Paul -- A Basic Stylometric Study

[Peter Kirby]

Does the shorter Romans map fairly well to JC O'Neill's reconstruction?

No, not really.

It's based on the research mentioned in the OP; the list of differences is also on the first page of the thread.

The 'shorter' Romans omits these passages (see the 'shorter readings' page in the OP):

Romans 1:1b-5a
Romans 1:19-2:1
Romans 2:3-2:11
Romans 3:25-26
Romans 6:13, 6:19
Romans 8:29-30
Romans 9:4-10:1
Romans 10:5-11:32
Romans 15:1-16:27

J. C. O'Neill doesn't seem to map to anything but J. C. O'Neill.

Would Phillipians 1-3 be too short of a sample size to test against all of Phillippians?

Yes, at this time, with this technique.

[Ben C. Smith]

Author Candidate #5 is being called "Paul" and consists of (a basically 'confirmed' set of works written by the author of 1 Cor):

1 Corinthians, 2 Corinthians, (shorter) Galatians, and 1 Thessalonians

You have created your own Hauptbriefe!

[Ben C. Smith]

Some random thoughts and suggestions:

We still see the same thing happening with 'shorter' Romans: one match. Possibly the first half has not removed all the 'additions'.

William O. Walker, IIRC, suggests that the entirety of Romans 1.18-2.29 is an interpolation; your own shorter Romans retains 1.18 and 2.2, 12-29, if I am understanding you correctly. Perhaps that is an avenue to explore in later tests to try to pin this part of Romans down.

The next text to be tested is the one called 1 Thessalonians, in full. (There is no way that an interpolation of 4 verses or less can be detected by this stylometry.)

I know 1 Thessalonians tested positive already, but I am wondering whether it would make a difference in the stats to remove both 1 Thessalonians 2.13-16 and 5.1-11.

Not looking so good for proponents of the 'longer' text of Romans.

Agreed. OTOH, chapter 16 is pretty unusual for Paul, with lots of greet so-and-so sentences and proper names that might make a difference as to the choice of words. Similar sections in the other epistles take up only a handful of verses, whereas this section takes up most of an entire chapter. I wonder whether keeping your longer version of Romans but lopping off only chapter 16 would make a difference. (A version of Romans has been hypothesized that contained only chapters 1-15 plus the doxology, anyway.) This move would be less obvious than, but perhaps in the same spirit as, removing the genealogy from Luke before using that text.

This must be admitted to be a match. It appears that the stylometry favors the hypothesis that Colossians were by "Paul."

Next we'd like to know whether 2 Corinthians were by "Paul."

Yes, if you are a total "Paul" skeptic, this approach may be less useful to you. But--and this everyone should find interesting--it does look like 'shorter' Romans is likely authored by the rest of the epistles canvassed here, while it seems unlikely that 'longer' Romans were.

What is up with those ubiquitous subjunctives of yours??

Ben.

[Peter Kirby]

Author Candidate #5 is being called "Paul" and consists of (a basically 'confirmed' set of works written by the author of 1 Cor):

1 Corinthians, 2 Corinthians, (shorter) Galatians, and 1 Thessalonians

You have created your own Hauptbriefe!

Indeed!

Not looking so good for proponents of the 'longer' text of Romans.

Agreed. OTOH, chapter 16 is pretty unusual for Paul, with lots of greet so-and-so sentences and proper names that might make a difference as to the choice of words. Similar sections in the other epistles take up only a handful of verses, whereas this section takes up most of an entire chapter. I wonder whether keeping your longer version of Romans but lopping off only chapter 16 would make a difference. (A version of Romans has been hypothesized that contained only chapters 1-15 plus the doxology, anyway.) This move would be less obvious than, but perhaps in the same spirit as, removing the genealogy from Luke before using that text.

This is a very good suggestion. I like it!

Especially because it's completely actionable: even without chapter 16, there is enough text in the 'additions' to test.

Let's start with the Neue Hauptbriefe of 1 Cor, 2 Cor, Gal(-), and 1 Thess as the basis for the style of "Paul." We get:

Bayesian Author Test: Posterior Probabilities from Equal Priors, Z-Score-Based Method
$VAR1 = '0.935740651387174'; $VAR2 = '0.00102002075759777'; $VAR3 = '0.0632393278552282';

Bayesian Comparison of Best Author to Best Control: from Equal Priors, Z-Score-Based Method
$VAR1 = 1; $VAR2 = '0.372128621220971'; $VAR3 = 25; $VAR4 = '0.627871378779029';

Percentage of Samples in the Best Author Candidate that Meet the P-Value>0.0492 Test, Z-Score-Based Method
1
Percentage of Samples outside the Best Author Candidate that Meet the P-Value>0.0492 Test, Z-Score-Based Method
0
Posterior Probability of a Sample Meeting the Test Being by the Best Author Candidate (with Prior = 0.5), Not Any Other, Z-Score-Based Method
1

Author Z-Score-Based P-Values
$VAR1 = '0.0492834708012318'; $VAR2 = '5.37223248227996e-05'; $VAR3 = '0.00333068095654756';
Poor compatibility. Z-Score-Based P-Value < 0.05.
Poor indicator. 24.3% of the rest have P-Value > 0.01.

