A Practical Measure of Offence Seriousness: Sentence Severity, continued
As Table 1 illustrates [and you will remember that I am not able to provide the tables here], the set of offenses in the dataset are discriminable not only by the descriptive characteristics suggested by their legal labels, but also by the degrees of two metric characteristics, namely sentence length and (judged) offence seriousness. The ordinal progression of offence serious-ness values shows a good correspondence to the rank order of the mean sentence severity scores, albeit with some mismatches. This apparent concordance is expressed in a Pearson correlation of .84 obtained between these two sets of scores.
Next, the two scales were plotted on linear co-ordinate paper, and it was observed that the rate of change in the upper ranges was greater for sentence severity than for offence seriousness. Thus, it seemed clear that the two variables did not follow a parallel linear path with respect to one another. This fact suggested the appropriateness of transforming scores to improve linearity. Unfortunately, for want of a criterion on which to scale the real intervals between offence categories, it was not possible to determine which of the two variables to transform or which type of transformation might be expected to make appropriate corrections to either variable. From the point of view of offence seriousness, sentence severity accelerates in the upper ranges; and from the point of view of sentence severity, offence seriousness is truncated in the upper ranges. Moreover, to apply a transformation to the sentence severity measure would add another minor complexity to the task of the correctional evaluation researcher working with sentence severity as a measure of seriousness. These two considerations seemed sufficient to warrant trying transformations on both of the variables. Table 3 presents the results of the regressions of untransformed offence seriousness on variously transformed sentence severity, and of untransformed sentence severity on variously transformed offence seriousness. It is worth noting that, although some transformations do improve the correlation between the two scales, — particularly the logarithmic (r=.93), square root (r=.92) and quadratic (r=.91) transformations of sentence severity and the quadratic (r=.99), exponential (r=.93), and power (r=.89) transformations of offence seriousness – it is almost unnecessary to transform the data since the basic relationship between the two variables (r=.84) appears reasonably robust even in untransformed form.
Insert Table 3 about here