Using different statistical tests

Using several different statistical methods, for example, an unpaired t-test, an analysis adjusted for centre effects, ANCOVA adjusting for centre and including baseline risk as a covariate, etc., and choosing that method which produces the smallest p-value is another form of multiplicity and is inappropriate. 

It is good practice to pre-specify in the protocol, or certainly in the statistical analysis plan, the statistical method to be used for analysis for each of the endpoints within the confirmatory part of the trial. This avoids the potential for bias at the analysis stage, which could arise if a method were chosen, for example, which maximised the treatment difference. As a consequence changing the method of analysis following unblinding of the study in an unplanned way, even if there seem sound statistical reasons for doing so, is problematic. Such a switch could only be supported if there was a clear algorithm contained within the statistical analysis plan which specified the rules for the switch. An example of this would be as follows  

The blind review does offer an opportunity to make some final changes to the planned statistical methods and this opportunity should not be missed but remember this is based on blinded data. 

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Using different statistical tests on the same data... 

The different statistical tests discussed in this book are all defined by the left column, that is, the initial situation Hq is known and circumscribed, whereas Hi is not (accordingly one should use the error probability a). 

Section 1.6.2 discussed some theoretical distributions which are defined by more or less complicated mathematical formulae they aim at modeling real empirical data distributions or are used in statistical tests. There are some reasons to believe that phenomena observed in nature indeed follow such distributions. The normal distribution is the most widely used distribution in statistics, and it is fully determined by the mean value p. and the standard deviation a. For practical data these two parameters have to be estimated using the data at hand. This section discusses some possibilities to estimate the mean or central value, and the next section mentions different estimators for the standard deviation or spread the described criteria are fisted in Table 1.2. The choice of the estimator depends mainly on the data quality. Do the data really follow the underlying hypothetical distribution Or are there outliers or extreme values that could influence classical estimators and call for robust counterparts ... 

If there are separate analysis plans for the clinical and economic evaluations, efforts should be made to make them as consistent as possible (e.g., shared use of an intention-to-treat analysis, shared use of statistical tests for variables used commonly by both analyses, etc.). At the same time, the outcomes of the clinical and economic studies can differ (e.g., the primary outcome of the clinical evaluation might focus on event-free survival, while the primary outcome of the economic evaluation might focus on quality-adjusted survival). Thus, the two plans need not be identical. 

What about the risks of decisions As we already know from the construction of confidence intervals, the probability, P, is connected with the complementary error probability, a. In a similar manner here the probability, a, characterizes the risk (of the first kind) of making a wrong decision as a result of using a statistical test. But the notion wrong may be seen from two different sides. 

Normal Distribution is a continuous probability distribution that is useful in characterizing a large variety of types of data. It is a symmetric, bell-shaped distribution, completely defined by its mean and standard deviation and is commonly used to calculate probabilities of events that tend to occur around a mean value and trail off with decreasing likelihood. Different statistical tests are used and compared the y 2 test, the W Shapiro-Wilks test and the Z-score for asymmetry. If one of the p-values is smaller than 5%, the hypothesis (Ho) (normal distribution of the population of the sample) is rejected. If the p-value is greater than 5% then we prefer to accept the normality of the distribution. The normality of distribution allows us to analyse data through statistical procedures like ANOVA. In the absence of normality it is necessary to use nonparametric tests that compare medians rather than means. 

After these preprocessing steps, raw data can be used for biological interpretation. In a typical experiment comparing two conditions, raw gene expression data is converted to log 2 fold-changes. Significances are calculated with different statistical tests. 

The two-sample t-test (or Student s t-tesi) is the most widely used parametric statistical test. This test compares the means of two populations that should be normally distributed when a sample size is small. The test statistic is formed as the mean difference divided by its standard error, that is, the difference of measured expressions normalized by the magnitude of noises. If the difference of the measured expressions is very large relative to its noise, it is claimed as being significant. Formally, suppose we want to test null hypotheses, H/. pji = pj2, against alternative hypotheses, Hj pji pp, foij= 1, 2,..., m. The test statistic for each j is... 

However, concerning the field data we face a theoretical problem. The data set is apparently different concerning a digit place in terms of the operation time of the item sets. It means that currently produced items obviously operate for a shorter time than the ones manufactured previously. This situation can affect a calculation procedure as weU as a comparison of the results. Taking into account this situation it is necessary to test the field data using the statistical test which is supposed to prove their comparabdity. The results of the test are mentioned in the second paper named Statistical comparing of rehabdity of two sets of highly reliable items . For more details see e.g. Neson(1982). 

