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Nonparametric tests tend to reject less null hypotheses than the related parametric tests and have lower sensitivity, which leads to an increased rate of false negative errors. They are more appropriate when the assumptions for parametric tests are not satis ed, as is often the case with microarray data (see Fig. 4.9). However, this does not imply that nonparametric tests will necessarily identify a smaller number of genes as differentially expressed than the parametric test, or that the sets of genes identi ed by one parametric test and one nonparametric test will necessarily be in a subset relationship. To illustrate the difference in results we used both ANOVA and the Kruskal Wallis test to identify differentially expressed genes in the acute leukemia data set. Out of 7129 genes, 1030 genes were identi ed as differentially expressed by both methods. In addition to that, 155 genes were identi ed only by ANOVA, while 210 genes were identi ed only by the Kruskal Wallis test. 4.3.1.3 Advanced Statistical Models Recently, more sophisticated models and methods for the identi cation of differentially expressed genes have been proposed [26,27]. For example, when considering the factors of array (A), gene (G), and biological condition (T), a two-step mix-model [21] rst ts the variance of arrays, biological conditions, and interactions between arrays and biological conditions using one model, and then uses the residues from tting the rst model to t the second model. An overview of mix-model methods is provided in the work by Wol nger et al. [28]. Other advanced statistical approaches with demonstrated good results in identifying differentially expressed genes include the signi cance analysis of microarray (SAM) [29], regression model approaches [30], empirical Bayes analysis [31], and the bootstrap approach to gene selection (see the case study below).



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The GSM Memorandum of Understanding (MoU) was signed in September 1987 by 14 network operators from 13 countries. In November 1988 there were already 19 signatories from 18 countries. These network operators committed themselves to open service to their capital city and its airport in 1991. This agreement was a good starting point. But the implementation was not easy. The biggest problem was that manufacturers needed to be convinced that GSM was meant seriously. This was achieved nally in autumn 1998 by the award of ten contracts to a number of manufacturers for the supply of infrastructure. But this meant also that nine network operators who had signed the GSM MoU had not ordered infrastructure in the autumn of 1988. In addition several of the ten contracts ordered only a validation system. There were only two contracts with substantial quantities of infrastructure equipment, the contracts of Deutsche Telekom and France Telecom. Both operators had decided not to implement a large capacity analogue interim system. These volumes were the rst orders of large amounts of real serial equipment. GSM had a dif cult competitive situation in the case of operators who had implemented large capacity analogue interim systems 4 GSM had an inferior coverage in the beginning. Analogue hand-helds were available since the late 1980s. GSM hand-helds became available in quantities in 1993 and were in the beginning bigger than advanced analogue hand-helds.

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