Omnibus tests

Again, even this information does not provide the most comprehensive answer possible in this situation. In this context of more than two treatment groups, the ANOVA is called an omnibus test. It is an overall test of statistical significance. The statistically significant result says that, somewhere, there is at least one statistically significant difference between pairs of the dose treatment groups. There are three pairs of dose treatment groups to consider ... 

In situations such as the one introduced in Section 7.9.2, i.e., one in which an omnibus test reveals a partial answer to the research question, multiple comparisons are performed. These are tests that facilitate the comparison of the means of each pair of treatment groups to see which pair(s) differ statistically significantly from each other. Multiple comparisons therefore provide a more detailed understanding of data than is provided by the initial omnibus test. (In cases where an omnibus test yields a nonsignificant result, it is not appropriate to continue to perform multiple comparisons.)... 

Use a single ( omnibus ) test to avoid a series of pair-wise comparisons... 

Multiple endpoints For this scenario, there is a whole other area of analysis referred to as multivariate statistics. These methods also allow omnibus testing - all endpoints are considered simultaneously. Multivariate stats are among the most complex to perform and interpret - there are generally six different ways to do any one... 

Bonferroni keeps the rate of type I errors down to 5 percent... In many instances, omnibus tests are not possible. If there are several comparisons to be made, each involving different groups of individuals and different endpoints, there may be no choice but to use a series of discrete statistical tests. In these circumstances, the Bonferroni correction may be applied to maintain the overall risk of false positives at the standard level of 5 per cent. 

Where several treatments are compared against each other, the first step in analysis should be an omnibus test (such as an ANOVA) and, if this proves significant, more detailed analyses can then be undertaken. 

The omnibus test statistic, X, follows a distribution with it — 1 df. If the omnibus test is rejected the pairs of groups can be evaluated using a Bonferroni-type approach. This requires the assumption that the ranks are normally distributed. As with the parametric one-way ANOVA, a minimally significant difference in ranks can be calculated for this purpose as ... 

Under the null hypothesis that the sample comes from a normal distribution, Zj is approximately normally distributed. Eqs. (4.39)-(4.43) to are based on the skewness of the samples. The other half of the omnibus test is based on the kurtosis. Compute... 

D Agostino, R.B. An omnibus test of normality for moderate and large sizes. Biometrika 1971 58 341-348. 

The hazardous waste regulations of Alabama, Arkansas, Oregon, and Utah do not require an HRA as a condition for obtaining a RCRA hazardous waste incinerator permit. However, state authorities have required HRAs at each of the chemical agent disposal facilities based on the RCRA omnibus authority. The RCRA permits for ANCDF, PBCDF, UMCDF, and TOCDF all require that an HRA or an HRA addendum be submitted after each trial burn or performance test. 

Bonferroni s test is the most straightforward of several statistical methodologies that can appropriately be used in the context of multiple comparisons. That is, Bonferroni s test can appropriately be used to compare pairs of means after rejection of the null hypothesis following a significant omnibus F test. Imagine that we have c groups in total. Bonferroni s method makes use of the following inequality ... 

The significant result of the omnibus F test led to the rejection of the null hypothesis of no significant differences, thereby revealing the presence of a significant difference between at least one pair of means. It is now of interest to determine precisely which pair or pairs of means are significantly different. 

The first step in our analytical strategy was to conduct an ANOVA. This ANOVA tested the null hypothesis that there were no differences among the three means. The null hypothesis was tested at an a level of O.OS, and was rejected on the basis of the significant omnibus f test. 

If the omnibus F test is significant, what are the pairwise comparisons that would be of interest ... 

In Chapter 11 we discussed the issue of multiple comparisons and multiplicity in the context of pairwise treatment comparisons following a significant omnibus F test. When we adopt the 5% significance level (a = 0.05), by definition it is likely that a type 1 error will occur when 20 separate comparisons are made. That is, a statistically significant result will be "found" by chance alone. The greater the number of objectives presented in a study protocol, the greater the number of comparisons that will be... 

Alternatively, instead of using the EBE of the parameter of interest as the dependent variable, an estimate of the random effect (t ) can be used as the dependent variable, similar to how partial residuals are used in stepwise linear regression. Early population pharmacokinetic methodology advocated multiple linear regression using either forward, backwards, or stepwise models. A modification of this is to use multiple simple linear models, one for each covariate. For categorical covariates, analysis of variance is used instead. If the p-value for the omnibus F-test or p-value for the T-test is less than some cut-off value, usually 0.05, the covariate is moved forward for further examination. Many reports in the literature use this approach. 

Another approach to multiple comparisons is the Bonferroni test. The strategy in this case is to divide a (typically 0.05 when a single comparison is being made) by the number of tests conducted following a significant omnibus ANOVA test. Hence, if ten comparisons were to be made, the a-level used for each comparison would become 0.05/10, i.e., 0.005, a considerably more conservative value. 

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