Timothy Finney, How to Discover Textual Groups
Multivariate analysis (MVA) can be applied to the New Testament textual tradition in order to investigate grouping among its witnesses. This article applies certain MVA methods to a number of example data sets. Each method operates on a matrix that tabulates distances between pairs of items in a data set. The simple matching distance, which is the proportion of disagreements, can be used as a metric for calculating distances between New Testament witnesses. Analysis methods called classical multidimensional scaling (CMDS) and divisive clustering (DC) are useful for revealing group structure when it is well defined. However, they are less useful when grouping is not very distinct. A method called partitioning around medoids (PAM) provides another way to divide a data set into groups. Local maxima in a plot of a statistic called the mean silhouette width (MSW) indicate preferred numbers of groups. Statistical analysis of a data set allows upper and lower critical limits to be defined for the distance between a pair of witnesses. Distances between these limits are not significant in the sense that the same range of distances is expected to occur for generated pairs whose states are randomly chosen from the available pool. Distances that are either less than or greater than these critical limits are not likely to happen by chance. A distance less than the lower critical limit indicates an adjacent relationship while one greater than the upper limit implies an opposite relationship. Applying CMDS, DC, and PAM analysis to data for the Gospel of Mark reveals interesting features of the textual landscape. Witnesses tend to form groups that have points of contact with conventional categories such as the “Alexandrian,” “Byzantine,” “Western,” and “Eastern” types identified by prior generations of researchers. Multivariate analysis can also be used for novel purposes such as identifying group representatives, group cores, and readings useful for classification purposes.
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