Cluster analysis takes a set of people (or whatever) that have been measured on a range of variables and puts them into groups based on how similar they are to each other in terms of those variables. The aim is to identify groups (clusters) or participants that belong together.

It works by using the variable measures as co-ordinates in space, so that each participant represents one point in that space. It then measures the distance of each point from each of the other points. Points that are close together are clustered. In the first step, each point is clustered with its nearest neighbour. In the next step, neighbouring pairs of points are clustered together to form a bigger cluster, and so on. At the final stage of the analysis, all the points are clustered together into one giant cluster.

Of course, it's not very interesting to see all our participants clustered together into one big group - we want them in smaller groups where the people in each group are alike. Therefore, we look at the coefficient table and stop the clustering process where we see a big jump in the coefficients. Sometimes, judgement will be needed to see how many clusters should be taken from the analysis.

It's done with Analyse > Classify > Hierarchical cluster