Alternatively, stability can be assessed over at least three intervals (including the initial analysis as one interval) to determine if any instability trends are present. Determination of the statistical significance of any differences in concentration observed at the different time intervals can in the first instance use standard statistical tests for differences between means and variances (Section 8.2.5). It is more difficult to determine whether or not any such differences represent a trend. In principle the analyst could determine the slope of the plot of measured concentration vs time and apply statistical tests to the variance of the slope to determine whether the slope differs significantly from zero (Section 8.3) three points on such a plot are the bare minimum to establish a slope, and in any event for any statistical test of significance, appropriate confidence limits and confidence levels must first be decided on. Thus, while... 

From a methodological point of view, we use entry, exit and persistence indicators to highlight differences in the contracting behaviour of laboratories over the nine year period and to underline that persistence in contracting is a major phenomenon. We use appropriate statistical tests to analyse whether persistent and non-persistent laboratories have the same portfolio of contracts and whether the demand side or the experience hypothesis dominates, or both co-exist. Overall, our contribution aims at shedding new light on how past behaviour in terms of contracting influences the current portfolio of contracts of academic laboratories. 

In this experiment students standardize a solution of HGl by titration using several different indicators to signal the titration s end point. A statistical analysis of the data using f-tests and F-tests allows students to compare results obtained using the same indicator, with results obtained using different indicators. The results of this experiment can be used later when discussing the selection of appropriate indicators. 

Using an appropriate statistical test, determine whether there is any significant difference between the standard and new methods at a = 0.05. 

Once a significant difference has been demonstrated by an analysis of variance, a modified version of the f-test, known as Fisher s least significant difference, can be used to determine which analyst or analysts are responsible for the difference. The test statistic for comparing the mean values Xj and X2 is the f-test described in Chapter 4, except that Spool is replaced by the square root of the within-sample variance obtained from an analysis of variance. 

Interpreta.tlon, Whereas statistical tests estabhsh whether results are or are not different from (over) an exposure criteria, the generaUty of this outcome must be judged. What did the samples represent May the outcome, which is inferred to cover both sampled and unsampled periods, be legitimately extrapolated into the future In other words, is the usual assumption of a stationary mean vaUd AH of these questions are answered by judgment and experience appHed to the observations made at the time of sampling, and the answers are used to interpret the quantitative results. 

Different tests for estimation the accuracy of fit and prediction capability of the retention models were investigated in this work. Distribution of the residuals with taking into account their statistical weights chai acterizes the goodness of fit. For the application of statistical weights the scedastic functions of retention factor were constmcted. Was established that random errors of the retention factor k ai e distributed normally that permits to use the statistical criteria for prediction capability and goodness of fit correctly. 

It must be appreciated that the selection of the best model—that is, the best equation having the form of Eq. (6-97)—may be a difficult problem, because the number of parameters is a priori unknown, and different models may yield comparable curve fits. A combination of statistical testing and chemical knowledge must be used, and it may be that the proton inventory technique is most valuable as an independent source capable of strengthening a mechanistic argument built on other grounds. 

In the course of pharmacological experiments, a frequent question is Does the experimental system return expected (standard) values for drugs With the obvious caveat that standard values are only a sample of the population that have been repeatedly attained under a variety of circumstances (different systems, different laboratories, different investigators), there is a useful statistical test that can provide a value of probability that a set of values agree or do not agree with an accepted standard value. Assume that four replicate estimates of an antagonist affinity are made (pKb values) to yield a mean value (see Table 11.14). A value of t can be calculated that can give the estimate probability that the mean value differs from a known value with the formula... 

In these cases it is not necessary to determine the absolute bioavailability or the absorption rate constant for the product under study. It is only necessary to prove that the plasma concentration versus time curve is not significantly different from the reference product s curve. This is done by comparing the means and standard deviations of the plasma concentrations for the two products at each sampling time using an appropriate statistical test. 

Many statistical methods have been developed for association studies [52, 53] that mostly consist of testing each polymorphism separately with the disease. It has been shown that the power of such methods decreases rapidly when the markers are in low or even moderate LD with the risk-conferring polymorphism [54]. One way to overcome this defect is to use haplotype-based tests [47, 55, 56] that combine different alleles of different markers. Haplotypes are likely to capture... 

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