The expectation concerning the pattern of covariances differs depending on the premise. Consider MAXCOV-HITMAX. The procedure uses three continuous items, X, Y and Z. One of the variables, say X, is used to partition the sample into two groups. The focus is on the covariance between Y and Z in the group below the cut point on X. If the premise regarding taxonicity is true, then the expectation is that the covariance between Y and Z is near zero if the cut point on X optimally divides the sample into taxon (=high on X) and complement members (=lower on X). Sliding the cut point along the range of X will produce an increasing and then a decreasing covariance between Y and Z because within the taxon and within the complement groups the covariance is assumed to be negligible, but when the partition includes members of both groups then the covariance will be larger than zero. However, if the premise regarding dimensionality is true, no substantial change in covariance of Y and Z is expected when moving the cut point along
