3.2. CORRELATIONS

Correlative analysis is a commonly used tool in the study of normal galaxies, and provides a more powerful tool than analysis of individual parameters, as illustrated in Section 3.1.4. Correlations however may be easier to establish than to interpret correctly. Many correlations are well known between various indicators of star formation activity, for instance IR/B, R(60, 100) and L(FIR) are all positively correlated, to an extent that varies with the sample used (Soifer & Neugebauer 1991; Bothun et al. 1989). In principle these correlations contain information on geometry and physical parameters such as density and heating intensity, and on the manner in which star formation affects these parameters, is affected by them, and whether there are balancing forces. In practice however, it can be very difficult to derive such inferences.

Particularly easy to generate are correlations between extensive parameters, those which scale with the extent of a system. Luminosity is such an extensive parameter, scaling with the square of the distance to the galaxy, as opposed to color ratio for instance, which is distance independent. Correlations between extensive parameters are of limited interest because they tend to be exaggerated by the distance scaling, since errors on the distance will affect all such estimators equally, reinforcing the appearance of a positive correlation. Such correlations are also exaggerated by the spread of system sizes, suggesting great significance, whereas the main information content is that all extensive quantities tend to be greater in larger systems. The accepted procedure to avoid such vacuous correlations is to normalize extensive quantities by a system size parameter such as luminosity or mass, thereby reducing as many parameters as possible to distance-independent expressions. Examples of correlations and their interpretation appear in Section 3.3 and in Section 5.