Metrika (2009) 70:165–176 DOI 10.1007/s00184-008-0185-4 Comparing means of several treatments with a control when one observation exists per treatment Mahmood Kharrati-Kopaei Received: 25 April 2006 / Published online: 19 June 2008 © Springer-Verlag 2008 Abstract 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. Keywords Control group · F -distribution · Power · p-value · Two-way ANOVA 1 Introduction Suppose that we have n + 1 Normal populations (treatments) with different means and equal variances and, without loss of generality, assume that the (n + 1)-th treatment is the standard treatment (control group). In addition, suppose that only one observation is available from each treatment. We call such a design an unreplicated one-way design. This design is used when the experiments are too expensive or only the means of each treatment are available. In the latter case, a researcher might do his/her experi- ments with some replications, but the original data are missing and only the means are available. A more practical usage of the unreplicated one-way designs is in unreplica- ted two-way layouts (there is only one observation per cell in such designs). Generally, M. Kharrati-Kopaei (B ) Department of Statistics, College of Sciences, Shiraz University, Shiraz, Iran e-mail: kharati@susc.ac.ir 123