Control Z-Score-Based P-Values
$VAR1 = '0.00186226362093513'; $VAR2 = '0.00826950979223098'; $VAR3 = '3.56288519902035e-07'; $VAR4 = '0.00120753863024787'; $VAR5 = '1.25991133879099e-05'; $VAR6 = '0.000246754789820377'; $VAR7 = '0.00029814187323343'; $VAR8 = '0.000477845100742534'; $VAR9 = '0.000860595222963254'; $VAR10 = '0.00410912127798894'; $VAR11 = '8.46105963002622e-08'; $VAR12 = '0.000121784301269535'; $VAR13 = '4.75468819484395e-10'; $VAR14 = '1.63902172963242e-11'; $VAR15 = '5.69370749656434e-07'; $VAR16 = '0.00632554066639301'; $VAR17 = '0.00424405979126409'; $VAR18 = '0.0120929923273112'; $VAR19 = '0.00574739415955842'; $VAR20 = '5.8619240394504e-09'; $VAR21 = '0.0825761800124696'; $VAR22 = '0.00749635940221311'; $VAR23 = '0.0759740167087431'; $VAR24 = '0.054530847200257'; $VAR25 = '0.0831531868241088'; $VAR26 = '0.0766967263628026'; $VAR27 = '0.0259977934350781'; $VAR28 = '0.05214281693783'; $VAR29 = '0.00338055299838832'; $VAR30 = '0.00380773824615918';

The tide has not, apparently, turned for the so-called 'additions'.

Let's add "Philippians" to the Neue Hauptbriefe

testsize: 2457


Bayesian Author Test: Posterior Probabilities from Equal Priors, Z-Score-Based Method
$VAR1 = '0.943982312631043'; $VAR2 = '0.00103379117890757'; $VAR3 = '0.0549838961900497';

Bayesian Comparison of Best Author to Best Control: from Equal Priors, Z-Score-Based Method
$VAR1 = 1; $VAR2 = '0.375386151829547'; $VAR3 = 25; $VAR4 = '0.624613848170453';

Percentage of Samples in the Best Author Candidate that Meet the P-Value>0.0499 Test, Z-Score-Based Method
1
Percentage of Samples outside the Best Author Candidate that Meet the P-Value>0.0499 Test, Z-Score-Based Method
0
Posterior Probability of a Sample Meeting the Test Being by the Best Author Candidate (with Prior = 0.5), Not Any Other, Z-Score-Based Method
1

Author Z-Score-Based P-Values
$VAR1 = '0.0499741606239951'; $VAR2 = '5.47286169826666e-05'; $VAR3 = '0.00291083214501773';
Poor compatibility. Z-Score-Based P-Value < 0.05.
Poor indicator. 24.3% of the rest have P-Value > 0.01.

Control Z-Score-Based P-Values
$VAR1 = '0.00186224088360505'; $VAR2 = '0.00826955502477946'; $VAR3 = '3.56334110069016e-07'; $VAR4 = '0.00120754354746219'; $VAR5 = '1.25984484417957e-05'; $VAR6 = '0.000246752092554052'; $VAR7 = '0.000298137939292791'; $VAR8 = '0.000477840639903089'; $VAR9 = '0.000860575395344218'; $VAR10 = '0.0041090547185714'; $VAR11 = '8.4609081731076e-08'; $VAR12 = '0.000121785065919954'; $VAR13 = '4.75507981859391e-10'; $VAR14 = '1.63890097288282e-11'; $VAR15 = '5.69362885370815e-07'; $VAR16 = '0.00632547375689066'; $VAR17 = '0.00424433963737187'; $VAR18 = '0.0120930266656228'; $VAR19 = '0.00574742217922966'; $VAR20 = '5.86248245147842e-09'; $VAR21 = '0.0825761837489678'; $VAR22 = '0.0074963931188114'; $VAR23 = '0.075973953699585'; $VAR24 = '0.0545307340520087'; $VAR25 = '0.0831531813955021'; $VAR26 = '0.0766967139007497'; $VAR27 = '0.0259976819076943'; $VAR28 = '0.052142814410607'; $VAR29 = '0.003380535388244'; $VAR30 = '0.00380769565555527'; $VAR31 = '0.00289178721333236'; $VAR32 = '0.00228942300927206'; $VAR33 = '2.75581382210024e-89'; $VAR34 = '0.000141634363013815'; $VAR35 = '2.04227326531006e-122'; $VAR36 = '0.0169994302685606'; $VAR37 = '0.00399418002741304'; $VAR38 = '0.0247128273944475'; $VAR39 = '0.00159631251970485';

No change there. Let's add "Colossians" also.

testsize: 2457


Bayesian Author Test: Posterior Probabilities from Equal Priors, Z-Score-Based Method
$VAR1 = '0.953604714000737'; $VAR2 = '0.000726820144442035'; $VAR3 = '0.0456684658548212';

Bayesian Comparison of Best Author to Best Control: from Equal Priors, Z-Score-Based Method
$VAR1 = 1; $VAR2 = '0.45753081436492'; $VAR3 = 25; $VAR4 = '0.54246918563508';

Percentage of Samples in the Best Author Candidate that Meet the P-Value>0.0701 Test, Z-Score-Based Method
1
Percentage of Samples outside the Best Author Candidate that Meet the P-Value>0.0701 Test, Z-Score-Based Method
0.00854700854700855
Posterior Probability of a Sample Meeting the Test Being by the Best Author Candidate (with Prior = 0.5), Not Any Other, Z-Score-Based Method
0.991525423728814

Author Z-Score-Based P-Values
$VAR1 = '0.0701332849483606'; $VAR2 = '5.34543124084457e-05'; $VAR3 = '0.00335870773489924';
Decent compatibility. Z-Score-Based P-Value > 0.05.
Decent indicator. 14.6% of the rest have P-Value > 0.05.

