ANOVA and Nonparametric Alternatives: Influence of Statistical Nuisance Factors to the Analysis of the relations between the Danube River and its Major Tributaries

Abstract

One-way ANOVA, nonparametric Kruskal-Wallis and Mann-Whitney tests were used to explore influence of the major tributaries (the Rivers Tisa, Sava and Velika Morava) to the eco-chemical status of the Danube. Various nuisance factors (outliers, departures from normality, seasonality, heteroscedasticity) affect objectivity these tests, therefore it was important to estimate their robustness, but also to apply proper procedures to detect presence of nuisance factors and mitigate their influence. The analysis of selected eco-chemical parameters: BOD-5, COD, UV extinction at 254nm, DO, Oxygen saturation, TDS, Electrical conductivity, Suspended matter, Total P, Phosphates, Nitrates, Ammonia, pH, Tot. alkalinity, m-2p alkalinity, CO2 and Temperature was performed for 15 years period. Because many eco-chemical parameters are subjected to changes over the time, relations determined during one year may not be the identical after 5 years or a decade. Advantage a large data base is that enables us to expand analysis to longer time periods and cover cyclic or linear variations of parameters which expand to longer periods of time than one year. We investigated applicability of ANOVA, post-hoc and related nonparametric tests (Kruskal-Wallis and Mann-Whitney test) combined with statistical tests developed to detect presence of various nuisance factors (Grubbs’ test for identification of outliers, Kolmogorov-Smirnov test for departures from normality, turning point test, Wald–Wolfowitz runs test and pairwise rank test for seasonality, Bartlett’s test for heteroscedasticity) and tested their performance, especially when they are combined with data transformations (e.g. Box-Cox transformations) whose role was to mitigate the effect of nuisance factors. ANOVA is generally robust enough to resist violations of required preconditions by various levels of the nuisance factors found in the environmental data sets collected from analyzed rivers, which suggests that these statistical methods are suitable for evaluating the influence of the tributaries in any other similar river system. Influence of the most of the nuisance factors can be reduced or avoided by using nonparametric methods and data transformations. The most severe negative influence resulted from the lack of independence related to the pronounced seasonality. The River Tisa was the most polluted tributary, but its pollution load was not substantial enough to exceed the Danube self-purification potential. The Belgrade city was also identified as serious pollution source.