A Model for Using Qualitative Variables as Covariates in the Analysis of Covariance
Abstract
The powers of fixed effects randomized block (RB) and analysis of covariance (CANCOVA) using qualitative concomitant variables were analytically and empirically compared. Analytical comparisons were made of the powers of RB and CANCOVA in which the number of observations (n sub i) within each of the I categories of the concomitant variable was a constant. Empirical comparisons were made of the power of CANCOVA in which (n sub i) was a random variable (RCANCOVA) with RB in which (n sub i) was a constant. A Monte Carlo program simulated fixed effects with two levels of treatment, one criterion variable, and a qualitative concomitant variable with I categories. Three 'design types' in which I was equal to 2, 3, and 4 were studied. The parameters varied for each design type were: (1) total sample size (n..) (I=2, n..=20, 80; I=3, n.. =36, 144; I=4, n..=56, 224); (2) ratio of number of row observations (I=2, 1:1, 4:1; I=3, 1:1:1, 4:1:1; I=4, 1:1:1:1, 4:1:1:1); (3) eta (0.0, 0.3, 0.9); and (4) magnitude of treatment effect (0.0, 0.2, 0.5). Analytically, the RB and CANCOVA provided the same information in terms of component sums of squares. However, the power relationship was shown to be a function of sample size, design type, and amount of heterogeneity (interaction) present. Empirically no interpretable differences were found, either in magnitude and direction, between the power of the RB and RCANCOVA for any of the design type and parameter combinations studied.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 01, 1975
- Accession Number
- ADA014936
Entities
People
- N. P. Ross
Organizations
- U.S. Army Research Institute for the Behavioral and Social Sciences