Spatial dependency is commonly measured and tested with Moran's I statistic. The question to be answered is, whether far-off objects affect this statistic and influence the test. Far-off objects are observations that are far apart from all other objects in the dataset, i.e. they do not have spatial links to other design points. In the paper different possibilities of treating such objects are discussed, and their influence on Moran's I and the corresponding spatial autocorrelation test is analysed. (author's abstract) / Series: Research Report Series / Department of Statistics and Mathematics