Control Z-Score-Based P-Values
$VAR1 = '0.00186225196705744'; $VAR2 = '0.0082695055754528'; $VAR3 = '3.56333903257483e-07'; $VAR4 = '0.00120753299721451'; $VAR5 = '1.25984659956673e-05'; $VAR6 = '0.000246753796724363'; $VAR7 = '0.000298144645529362'; $VAR8 = '0.000477839127991407'; $VAR9 = '0.000860584775993519'; $VAR10 = '0.00410912723409554'; $VAR11 = '8.4612854639493e-08'; $VAR12 = '0.000121785861114613'; $VAR13 = '4.75521073617665e-10'; $VAR14 = '1.63891411626099e-11'; $VAR15 = '5.69353155507161e-07'; $VAR16 = '0.00632566614191277'; $VAR17 = '0.00424439077131652'; $VAR18 = '0.0120930145972459'; $VAR19 = '0.00574740567932526'; $VAR20 = '5.86243027709709e-09'; $VAR21 = '0.0825761817759418'; $VAR22 = '0.00749635516960693'; $VAR23 = '0.0759738516772441'; $VAR24 = '0.0545307263832065'; $VAR25 = '0.0831531883260345'; $VAR26 = '0.0766967257114399'; $VAR27 = '0.0259976968528734'; $VAR28 = '0.0521428170644012'; $VAR29 = '0.00338053449445615'; $VAR30 = '0.00380765624041403'; $VAR31 = '0.00289176786762523'; $VAR32 = '0.00228942673206768'; $VAR33 = '2.7558352026776e-89'; $VAR34 = '0.000141636736884806'; $VAR35 = '2.0422677769683e-122'; $VAR36 = '0.0169994283862486'; $VAR37 = '0.00399416283221166'; $VAR38 = '0.0247128114387147'; $VAR39 = '0.00159631049124646';

Still negative. Let's add Ephesians to the bunch.

testsize: 2457


Bayesian Author Test: Posterior Probabilities from Equal Priors, Z-Score-Based Method
$VAR1 = '0.969875668121359'; $VAR2 = '0.000467450577034875'; $VAR3 = '0.0296568813016065';

Bayesian Comparison of Best Author to Best Control: from Equal Priors, Z-Score-Based Method
$VAR1 = 1; $VAR2 = '0.567080330404173'; $VAR3 = 25; $VAR4 = '0.432919669595827';

Percentage of Samples in the Best Author Candidate that Meet the P-Value>0.1 Test, Z-Score-Based Method
1
Percentage of Samples outside the Best Author Candidate that Meet the P-Value>0.1 Test, Z-Score-Based Method
0.0056980056980057
Posterior Probability of a Sample Meeting the Test Being by the Best Author Candidate (with Prior = 0.5), Not Any Other, Z-Score-Based Method
0.994334277620397

Author Z-Score-Based P-Values
$VAR1 = '0.108922028827443'; $VAR2 = '5.24971054545792e-05'; $VAR3 = '0.00333062039418173';
Good compatibility. Z-Score-Based P-Value > 0.1.
Excellent indicator. 0% of the rest have P-Value > 0.1.

Control Z-Score-Based P-Values
$VAR1 = '0.00186226082809374'; $VAR2 = '0.0082694921384563'; $VAR3 = '3.56297413546805e-07'; $VAR4 = '0.00120753486407409'; $VAR5 = '1.25988729063568e-05'; $VAR6 = '0.000246755209672897'; $VAR7 = '0.000298145087134831'; $VAR8 = '0.000477839430676654'; $VAR9 = '0.000860587544961813'; $VAR10 = '0.00410911531222341'; $VAR11 = '8.46092138373028e-08'; $VAR12 = '0.000121785351538786'; $VAR13 = '4.75510751095621e-10'; $VAR14 = '1.63890372721623e-11'; $VAR15 = '5.6931792283275e-07'; $VAR16 = '0.00632561525944539'; $VAR17 = '0.00424436162220432'; $VAR18 = '0.0120930068239047'; $VAR19 = '0.00574739446016318'; $VAR20 = '5.86239337432678e-09'; $VAR21 = '0.082576180805325'; $VAR22 = '0.00749635454771991'; $VAR23 = '0.0759739787762033'; $VAR24 = '0.0545307290273313'; $VAR25 = '0.0831531023092891'; $VAR26 = '0.0766967221081683'; $VAR27 = '0.0259976073938762'; $VAR28 = '0.0521428166715033'; $VAR29 = '0.00338056255489657'; $VAR30 = '0.00380770302834837'; $VAR31 = '0.00289178947515376'; $VAR32 = '0.00228945260558413'; $VAR33 = '2.75625191964828e-89'; $VAR34 = '0.000141635095307308'; $VAR35 = '2.04104285550107e-122'; $VAR36 = '0.0169994764026071'; $VAR37 = '0.00399419327053094'; $VAR38 = '0.0247128258920269'; $VAR39 = '0.0015963064622587';

Now it turns positive.

Let's backtrack a bit and repeat the original comparison against just 'shorter' Romans and 1 Corinthians.

testsize: 2457


Bayesian Author Test: Posterior Probabilities from Equal Priors, Z-Score-Based Method
$VAR1 = '0.967854566456962'; $VAR2 = '0.000559647272607322'; $VAR3 = '0.0315857862704309';

Bayesian Comparison of Best Author to Best Control: from Equal Priors, Z-Score-Based Method
$VAR1 = 1; $VAR2 = '0.529540963663074'; $VAR3 = 25; $VAR4 = '0.470459036336926';

Percentage of Samples in the Best Author Candidate that Meet the P-Value>0.0935 Test, Z-Score-Based Method
1
Percentage of Samples outside the Best Author Candidate that Meet the P-Value>0.0935 Test, Z-Score-Based Method
0
Posterior Probability of a Sample Meeting the Test Being by the Best Author Candidate (with Prior = 0.5), Not Any Other, Z-Score-Based Method
1

Author Z-Score-Based P-Values
$VAR1 = '0.0935958593999659'; $VAR2 = '5.41203908685165e-05'; $VAR3 = '0.00305448660703931';
Decent compatibility. Z-Score-Based P-Value > 0.05.
Decent indicator. 14.6% of the rest have P-Value > 0.05.

