Table of Contents
 The apparatus of a critical edition of the biblical text can be encoded as a tabular structure called a data matrix. By counting how often witnesses disagree in their readings, another tabular structure called a dissimilarity matrix is obtained which records the distance between each pair of witnesses. This article begins by applying statistical reasoning to determine what constitutes a statistically significant distance between two witnesses and how sample size affects the margin of error for a distance estimate. Following this, two modes of multivariate analysis called “multidimensional scaling” and “divisive clustering” are introduced then applied to data extracted from the apparatus of the Letter to the Hebrews in the fourth edition of the United Bible Societies' Greek New Testament (UBS4).
 The results offer fresh ways to comprehend relationships among ancient witnesses of the text. Multidimensional scaling produces a map that reveals the structure of the “textual space” occupied by these witnesses while divisive clustering produces a tree-like structure that progresses from broad to narrow categories. Some of the clusters revealed by the analysis are evocative of the conventional “Alexandrian,” “Byzantine,” and “Western” text-types. However, the analysis results also exhibit important differences relative to these text-types.
 It is natural to ask what each cluster revealed by the analysis represents and how the overall picture came to have its present form. A geographical interpretation can be applied to the multidimensional scaling map whereby concentrations of witnesses are correlated with regions around the Mediterranean rim. If this is a valid interpretation of the data then Streeter's theory of local texts deserves to be reconsidered.
 The apparatus of a critical edition specifies the readings of various witnesses to the text at places where the witnesses differ. A variation unit is a place where the text varies across witnesses, and is comprised of the readings encountered at that site. In the case of the New Testament, where thousands of witnesses survive, critical editions usually report only substantive variations (i.e. those which affect the meaning), thus sparing the reader from a miriad of orthographic variations (i.e. differences of spelling, diacritics, and punctuation which don't affect meaning). Editions which take this approach include UBS4 and the 27th edition of the Nestle-Aland Novum Testamentum Graece (NA27). NA27 covers many more variation units than UBS4 but, due to space restrictions, does not always include the full attestation (i.e. list of supporting witnesses) for each reading. Instead, the reader has to consult the introduction and an appendix to see whether absence of a witness from the attestation for a reading is because it is undefined at the relevant place or has been subsumed under a set of “constant witnesses.” By contrast, UBS4 reports fewer variation units but gives the full attestation for each reading of a variation unit. Thus, absence of a witness from the attestations of all readings of a variation unit in UBS4 implies that the witness is undefined there, perhaps because it is illegible or is a version whose back-translation into Greek cannot be taken as support for a single reading. This makes the UBS4 apparatus a more convenient basis for producing a data matrix.
 A data matrix is a grid which shows the reading of each witness at each variation
unit. By convention, rows are devoted to witnesses and columns to variation units. At the
intersection of each row and column is a cell which specifies the reading of the witness at
that variation unit. Instead of placing the entire reading in the cell, it is enough to encode
the reading as a numeral using a one-to-one correspondence between readings and numerals for
each variation unit. While the assignment of numerals to readings is arbitrary, I prefer to
give the first reading of a variation unit in the UBS4 apparatus the numeral
2, the third
3, and so on. A special code,
NA, which stands for “not available,”