Application of two statistical goodness-of-fit tests in complex samples: A practical case in forest field

摘要

In this research two goodness-of-fit tests are compared in terms of their type I error: Pearson's Chi-square test and Rao-Scott test with correction of second order, applied to data collected using sampling methods that do not fulfill the assumptions of independence and equal probability of inclusion of observations, methods called complex surveys. Both tests were utilized to fit diametric categories in a gmelina plantation (Gmelina arborea), applying systematic sampling with fixed area plots and with variable area plots (Bitterlich Sampling or variable radius plot), and employing simulation techniques. The Rao-Scott test with correction of second order registered a lower Type I error, close to the nominal a, when compared to the Pearson Chi-square test, due to the fact that the former takes into account the effects of the sample design and corrects the violation of the assumptions. The results obtained in this research show that the use of Pearson's Chi-square goodness-of-fit test is inappropriate in data obtained applying fixed area and variable area plots, widely used in forestry inventories. Therefore, it is important to use statistical tests that take into account sampling design complexity, in order to achieve valid inferences.