Statistical analysis adequacy

Statistical testing of model adequacy and significance of parameter estimates is a very important part of kinetic modelling. Only those models with a positive evaluation in statistical analysis should be applied in reactor scale-up. The statistical analysis presented below is restricted to linear regression and normal or Gaussian distribution of experimental errors. If the experimental error has a zero mean, constant variance and is independently distributed, its variance can be evaluated by dividing SSres by the number of degrees of freedom, i.e. 

Two important aspects are internal audits and product quality review. Internal audits are implemented to regularly monitor the compliance activities in drug manufacture and to ensure rectification to these activities if deviations occur. Trending and statistical analysis of data provide early warning of impending problems. Product quality review checks the relevance and adequacy of the manufacturing activities. It provides input to update and improve the quality system. 

The goodness of different equations fitted to the experimental data points is assessed by the results of statistical analysis or by simply considering the standard error of the estimate. It should be also considered that the adequacy of the calibration function for the determination of correct MW values is also dependent on the quality of the narrow MWD standards. Their nominal MWs are determined with independent absolute methods and are affected by experimental errors which may be different between samples with different MWs, or coming from different producers. A check of the quality of the narrow standards may be obtained by calculating the percent MW deviation of each standard from the calibration curve ... 

In considering the adequacy of specific investigations as a basis to identify hazard in risk assessment, several features of study design are considered including the purity of the compound administered, the size of the study (i.e., numbers of exposed and control animals), whether the study was performed under Good Laboratory Practice standards, the relevance of the route of exposure to that of humans, duration of exposure, the number and suitability of the dose levels administered, the extent of examination of various toxicological endpoints, and the statistical analysis of the data (HC 1994 Meek et al. 1994). Criteria for the technical adequacy of animal carcinogenicity studies have been published (e.g., Chhabra et al. 1990 NTP 1984 OSTP 1986). 

Risk control status is achieved through field observations, regular and independent inspections, statistical analysis and in discussion with all levels of the workforce. The task is to ensure, as accurately as possible, that the barriers in place to control hazards are appropriate and effective. The safety precedence sequence mentioned in Chapter 1 is useful as a guide in establishing the adequacy of risk control strategies ... 

In the study of simulation, Hicks and Earl (2001) explained the importance of validation to simulation models. They supported the theory of Schlesinger (1980) and suggested that the components were (1) analysis generated a conceptuai model (2) model qualification determined the adequacy of the conceptual model (3) programming the model (4) model verification confirmed that the computerised model could represent the conceptual model within specified limits of accuracy using carefully chosen test cases and (5) in the process of validation, tested the input-output transformation of the simulation by statistical analysis. 

For the most part, the statistical analysis of SAW Monte Carlo data uses the same methods as are employed in other types of Monte Carlo simulation. In particular, with dynamic Monte Carlo data it is essential to carry out a thorough autocorrelation analysis, only in this way can one test the adequacy of the thermalization interval and the run length and properly assess the statistical error bars. For details, see e.g.. Ref. 36, Section 3 Ref. 37, Section 2 Ref. 96, Appendix C and Ref. 11, Sections 9.2.2 and 9.2.3. 

The adequacy of the 60-percent sampling has also been confirmed by a WSRC statistical analysis. 

The several modeling methods discussed in the accompanying sections are quite useful in testing the ability of a model to fit a particular set of data. These methods do not, however, supplant the more conventional tests of model adequacy of classical statistical theory, i.e., the analysis of variance and tests of residuals. 

We will learn the most appropriate methods for solving Eq. (6.14) in Section 6.2. The statistical tests for the adequacy of the regression model are based on an analysis of variances (ANOVAs) (cf. Section 2.3). 

The analysis of variance (ANOVA) was used to determine the adequacy of the model to describe the observed data. The statistic indicates the degree of variability of the optimization parameters that are explained by the model. 

Exploratory factor analysis (EFA) would discern the thematic patterns of mFSMAS on the basis of the sample data. However, as the sample size is limited to N =29, which means the sample to variable ratio is less than 3 1 (please see Brown and Onsman 2013) for arguments on sampling adequacy for factor analysis), the data is not sufficient to run EFA. Therefore, the factorial structure of an earlier study of mFSMAS on Turkish students in the context of chemistry education is used as a reference for the analysis (Kahveci, 2009). Table 1 shows the item-based factorial categories as drawn from Kahveci (2009) and Cronbach alpha values and the standardized descriptive statistics for the current sample N = 29) in the context of PChem II. There were six factors applied to this research as follows (1) confidence in learning physical chemistry, (2) satisfaction, (3) relevance, (4) personal ability, (5) gender difference, and (6) interest. 

---