7.1 Score transformations: details

Before distributing the derived scores through the 'index' files, we usually choose to transform them to a consistent set of values. There are several transformation procedures available of which we concentrate on two: range transformations, which adjust the scores to fit within a specified range of the minimum and maximum values, and mean standardisation procedures, which can adjust the scores in line with their mean and standard deviation values over a given population. (Other possible transformations include, for example, ranking and normalisation, which assign scores based upon ranked positions rather than the magnitudes involved in original score values.)

The two procedures have alternative attractions. Using range transformations, we can ensure that every scale version has the same start and endpoints. We do not ensure, however, that different versions of the scale have the same population means, so the midpoint of a range transformation can be misleading and does not have a strong substantive interpretation.

Mean standardisation transformations can be used to force every scale version to have the same population mean value and variance parameters - such transformations are therefore more attractive when attempts to compare scales from different versions are made. However, a weakness with standardisation transformations is that there is no guarantee of where the endpoints of the distribution will lie, and it could be the case in some applications that extreme original scale values lead to standardised scores which are outside the range of data values we would like to use.

We choose to present CAMSIS derived scales through their mean standardised transformed values. However, reflecting the latter issue of the possibility of extreme values, we also impose a constraint on the range of the mean standardised scores, by 'cropping' any extreme values which do occur in order to fit within the desired range. In practice, such 'cropping' does not occur frequently, and does not usually have a significant substantive impact when it does, although we use notes made available in the version specific downloadable archives to highlight any occassions when the occurrences are high.

(Note that until a revision dated 4.4.02, we used only range transformation procedures. These presented a risk in that they could confuse users that the mean values of different versions have little substantive relation; in fact we found that early users almost immediately did fall down this path. There are further comments on this transition in the plain text updates file).

Specifically, we disseminate CAMSIS scale scores which are standardised around a continuous normal distribution, so that, on a nationally representative population within a gender group, the mean value of any version is 50.0, the standard deviation 15, with a range from 1.0 to 99.0 (with higher positive scores being associated with greater 'generalised advantage'), and with a precision of 1 decimal point.

The accompanying sample SPSS command syntax shows how such transformations to the distribution of score values can be made.


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