5 Summary

We have described in detail the statistical operations involved in, and the use of SAS and PRELIS for, the measurement of variation and covariation. When we have continuous measures, the calculations are quite simple and can be done by hand, but for ordinal data the process is more complex. We obtain estimates of polychoric and polyserial correlations by using software that numerically integrates the bivariate normal distribution. In the process, we are effectively fitting a model of continuous multivariate normal liability with abrupt thresholds to the contingency table. This model cannot be rejected when there are only two categories for each measure, but may fail as the number of cells in the table increases. While ordinal data are far more common than continuous measures in the behavioral sciences, we note that as the number of categories gets large (e.g., more than 15) the difference between the continuous and the ordinal treatments gets small. In general, the researcher should try to obtain continuous measures if possible, since considerable statistical power can be lost when only a few response categories are used, as we shall show in Chapter 7.