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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.

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** Index**
Jeff Lessem
2002-03-21