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,” is used when the reading of
a witness cannot be confidently determined for the variation unit in question.
 Taking the UBS4 apparatus of Hebrews as an example, a variation unit with three readings is found at Heb 1:3:
τῆς δυνάμεως αὐτοῦ, καθαρισμόν (01 A B H* P 044 075 0150 33 81 436 1175 1962 2464 itt, v vg syrpal arm geo1 Didymusdub Cyril John-Damascusmss)
τῆς δυνάμεως, δι᾽ ἑαυτοῦ καθαρισμόν (P46 0243 6 424c 1739 1881*)
τῆς δυνάμεως αὐτοῦ, δι᾽ ἑαυτοῦ (D Hc K L 104 256 263 365 424* 459 1241 1319 1573 1852 1881c 1912 2127 2200 Byz Lect itar, b, comp, d vgms syr(p), hcopsa, bo, fay (eth) geo2 slav Chrysostom John-Damascus Augustine Varimadum)
 Encoding these readings as numerals produces a single column of the data matrix. Including all 44 variation units in the UBS4 apparatus of Hebrews produces a data matrix with 154 rows and 44 columns. A separate row is devoted to each scribe and corrector of a manuscript. Some sigla are reformatted to facilitate the eventual plotting of analysis results. In particular, superscripts are replaced with inline forms, and Gregory-Aland numbers are employed for majuscules not represented by Roman letters. Thus, for example, P46 becomes P46, Codex Sinaiticus is represented by the Gregory-Aland number 01, Codex Vaticanus is represented by the letter B, and syrpal becomes syr-pal. This article employs these reformatted sigla from this point forwards.
 Analysis can begin once the data matrix is in hand. Some analytical methods operate directly on the data matrix while others begin with a dissimilarity matrix constructed by calculating the distance between each pair of witnesses.
 Dissimilarity is a measure of how unlike two objects are with respect to each other. When calculating the dissimilarity of two objects contained in a data matrix, it is important to compare them in a meaningful way. Data which encodes the state of an object with a numeral is called “nominal” because each numeral simply nominates the state. Even though the state is represented by a numeral, it does not make se