Power analysis

Quantitative risk analysis (QRA) is a powerful analysis approach used to help manage risk and improve safety in many industries. When properly performed with appropriate respect for its theoretical and practical limitations, QRA provides a rational basis for evaluating process safety and comparing improvement alternatives. However, QRA is not a panacea that can solve all problems, make decisions for a manager, or substitute for existing safety assurance and loss prevention activities. Even when QRA is preferred, qualitative results, which always form the foundation for QRA, should be used to verify and support any conclusions drawn from QRA. 

Kolas, T.J. (1985), The Exergy Method of Thermal Power Analysis, Butterworth, London. 

GPC has many uses and is a powerful analysis technique for acrylate polymers. With care in selecting solvents and stationary phases, one finds that many polymers can be analyzed successfully. Opportunities always exist to use analytical GPC columns in nonstandard ways (semiprep, HDC, pseudo-ElPLC combined with GPC ) to the benefit of the analyst, but the analyst must always be keenly aware of which mode of operation is dominating when practicing such nonroutine analyses. 

FIGURE 11.23 Power analysis.The desired difference is >2 standard deviation units (X, - / = 8). The sample distribution in panel a is wide and only 67% of the distribution values are > 8. Therefore, with an experimental design that yields the sample distribution shown in panel a will have a power of 67% to attain the desired endpoint. In contrast, the sample distribution shown in panel b is much less broad and 97% of the area under the distribution curve is >8. Therefore, an experimental design yielding the sample distribution shown in panel B will gave a much higher power (97%) to attain the desired end point. One way to decrease the broadness of sample distributions is to increase the sample size. 

This latter value (tp) is given by power analysis software ancl can be obtained as a power curve. Figure 11.24 shows a series of power curves giving the samples sizes required to determine a range of differences. From these curves, for example, it can be seen that a sample size of 3 will be able to detect a difference of 0.28 with a power of 0.7 (70% of time) but that a sample size of 7 would be needed to increase this power to 90%. In general, power analysis software can be used to determine sample sizes for optimal experimental procedures. 

Power analysis can be used to optimize experiments for detection of difference with minimal resources. 

Power Analysis for ANOVA Designs can be used to calculate sample size for one and two-way factorial designs with fixed effects http //evall.crc.uiuc.e du/ fp o wer. html/... 

The results were not completely consistent, but these findings seem to favor a dimensional model of depression. However, this may reflect inadequate indicator selection. Taxometric power analysis suggests this is not the case, but the power analyses may have presented an overly optimistic view of indicator quality. In addition, the construct validity of the indicators used in this study is unknown. The validity of the BDI and the MMPI Scale 2 are well established, but the authors used indicators derived from these instruments, not the scales themselves. We cannot assume that the indicators assessed depression as accurately as the original scales. In fact, we don t know whether the derived scales are reliable. It is possible that the indicators actually did not tap syndromal depression, but instead they tapped a closely related factor such as negative affect, and thus are largely irrelevant to the question about the taxonicity of depression per se. 

Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nded.). Hillsdale, NJ Erlbaum. 

Kraemer, H.C. and Thiemann, G. (1987). How Many Subjects Statistical Power Analysis in Research. Sage Publications, Newbury Park, CA. 

Chiang, A.Y., Smith, W.C., Main, B.W., and Sarazan, R.D., Statistical power analysis for hemodynamic cardiovascular safety pharmacology studies in beagle dogs, /. Pharmacol. 

Seo J, Gordish-Dressman H, Hoffinan EP (2006) An interactive power analysis tool for microarray hypothesis testing and generation. Bioinformatics 22 808-814. doi btk052 (pii) 10.1093/bioinformatics/btk052... 

This technique is called analysis of covariance (ANCOVA) and size of the primary tumour is termed the covariate. Taking account of the covariate here has led to a much more powerful analysis than that provided by the simple unpaired t-test. Of course the main reason why we are seeing such an improvement in sensitivity is that the covariate is such a strong predictor of outcome. These improvements will not be quite so great with weaker predictors. 

Several controlled studies of IMI involved less homogeneous samples of anxious children. Neither IMI nor alprazolam (a BZ) was superior to placebo in an 8-week study of 24 children (ages 7-18 years) with school refusal, which included subjects with anxiety and depression (Bernstein et ah, 1990). A more recent placebo-controlled study of IMI -I- CBT for 47 adolescents (ages 12-18 years) with school refusal, anxiety, and/or depression was designed to address the limitations of previous studies of TCA treatment for pediatric anxiety disorders (Bernstein et ah, 2000). Accordingly, sample size was based on proposed power analysis IMI dose and serum level were monitored to ensure adequate exposure (mean IMI dose 180 mg/day mean serum IMI180 pg/L and mean IMI -I- DMI 250 pg/L at week 3 and week 8) and CBT was manual based and closely monitored. Fifty-four percent of subjects treated with IMI -I- CBT met remission criteria (defined as > 75% school attendance at the end of the study), compared to 17% of subjects treated with placebo -I- CBT. No between-group differences were noted... 

Borenstein, M., Rothstein, H., and Cohen, J. (2000) Powet and pte-cision a computet ptogtam for power analysis and confidence intervals. Biostat, http //www.Power-Analysis.com. 

Hoeven, N. van der, Kater, B.J. and Pieters, J.F. (2002). Statistical tests and power analysis for three in vivo bioassays to determine the quality of marine sediments. Environmetrics 13, 281-293. 

A wide range of transformations can be applied to spectral data before they are analyzed. The main purpose of transformations is to make the latent variables better available for powerful analysis. One of the most widely used is logarithmic transformation, which is especially useful to make skewed variables more symmetrically... 

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