Significance level, statistical term

Data were subjected to analysis of variance and regression analysis using the general linear model procedure of the Statistical Analysis System (40). Means were compared using Waller-Duncan procedure with a K ratio of 100. Polynomial equations were best fitted to the data based on significance level of the terms of the equations and values. 

There is a fair amount of language that we wrap around this process. We talk in terms of a test of significance. If p < 0.05, we declare statistical significance, and reject the null hypothesis at the 5 per cent level. We call 5 per cent the significance level, it is the level at which we declare statistical significance. If p > 0.05, then we say we have a non-significant difference and we are unable to reject the null hypothesis at the 5 per cent level. 

Odhiambo and Manene presented a performance analysis of stepwise screening that assumes a2 > 0, where statistical tests are fallible even if all assumptions are correct. They derived expected values of the number of runs required, the number of factors mistakenly classified as active, and the number of factors mistakenly classified as not active, in terms of p, f, k, and the significance level and power of the tests used. These expressions are fairly complicated and are not repeated here, but Odhiambo and Manene also provide simpler approximations that are appropriate for small values of p. 

Analysis of data To be considered as evidence, results must achieve the statistical significance level of p < 0.05, which can also be stated in terms of 95 per cent confidence intervals. Failure of study results to demonstrate a statistically significant difference in the measured effect is not sufficient to support a claim of equivalence between the treatments studied. 

The issue of multiplicity is that when performing multiple statistical tests, the error probability associated with the inferences made is inflated. To see this, let us consider a simple situation where one is interested in performing two statistical tests on independent sets of data, each at a significance level of 0.05. Thus, the probability that each of the two tests will be declared significant erroneously (type I error) is 0.05. However, the probability that at least one of the two tests will be declared significant erroneously is 0.0975. The probability that at least one of the tests of interest will be declared significant erroneously is called the experiment-wise error rate. If we perform three 0.05 level tests, the experiment-wise error rate increases to 0.143. In practical terms, this means that if we perform multiple tests and make multiple inferences, each one at a reasonably low error... 

In practical terms, this means that if we perform multiple tests and make multiple inferences, each one at a reasonably low error probability, the likelihood that some of these inferences will be erroneous could be appreciable. To correct for this, one must conduct each individual test at a decreased significance level, with the result that either the power of the tests will be reduced as well, or the sample size must be increased to accommodate the desired power. This could make the trial prohibitively expensive. Statisticians sometimes refer to the need to adjust the significance level so that the experimentwise error rate is controlled, as the statistical penalty for multiplicity. 

AU terms in the model are now statistically significant at 5 % significance level, and the predictive power of the model is fairly good according the Q2 value. Section 4.3 shows how this model has been used in search for improvement. 

The computed F statistics are now compared to their common critical value at the specified significance level, say, a = 0.05, that is, Fo osCl, ) = 161. Since none of these is greater than 161,we do not have sufficient evidence to conclude that any of the main effects and interactions are significant at a = 0.05. However, the computed F statistics do reveal that while the interaction DIET X EXR is relatively larger than the others, the factor SEX and another interaction DIET X SEX are negligible and thus can be merged with the error term. The resulting ANOVA table is listed in Table 12B. 

It is necessary to emphasize that it is very difficult to submit the proofs of NIEMF long-term effects on the statistically significant level of probability. First of... 

It is probably fair to say that for measures of safety performance that occur less than fifty times a year, the size of the year-to-year variation is so large in percentage terms that it may be difficult in practice to draw meaningful statistical conclusions. Fortunately, the situation is less discouraging if a railroad is observed over multiple years. Consider the twenty-five-percent significance level. A railroad would have an occurrence count above this level by pure chance one year in every four. However, if the railroad falls above the critical value for two years in a row, then the probability that this event will occur purely by chance, and not due to poor safety precautions by the railroad will be 14 or one chance in sixteen. The probability that the railroad would fall above the critical value by pure chance for three years in a row is or year in sixty-four, a very small probability. On this... 

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... 

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