Control Z-Score-Based P-Values
$VAR1 = '0.00186225145514376'; $VAR2 = '0.00826953186394238'; $VAR3 = '3.5628840224262e-07'; $VAR4 = '0.00120754341778157'; $VAR5 = '1.25986517163099e-05'; $VAR6 = '0.000246752858869475'; $VAR7 = '0.000298140791110689'; $VAR8 = '0.000477845894586791'; $VAR9 = '0.000860575812468344'; $VAR10 = '0.00410912313385426'; $VAR11 = '8.46092182082422e-08'; $VAR12 = '0.000121781515237684'; $VAR13 = '4.75456219756542e-10'; $VAR14 = '1.63909248270097e-11'; $VAR15 = '5.69372106971635e-07'; $VAR16 = '0.00632553593861285'; $VAR17 = '0.00424411815523733'; $VAR18 = '0.0120929933251556'; $VAR19 = '0.00574739328111263'; $VAR20 = '5.86188922771766e-09'; $VAR21 = '0.082576180705838'; $VAR22 = '0.0074963108697779'; $VAR23 = '0.0759740793601885'; $VAR24 = '0.0545308981548625'; $VAR25 = '0.0831531851923941'; $VAR26 = '0.076696723199532'; $VAR27 = '0.0259978094631105'; $VAR28 = '0.0521428161275921'; $VAR29 = '0.003380552701312'; $VAR30 = '0.00380773997235991'; $VAR31 = '0.00289178893514899'; $VAR32 = '0.00228945382300679'; $VAR33 = '2.7552014904796e-89'; $VAR34 = '0.000141634287231131'; $VAR35 = '2.03982376156719e-122'; $VAR36 = '0.0169993859076548'; $VAR37 = '0.00399419613587115'; $VAR38 = '0.0247128250348976'; $VAR39 = '0.00159630265545535';

Let's add together shorter 'Romans', 1 Corinthians, and 2 Corinthians.

testsize: 2457


Bayesian Author Test: Posterior Probabilities from Equal Priors, Z-Score-Based Method
$VAR1 = '0.974230636490462'; $VAR2 = '0.00040505782916938'; $VAR3 = '0.0253643056803684';

Bayesian Comparison of Best Author to Best Control: from Equal Priors, Z-Score-Based Method
$VAR1 = 1; $VAR2 = '0.607256360646455'; $VAR3 = 25; $VAR4 = '0.392743639353545';

Percentage of Samples in the Best Author Candidate that Meet the P-Value>0.12 Test, Z-Score-Based Method
1
Percentage of Samples outside the Best Author Candidate that Meet the P-Value>0.12 Test, Z-Score-Based Method
0
Posterior Probability of a Sample Meeting the Test Being by the Best Author Candidate (with Prior = 0.5), Not Any Other, Z-Score-Based Method
1

Author Z-Score-Based P-Values
$VAR1 = '0.128570640628691'; $VAR2 = '5.34560735798457e-05'; $VAR3 = '0.00334736448257736';
Good compatibility. Z-Score-Based P-Value > 0.1.
Excellent indicator. 0% of the rest have P-Value > 0.1.

Control Z-Score-Based P-Values
$VAR1 = '0.00186224744550061'; $VAR2 = '0.00826953781541641'; $VAR3 = '3.5633063955149e-07'; $VAR4 = '0.0012075362205514'; $VAR5 = '1.25984609588903e-05'; $VAR6 = '0.000246753191931779'; $VAR7 = '0.00029814369351529'; $VAR8 = '0.000477840156041966'; $VAR9 = '0.000860580845309692'; $VAR10 = '0.00410908321060521'; $VAR11 = '8.46116526411823e-08'; $VAR12 = '0.000121785569631331'; $VAR13 = '4.75523511950782e-10'; $VAR14 = '1.63889998226168e-11'; $VAR15 = '5.69359237598905e-07'; $VAR16 = '0.00632588188627894'; $VAR17 = '0.00424432258688368'; $VAR18 = '0.0120930207222749'; $VAR19 = '0.00574742642974218'; $VAR20 = '5.8624682976224e-09'; $VAR21 = '0.0825761799085556'; $VAR22 = '0.00749636979468802'; $VAR23 = '0.0759739220548887'; $VAR24 = '0.0545307285779784'; $VAR25 = '0.0831531863425426'; $VAR26 = '0.0766967226810829'; $VAR27 = '0.0259977086651422'; $VAR28 = '0.0521428163343538'; $VAR29 = '0.00338053476962128'; $VAR30 = '0.00380768153704909'; $VAR31 = '0.00289177660379048'; $VAR32 = '0.00228942736926259'; $VAR33 = '2.75557643213645e-89'; $VAR34 = '0.000141636409979664'; $VAR35 = '2.04244810996627e-122'; $VAR36 = '0.0169994286807426'; $VAR37 = '0.00399416408803193'; $VAR38 = '0.0247128264922022'; $VAR39 = '0.00159631564498169';

It looks as though the situation does improve for some comparisons when chapter 16 is removed, while for some it is still negative.

Perhaps the stylometry cannot actually say anything about the so-called 'additions', other than that it cannot verify them.

(They 'additions' seem to be in a similar position to Ephesians--excluded for several tests, but sometimes included with other tests.)

