# Accession Number:

## ADA014936

# Title:

## A Model for Using Qualitative Variables as Covariates in the Analysis of Covariance

# Descriptive Note:

## Final rept.

# Corporate Author:

## ARMY RESEARCH INST FOR THE BEHAVIORAL AND SOCIAL SCIENCES ALEXANDRIA VA

# Personal Author(s):

# Report Date:

## 1975-07-01

# Pagination or Media Count:

## 47.0

# 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.. I2, n..20, 80 I3, n.. 36, 144 I4, n..56, 224 2 ratio of number of row observations I2, 11, 41 I3, 111, 411 I4, 1111, 4111 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.

# Descriptors:

# Subject Categories:

- Statistics and Probability