Terms of statistical significance

If the 95 per cent confidence interval for the treatment effect not only lies entirely above - A but abo above zero, then there is evidence of superiority in terms of statistical significance at the 5 per cent level (p < 0.05). In this case, it is acceptable to calculate the exact probability associated with a test of superiority and to evaluate whether this is sufficiently small to reject convincingly the hypothesis of no differenc... Usually this demonstration of a benefit is sufficient for licensing on its own, provided the safety profiles of the new agent and the comparator are similar. ... 

Table IV. Terms of Statistical Significance to Mathematical Models...

Upon formulating these relationships, phenols with branched alkyl substituents were not included in the data of a-cyclodextrin systems, though they were included in (3-cyclodextrin systems. In all the above equations, the n term was statistically significant at the 99.5 % level of confidence, indicating that the hydrophobic interaction plays a decisive role in the complexation of cyclodextrin with phenols. The Ibrnch term was statistically significant at the 99.5% level of confidence for (3-cyclo-dextrin complexes with m- and p-substituted phenols. The stability of the complexes increases with an increasing number of branches in substituents. This was ascribed to the attractive van der Waals interaction due to the close fitness of the branched substituents to the (3-cyclodextrin cavity. The steric effect of substituents was also observed for a-cyclodextrin complexes with p-substituted phenols (Eq. 22). In this case, the B parameter was used in place of Ibmch, since no phenol with a branched... 

Statistical significance. This term relates to the probability that an event or difference occurred by chance alone. Thus, it is a measure of whether a difference is likely to be real, but it does not indicate whether the difference is small or large, important or trivial. The level of statistical significance depends on the number of patients studied or observations made, as well as the magnitude of difference observed. 

The p in p-value stands for probability and as such it therefore lies between 0 and 1. I am sure we all know that if the p-value falls below 0.05 we declare statistical significance and conclude that the treatments are different, that is pi 7 p2. In contrast if the p-value is above 0.05 then we talk in terms of non-significant differences. We will now explore just how this p-value is defined and later we will see the principles behind its calculation. 

Without introduction of IAF into the Kraus plot, the coefficients of determination generated for the rubber nanocomposites are found to be significantly less than unity (around 0.608). In terms of statistics, it means that although the present function relating the independent variable to the dependent variable is robust, its accuracy of mapping is hindered possibly because of neglecting certain other parameters that influence the independent variable. 

Whether the volume transition occurs with respect to temperature, salt or solvent composition, each model works well. Furthermore, neither model outperforms the other in terms of statistical quality of fit of data to theory. Also, the diffusion coefficients obtained from either model are normally comparable, even if a correction for the difference in reference frames is applied [119, 121, 153]. Theoretically, the value of D obtained from the different models differ significantly only for very large volume changes. Thus, if the desire is to correlate different experiments or to reduce kinetic data to a single parameter either model can be used satisfactorily. 

Here the terms are in order of statistical significance. It is reasonable to suspect that if 02 consumption were a first-order function of its concentration, growth would be likewise. The regression equation above would be dominated by the first-order 02 term. In fact, in Eq. (18), growth is a relatively weak function of 02. This suggests that metabolic activity was not a first-order function of 02 concentration in the concentration range we investigated. 

Strength of evidence involves the enumeration of tumours in human and animal studies and determination of their level of statistical significance. Sufficient human evidence demonstrates causality between human exposure and the development of cancer, whereas sufficient evidence in animals shows a causal relationship between the agent and an increased incidence of tumours. Limited evidence in humans is demonstrated by a positive association between exposure and cancer, but a causal relationship cannot be stated. Limited evidence in animals is provided when data suggest a carcinogenic effect, but are less than sufficient. The terms sufficient and limited are used here as they have been defined by the International Agency for Research on Cancer (lARC) and are outlined in 3.6.5.3.I. 

The term Zrz in the numerator of the expression is the normal deviate for the level of statistical significance to be employed. As this is usually the 0-05 level of statistical significance, Za is set to 1-96. Note that this is a two-tailed 95% normal deviate. A Type I error occurs if, by chance, P < 0 05 when the true difference between the treatments is zero. Chance is impartial, and such a difference could occur in either direction. 

The answer is no. In cases where there are only two levels, either test is applicable. The values obtained in the calculations of the respective tests will be different, but the tests will give precisely the same answer in terms of the degree of statistical significance obtained by the respective test statistic. That is, the t value and F value... 

We use this term in the restricted sense of statistical significance. In other words, if an effect is "significant", there is a high probability (95%, 99%, 99.9%) that the effect is "real" - that is, different from zero. The determination of the significance of an effect or of a mathematical model is an essential tool for the experimenter. 

In particular, we shall see that the regression sum of squares can also be subdivided, each part being associated with certain terms in the model - a sum of squares for the linear model, another for the quadratic and interaction terms. The statistical significance of the different terms in the model can then be assessed. 

A large number of the terms are statistically significant and numerically important, main effects, square terms and interactions. Significant effects (< 5%) are shown in bold type. 

Three terms are widely used to describe the precision of a set of replicate data standard deviation, variance, and coefficient of variation, dliese terms have statistical significance and are defined in Section alB-l. 

Usually one does not know if each potential descriptor will be important for the fit, so the usual procedure is to calculate all possible equations in order to find the ones in which all terms are significant. If there are many possible equations then stepwise strategies may be used. At the end of the process the user will select one or more best equations, based on the overall quality of the fit and the contribution of each term to the final fit. The latter criterion is necessary because it sometimes happens that one term is statistically significant but increases and decreases s so little that how necessary it is to include it in later predictions is questionable. 

The analysis of variance shows that the linear model is unsatisfactory, and that the other two models do not show lack of fit (Table 7A.4). This time, however, the special cubic model seems superior. The explained variation is larger, the MS of/MS ratio is smaller, and the cubic term is statistically significant. The contour curves for the cubic model are presented in Fig. 7A.3. The largest tensile strength values are obtained close to the base of the triangle, toward the left vertex, which corresponds to a blend that is predominantly PVDF, with httle or no polystyrene. 

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