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Full-Text Articles in Statistics and Probability
On Optimizing Multi-Level Designs: Power Under Budget Constraints, Todd C. Headrick, Bruno D. Zumbo
On Optimizing Multi-Level Designs: Power Under Budget Constraints, Todd C. Headrick, Bruno D. Zumbo
Todd Christopher Headrick
This paper derives a procedure for efficiently allocating the number of units in multi-level designs given prespecified power levels. The derivation of the procedure is based on a constrained optimization problem that maximizes a general form of a ratio of expected mean squares subject to a budget constraint. The procedure makes use of variance component estimates to optimize designs during the budget formulating stages. The method provides more general closed form solutions than other currently available formulae. As such, the proposed procedure allows for the determination of the optimal numbers of units for studies that involve more complex designs. A …
An Investigation Of The Rank Transformation In Multple Regression, Todd C. Headrick, Ourania Rotou
An Investigation Of The Rank Transformation In Multple Regression, Todd C. Headrick, Ourania Rotou
Todd Christopher Headrick
Real world data often fail to meet the underlying assumptions of normal statistical theory. The rank transformation (RT) procedure is recommended and used in the context of multiple regression analysis when the assumption of normality is violated. There is no general supporting theory of the RT. In view of this, the current study examined the Type I error and power properties of the RT in terms of multiple regression. The investigation included both additive and nonadditive models. Results indicated that there were severely inflated Type I error rates associated with the RT procedure under both normal and nonnormal distributions (e.g., …