Short statistical analysis

Simulation runs are typically short (t 10 - 10 MD or MC steps, correspondmg to perhaps a few nanoseconds of real time) compared with the time allowed in laboratory experiments. This means that we need to test whether or not a simulation has reached equilibrium before we can trust the averages calculated in it. Moreover, there is a clear need to subject the simulation averages to a statistical analysis, to make a realistic estimate of the errors. 

The liquid mean residence time, tm, in counter-current mode was significantly lower than in co-current mode. Statistical analysis (Yates method of ANOVA) indicates that along with the liquid flowrate, the direction of liquid travel is the most significant factor in the liquid mean residence time. This variation in the liquid phase mean residence time, suggests an increase in short-circuiting or channeling in the counter-current mode as a result of the gas-liquid interactions. 

If significant change at any time during the six-month period of the accelerated (short-term) condition is observed, then extrapolation is not considered appropriate. If the long-term data show variability, the proposed shelf life can be verified by statistical analysis. 

Although the results of these studies mostly support the notion that yogurt has immunostimu-latory effects, poor study design, lack of appropriate controls, and short duration of most of the studies limit the value of the conclusions that can be drawn from them. Most early animal and human studies included too few animals or subjects in each group and most did not include statistical analysis. Although more recent studies addressed these points, none provided the statistical basis for the selected number of subjects that is, it seems that no power calculations were performed. 

Fig. 7A, B Statistical analysis of the density of BrdU+ in DG. A In the short-term survival group after BrdU, the density peaked on day 9. B In the long-term-survival monkey DG, density was significantly higher in postischemic compared to control brains. p < 0.001 versus controls, one-way ANOVA followed by Tukey-Kramer post hoc...

Statistical analysis demonstrated that the postischemic increase of BrdU+ cells in the short-term monkey group was significant only on days 9 and 15, while the postischemic day-4 SVZi did not show statistically significant differences to... 

This comparison is performed on the basis of an optimality criterion, which allows one to adapt the model to the data by changing the values of the adjustable parameters. Thus, the optimality criteria and the objective functions of maximum likelihood and of weighted least squares are derived from the concept of conditioned probability. Then, optimization techniques are discussed in the cases of both linear and nonlinear explicit models and of nonlinear implicit models, which are very often encountered in chemical kinetics. Finally, a short account of the methods of statistical analysis of the results is given. 

Bravo and Fair (122) statistically analyzed the reliability of their model. They concluded that multiplying an HETP calculated from their model by a safety factor of 1.6 will give 95 percent confidence that the column is not too short This factor is slightly lower than the Bolles and Fair (55,96) and the Onds et al. (123) correlations. MacDougall (58) repeated the statistical analysis after he rearranged the data bank, and showed that a safety factor of 1.3 is more appropriate, making the Bravo and Fair correlation much better than the others. 

Overall, DSC is an excellent method to measure the wax appearance and crystallization temperatures of vegetable oils. Due to the complexity of the vegetable oil composition with respect to their FA distribution, the situation is not as simple as pure triacylglycerol molecules. Moreover, there is significant influence of the nature, relative abundance, and orientation of C=C bonds on the wax appearance temperatures. Further, presence of other saturated short-chain-length FAs in vegetable oil structure is found to affect the crystallization process. Statistical analysis of NMR-derived vegetable oil structure support the influence of several predictor variables associated with FA unsaturation on the crystalhzation process. 

Loop structure prediction is always based in one way or another on an understanding of loop conformations in experimentally determined structures. Loop conformational analysis has been performed on a number of levels, ranging from classification of loops into a number of distinct types to statistical analysis of backbone dihedral angles. Loop classification schemes have usually been restricted to loops of a particular size range short loops of 1-4 residues, medium loops of 5-8 residues, and long loops of 9 residues or longer. 

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