sample decreases. A distance calculated from a sample of five or less variation units is entirely worthless because the associated confidence interval covers all possible distances. Unfortunately, increasing the sample size excludes witnesses that do not have a full complement of variation units. It is therefore necessary to reach a compromise which produces a confidence interval of tolerable width while not excluding too many interesting witnesses. For calculations related to this article, a minimum sample size of twelve has been used, corresponding to a relative interval width of just over 50% (actually 53.8%). The main reason for choosing this rather than a larger sample size is to include Codex Vaticanus (B) in the results.
 Three distance matrices are used to produce the results which follow:
 The first two are contrived examples that will be used to illustrate certain aspects of multivariate analysis. The third is derived from the previously mentioned data matrix which is based on the UBS4 apparatus of Hebrews. In constructing this distance matrix, a constraint was introduced to ensure that each distance was calculated from at least twelve variation units. Due to the added constraint, only 54 objects are represented.
 Multidimensional scaling (MDS) takes a distance matrix and derives a configuration of points in a space with a specified number of dimensions so that distances between the derived points are a best match to the original distances. As Venables and Ripley say, “We can think of 'squeezing' a high-dimensional point cloud into a small number of dimensions ... whilst preserving as well as possible the inter-point distances.” The configuration found by a popular variety of multidimensional scaling called “classical” MDS minimises the sum of squared differences between the original and derived distances. In general, the maximum number of dimensions required to perfectly reproduce the original distances is one less than the number of objects. However, a reasonably good approximation can sometimes be obtained with only a few dimensions.
 The following cases illustrate how the given number of dimensions affects the procedure's ability to arrive at a configuration of points that adequately reflects the supplied distances. Using classical MDS to analyse the distance matrix for Australian cities with only two dimensions produces this result:
 The resulting map has an unconventional orientation, which is to be expected because the underlying mathematical analysis does not include any constraints concerning what should be regarded as up, down, left, or right. Consequently, it is quite appropriate to rotate or reflect such a map in order to place it in a preferred orientation. Even though it has an unconventional orientation, this map accurately reflects the relative positions of the cities included in the distance matrix. A figure called the “proportion of variance” indicates how well the procedure has managed to fit the extracted configuration of points into the available number of dimensions. In this case, the proportion of variance is 1.00 which indicates that two dimensions are sufficient to achieve a perfect fit between the original distances and those derived from the extracted coordinates. This is because the original distance matrix was derived from a flat (i.e. two-dimensional) map.
 Subjecting the distance matrix for the apexes of a tetrahedron to classical MDS while allowing only two dimensions produces a proportion of variance figure of 0.67, indicating that the resulting map conveys two-thirds of the analysed distance information. Allowing three dimensions produces a perfect score of 1.00. Three dimensions is sufficient to produce a perfect configuration for any four points. Two dimensions would be sufficient if all of the points were in a plane, and only one dimension would be required if they were all in a line.
 The distance matrix derived from the UBS4 apparatus data for Hebrews can be analysed by classical MDS as well. This matrix includes 54 objects, meaning that up to 53 dimensions would be requir