Approximate Confidence Intervals for Contrasts in the Balanced Three Factor Mixed Model

✍ Scribed by Michael C. Mosier; Franklin A. Graybill

• Publisher: John Wiley and Sons
• Year: 1995
• Tongue: English
• Weight: 949 KB
• Volume: 37
• Category: Article
• ISSN: 0323-3847
• DOI: 10.1002/bimj.4710370304

✦ Synopsis

When conducting a statistical analysis of data from a designed experiment, an investigator is often interested in coddeuce intervals for contrasts of the fixed effects. If the analysis involves a mixed linear model, exact confidence intervals for contrasts of the fixed effects are not always available. In such cases, confidence intervals with approximate coverage probabilities must be used.

As will be shown, this problem may be generalized to that of constructing a confidence interval for the parameter p, where X is a normal random variable with mean p and variance uqflq, where a , , ... , a, are known constants, U, =nqS:/flq is a chi-squared random variable witi n, degrees of freedom, for each q = l , ..., Q, and X, U, ,_.., U, are mutually independent. In this paper, we consider the case where Q = 3 and aj <O.