TESTING SUBHYPOTHESES AND ESTIMATING σ2 IN THE NONREPLICATED THREE-WAY MULTIPLICATIVE INTERACTION MODEL

ABSTRACT

Standard statistical techniques do not provide methods for analyzing data from nonreplicated factorial experiments. Such experiments occur for several reasons. Many experimenters may prefer conducting experiments having a large number of factor levels with no replications than conducting experiments with a few factor levels with replications particularly in pilot studies. Such experiments may allow one to identify factor combinations to be used in follow-up experiments. Another possibility is when the experimenter thinks that an experiment is replicated when in fact it is not. This occurs when a naive researcher believes that sub-samples are replicates when in reality they are not. Nonreplicated two-way experiments have been extensively studied. This paper discusses the analysis of nonreplicated three-way experiments. In particular, estimation of σ² is discussed and a test is derived for testing whether three-factor interaction is absent in sub-areas of three-way data using a nonreplicated three-way multiplicative interaction model with a single multiplicative term. Approximate null distribution of the derived test statistic is studied using Monte Carlo studies and results are illustrated through an example.     

A NOTE ON THE HOMOGENETIC ESTIMATE FOR THE VARIANCE OF THE KAPLAN–MEIER ESTIMATE

ABSTRACT

The Greenwood estimate (GE) is commonly employed for estimating the variance of the Kaplan–Meier estimate (KME) even though it underestimates the variance. To reduce the bias of the GE, Zhao (1996) proposed an alternative, called the homogenetic estimate (HE). In this note, we point out that the HE actually esimates the variance of the reduced sample estimate (RE) and can seriously overestimate that of the KME. We also derive the explict relationship between the HE and the GE and discuss the use of the HE.