Pairwise comparisons multiple

In summary, there is not much to be gained in using one-way analysis of variance with multiple treatment groups. A simpler analysis structuring the appropriate pairwise comparisons will more directly answer the questions of interest. One final word of caution though undertaking multiple comparisons in this way raises another problem, that of multiplicity. For the time being we will put that issue to one side we will, however, return to it in Chapter 10. 

In this context, each patient would be receiving each of the multiple treatments. In the cross-over trial with three treatments this would likely be a three-period, three-treatment design and patients would be randomised to one of the six sequences ABC, ACB, BAC, BCA, CAB or CBA. Although there are again ways of asking a simultaneous question relating to the equality of the three treatment means through an analysis of variance approach this is unlikely to be of particular relevance questions of real interest will concern pairwise comparisons. 

The discussion so far in this section has assumed that the treatment groups are unordered. There are, however, situations where these multiple treatment groups correspond to placebo and then increasing dose levels of a drug. It could still be in these circumstances that we are looking to compare each dose level with placebo in order to identify, for example, the minimum effective dose and again we are back to the pairwise comparisons. 

The Tar—Tar sequence as well as the A-form RNA and B-form DNA equivalents of Tar—Tar (see Fig. 20.3) do not contain palindromes. However, we have data from multiple independent simulations and the analysis of Ponomarev et al. can be repeated using data from pairs of simulations. The equivalent test is to compare the residue-resolved ion-contact distributions between replicate trajectories. Such comparisons are a stringent test if each simulation was separately initialized with randomized ion starting positions and velocities. The PCCs for the A-form RNA simulations are shown in Fig. 20.4. Error bars denote the standard errors across the six possible pairwise comparisons across four independent trajectories, each of... 

Duration of action of the compounds is assessed by determining the period of time for which the inhibitory effects remain significantly different from vehicle controls. Statistical analysis of the data is performed by a repeated measure analysis of variance (ANOVA) followed by pairwise comparisons against control at each time period using Fisher s LSD multiple comparison test. 

The important point to note here is that the a = 0.05 level is deemed appropriate when a single test is being conducted. Multiple comparisons, by definition, mean that more that one test is being conducted. When testing a number of pairwise comparisons - for example, after an ANOVA where the null hyqiothesis has been rejected - it is not acceptable to test each pairwise comparison at the a = 0.05 level because of the potential inflation of the overall type I error rate. 

The issue of type I error inflation caused by multiple testing appears in many guises in the realm of new drug development. This issue is of great importance to decision-makers, and we discuss this topic again later in the chapter. For now, we have not yet provided a full answer to our research question our description of analysis of variance is incomplete without a discussion of at least one analysis method that controls the overall type I error rate when evaluating pairwise comparisons from an ANOVA. 

May, A. C. and M. S. Johnson, Improved genetic algorithm-based protein structure comparisons pairwise and multiple superpositions. Protein Eng, 1995. 8(9) p. 873-82. 

Pairwise and multiple sequence comparisons creation, editing, display, and analysis searching of nucleic acid and protein sequence databases for similar sequences to an input sequence or pattern using BLAST and FASTA in their various forms... 

Takeda, E., and Yu, P. L. (1995), Assessing Priority Weights from Subsets of Pairwise Comparisons in Multiple Criteria Optimization Problems, European Journal of Operational Research, Vol. 86. Werners, B. (1987), Interactive Multiple Objective Programming Subject to Flexible Constraints, European Journal of Operational Research, Vol. 31, pp. 342-349. 

Pairwise comparisons among 80 adult E. rufescens using a distribution-free multiple comparison test based upon the Kruskal-Wallis ranked sums test (Hollander Wolfe, 1973) indicate that the active surface area of paired males is significantly larger than that of single males and those of both paired and single females (P < 0.05 for each comparison)... 

We used t-tests with a Bonferroni adjustment for multiple comparisons when appropriate. When assumptions for parametric analysis were not met, we used Kruskal-Wallis (H) analysis of variance on rank, followed by planned pairwise comparisons of interest using Dunn s (Q) method. 

Accommodates multiple criteria Length of the process, which increases with the number of levels and number of pairwise comparisons... 

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