The structural polarity of cellular microtubules can be visualized in situ by lysing cells in special buffers containing tubulin. Under these conditions, the tubulin polymerizes to form curved sheets which attach to the walls of the endogenous microtubules. When such decorated microtubules are cut in cross section and viewed in the electron microscope, they appear to bear hooks curving clockwise or counter-clockwise. The direction of hook curvature is defined by the orientation of the decorated microtubule and thus serves as a probe for microtubule polarity. In this paper we describe a way to analyze the relative frequencies of hooks of different curvatures so as to measure the fidelity of the relation between hook curvature and microtubule polarity. The assumptions of the method are tested and found to be valid to a reasonable accuracy. The correlation between hook curvature and microtubule orientation is shown to be at least 0.98 for the spindles of PtK cells and Haemanthus endosperm at all stages of division and at all places in the spindle. The correlation is shown to be valid for each hook that forms, so the polarity of those microtubules that bear multiple hooks is specified with even better certainty than 0.98. This property of hook decoration is used to reinvestigate the possibility that some of the microtubules of the kinetochore fiber might be oriented with their plus ends distal to the kinetochore (opposite to the direction previously shown to predominate). Close analysis fails to identify such oppositely oriented microtubules. The scoring of tubules bearing multiple hooks also shows that individual interzone fibers at anaphase are constructed from clusters of antiparallel microtubules. The method for estimating the correlation between hook decoration and microtubule polarity is shown to be applicable to many structures and circumstances, but we find that the hook decoration assay for microtubule polarity is not uniformly accurate. We suggest that future studies using hook decorations should employ the method of data analysis presented here to assess the accuracy of the results obtained.