[Ben C. Smith]

This is a very good suggestion. I like it!

Especially because it's completely actionable: even without chapter 16, there is enough text in the 'additions' to test.

Thanks for indulging me here.

Perhaps the stylometry cannot actually say anything about the so-called 'additions', other than that it cannot verify them.

Perhaps, but it seems a bit suspicious to me that Romans is the supposedly genuine letter that your stylometer has the most trouble with, and Romans is also the supposedly genuine letter for which various scholars have argued for the longest, most substantial additions, compared to the other letters.

Ben.

[Peter Kirby]

Good points.

Now hold on to your chairs folks... because I'm about to rock your world.

Using just this 'Neue Hauptbriefe', i.e. 1 Cor-2 Cor-Gal-1 Thess, we get these comparisons for 1 Timothy, 2 Timothy, and Titus.

This is even after I added 9 more controls to the stylometer (yes, I'm bad) just to make sure it wasn't a complete fluke.

At least for these very common words that are measured, and at least for 1 Timothy, there's some 'splainin to do.

At least 2 Timothy and Titus (sort of) know their place here! Harumph!

1 Timothy VS the Neue Hauptbriefe:

testsize: 1590


Bayesian Author Test: Posterior Probabilities from Equal Priors, Z-Score-Based Method
$VAR1 = '0.823669152722151'; $VAR2 = '0.042389397305391'; $VAR3 = '0.133941449972458';

Bayesian Comparison of Best Author to Best Control: from Equal Priors, Z-Score-Based Method
$VAR1 = 1; $VAR2 = '0.612786900029935'; $VAR3 = 38; $VAR4 = '0.387213099970065';

Percentage of Samples in the Best Author Candidate that Meet the P-Value>0.15 Test, Z-Score-Based Method
1
Percentage of Samples outside the Best Author Candidate that Meet the P-Value>0.15 Test, Z-Score-Based Method
0
Posterior Probability of a Sample Meeting the Test Being by the Best Author Candidate (with Prior = 0.5), Not Any Other, Z-Score-Based Method
1

Author Z-Score-Based P-Values
$VAR1 = '0.154443265231539'; $VAR2 = '0.00794828470801069'; $VAR3 = '0.0251148835855109';
Good compatibility. Z-Score-Based P-Value > 0.15.
Excellent indicator. 0% of the rest have P-Value > 0.15.

Control Z-Score-Based P-Values
$VAR1 = '0.0170243332105464'; $VAR2 = '0.0564052460203599'; $VAR3 = '0.000928280503493673'; $VAR4 = '0.0131644953216068'; $VAR5 = '0.000492662296617979'; $VAR6 = '0.00445119394812572'; $VAR7 = '0.000852237277813012'; $VAR8 = '0.00692609880757475'; $VAR9 = '0.00776293334417129'; $VAR10 = '0.00732755530279445'; $VAR11 = '9.7436698172509e-05'; $VAR12 = '0.000893211186579737'; $VAR13 = '4.75732365830095e-05'; $VAR14 = '5.93607522243107e-05'; $VAR15 = '0.00037821460817371'; $VAR16 = '0.014892394438101'; $VAR17 = '0.013605109242933'; $VAR18 = '0.00432614679033096'; $VAR19 = '0.0258308580962214'; $VAR20 = '0.000101008472015055'; $VAR21 = '0.0709847677823983'; $VAR22 = '0.0269248479115905'; $VAR23 = '0.0408183265953848'; $VAR24 = '0.0660254346476931'; $VAR25 = '0.0851172573158174'; $VAR26 = '0.0825854242307653'; $VAR27 = '0.0335936110829929'; $VAR28 = '0.0521758897038511'; $VAR29 = '0.00312471775322001'; $VAR30 = '0.0177039344297022'; $VAR31 = '0.00851151563161336'; $VAR32 = '0.0119973976579309'; $VAR33 = '1.32974656496141e-66'; $VAR34 = '0.0184974248062306'; $VAR35 = '6.45375394491338e-09'; $VAR36 = '0.0604925006563526'; $VAR37 = '0.0365023441868827'; $VAR38 = '0.0975909496382541'; $VAR39 = '0.0328799151167084';

2 Timothy VS the Neue Hauptbriefe:

testsize: 1238


Bayesian Author Test: Posterior Probabilities from Equal Priors, Z-Score-Based Method
$VAR1 = '0.534484554201049'; $VAR2 = '0.187339711333116'; $VAR3 = '0.278175734465835';

Bayesian Comparison of Best Author to Best Control: from Equal Priors, Z-Score-Based Method
$VAR1 = 1; $VAR2 = '0.493392338215285'; $VAR3 = 25; $VAR4 = '0.506607661784715';

Percentage of Samples in the Best Author Candidate that Meet the P-Value>0.16 Test, Z-Score-Based Method
1
Percentage of Samples outside the Best Author Candidate that Meet the P-Value>0.16 Test, Z-Score-Based Method
0
Posterior Probability of a Sample Meeting the Test Being by the Best Author Candidate (with Prior = 0.5), Not Any Other, Z-Score-Based Method
1

Author Z-Score-Based P-Values
$VAR1 = '0.165304166790892'; $VAR2 = '0.057939999660155'; $VAR3 = '0.0860335582120905';

