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On the post hoc power in testing mean differences
 Journal of Educational and Behavioral Statistics
, 2005
"... Retrospective or post hoc power analysis is recommended by reviewers and editors of many journals. Little literature has been found that gave a serious study of the post hoc power. When the sample size is large, the observed effect size is a good estimator of the true effect size. One would hope th ..."
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Retrospective or post hoc power analysis is recommended by reviewers and editors of many journals. Little literature has been found that gave a serious study of the post hoc power. When the sample size is large, the observed effect size is a good estimator of the true effect size. One would hope that the post hoc power is also a good estimator of the true power. This article studies whether such a power estimator provides valutble infonnation about the true power. Using analytical, numerical, and Monte Carlo approaches, our results show that the estimated power does not provide usefidl infonnation when the true power is small. It is almost always a biased estimator of the true power. The bias can be negative or positive. Large sample size alone does not guarantee the post hoc power to be a good estimator of the true power. Actually, when the population variance is known, the cumulative distribution function of the post hoc power is solely a function of the population power. This distribution is uniform when the true power equals 0.5 and highly skewed when the true power is near 0 or 1. When the population variance is unknown, the post hoc power behaves essentially the same as when the variance is known.
SYSTEMS
"... The impact of reftigeration systems on the environment can be reduced by the use of alternative reffigerants which are less harmful to the atmosphere and the optimisation of systems and control strategies to deliver increased levels of energy efficiency. Mathematical modelling offers the opportunity ..."
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The impact of reftigeration systems on the environment can be reduced by the use of alternative reffigerants which are less harmful to the atmosphere and the optimisation of systems and control strategies to deliver increased levels of energy efficiency. Mathematical modelling offers the opportunity to test the performance of systems under different operating conditions and with alternative reffigerants. Dynamic models allow comparison of both transient and steadystate behaviour and this is of particular importance for liquid chillers, since these systems can operate under transient conditions for long periods. This thesis details the development of a general dynamic model for the simulation of liquid chillers. Mathematical models of the reciprocating compressor, expansion valve, evaporator and condenser are presented. The models are integrated to form the overall system model by passing conditions from one component to another. A series of steadystate and transient experimental tests were carried out on a liquid chiller and the model was used to simulate these tests. Validation was carried out by comparison of these measured results to those predicted by the simulation for both the steadystate and transient tests. Once validated, the model was used to investigate the steadystate and dynamic performance of liquid chillers operating with various refrigerants. The effect of the mass of the system refrigerant charge was examined for a number of refrigerants. The steadystate performance for a range of evaporator and condenser coolant temperatures was also investigated. Finally, the effect of different system refrigerants on startup transients was examined and the losses in cooling capacity due to cycling quantified. The e ffect of the expansion valve's initial superheat spring setting on the dynamic response and transient losses was also investigated. ii ACKNOWLEDGEMENTS I would like to express special gratitude to my supervisor, Professor Sawas Tassou, for his guidance and support throughout this project. IIis advice and encouragement have been invaluable. I am also grateful to the Mechanical
SMAC2003: The Automatic Iteration of SMAC
, 2003
"... Copyright © 2003 SAE International In prior studies researchers have been interested in automating the process by which the Simulation Model of Automobile Collisions (SMAC) is used to reconstruct an accident. The SMAC program requires an initial approximation of the impact speeds and the positions a ..."
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Copyright © 2003 SAE International In prior studies researchers have been interested in automating the process by which the Simulation Model of Automobile Collisions (SMAC) is used to reconstruct an accident. The SMAC program requires an initial approximation of the impact speeds and the positions and orientations at impact. And with a SMAC reconstruction you can sometimes get a reasonably close match and then spend many hours on iterative runs trying to match as best as possible the overall body of physical evidence. The prior research on automation of SMAC (during the time period 19751980) was constrained by computer time and resources. Those research projects were performed on mainframe computers where all applications included charges for CPU time and memory resources. Today with gigahertz Pentium computers and unlimited memory, aside from the initial cost of the computer, the cost per SMAC run is virtually free and the time for a run is measured in seconds rather than minutes. This paper describes an automatic iterative procedure which can quickly and efficiently iterate to a "best match" of the physical evidence with SMAC. Quantitative measures of the overall "fit " to the evidence, which guide the procedure, are discussed. Representative results from applications to experimental tests are presented.