Data analysis comparison between products

This section introduces two approaches to compare products based on TDS data. 

Note that this approach does not account for any correction for multiplicity of tests even though the number of tests is very high (number of time points x number of attributes, which represents generally hundreds of tests). The results should therefore simply be considered as a descriptive view of the most probable reasons for product differences, and not as a valid inference test to prove the significance of product differences. 

The example presented in Pineau et al. (2009) shows that it is easy to evidence the specificities of the two products (Fig. 13.11). Product FC is more pasty at the 

Rapid Sensory Profiling Techniques and Related Methods 

To get an idea of the specificity of one product compared to the oflier products of the test, it is also possible to calculate an average TDS profile of the other products by calculating the mean of the dominance proportion for each attribute x time point over the products, and using this average TDS profile to compare the remaining product to the others. As for the difference between two products, the curves of the difference will exhibit the specificities of one product versus the other ones. 

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Detailed quantitative analyses of the data allowed the production of a mathematical model, which was able to reproduce all of the characteristics seen in the experiments carried out. Comparing model profiles with the data enabled the diffusion coefficients of the various components and reaction rates to be estimated. It was concluded that oxygen inhibition and latex turbidity present real obstacles to the formation of uniformly cross-linked waterborne coatings in this type of system. This study showed that GARField profiles are sufficiently quantitative to allow comparison with simple models of physical processes. This type of comparison between model and experiment occurs frequently in the analysis of GARField data. 

Although the concept of patient variability had been articulated by the middle of the twentieth century, the concept that a difference between two groups could be due to chance was slow to be accepted. The first clinical trial to use a formal statistical analysis reportedly occurred in 1962. The study involved a comparison of antibody production after yellow fever vaccination by two different methods. Several years later (1966) a critique of statistical methods used in medical journal manuscripts suggested a lack of proper study design and data analysis. In this critique, the authors canonized the criterion of P < 0.05 for a difference between two groups to be considered not due to chance. 

As stated above, their shape, their velocity, and their collisions characterize soliton-like waves. In the present state of knowledge, comparison between theoretical analysis and experimental data can be obtained in two basic situations when there is predominance of the nonlinearity dispersion balance, as in BKdV solitons (case A) and when the (free)-energy production dissipation terms dominate (case B). ... 

Valuable information on the mechanism of the process and on the confirmation of the formulated assumptions was obtained by analyzing the low-molecular-weight by-products of trioxane polymerization reaction 1,3,5,7-tetraoxane and formaldehyde. Theoretical analysis has shown that, depending on the state of active centers (surface or dissolved) and the length of the dissolved portion of the polymer chain, the steady-state concentration of 1,3,5,7-tetraoxane and formaldehyde changes. A comparison between experimental and theoretical data has shown that at monomer... 

Data obtained from these experiments are given in Table I. To permit comparison between different experiments, reaction product yields are all quoted in terms of moles of hydrocarbon formed per mole of molecular hydrogen fed to the reactor at the stated molecular hydrogen feed rate. Quantitative yields for the C4 hydrocarbons are not given in Table I because their amounts were too small for meaningful analysis. 

B) Comparison between calculated and experimental distribution of a water-soluble marker (ferritin) inside POPC vesicles. Detailed data analysis shows that in some cases ferritin can be entrapped with efficiency higher than what expected on theoretical basis (Poisson distribution). Data taken from Berciaz et al. (C) Probability of co-entrapment of all macromolecular components of transcription-translation kit inside lipid vesicles of a given radius. The entrapment of each molecule is modelled as a poissonian process, and the cumulative probability is calculated as product of probabilities of independent events. The curve (a) indicates the probability of entrapping at least one copy of each molecular specie inside the same vesicle. The curve (b) indicates the probability of entrapping at least one copy of each molecular species under the hypothesis that their concentrations are all 50 times higher than the nominal (bulk) concentrations. Adapted from Souza et aP ... 

When the evaluation protocol is not standardized, the duration of an evaluation can vary from one product to another (and/or from one subject to another). In this case, it is useful to compare the evaluation durations between products to know whether some products generally need a longer duration to be evaluated than others. To do so, the 2-way ANOVA model usually used for Descriptive Analysis data (product as fixed effect, subject as random effect, with interaction in case there is replicates) can be simply applied to the evaluation duration variable. A multiple comparison test can also be conducted to identify which products have significantly different evaluation durations from which other products. 

One of the most important branches of theoretical organic chemistry deals specifically with the determination of these parameters. It should be noted that they cannot, with rare exceptions, be determined by experimental methods. Indeed, studying of reaction kinetics and isotopic effects, analysis of various correlational relationships of the steric structure of reaction products etc. give data which allow only indirect conclusions as to the overall reaction pathway since they all are invariably based on the studies of only the initial and the final state of every elementary step of the reaction. This situation may remind one of the black box direct access to the information therein is impossible, it can be deduced only through a comparison between the input and the output data. 

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