Statistical test, possible results

All clinical trials should have a pre-specified research question, which may be stated in the form of a primary hypothesis (or possibly a few primary hypotheses). An objective outcome measure or measures should also be clearly identified, such as the results of a biochemical test or the score on a validated scale. This allows statistical tests to be applied in order to assess the likelihood that any differences in response between treatment groups resulted from the active treatment and were not due to chance. 

Statistics should follow the technical scrutiny, not the other way round. A statistical analysis of data of an interlaboratory study cannot explain deviating results nor can alone give information on the accuracy of the results. Statistics only treat a population of data and provide information on the statistical characteristics of this population. The results of the statistical treatment may give rise to discussions on particular data not belonging to the rest of the population, but outlying data can sometimes be closer to the true value than the bulk of the population (Griepink et al., 1993). If no systematic errors affect the population of data, various statistical tests may be applied to the results, which can be treated either as individual data or as means of laboratory means. When different methods are applied, the statistical treatment is usually based on the mean values of replicate determinations. Examples of statistical tests used for certification purposes are described elsewhere (Horwitz, 1991). Together with the technical evaluation of the results, the statistical evaluation forms the basis for the conclusions to be drawn and the possible actions to be taken. 

Second, there are biometrical requirements. Various exposure response models may be used and compared. The models need to be clearly defined, and goodness of fit should be reported, both for the separate exposures as well as for the mixtures. Concentration addition, response addition, and mixed-model results may be compared as possible alternatives, especially when underpinning of mechanistic assumptions is weak. Results at one exposure level (e.g., EC50) do not necessarily predict results at other exposure levels due to different slopes and positions of the curves for separate compounds and the mixtures. Statistical tests should be executed properly to compare predicted and observed responses. If any statements about the significance of results are made, the methods of dose-response analysis need to be reported. 

Difference Gel Electrophoresis Next Generation of Protein Detection in 2-DE 51 Table 3.4 Possible results of a statistical test. 

Accuracy by Comparison. For drug substance, the only possibility of a quantitative assessment of accuracy is the comparison to the results of another analytical procedure or to a reference (if established with other procedures and/or additional characterization). This can be performed statistically with a r-test (see statistical textbooks or corresponding software). However, the shortcomings of these statistical tests (or better the justification of their use) are especially important here. It must be taken into consideration that two independent analytical procedures most probably differ in their specificity. This may lead to a systematic influence on the results (Table 2). If the effect can be quantified, the means should be corrected before performing the statistical comparison. If a... 

It is also often possible to reduce the number of animals used in the evaluation of a chemical or toxic waste site by carefully designing the experiment to maximize the data acquired or by accepting a compromise in the statistical significance and power. Often a slight decrease in the statistical power can result in a large reduction in the number of animals required in a toxicity test. 

If standard samples are not available, a second independent and reliable analytical method can be used in parallel with the method being evaluated. The independent method should differ as much as possible from the one under study. This minimizes the possibility that some common factor in the sample has the same effect on both methods. Here again, a statistical test must be used to determine whether any difference is a result of random errors in the two methods or due to bias in the method under study (see Section 7B-2). 

The preciseness of the primary parameters can be estimated from the final fit of the multiexponential function to the data, but they are of doubtful validity if the model is severely nonlinear (35). The preciseness of the secondary parameters (in this case variability) are likely to be even less reliable. Consequently, the results of statistical tests carried out with preciseness estimated from the hnal ht could easily be misleading—thus the need to assess the reliability of model estimates. A possible way of reducing bias in parameter estimates and of calculating realistic variances for them is to subject the data to the jackknife technique (36, 37). The technique requires little by way of assumption or analysis. A naive Student t approximation for the standardized jackknife estimator (34) or the bootstrap (31,38,39) (see Chapter 15 of this text) can be used. 

There are a variety of statistical tests that have been used to decide if a data point should be rejected, as well as some rules of thumb . The range chosen to guide the decision will limit all of these tests and guidelines. A large range will retain possibly erroneous results, while a very small range will reject valid data points. It is important to note that the outlier must be either the highest value in the set of data or the lowest value in the set. A value in the middle of a data set cannot be discarded unless the analyst knows that an error was made. 

This test is probably the most used of all statistical tests. It is very valuable when systematic differences between samples are caused by a single factor, and is entirely appropriate for comparing two independent averages. Arrhenius and Berzelius, however, made determinations on samples from five different vinegar producers. It is natural to suspect that these samples have different concentrations of acetic acid, and that samples from the same manufacturer are likely to be more similar to each other than to those coming from different producers. For this reason alone the results of the analyses are already expected to vary, blurring a possible difference in analytical technique. Since we are interested in a possible difference between the analysts, we need an improved method, which eliminates the variation caused by the different producers on the final result. 

The standardization and quantification of technique, and the rigorous application of statistics to the results has, in the last four decades, provided pharmacodynamics with a solid base such as it had not previously known. The use of experimental and control groups in tests on laboratory animals followed by similar tests on the human subject, have made it possible to evaluate the efficacy and side effects of drugs reliably, and also to make meaningful comparisons with established remedies. 

A source of random numbers is required by any Monte Carlo experiment. It is certainly possible, in principle, to produce numbers that are random in that they are the result of some random physical process such as radioactive decay, but such techniques are almost never used today. Instead one uses a mathematical relation that produces a sequence of numbers that will pass a specified battery of statistical tests. The numbers are not random in that their sequence is determined by the generator, but various statistical tests cannot distinguish them from random numbers. To be more specific we want a sequence of numbers / = 1,2,3,... that are uniform in the interval (0,1) and that are not seriously correlated. A possible sequence of statistical tests would examine uniformity of < in the unit interval, of 2i 2i+i in the unit square, of 3h 3i+u 31+2 in the unit cube, and so on until correlation behavior of a sufficient order (for the experiment in question) has been considered. 

A combination of the molecular polyelectrolyte theory with the methods of statistical mechanics can be used at least for the description of the chain expansion due to charges along the polysaccharide chain. The physical process of the proton dissociation of a (weak) polyacid is a good way to assess the conformational role of the poly electrolytic interactions, since it is possible of tuning poly electrolyte charge density on an otherwise constant chemical structure. An amylose chain, selectively oxidized on carbon 6 to produce a carboxylic (uronic) group, has proved to be a good example to test theoretical results. ... 

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