Normal probability plots problem

Small departures of normality do not significantly influence the use of the calibration model in residue analysis. However, major departures of normality are mostly related to analytical or instrumental problems. The use of an inappropriate calibration model can give rise to nonnormality of the residuals. In this case also, one or more of the other four basic assumptions have been violated. Normality can be evaluated by means of several statistical tests (i.e., Kolgomorov-Smirnov, Shapiro-Wilk W) or by constructing normal probability plots [8]. 

Ideally, at the end of a determination that has made use of hundreds or thousands of observations and is thus amenable to statistical analysis at a reasonably high level, one should not merely take comfort in satisfactory values of parameters such as R and ax but rather undertake an overall statistical analysis of the residuals to ascertain whether the uncertainties in the data were properly assessed and whether there is an opportunity to detect errors in the model or systematic errors in the data. In the past this has rarely been done, in part because it is a lot of work and in part because most crystallographers do not really know how to go about it. Recently, Abrahams and Keve17 (later also Hamilton and Abrahams18 ) showed that the objectives sought can be largely achieved by use of an (normal probability plot. In the application of this technique to the problem at hand, the normalized residual... 

It can be noted that adding a quadratic term has improved the size of the parameter estimate confidence intervals, as well as increasing R. Furthermore, the normal probability plot of the results seems to suggest that there could be some problems due to the clustering of values. The residuals as a function of temperature plot does not show any real issues. There does seem to be a small increase in variability of the values as the temperature increases. There are no discernible parameters that would improve the fit. 

Description a screenshot of the plain template is shown in Fig. 8.26. The yellow blocks are where the required data are entered. Note that Solver needs to be used to obtain a solution to the problem. The configuration of Solver is shown as an inset in Fig. 8.26. The layout and formatting of the results are similar to the linear regression case. Two important differences are that the model and its Jacobian must be entered as a macro and that Solver must be used. The spreadsheet automatically creates the normal probability plot for the residuals and plots of the residuals as a function of y and y, as well as a time series plot of the residuals. Additional plots can be created by the user. An example of how to use the template is provided in Sect. 8.7.2 Nonlinear Regression Example. 

Figure 1.9 shows examples of how these kinds of problems can appear on a probabiUty plot. Figure 1.9a shows a normal probability distribution with mean 0 and variance 1 with 2 outliers (circled). Notice how the outliers can cause some of the adjacent points to also be skewed from the ideal location. Figure 1.9b shows the case where the tails of the distribution do not match. In this case, a 2-degree-of-freedom Student s f-distribution was compared against the normal distribution. The f-distribution has larger tails than the normal distribution. This can clearly be seen by the deviations on both sides from the central line. Figure 1.9c shows the case... 

The assumption of global kinetic control is probably valid for only a handful of catalytic reaction processes. Nevertheless, some typical simulation results of the model of catalyst deactivation under kinetic control are presented here in order to emphasize some of the unique percolation-type aspects of the problem. The overall plugging time 0p, i.e., the time at which the catalyst becomes completely deactivated is shown is Figure 1, where it is plotted versus Z, the average coordination number of the network of pores, (in industrial applications, of course, the useful lifetime of the catalyst is significantly smaller than 0p). Note that as Z increases, (higher values of Z mean a more interconnected catalyst pore structure) 0p increases, i.e., the catalyst becomes more resistant to deactivation. The dependence of normalized catalytic activity (r/rQ) ([Pg.176]

Before the computer age, the friction factor plot and the convenience plots made from it were the only means that engineers had of solving fluid friction problems in pipes. For an occasional such calculation or a problem outside the normal range of the engineer s experience, they are probably still the best way. However, for routine pipe friction calculations, engineers use computers. To do so, they need equations equivalent to the friction factor plot. 

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