We give a review of recent ANOVA-like procedures for testing group differences based on data in a metric space and present a new such procedure. Our statistic is based on the classic Levene's test for detecting differences in dispersion. It uses only pairwise distances of data points and and can be computed quickly and precisely in situations where the computation of barycenters ("generalized means") in the data space is slow, only by approximation or even infeasible. We show the asymptotic normality of our test statistic and present simulation studies for spatial point pattern data, in which we compare the various procedures in a 1-way ANOVA setting. As an application, we perform a 2-way ANOVA on a data set of bubbles in a mineral flotation process.

翻译：我们审视了最近根据计量空间数据测试群落差异的ANOVA类似程序,并提出了一种新的程序。我们的统计数据以经典的Levene的测试为基础,以探测分散差异。它只使用数据点的对称距离,在数据空间中“通用手段”的计算缓慢、近似甚至不可行的情况下可以快速精确地计算。我们展示了我们的测试统计和模拟空间点模式数据研究的无症状性常态性,其中我们比较了单向的ANOVA设置的各种程序。作为一个应用,我们在矿物漂浮过程中对一组泡沫数据进行了双向的 ANOVA。