Non-significance interval

C. Non-significance Intervals for Significant Quantitative Factors DETERMINATION OF SST LIMITS REVIEW OF CASE STUDIES... 

For example, the effect of factor A on response CR t at ot = 0.05 was found significant when using the variance from duplicated design experiments to estimate the critical effect (see Table 11). However, since this factor represents different CE equipments, i.e., is discrete, calculating a non-significance interval is irrelevant. 

Suppose a factor X has 45, 50, and 55 as extreme low, nominal, and extreme high levels, respectively, and an effect of 100 on response Y, with the critical effect equal to 80. Then the non-significance interval limits for this factor are [46.0,54.0], which means that when restricting the levels of X to this interval, the quantitative aspect of the method is considered robust. It can be noticed that the interval is symmetrically around the nominal level and meant for factors thus examined, i.e., with extreme levels symmetrically around the nominal. 

Most frequently, the design results, or more specifically the factor effects, are analyzed graphically and/or statistically, to decide on method robustness. A method is considered robust when no significant effects are found on responses describing the quantitative aspects. When significant effects are found on quantitative responses, non-significance intervals for the significant quantitative factors can be defined, to obtain a robust response. However, no case studies were found in CE where such intervals actually were determined. 

Trial 3 has given non-significance statistically and inspecting the confidence interval tells us that there is nothing in terms of clinical importance either at most with 95 per cent confidence the benefit of the active treatment is only 3.1 mmHg. 

Figure 6.7 shows the influence of the size of the experimental effect. If the mean clearances differ to only a very small extent (as in the two lower cases in Figure 6.7), then the 95 per cent confidence interval will probably overlap zero, bringing a non-significant result. However, with a large effect (as in the two upper cases), the confidence interval is displaced well away from zero and will not overlap it. 

One of the factors that feeds into the calculation of a two-sample /-test is the sample size. If we investigate a case where there is a real difference, but use too small a sample size, this may widen the 95 per cent confidence interval to the point where it overlaps zero. In that case, the results would be declared non-significant. This is a different kind of error. We are now failing to detect an effect that actually is present. This is a false negative or type II error . 

Variability of the data We know that the width of the 95 per cent Cl depends upon the variability of the data (Section 5.9). If data vary greatly, the confidence interval will be wider and more likely to overlap zero, implying non-significance. Greater SDs bring less power. 

Eighteen times out of 20, the 90per cent confidence interval will span zero — the lower limit is below zero, so the null hypothesis cannot be rejected. The result is correctiy declared as non-significant. 

One time in 20, the entire interval will be below zero — the lower limit is again below zero and the result is correctiy interpreted as non-significant. 

The confidence interval includes zero, so the result is non-significant. The P value (0.155) confirms non-significance. 

Next, there is a block comparing palladium-iridium with all other catalysts except palladium (already considered). In this case, the gap between palladium-iridium and it is nearest rival (iridium) is just a little too small to be statistically significant however, the alloy was shown to be superior to the other two metals. For all the remaining comparisons among iridium, rhodium and platinum, the interval includes zero and they are non-significant. 

As for full factorial designs the levels of the variables are situated at the borders of the experimental interval for that variable. It is possible that the response function of that variable is curved with an optimum at an intermediate factor level (see Fig. 6.11). The effect calculated from the design can then be small and the variable may be incorrectly considered as non-significant 45. When such intermediate optima are considered possible, a solution can be to perform the screening at three levels by reflecting a... 

Some remarkable case reports have previously been published (SEDA-25, 169) and reports continue to appear, supplemented by prospective studies and other analyses. For instance, 11 studies involving ropinirole or pramipexole in a total of 2066 patients have been reviewed (24). Four of these (two each with ropinirole and pramipexole) were placebo-controUed. The pooled relative risk of somnolence was 4.98 compared with placebo there was a non-significant trend for greater somnolence with ropinirole, but the confidence intervals were much wider than with pramipexole. In the other studies levodopa alone was compared with levodopa plus the newer drugs the relative risk was 2.06 compared with levodopa alone. It must be borne in mind that somnolence and sleep attacks may be separate phenomena, although this is controversial. 

The only intervals, that do not contain zero, i.e., those concerning the main effects of silica (A), sodium hydroxide (B) and their interaction (AB), must be considered statistically significant. From the practical point of view, the statistically non significant effect of the crystallization times tested means that once the zeolite FAU starts to crystallize alone it is thermodynamically stable for the given experimental conditions. 

A study in 16 healthy men given zafirlukast 160 mg twice daily for 16 days with terfenadine 60 mg twice daily on days 8 to 16 found that the mean maximum serum levels and AUC of zafirlukast were reduced by 70% and 60%, respectively. There was a small, non-significant reduction in the terfenadine AUC and serum levels. A study in 8 healthy subjects given zafirlukast 160 mg twice daily with terfenadine 60 mg twice daily for 8 days found that the AUC of terfenadine and the QTc interval were not significantly increased with concurrent use, despite the fact that zafirlukast appears to inhibit CYP3A4 in vitro, the major enzyme involved in terfenadine metabolism. The reduction in zafirlukast serum levels would be expected to reduce its antiasthmatic effects, but this needs assessment. If both drugs are given be alert for a reduced response to zafirlukast. 

The kinetic parameters of the equations were determined by the least square method, where the sum of Z (X exp-X modei) has teen minimized. In order to test the adequacy of models two statistica tests have been realized as it is proposed by [Froment and Bishoff, (1990)]. Lack of fit (F) test was applied as well as 95% confidence interval of the parameters was estimated. Models that show lack of fit or whose parameter(s) is non-significantly different from zero or negative were rejected A block diagram of model discrimination is shown in the Figure 3. 

It is useful to obtain a predictive equation for the responses so that responses for intermediate factor levels can be predicted with a confidence interval. This can be done using ANOVA or regression if some of the factors can be assumed to be non-significant so that an error term can be estimated. The danger is that by choosing the smallest sums of squares the error estimate is biased to the small side. The half normal plot can be used to decide which factors should be included in the regression model. 

Significant evidence for the extreme stability of the carbenium ions derived from isopropenylferrocene was also provided by its -H-NMR spectrum in trifluoroacetic acid at 20°C which was similar to that reported earlier. However, repeated scans of this sample at 1 h intervals showed no changes until a period of 10 h had elapsed. Thus it seems that the formation of the carbenium ion is very facile and once formed it is extremely stable in a non-nucleophilic environment. On pouring the contents of the NMR tube into methanol, no precipitate was seen. 

A realistic uncertainty interval has to be estimated, namely by considering the statistical deviations as well as the non-statistical uncertainties appearing in all steps of the analytical process. All the significant deviations have to be summarized by means of the law of error propagation see Sect. 4.2. 

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