different levels of a discrete group-labeling variable Z. How can the true degree of relationship between X and Y conditionally given Z be summarized nonparametrically ?

To answer this question, this paper presents and compares two new definitions for partial rank correlations: (1) S1, a rank correlation computed from X and Y after linearly correcting them by their group means within levels of Z, and (2) S2, a weighted linear combination of within Z-group rank correlations.

We investigate the comparative asymptotic performance of statistics S1 and S2, and apply them in detecting within group relationships in data obtained from a machine-translation experiment. The large-sample power of each statistic to detect real within group relationships is determined and illustrated by simulation for a broad range of within group dependence models. Further modifications of these statistics to take account of group-Z scale-factors are considered for various potential applications.