Comparing means of several treatments with a control when one observation exists per treatment

In an one-way analysis of variance with standard assumptions suppose that only one observation exists per treatment. In addition, assume that one of the treatments is a control group. Because of insufficient observations, the variance of the populations cannot be estimated and hence the usual methods for comparing treatments with the control group fail. In this paper, we present a method to compare treatments with a control when one observation exits per treatment. An algorithm is given to estimate the critical values of the test. The power of the test is investigated by a Monte Carlo simulation; numerical studies show that when there is a treatment whose mean is close to the control group, the power of the test is satisfactory.