Paul -- A Basic Stylometric Study

[Peter Kirby]

Okay, then, well, back to the stylometry and back to measuring how well the sections of Romans rate against the rest of "Paul." Perhaps we'll find some clues to our questions here yet.

We've now subtracted 2 Thessalonians from the training set.

The two 'shorter' sections still are matched closest by "Paul."

testsize: 2087


Bayesian Author Test: Posterior Probabilities from Equal Priors, Z-Score-Based Method
$VAR1 = '0.971166760870072'; $VAR2 = '9.74237373074236e-118'; $VAR3 = '3.60260961566067e-09'; $VAR4 = '0.0288332355273188';

Bayesian Comparison of Best Author to Best Control: from Equal Priors, Z-Score-Based Method
$VAR1 = 1; $VAR2 = '0.542875072126294'; $VAR3 = 26; $VAR4 = '0.457124927873706';

Percentage of Samples in the Best Author Candidate that Meet the P-Value>0.0503 Test, Z-Score-Based Method
1
Percentage of Samples outside the Best Author Candidate that Meet the P-Value>0.0503 Test, Z-Score-Based Method
0.105820105820106
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
0.904306220095694

Author Z-Score-Based P-Values
$VAR1 = '0.0503614510414053'; $VAR2 = '5.05206826918468e-119'; $VAR3 = '1.86819251945819e-10'; $VAR4 = '0.00149519489121873';
Decent compatibility. Z-Score-Based P-Value > 0.05.
Excellent indicator. 0% of the rest have P-Value > 0.05.

Control Z-Score-Based P-Values
$VAR1 = '0.000166244460746957'; $VAR2 = '0.00437918152412954'; $VAR3 = '2.03084269349196e-13'; $VAR4 = '0.000633496172218769'; $VAR5 = '9.78683271131006e-07'; $VAR6 = '2.89971845328016e-05'; $VAR7 = '8.71356629099173e-05'; $VAR8 = '0.000278069865744261'; $VAR9 = '0.000333599689988833'; $VAR10 = '0.00459271006361686'; $VAR11 = '4.34831125141852e-08'; $VAR12 = '1.45400185975014e-05'; $VAR13 = '5.6711477766175e-10'; $VAR14 = '1.2637000573602e-10'; $VAR15 = '6.90469026884163e-07'; $VAR16 = '0.000906132146329434'; $VAR17 = '0.0022602739988705'; $VAR18 = '0.00463330351309094'; $VAR19 = '0.00196703356402824'; $VAR20 = '1.32328723515804e-08'; $VAR21 = '0.0387289907982187'; $VAR22 = '0.0029704066489141'; $VAR23 = '0.0309582933368472'; $VAR24 = '0.0269848798411817'; $VAR25 = '0.0393066711157513'; $VAR26 = '0.0424065790767455'; $VAR27 = '0.00577801730782261'; $VAR28 = '0.0225006161758183'; $VAR29 = '0.000965232865008366'; $VAR30 = '0.00116799246714527';

testsize: 2134


Bayesian Author Test: Posterior Probabilities from Equal Priors, Z-Score-Based Method
$VAR1 = '0.991153418030528'; $VAR2 = '2.32304520280344e-145'; $VAR3 = '1.36492857463184e-13'; $VAR4 = '0.00884658196933518';

Bayesian Comparison of Best Author to Best Control: from Equal Priors, Z-Score-Based Method
$VAR1 = 1; $VAR2 = '0.683079592916667'; $VAR3 = 26; $VAR4 = '0.316920407083333';

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
0.010840108401084
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
0.989276139410188

Author Z-Score-Based P-Values
$VAR1 = '0.101364398666'; $VAR2 = '2.37575813968341e-146'; $VAR3 = '1.39590059089455e-14'; $VAR4 = '0.000904732249577448';
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 = '2.08746144982065e-07'; $VAR2 = '0.00195145039988182'; $VAR3 = '2.21130853323069e-10'; $VAR4 = '0.000878161148827971'; $VAR5 = '1.35528687878506e-08'; $VAR6 = '1.29709282077259e-05'; $VAR7 = '0.000229786406678742'; $VAR8 = '0.000653287169891307'; $VAR9 = '0.000735810650089514'; $VAR10 = '0.00710008708542592'; $VAR11 = '5.05437094863628e-09'; $VAR12 = '1.3183352442716e-05'; $VAR13 = '4.06278944250575e-07'; $VAR14 = '1.3911444916948e-08'; $VAR15 = '0.000359648574849108'; $VAR16 = '0.0025370958263097'; $VAR17 = '0.0049645926323386'; $VAR18 = '0.0176711214763852'; $VAR19 = '0.00517231877152688'; $VAR20 = '4.01257970304954e-06'; $VAR21 = '0.0294539963741836'; $VAR22 = '0.00544038164571944'; $VAR23 = '0.0452650376343735'; $VAR24 = '0.0452192706943131'; $VAR25 = '0.0419005826781921'; $VAR26 = '0.0470288482075981'; $VAR27 = '0.0180258456055121'; $VAR28 = '0.0388667077581223'; $VAR29 = '0.00193596500538218'; $VAR30 = '0.00111233964578893';

The 'additions' do happen to get a positive here as well.

testsize: 2881


Bayesian Author Test: Posterior Probabilities from Equal Priors, Z-Score-Based Method
$VAR1 = '0.905270474246813'; $VAR2 = '1.30523129568126e-125'; $VAR3 = '3.79957712472476e-66'; $VAR4 = '0.0947295257531867';

Bayesian Comparison of Best Author to Best Control: from Equal Priors, Z-Score-Based Method
$VAR1 = 1; $VAR2 = '0.558768128659212'; $VAR3 = 26; $VAR4 = '0.441231871340788';

