Integral evaluation of indicators in models of parametric and non-parametric analysis of variance. Use of the categorical principal component - Herrera, M.; Guerra, C. W.; Medina, Y. (Cuban Journal of Agricultural Science, 2016)
In order to establish possible relations among statistical indicators in models of parametric and non-parametric analysis of variance, belonging to completely randomized and random block experimental designs, the categorical principal component analysis was used because they are quantitative and qualitative. The models of analysis of variance of simple classification, with 16 experiments, were selected, as well as those of double classification with five experiments. An amount of 100 discrete and categorical variables were analyzed. A matrix of data was designed using the indicators of completely randomized designs and the test of Kruskal-Wallis, which is its non-parametric homologue, the model of random blocks with its non-parametric homologue, and the test of Friedman. The categorical principal component analysis showed adequate reliability and a variability percentage explained with 0.94. The indicators with more importance in the first dimension are related to probability of type I error and power, showing absolute values close to one and allowing to determine their contribution in this study. The results evidenced the existing relations among the analyzed statistical indicators, from the high degree of positive correlation over 0.90 among the values of probability of type I error in the F test of Fisher (with and without transformation) and its non-parametric homologue test, as well as the high negative correlations, existing between around 0.8 and 0.93 of them with values of power (with or without data transformation). It is necessary to continue the analysis for different data distributions and sample sizes. Key words: statistical indicators, models of simple and double variance analysis, categorical principal component analysis