Statisticians are interested in testing the structure of covariance matrices, especially under the high-dimensional scenario in which the dimensionality of data matrices exceeds the sample size. Many test statistics have been introduced to test whether the covariance matrix is equal to identity structure (<img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?H_%7B01%7D:%20%5CSigma%20=%20I_p" />), sphericity structure (<img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?H_%7B02%7D:%20%5CSigma%20=%20%5Csigma%5E2I_p" />) or diagonal structure (<img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?H_%7B03%7D:%20%5CSigma%20=%20diag(d_1,%20d_2,%5Cdots,d_p)" />). These test statistics work under the assumption that data follows the multivariate normal distribution. In our thesis work, we want to compare the performance of test statistics for each structure test under given assumptions and when the distributional assumption is violated, and compare the test sensitivity to outliers. We apply simulation studies with the help of significance level, power of test, and goodness of fit tests to evaluate the performance of structure test statistics. In conclusion, we identify the recommended test statistics that perform well under different scenarios. Moreover, we find out that the test statistics for the identity structure test are more sensitive to the changes of distribution assumptions and outliers compared with others. The test statistics for the diagonal structure test have a better tolerant to the change of the data matrices.

Diploma thesis focuses on examination of the use of Intelligence Structure Test IST 2000 R in diagnostics of high school students with dyslexia. To verify the suitability of its use, the thesis compares overall results of 56 dyslexic students with results of their peers who attend the same high schools in Prague 10 (Gymnázium Voděradská, Omská a Přípotoční, Střední průmyslová škola elektrotechnická V Úžlabině, Obchodní Akademie Heroldovy Sady). Afterwards, the results of 35 students with dyslexia are compared with their results of different in the past administrated intelligence tests (Pražský dětský wechsler, Wechslerova inteligenční škála pro děti). The results of the study showed that students with dyslexia scored significantly lower than their peers from intact population in the IST 2000 R test and their final score is significantly lower than their own results from different intelligence tests. Therefore, it is not correct to evaluate the IST 2000 R test as suitable for assessment of high school students with dyslexia.