Vaticanus has many horizontal bars that extend into the margin. An example is shown to the left. It is agreed that most or all indicate paragraphs, hence the term paragraphoi. The margins also contain distigmai (pairs of dots), such as shown to the right, and Payne counts nearly 800 such cases in Vaticanus.He has shown that the dots tend to correspond to textual variants and Peter Head has argued that they were added in the sixteen century (see here and here). Payne finds 28 places where the two dots and a bar appear together. He then argues that, in such cases, the bars fall into two categories. He finds 20 "undisputed paragraphoi", and 8 "characteristic bars". The "primary graphic distinction" of the "characteristic bars" is that they extend further into the margin, he claims. Of the 28 cases, he finds 10 that correspond to locations where NA28 identifies a "multi-word variant". Now, Payne's 8 "characteristic bars" all belong to the group of 10 cases that have "multi-word variants". He shows that this could not happen by chance, and concludes that 1 Cor 14:33-4, which is one of the 8, marks the beginning of added text. This would then support the view that Paul did not write 1 Cor 14:34-35, the text that many take to mean that Paul did not allow women to speak in church.
The purpose of this blog post is not to assess the whole paper (I am not qualified to do that), but merely to comment on the bar measurements and the statistical argument about the correlation between the bar measurements and presence of a multi-word variant.
Using online images, I measured the extension into the margin of the bars in all 28 cases. I measured them three times each and took the average (I then adjusted all the values down by the same amount to make my definition of the margin consistent with Payne's). The results are plotted below. Here the cases have been placed in ascending order of the number of added words in the textual variants, as given by Payne in his comments on the ETC blog. Thus, the first six points, on the left, have no added words (and are in a random order), and the 28th point, on the right, represents 1 Cor 14:33-4, where 36 words may have been added. The order, with Vaticanus locations is Col 3:18 (1505B), Matt 24:6 (1268A), Col 2:15 (1504B), Acts 13:16 (1401B), Mark 3:5 (1280C), Jas 4:4 (1428C), 2 John 8 (1442C), Luke 22:58 (1345B), Matt 21:3 (1262C), Luke 21:19 (1342C), Col 3:20 (1505B), Acts 14:13 (1403A), John 9:41 (1365A), 1 Cor 10:24 (1470A), Matt 3:9 (1237B), Rom 16:5 (1460B), Phil 2:24 (1500C), John 7:39 (1361A), Mark 5:40 (1284C), Luke 1:28 (1305A), Matt 13:50 (1253B), Mark 14:70 (1301B), Acts 14:18 (1403B), Luke 14:24-5 (1332C), Acts 2:47 (1385B), Matt 18:10, 12 (1259A), Acts 6:10 (1390A), 1 Cor 14:33-4 (1474A).
As you can see, the data demonstrate no particular relationship between extension into margin and size of textual variant. To avoid bias I took the measurements without knowing which images were associated with textual variants. That is to say, when measuring the Y-value of each point, I was blind to its X-value. (I should mention that there is some ambiguity about the bar at Matt 18:10, 12, shown to the right. Payne includes the dot as part of the bar, but I did not).So how does Payne arrive at the conclusion that "The standard probability test shows that the likelihood of such a stark difference occurring at random is far less than one in 10,000."? Well, he kindly shared his own data in the comments section of the blog post at ETC. The graph below shows Payne's measurements together with mine.
We see immediately that Payne gets smaller measurements for all 20 "undisputed paragraphoi", and he gets greater measurements for all but one of the "characteristic bars". With his measurements he is able to claim that the 8 "characteristic bars" "extend on average almost twice as far into the margin as these twenty undisputed paragraphoi."
Payne also discusses bar length, so I have pasted the graph for bar length below. Note that bars that extend far into the margin are naturally often long (they are not statistically independent variables).
Let us compare, for example, Matt 21:3 (the 9th point in the graph), with 1 Cor 14:33-34 (the last point in the graph). Payne measures the bar at 1 Cor 14:33-34 to be 20% longer than the bar at Matt 21:3, but the image to the right shows that they are the same. Payne's numbers come from his comment on the ETC blog, and he gives them to one decimal place. However 13 of his 28 length measurements, including at 1 Cor 14:33-34, are whole numbers, as you can see above. We would expect just 3 and the probability of getting 13 or more is less then one in a million. He has clearly favoured whole numbers and it does appear that he has shown a bias in his decisions about which numbers to round down or up.
With Payne's measurements there is no "characteristic bar" that is shorter than any of the "undisputed paragraphoi".
Philip tells me that it is a combination of features that define "characteristic bars", so here is the plot of extension into the margin against length.
In his paper Payne claims that "All eight combine noticeably greater extension into the margin with noticeably greater length than the other twenty." This is just not true, however we interpret it.
There is no bi-modal distribution of extensions into the margin or lengths: the points do not fall into two categories, even with Payne's measurements. He uses arbitrary thresholds to define a "characteristic bar" and a "multi-word variant", but uses a statistical test that is appropriate only when the categories are distinct.
Payne claims in his paper (section 3) that only one paragraphos in 1 Cor extends as far into the margin as the bar at 14:33-4, but I did not have to look far to find another (at 1468B).
So, there are serious flaws in Payne's data, and in his use of those data. What lessons can we draw from this?
We cannot conclude, of course, that Paul wrote 1 Cor 14:34-35, still less that he silenced women there. This text remains a mystery to me. It is almost certain that Paul gave leadership roles to women. I have argued that Paul gave Lydia the "leadership name", Euodia. See page 254 of the Tyndale Bulletin paper embedded here.
What we can conclude is that the peer review process has failed us yet again. The measurement errors and questionable statistical method should have been spotted by reviewers.
We can also conclude that online discussion can make much faster progress then peer reviewed journals. The blog posts and comments on the ETC blog have advanced the debate, in large part because Philip Payne and others have been so willing to share their ideas and data. He has also exchanged multiple emails with me. If only all scholars were as willing to engage in online and offline discussion!
