There is considerable interest in cell biology in determining whether, and to what extent, the spatial arrangement of nuclear objects affects nuclear function. A common approach to address this issue involves analyzing a collection of images produced using some form of fluorescence microscopy. We assume that these images have been successfully pre-processed and a spatial point pattern representation of the objects of interest within the nuclear boundary is available. Typically in these scenarios, the number of objects per nucleus is low, which has consequences on the ability of standard analysis procedures to demonstrate the existence of spatial preference in the pattern. There are broadly two common approaches to look for structure in these spatial point patterns. First a spatial point pattern for each image is analyzed individually, or second a simple normalization is performed and the patterns are aggregated. In this paper we demonstrate using synthetic spatial point patterns drawn from predefined point processes how difficult it is to distinguish a pattern from complete spatial randomness using these techniques and hence how easy it is to miss interesting spatial preferences in the arrangement of nuclear objects. The impact of this problem is also illustrated on data related to the configuration of PML nuclear bodies in mammalian fibroblast cells.