On the Sample Size of the One-Stage and Two-Stage Sampling Procedures Under Heteroscedasticity

• Activity Number: 661
• Type: Contributed
• Date/Time: Thursday, August 4, 2011 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Computing
• Author(s): Shun-Yi Chen*+ and Ching-Feng Hsu
• Companies: Tamkang University and Tajen University
• Keywords: Unknown and unequal variances ; ANOVA ; Range of independent $t$ variables

Abstract

The level and the power of conventional F-test in analysis of variances are sensitive to unequal variances. When the variances are unknown and unequal, both level and power associated with the tests derived using the general one-stage and two-stage sampling procedures are controllable at the nominal values and are independent of the unknown variances. This paper presents a further investigation on the sample size of these two sampling procedures under heteroscedasticity. We conclude that when the initial sample size of the two-stage procedure ($n_{02}$) is larger (usually larger than 6), the general one-stage procedure loses little power relative to the two-stage procedure, but it performs relatively good for smaller $n_{02}.$ We also note that the powers of the general one-stage procedure employing unequal sample size outperform the equal sample size case except when both variances and $n_{02}$ are very small.