Statistical analysis significance

The probabilistic nature of a confidence interval provides an opportunity to ask and answer questions comparing a sample s mean or variance to either the accepted values for its population or similar values obtained for other samples. For example, confidence intervals can be used to answer questions such as Does a newly developed method for the analysis of cholesterol in blood give results that are significantly different from those obtained when using a standard method or Is there a significant variation in the chemical composition of rainwater collected at different sites downwind from a coalburning utility plant In this section we introduce a general approach to the statistical analysis of data. Specific statistical methods of analysis are covered in Section 4F. 

A statistical analysis allows us to determine whether our results are significantly different from known values, or from values obtained by other analysts, by other methods of analysis, or for other samples. A f-test is used to compare mean values, and an F-test to compare precisions. Comparisons between two sets of data require an initial evaluation of whether the data... 

In this experiment students measure the length of a pestle using a wooden meter stick, a stainless-steel ruler, and a vernier caliper. The data collected in this experiment provide an opportunity to discuss significant figures and sources of error. Statistical analysis includes the Q-test, f-test, and F-test. 

In all antiseptic testing, it is recognized that skin and mucous membranes to which products ate appHed cannot be disinfected or sterilized but it is possible to significantly reduce the population of transient and resident pathogenic bacterial flora. AH in vivo test methods requite a deterrnination of the bacteria on the skin before and after treatment. Because of the normal variation in bacterial population of the skin of different people, a number of people must be tested in order to make a statistical analysis of the results. Different parts of the body are used for different tests. In aH of the tests the details of the protocol ate extremely important and must be strictly adhered to in order to obtain reproducible results. 

The parameters Ci, t2 were postulated to be dependent only upon the substrate, and d, d2, upon the solvent. A large body of kinetic data, embodying many structural types and leaving groups, was subjected to a statistical analysis. In order to achieve a unique solution, these arbitrary conditions were imposed cj = 3.0 C2 for MeBr Cl = C2 = 1.0 for f-BuCl 3.0 Ci = C2 for PhsCF. Some remarkably successful correlations [calculated vs. experimental log (fc/fco)l were achieved, but the approach appeared to lack physical significance and was not much used. Many years later Peterson et al. - showed a correspondence between Eqs. (8-69) and (8-74) in particular, the very simple result di + d, = T was found. 

Besides, the statistical analysis of the results obtained confirmed that the xylan samples did not present a significant effect on the cell viability and cell proliferation rate when in direct contact with HeLa cells at the concentrations used in this study and compared to the control. 

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. 

Statistical analysis did not reveal any significant interactions between Na and K. Three-dimendonal plots for each deagn showed that the data of each mixtiu e design could be easily described by the data belonging to the border lines of the defined fields, because minimum and maximum values were located there. Thus, without loss of information, figure 1 gives a representative idea of the influence, which the studied cations exert on the sol / gel transition of the three pectins. The curvature in the dotted curves reveal the interactions between Ca and a monovalent cation. 

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. 

Each oil-dispersant combination shows a unique threshold or onset of dispersion [589]. A statistic analysis showed that the principal factors involved are the oil composition, dispersant formulation, sea surface turbulence, and dispersant quantity [588]. The composition of the oil is very important. The effectiveness of the dispersant formulation correlates strongly with the amount of the saturate components in the oil. The other components of the oil (i.e., asphaltenes, resins, or polar substances and aromatic fractions) show a negative correlation with the dispersant effectiveness. The viscosity of the oil is determined by the composition of the oil. Therefore viscosity and composition are responsible for the effectiveness of a dispersant. The dispersant composition is significant and interacts with the oil composition. Sea turbulence strongly affects dispersant effectiveness. The effectiveness rises with increasing turbulence to a maximal value. The effectiveness for commercial dispersants is a Gaussian distribution around a certain salinity value. 

Data were subjected to analysis of variance and regression analysis using the general linear model procedure of the Statistical Analysis System (40). Means were compared using Waller-Duncan procedure with a K ratio of 100. Polynomial equations were best fitted to the data based on significance level of the terms of the equations and values. 

Statistical analysis of the data in Table IV shows the selenium residue on and in the peel to be highly significant over the residue on and in the peel of nonsprayed apples. There is no significant difference between varieties. Selenium residue is evenly distributed on the trees. 

Statistical analysis of the data in Table II shows no significant difference between varieties or between positions on the tree. The average parathion residue on all varieties is equal to or slightly less than the variation between samples. 

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