Pairwise comparison

Table 4.5-8 Requirements for Paired Coinparisons List of all human errors analyzed using this method, Expert tables generated during the pairwise comparisons,...

Results of pairwise comparison of three produets in two presentation orders by 13 panellists. 

The overall mean chlorpromazine-equivalents per day (CPZe) dose prescribed differed significantly, with lower dosing in Thailand compared with Malaysia and Australia (p < 0.001) (see Table 11.4). Pairwise comparisons revealed that the mean typical antipsychotic dose was significantly higher in Malaysia compared with Thailand (p < 0.001) and NWMH (p < 0.001). There were significant differences observed (p < 0.001) while comparisons of the mean atypical antipsychotic dose showed that Australia was significantly higher compared with Thailand (p < 0.001) and Malaysia (p < 0.001). 

After a number of new solutions are produced by crossover (or more generally, recombination) and mutation operations, improved solutions must be incorporated into the population. The best solution found thus far is almost always retained. A common strategy replaces a certain fraction of the remaining individuals, either with improved offspring or with new individuals chosen to maintain diversity. Another strategy is tournament selection, in which new solutions and current population members compete in a tournament. Each solution competes with K other solutions, which may be randomly selected, and, in each pairwise comparison, the solution with best fitness value wins. If P is the population size, the P solutions with the most wins become the new population. 

Rc will also depend on the initial absorbance (greater initial absorbance implies larger Rc (15)), and so all of the curves in the three figures cannot be strictly compared to one another. However, several pairwise comparisons are precisely valid, and the absorbances are close enough that a common comparison among afl of them is useful. The following points are evident ... 

As a general approach, most pharmaceutical statisticians begin by testing for the presence of a dose-related trend in tumor proportions. If the trend test is significant, that is, the p value is less than or equal to 0.05, pairwise comparisons are performed... 

Although in most cases the use of trend tests is appropriate since most biological responses are dose related, there are exceptions to this rule. Certain drugs, especially those with hormonal activity, may not produce classical dose responses and may even induce inverse dose-response phenomena. In these cases, a pairwise comparison may be appropriate in the absence of a significant positive trend. 

Note that the testing for trend is seen as a more sensitive way of picking up a possible treatment effect than simple pairwise comparisons of treated and control groups. Attempting to estimate the magnitude of effects at low doses, typically below the lowest positive dose tested in the study, is a much more complex procedure, and is heavily dependent on the assumed functional form of the dose-response relationship. 

It tests all linear contrasts among the population means (the other three methods confine themselves to pairwise comparison, except they use a Bonferroni type correlation procedure). 

New domains and their boundaries have been defined manually from sequence alone for literally hundreds of protein domains. Finding regions of similarity between proteins allows detection of domains. However, defining the exact boundaries of the domain is often a more difficult problem. Certain rules can be used to find the maximum size of a domain from pairwise comparisons of proteins in a related family. 

Lastly, it is desirable that parameters are able to discriminate between positive and negative conditions in a variety of experimental conditions. In other words they should be robust and reproducible. For this purpose, the Pearson correlation coefficient between all experimental repeats using control wells is calculated. Robust parameters have high Pearson correlation coefficients (above 0.7) in pairwise comparisons of experimental repeats. For this analysis we have developed another R template in KNIME to calculate the Pearson correlation coefficient between experimental runs. 

A significant p-value from this test would cause us to reject the null hypothesis, but the conclusion from this only tells us that there are some differences somewhere at least two of the ps are different. At that point we would want to look to identify where those differences lie and this would lead us to pairwise comparisons of the... 

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. 

Comments as above for the between-patient designs apply also for the within-patient designs and in many cases the best approach will be to focus on a sequence of pairwise comparisons using the paired t-test. 

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. 

Carlo test (Manly, 1997) using the chi statistic (Snedeeor and Coehran, 1967) because of the many low-number (or zero) observations. In the simulations, the number of observations per loeation was kept fixed. For eaeh test, 10,000 simulations were performed and pairwise comparisons were also made using this method. 

In the third portion of the study, the results using five different sampler and analytical method combinations were compared. When obvious outliers were excluded from the data, the normalized percentage differences compared to the mean value for sulfur varied from -21 to +23%. Pairwise comparisons for other elements showed similar variability. The agreement overall for X-ray fluorescence compared to PIXE was good, although there was scatter in the individual measurements, perhaps due to differences in sampling (Nejedly et al., 1998). 

Table 2. Stomatal density (SD), Epidermal cell density (ED) and stomatal index (SI) of modern Quercus kelloggii leaves, assigned to light regime during growth by degree of undulation, and p-values from a pairwise comparison using a nested mixed-model ANOVA based on a general linear model.

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