Statistical conclusion

A minimum of five laboratories should be used to provide meaningful statistical conclusions from interlaboratory studies... 

With such tables established for each group in a study, we may now proceed to test the hypotheses that each of the treated groups has a significantly shorter duration of survival, or that of the treated groups died more quickly (note that plots of total animals dead and total animals surviving will give one an appreciation of the data, but can lead to no statistical conclusions). 

The results of the CSB incident data analysis are acknowledged as representing only a sampling of recent reactive incident data. This limitation precludes CSB from drawing statistical conclusions on incidence rates or inferring trends in the number or severity of incidents. However, despite these limitations, the data can be used to illustrate the profile and causes of reactive incidents. 

A basic assumption underlying r-tests and ANOVA (which are parametric tests) is that cost data are normally distributed. Given that the distribution of these data often violates this assumption, a number of analysts have begun using nonparametric tests, such as the Wilcoxon rank-sum test (a test of median costs) and the Kolmogorov-Smirnov test (a test for differences in cost distributions), which make no assumptions about the underlying distribution of costs. The principal problem with these nonparametric approaches is that statistical conclusions about the mean need not translate into statistical conclusions about the median (e.g., the means could differ yet the medians could be identical), nor do conclusions about the median necessarily translate into conclusions about the mean. Similar difficulties arise when - to avoid the problems of nonnormal distribution - one analyzes cost data that have been transformed to be more normal in their distribution (e.g., the log transformation of the square root of costs). The sample mean remains the estimator of choice for the analysis of cost data in economic evaluation. If one is concerned about nonnormal distribution, one should use statistical procedures that do not depend on the assumption of normal distribution of costs (e.g., nonparametric tests of means). 

GAC and Ozone-GAC. The Wilcoxon test was applied to compare results before and after GAC filtration. By using data for DCM or MeOH extracts, no interpretation of the variations observed and no statistical conclusions can be drawn. This situation is true for GAC treatment alone and for all combinations of dose, contact time, and GAC (Table III). 

Disinfection with Chlorine and Chlorine Dioxide. The comparison of the mutagenic activity of the DCM extract before and after disinfection treatment was studied by the Wilcoxon test. No statistical conclusions on disinfection effects can be drawn. However, the MeOH extract showed a significant decrease in mutagenic activity for the line 2 chlorine treatment. Comparison of the two disinfection treatments for the nonozonated GAC filtered water (treatment line 4) shows that chlorine disinfection yields greater mutagenic activity of the DCM extract than chlorine dioxide (Table V). 

Low ozonation rate treatments (lines 1 and 2) of this water source were observed to decrease mutagenic activity of low molecular weight and chromatrographable compounds. GAC treatment changed mutagenic activity, but no statistical conclusions could be drawn. 

Graphical methods are powerful tools for extracting the information contained in data sets and making statistical conclusions easier to understand. A variety of techniques have been developed in recent years. An excellent overview of these methods is given by James and Polhemus [18],... 

Insofar as the effect of the atomic size difference on the shape of the liquidus line is concerned, there are not enough suitable phase diagrams (containing congruent-melting AB3 compounds) to establish a statistical conclusion in support or nonsupport of the theoretical prediction. Nevertheless, the two related systems, Bi-Li (nearly equal atomic size) and Bi-Na (unequal atomic size) appear to be in support of the theoretical prediction. 

Statistics must not be viewed as a method of making sense out of bad data, as the results of any statistical test are only as good as the data to which they are applied. If the data are poor, then any statistical conclusion that can be made will also be poor. 

With sufficiently complex samples, particularly biological and environmental samples, the frequency of overlap can be estimated by statistical means. In a statistical model developed by Davis and this author [33], far-reaching conclusions follow from a simple basic assumption the probability that any small interval dx along the separation path x is occupied by a component peak center is A dx, where A is a constant. This assumption defines a Poisson process and leads to well-known statistical conclusions. 

The precision of an instrument must be considered. Many typical measurements, for example, in atomic spectroscopy, are recorded to only two significant figures. Consider a dataset in which about 95 % of the readings were recorded between 0.10 and 0.30 absorbance units, yet a statistically designed experiment tries to estimate 64 effects. The /-test provides information on the significance of each effect. However, statistical tests assume that the data are recorded to indefinite accuracy, and will not take this lack of numerical precision into account. For the obvious effects, chemo-metrics will not be necessary, but for less obvious effects, the statistical conclusions will be invalidated because of the low numerical accuracy in the raw data. 

Example 9 illustrates that the same relative distribution of data produces a different statistical conclusion when there are different amounts of data available. Chi-squared varies directly with the sample size when the relative distribution within the sample is unchanged. Thus, it is possible to determine the sample necessary to give a significant test... 

In the above example, t = (0.08/0.0436) /3 = 3.2. From the table, corresponding to — 1 = 2 degrees of freedom, t = 2.920 at the 90% confidence level and 4.303 at the 95% level. Thus a value of t = 3.2 or greater would occur by chance alone less than once in 10 trials, and therefore the differences between methods A and B may be judged to be real. Actually, it is risky to draw conclusions from a group of data as limited as the example presented here for the sake of simplicity on the other hand, valid statistical conclusions are not necessarily based on an enormous body of data. 

Comparing the p value of 0.623 to a = 0.05, the statistical conclusion is not to reject the null hypothesis. There is insufficient evidence to conclude that the alternate hypothesis is true. If the goal of a new antihypertensive therapy were to... 

After a study has been completed, a statistical analysis provides a means either to reject or to fail to reject the null hypothesis. The statistical conclusion will, in part, be used to justify whether or not further investment is made in the development of a test product. A sound business strategy would dictate that further investment be made only if objective information from the study suggests it. Inferential statistics... 

How likely is the sponsor to be misled by the result of the statistical conclusion from a hypothesis test with design parameters a and p ... 

Consider the following probabilities, which express the likelihood of the true state of affairs given the statistical conclusion at the end of the study ... 

Statistical conclusion validity. Statistical conclusion validity refers to the validity of conclusions about whether the observed covariation between variables is due to change. In other words, it refers to the confidence with which one can say that there is a real difference in Y scores between X cases and X cases. 

It will probably be apparent that the methods used to increase internal validity and statistical conclusion validity and the techniques to gain precision will threaten the external validity of that particular set of data, but the relation is not a symmetrical one. Things that aid external validity, e.g. large and varied samples, may either hinder or help internal validity or have no effect on it. Moreover, it is certainly not the case that things that decrease internal validity will somehow increase external validity. 

Experimental validity means that the conclusions drawn on inference are true, relative to the perspective of the research design. There are several threats to inference conclusions drawn from experimentation, and they include (1) internal validity, (2) external validity, (3) statistical conclusion validity, and (4) construct validity. 

Step 5 If one computes < f w < it is still prudent to suspect possible serial correlation, particularly when n < 40. So, in drawing statistical conclusions, this should be kept in mind. 

Don t blindly follow statistical conclusions without taking into account their practical significance and economic considerations Negligence of the nonstatistical aspects of the experimental design can prove to be vital. 

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