Power to detect additive treatment effects with randomized block and analysis of covariance designs

The power of analysis of covariance (ANCOVA) and 2 types of randomized block designs were compared as a function of the correlation between the concomitant variable and the outcome measure, the number of groups, the number of participants, and nominal power. ANCOVA had a small but consistent advantage over a randomized block design with 1 participant in each Block x Treatment combination (RB1). At correlations of .3 or greater, ANCOVA was superior to a randomized block design with n participants per Block x Treatment combination (RBn), with increasing differences as the correlation increased. RBn was superior to the other 2 designs only when the correlation was .2 or less. At those levels, however, the randomized group analysis of variance ignoring the concomitant variable was equally powerful, The findings held regardless of sample size, number of groups, of nominal power.