A new functional ANOVA test, with a graphical interpretation of the result, is presented. The test is an extension of the global envelope test introduced by Myllymäki et al. (2017, Global envelope tests for spatial processes, J. R. Statist. Soc. B 79, 381-404, doi: 10.1111/rssb.12172). The graphical interpretation is realized by a global envelope which is drawn jointly for all samples of functions. If a mean function computed from the empirical data is out of the given envelope, the null hypothesis is rejected with the predetermined significance level α. The advantages of the proposed one-way functional ANOVA are that it identifies the domains of the functions which are responsible for the potential rejection. We introduce two versions of this test: the first gives a graphical interpretation of the test results in the original space of the functions and the second immediately offers a post-hoc test by identifying the significant pair-wise differences between groups. The proposed tests rely on discretization of the functions, therefore the tests are also applicable in the multidimensional ANOVA problem. In the empirical part of the article, we demonstrate the use of the method by analyzing fiscal decentralization in European countries.
Latent toxoplasmosis is the most widespread parasite infection in developed and developing countries. I'he prevalence of Toxoplasma gondii infection varies mostly between 20 to 80% in different territories. This form of toxoplasmosis is generally considered to be asymptomatic. Recently published results, however, suggest that the personality profiles of infected subjects differ from those of uninfected controls. These results, however, were obtained on non-standard populations (biologists or former acute toxoplasmosis patients). Here we studied the personality profiles of 191 young women tested for anti-Toxoplasma immunity during gravidity. The results showed that the differences between Toxoplasma-negative and loxoplasma-posilive subjects exits also in this sample of healthy women. The subjects with latent toxoplasmosis had higher intelligence, lower guilt proneness, and possibly also higher ergic tension. The difference in several other factors (desurgency/surgency, alaxia/protension, naiveté/shrewdness, and selfsentiment integration) concerned changes in the variances, rather than the mean values of the factors.
The latent toxoplasmosis is usually considered to be asymptomatic, however, this paradigm has never been rigorously tested. Here we searched for symptoms of deterioration of physical health (decrease of weight) in infected people by analysis of clinical records of 758 women tested for toxoplasmosis in the 16th week of gravidity. Toxoplasma-positive women have a lower body weight in the 16th week of gravidity (p = 0.02) than Toxoplasma-negative women. Moreover, a negative correlation between weight and the duration of toxoplasmosis was found in a subset of 174 Toxoplasma-positive women (p = 0.04), suggesting that slow and cumulative effects of latent toxoplasmosis, rather than a transient effect of acute toxoplasmosis, are responsible for the decreased weight of infected subjects. Longer duration of gravidity estimated from the date of last menstruation in the set of Toxoplasma-positive women in the 16th week of gravidity estimated with ultrasonography (p = 0.04) suggests a possibility of retarded foetal growth in Toxoplasma-positive women. The prevalence of latent toxoplasmosis is extremely high. Therefore, even its mild symptoms such as the decreased body weight in Toxoplasma-positive pregnant women might in fact indicate an unrecognized serious public health problem.