Control Z-Score-Based P-Values
$VAR1 = '0.0460227353632688'; $VAR2 = '0.0545675925051056'; $VAR3 = '0.000498488307145953'; $VAR4 = '0.032050203808226'; $VAR5 = '0.0143427075782125'; $VAR6 = '0.0311274287155146'; $VAR7 = '0.0135061649141058'; $VAR8 = '0.0352786409746189'; $VAR9 = '0.0328813340739722'; $VAR10 = '0.0459096997119506'; $VAR11 = '0.00406548469466203'; $VAR12 = '0.00732083860260034'; $VAR13 = '0.000404659028948727'; $VAR14 = '0.000496172942368708'; $VAR15 = '0.00330680691248113'; $VAR16 = '0.051993387881794'; $VAR17 = '0.0312480035731725'; $VAR18 = '0.0385586890489967'; $VAR19 = '0.0500130193555795'; $VAR20 = '0.000377621586571602'; $VAR21 = '0.11359223528883'; $VAR22 = '0.0645878957477191'; $VAR23 = '0.12683957296688'; $VAR24 = '0.103675481207133'; $VAR25 = '0.169731775171311'; $VAR26 = '0.106850810826849'; $VAR27 = '0.0638803620943742'; $VAR28 = '0.0945179559638842'; $VAR29 = '0.037938539332624'; $VAR30 = '0.0293489220172324'; $VAR31 = '0.0338334270671696'; $VAR32 = '0.0482989460458862'; $VAR33 = '2.75264785388063e-10'; $VAR34 = '0.0530956357823437'; $VAR35 = '3.03899011219215e-05'; $VAR36 = '0.115141753498039'; $VAR37 = '0.0841751977083421'; $VAR38 = '0.124906438367498'; $VAR39 = '0.0947593632425605';

Titus VS the Neue Hauptbriefe:

testsize: 659


Bayesian Author Test: Posterior Probabilities from Equal Priors, Z-Score-Based Method
$VAR1 = '0.542026060603636'; $VAR2 = '0.294662196168917'; $VAR3 = '0.163311743227447';

Bayesian Comparison of Best Author to Best Control: from Equal Priors, Z-Score-Based Method
$VAR1 = 1; $VAR2 = '0.473758599709701'; $VAR3 = 36; $VAR4 = '0.526241400290299';

Percentage of Samples in the Best Author Candidate that Meet the P-Value>0.14 Test, Z-Score-Based Method
1
Percentage of Samples outside the Best Author Candidate that Meet the P-Value>0.14 Test, Z-Score-Based Method
0.0558823529411765
Posterior Probability of a Sample Meeting the Test Being by the Best Author Candidate (with Prior = 0.5), Not Any Other, Z-Score-Based Method
0.947075208913649

Author Z-Score-Based P-Values
$VAR1 = '0.149348083682433'; $VAR2 = '0.0811902554694061'; $VAR3 = '0.0449983823041539';

Control Z-Score-Based P-Values
$VAR1 = '0.0820936513475325'; $VAR2 = '0.0837963041341427'; $VAR3 = '0.0103778519158933'; $VAR4 = '0.0484530365557513'; $VAR5 = '0.0334806062209'; $VAR6 = '0.0462335250522526'; $VAR7 = '0.0099585059493663'; $VAR8 = '0.0317520860593213'; $VAR9 = '0.0201594571253324'; $VAR10 = '0.0138681886105674'; $VAR11 = '0.00416733144074063'; $VAR12 = '0.0169609070122515'; $VAR13 = '0.0158455979249957'; $VAR14 = '0.0141116862793918'; $VAR15 = '0.0162841519890944'; $VAR16 = '0.0222024776755815'; $VAR17 = '0.0401509863065157'; $VAR18 = '0.0245317790027318'; $VAR19 = '0.0347303749546803'; $VAR20 = '0.00821886215822706'; $VAR21 = '0.111156340140766'; $VAR22 = '0.0398931642921516'; $VAR23 = '0.0667736315172761'; $VAR24 = '0.0889342103874887'; $VAR25 = '0.086774896682145'; $VAR26 = '0.115597035106694'; $VAR27 = '0.0656315158928418'; $VAR28 = '0.0631417728384365'; $VAR29 = '0.0178886981898115'; $VAR30 = '0.0302292559395695'; $VAR31 = '0.0361919472405477'; $VAR32 = '0.0428552391799786'; $VAR33 = '0.0078320453130924'; $VAR34 = '0.0981873671331347'; $VAR35 = '0.0268062378076674'; $VAR36 = '0.165892808565111'; $VAR37 = '0.0582630957082599'; $VAR38 = '0.0927591332850181'; $VAR39 = '0.0780846355438502';

But here's the combined 2 Timothy & Titus reading:

testsize: 1897


Bayesian Author Test: Posterior Probabilities from Equal Priors, Z-Score-Based Method
$VAR1 = '0.913206946618373'; $VAR2 = '0.000188298871011871'; $VAR3 = '0.0866047545106156';

Bayesian Comparison of Best Author to Best Control: from Equal Priors, Z-Score-Based Method
$VAR1 = 1; $VAR2 = '0.560961574800625'; $VAR3 = 25; $VAR4 = '0.439038425199375';

Percentage of Samples in the Best Author Candidate that Meet the P-Value>0.11 Test, Z-Score-Based Method
1
Percentage of Samples outside the Best Author Candidate that Meet the P-Value>0.11 Test, Z-Score-Based Method
0
Posterior Probability of a Sample Meeting the Test Being by the Best Author Candidate (with Prior = 0.5), Not Any Other, Z-Score-Based Method
1

Author Z-Score-Based P-Values
$VAR1 = '0.112024483130811'; $VAR2 = '2.30989084975012e-05'; $VAR3 = '0.0106239367721071';
Good compatibility. Z-Score-Based P-Value > 0.1.
Excellent indicator. 0% of the rest have P-Value > 0.1.

