A more powerful test for incomplete block designs
We studied the behavior of a statistic that tests for treatment effects in incomplete block designs, Simulation was used to estimate the first four moments of a test statistic that combines intra- and inter-block estimates of treatment contrasts. For a wide range of alternative hypotheses, the moments are remarkably close to those of an F distribution with one degree of freedom in the numerator, and the denominator degrees of freedom equal to that of the mean square error in the usual intra-block analysis, The noncentrality parameter depends upon the block and unit variances and the eigenvalues of the incidence matrix of the design, The power of the test statistic can be estimated from standard power function charts.