Profile matrices contain measurements of variables for a set of items. Proximity matrices contain measurements of relations, or proximities, between items. If the measurements in a proximity matrix tell how close things are to each other then you have a similarity matrix. If the measurements in a proximity matrix tell how far apart things are from each other, then you have a dissimilarity matrix (box 15.2).

BOX 15.2

SIMILARITY AND DISSIMILARITY MATRICES

If you've had a course in statistics and seen a correlation matrix, then you've had experience with a similarity matrix. The bigger the number in each cell—the higher the correlation—the more alike two things are.

If you've ever read one of those tables of distances between cities that you see on road maps, you've had experience with a dissimilarity matrix. The bigger the number in the cells, the more ''dissimilar'' two cities are. In other words, the larger the number in any cell, the farther apart two cities are on the map.

Figure 15.2b shows a similarity matrix of variables. Imagine the list of variable names stretching several feet to the right, off the right-hand margin of the page, and several feet down, off the lower margin. That is what would happen if you had, say, 100 variables about each of your respondents. For each and every pair of variables in the matrix of data, you could ask: Are these variables related?

We’ll need the concept of a proximity matrix for all kinds of analyses coming up in the chapters that follow.