Control Z-Score-Based P-Values
$VAR1 = '0.00337474653502709'; $VAR2 = '0.0266200361752983'; $VAR3 = '9.0030172758527e-06'; $VAR4 = '0.0123644990002458'; $VAR5 = '0.00132850753017783'; $VAR6 = '0.00709492638297052'; $VAR7 = '0.00175257570262458'; $VAR8 = '0.00533457909709268'; $VAR9 = '0.00671201236496284'; $VAR10 = '0.00496067849716306'; $VAR11 = '3.49936936778673e-05'; $VAR12 = '0.00135314515113046'; $VAR13 = '4.07477857443668e-05'; $VAR14 = '9.70034537998303e-05'; $VAR15 = '0.00107058572184818'; $VAR16 = '0.0104469193460479'; $VAR17 = '0.00249362111301281'; $VAR18 = '0.00349743508675774'; $VAR19 = '0.0114736805833751'; $VAR20 = '2.37604830766775e-05'; $VAR21 = '0.0635974725031043'; $VAR22 = '0.0144236194199457'; $VAR23 = '0.0464990882304803'; $VAR24 = '0.0535010392360603'; $VAR25 = '0.0876763309055633'; $VAR26 = '0.0582419082013158'; $VAR27 = '0.0208341493994333'; $VAR28 = '0.0513936936733187'; $VAR29 = '0.00262889682683281'; $VAR30 = '0.00632074030281559'; $VAR31 = '0.00317891769079122'; $VAR32 = '0.00584224377384102'; $VAR33 = '3.98403945841793e-99'; $VAR34 = '0.000128983177380328'; $VAR35 = '1.95454177103593e-101'; $VAR36 = '0.0509308342409494'; $VAR37 = '0.0267388094870112'; $VAR38 = '0.0678909578596876'; $VAR39 = '0.037435219364268';

Oh dear, oh dear.

[Peter Kirby]

Okay so what the hell does a stylometer know anyway?

And here's the thing--this isn't the first time that stylometry results have reached similar conclusions.

Anthony Kenny's monograph/book on the stylometry of the New Testament, for example, concluded that he couldn't disprove that the same person wrote all 12 or 13 epistles (while conceding that the case of Titus was too short to make a sure decision).

Now we can explain it various ways, but I don't think that pure error is very high on the list of explanations here. Let's not shoot the messenger. And just to know that the stylometer hasn't decided to go haywire, or hasn't gotten too smart for its own good (and isn't hatching a plot to take over the world with phony results).... here's the case of Hebrews.

This is the first part of Hebrews, with "Paul" (Neue Hauptbriefe) as candidate #1 and with "Acts" as candidate #2.

testsize: 2520


Bayesian Author Test: Posterior Probabilities from Equal Priors, Z-Score-Based Method
$VAR1 = '0.132742491416456'; $VAR2 = '0.867257508583544';

Bayesian Comparison of Best Author to Best Control: from Equal Priors, Z-Score-Based Method
$VAR1 = 2; $VAR2 = '0.33154046916538'; $VAR3 = 25; $VAR4 = '0.66845953083462';

Percentage of Samples in the Best Author Candidate that Meet the P-Value>0.0567 Test, Z-Score-Based Method
1
Percentage of Samples outside the Best Author Candidate that Meet the P-Value>0.0567 Test, Z-Score-Based Method
0.0352941176470588
Posterior Probability of a Sample Meeting the Test Being by the Best Author Candidate (with Prior = 0.5), Not Any Other, Z-Score-Based Method
0.965909090909091

Author Z-Score-Based P-Values
$VAR1 = '0.00869369996555203'; $VAR2 = '0.056799269714195';
Decent compatibility. Z-Score-Based P-Value > 0.05.
Decent indicator. 15% of the rest have P-Value > 0.05.

Control Z-Score-Based P-Values
$VAR1 = '9.28584122504552e-05'; $VAR2 = '0.00238218311681104'; $VAR3 = '4.20863905986345e-16'; $VAR4 = '0.0159072532810663'; $VAR5 = '2.64375668191831e-05'; $VAR6 = '0.000899305562936673'; $VAR7 = '0.00481989535062233'; $VAR8 = '0.00678683795126769'; $VAR9 = '0.0116761822842448'; $VAR10 = '0.0158366294177911'; $VAR11 = '2.74042358886974e-06'; $VAR12 = '0.000528942647392273'; $VAR13 = '6.67844455919544e-07'; $VAR14 = '2.812710944671e-07'; $VAR15 = '5.55821771701027e-05'; $VAR16 = '0.023268841012523'; $VAR17 = '0.000814982473115154'; $VAR18 = '0.00521150269232162'; $VAR19 = '0.0210044362583153'; $VAR20 = '9.96332951687535e-07'; $VAR21 = '0.0936418691214611'; $VAR22 = '0.015790966032559'; $VAR23 = '0.0612583618231792'; $VAR24 = '0.0818767375946985'; $VAR25 = '0.114519995946439'; $VAR26 = '0.0908291208221726'; $VAR27 = '0.034471375374815'; $VAR28 = '0.0794156457588401'; $VAR29 = '0.0255938178356033'; $VAR30 = '0.00713331314871337'; $VAR31 = '0.0223981926963377'; $VAR32 = '0.00838686995696301'; $VAR33 = '1.92977673453916e-123'; $VAR34 = '3.09612492459792e-05'; $VAR35 = '6.62232547425069e-122'; $VAR36 = '0.0113714052708867'; $VAR37 = '0.0378954880612635'; $VAR38 = '0.00459154529214788'; $VAR39 = '0.00528454004652651';

It doesn't look like either "Paul" or "Acts" are the likely author. And here's the second part.

testsize: 2430


Bayesian Author Test: Posterior Probabilities from Equal Priors, Z-Score-Based Method
$VAR1 = '0.716918734447254'; $VAR2 = '0.283081265552746';

Bayesian Comparison of Best Author to Best Control: from Equal Priors, Z-Score-Based Method
$VAR1 = 1; $VAR2 = '0.223722632540084'; $VAR3 = 25; $VAR4 = '0.776277367459916';

Percentage of Samples in the Best Author Candidate that Meet the P-Value>0.0295 Test, Z-Score-Based Method
1
Percentage of Samples outside the Best Author Candidate that Meet the P-Value>0.0295 Test, Z-Score-Based Method
0.0112994350282486
Posterior Probability of a Sample Meeting the Test Being by the Best Author Candidate (with Prior = 0.5), Not Any Other, Z-Score-Based Method
0.988826815642458

Author Z-Score-Based P-Values
$VAR1 = '0.0295268734866187'; $VAR2 = '0.011658929126538';
Poor compatibility. Z-Score-Based P-Value < 0.05.
Terrible indicator. 42.5% of the rest have P-Value > 0.01.

Control Z-Score-Based P-Values
$VAR1 = '0.00488055894408815'; $VAR2 = '0.0101527494104495'; $VAR3 = '1.66072305892278e-06'; $VAR4 = '0.024066900135907'; $VAR5 = '0.000190772449589878'; $VAR6 = '0.00274410661865015'; $VAR7 = '0.00332922739595448'; $VAR8 = '0.00583987799780099'; $VAR9 = '0.0127402206234616'; $VAR10 = '0.00397630044125346'; $VAR11 = '5.83564884806747e-06'; $VAR12 = '0.00106429808671045'; $VAR13 = '8.77461783002632e-06'; $VAR14 = '6.43597983289021e-06'; $VAR15 = '0.000228120297445571'; $VAR16 = '0.0082569340248386'; $VAR17 = '0.00232500890489143'; $VAR18 = '0.00533345404320606'; $VAR19 = '0.0129813129272985'; $VAR20 = '2.64238526196255e-06'; $VAR21 = '0.0995366080158046'; $VAR22 = '0.0230098570555582'; $VAR23 = '0.050954500100249'; $VAR24 = '0.0498513337877205'; $VAR25 = '0.102452949705067'; $VAR26 = '0.0718610962327052'; $VAR27 = '0.0207582615210065'; $VAR28 = '0.0605704332148314'; $VAR29 = '0.00607387628416899'; $VAR30 = '0.00587109246542373'; $VAR31 = '0.0254515709237593'; $VAR32 = '0.00292768977513374'; $VAR33 = '3.04322067740003e-104'; $VAR34 = '0.000315664074696018'; $VAR35 = '3.98315558248133e-99'; $VAR36 = '0.0173132257701817'; $VAR37 = '0.0182909770485222'; $VAR38 = '0.0288428035101501'; $VAR39 = '0.00814768911020561';

Again it doesn't look like "Paul" or "Acts" is the author.

[Ben C. Smith]

Peter, I know nothing about Z-Scores and P-Values and such. Nothing. So far through all of this I have simply been taking your word for it on the positive and negative evaluations; I have tried to locate those specific values that you are interpreting as positive or negative, but to no avail. So, especially now you are sometimes just displaying results with no such pronouncements, I would love to be able to basically, sort of read the results and at least know what to look for, if that is possible. I have read and reread your initial explanation of the results on that first thread you started, too, but I cannot match the numbers to your stated results. (For example, it sounds easy enough when you talk about your Bayesian author test being a straight comparison of the different candidate authors, the most likely candidate having the highest number, but then I will find results you have called negative where the tested candidate appears to have the highest number, and results you have called positive where the tested candidate appears not to; and I am taking into account the scientific notation being used for the really low results.)

In short, I have no earthly idea what to look for.

Ben.

[Peter Kirby]

Peter, I know nothing about Z-Scores and P-Values and such. Nothing. So far through all of this I have simply been taking your word for it on the positive and negative evaluations; I have tried to locate those specific values that you are interpreting as positive or negative, but to no avail. So, especially now you are sometimes just displaying results with no such pronouncements, I would love to be able to basically, sort of read the results and at least know what to look for, if that is possible. I have read and reread your initial explanation of the results on that first thread you started, too, but I cannot match the numbers to your stated results. (For example, it sounds easy enough when you talk about your Bayesian author test being a straight comparison of the different candidate authors, the most likely candidate having the highest number, but then I will find results you have called negative where the tested candidate appears to have the highest number, and results you have called positive where the tested candidate appears not to; and I am taking into account the scientific notation being used for the really low results.)

In short, I have no earthly idea what to look for.

Ben.

In this thread, I have solely been making that call based on this number (e.g., this is a 'negative' result):

Bayesian Comparison of Best Author to Best Control: from Equal Priors, Z-Score-Based Method
$VAR1 = 2; $VAR2 = '0.33154046916538'; $VAR3 = 25; $VAR4 = '0.66845953083462';

Less than 0.5 is negative (the best "control" provides the closest match to the sample).

Greater than 0.5 is positive (the best "author candidate" provides the closest match to the sample).

[Peter Kirby]

One possible explanation for the phenomena found with the Pastorals and with Ephesians is that their respective authors may have had a broad familiarity with the published works of "Paul" and may have extensively drawn on the phrasing from that corpus. This is, in any case, the position of this monograph:

http://babel.hathitrust.org/cgi/pt?id=m ... 1up;seq=19

Several have attempted to show that both Ephesians and the Pastorals show this kind of broad allusional contact that might show that it used the other letters. This, then, is a plausible alternative explanation (for Pastorals, for Ephesians, or for both).