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
0.00371747211895911
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
0.996296296296296

Author Z-Score-Based P-Values
$VAR1 = '0.112123221966736'; $VAR2 = '1.61660788070395e-126'; $VAR3 = '4.70600601096259e-67'; $VAR4 = '0.0117328245480061';
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 = '1.14278448201574e-05'; $VAR2 = '0.00215579882246775'; $VAR3 = '1.48008079615149e-12'; $VAR4 = '0.000977986085557945'; $VAR5 = '9.50993834111158e-06'; $VAR6 = '0.000511449934184708'; $VAR7 = '0.000126380134921262'; $VAR8 = '0.00212920652338'; $VAR9 = '0.00211280549669375'; $VAR10 = '0.00510014618641654'; $VAR11 = '4.52178138198396e-08'; $VAR12 = '2.32663602816517e-05'; $VAR13 = '1.08454363270407e-11'; $VAR14 = '4.88029399703153e-12'; $VAR15 = '3.36808083886514e-06'; $VAR16 = '0.00583170290025606'; $VAR17 = '0.000456858847991808'; $VAR18 = '0.00752907583336433'; $VAR19 = '0.00700448821995009'; $VAR20 = '5.45348890310958e-10'; $VAR21 = '0.0656965025937909'; $VAR22 = '0.00585583005649278'; $VAR23 = '0.0714790273717603'; $VAR24 = '0.05396578762922'; $VAR25 = '0.0672424890810161'; $VAR26 = '0.0885382263441768'; $VAR27 = '0.01734968651736'; $VAR28 = '0.0501089211165585'; $VAR29 = '0.00357237672527834'; $VAR30 = '0.00486328547936382';

On the other hand, the start and end of "Romans" get a 'negative' when using the longer "Romans" (and identifying against 1 Cor, 2 Cor, shorter Gal, 1 Thessalonians, Philippians, Philemon, Colossians, and Ephesians).

testsize: 2355


Bayesian Author Test: Posterior Probabilities from Equal Priors, Z-Score-Based Method
$VAR1 = '0.900088328522161'; $VAR2 = '2.49152294662324e-149'; $VAR3 = '1.86483733012937e-05'; $VAR4 = '0.0998930231045377';

Bayesian Comparison of Best Author to Best Control: from Equal Priors, Z-Score-Based Method
$VAR1 = 1; $VAR2 = '0.485730156985343'; $VAR3 = 26; $VAR4 = '0.514269843014657';

Percentage of Samples in the Best Author Candidate that Meet the P-Value>0.0489 Test, Z-Score-Based Method
1
Percentage of Samples outside the Best Author Candidate that Meet the P-Value>0.0489 Test, Z-Score-Based Method
0.0725075528700906
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
0.932394366197183

Author Z-Score-Based P-Values
$VAR1 = '0.048974526313852'; $VAR2 = '1.35565757542163e-150'; $VAR3 = '1.01467291599511e-06'; $VAR4 = '0.00543525933353213';
Poor compatibility. Z-Score-Based P-Value < 0.05.
Decent indicator. 18.1% of the rest have P-Value > 0.01.

Control Z-Score-Based P-Values
$VAR1 = '3.40309045435088e-06'; $VAR2 = '0.000902296503603511'; $VAR3 = '8.75629404523119e-08'; $VAR4 = '0.00195779081887294'; $VAR5 = '1.36528331752382e-05'; $VAR6 = '0.000220383479020651'; $VAR7 = '0.000348303178027803'; $VAR8 = '0.000742914886524126'; $VAR9 = '0.000413337852657473'; $VAR10 = '0.00477580127036022'; $VAR11 = '5.33178395799041e-09'; $VAR12 = '4.35851303891826e-05'; $VAR13 = '6.96834196104292e-10'; $VAR14 = '1.04129972976392e-10'; $VAR15 = '7.47474588644823e-07'; $VAR16 = '0.000749823437481076'; $VAR17 = '0.000412965614386444'; $VAR18 = '0.0029488014674202'; $VAR19 = '0.00249778853207511'; $VAR20 = '2.90631016126241e-09'; $VAR21 = '0.0406049304317633'; $VAR22 = '0.00304064967103437'; $VAR23 = '0.0399564176848096'; $VAR24 = '0.0472552996014604'; $VAR25 = '0.0468325201988656'; $VAR26 = '0.051852086177762'; $VAR27 = '0.00394786170940485'; $VAR28 = '0.0287464981883643'; $VAR29 = '0.00207704377607761'; $VAR30 = '0.00175355355063183';

testsize: 2442


Bayesian Author Test: Posterior Probabilities from Equal Priors, Z-Score-Based Method
$VAR1 = '0.991225736299211'; $VAR2 = '3.60382725283672e-174'; $VAR3 = '1.96707234084705e-07'; $VAR4 = '0.00877406699355465';

Bayesian Comparison of Best Author to Best Control: from Equal Priors, Z-Score-Based Method
$VAR1 = 1; $VAR2 = '0.560173391478115'; $VAR3 = 28; $VAR4 = '0.439826608521885';

Percentage of Samples in the Best Author Candidate that Meet the P-Value>0.0489 Test, Z-Score-Based Method
1
Percentage of Samples outside the Best Author Candidate that Meet the P-Value>0.0489 Test, Z-Score-Based Method
0.0625
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
0.941176470588235

Author Z-Score-Based P-Values
$VAR1 = '0.0489384666517871'; $VAR2 = '1.77926957879667e-175'; $VAR3 = '9.71176399370017e-09'; $VAR4 = '0.000433190310985837';
Poor compatibility. Z-Score-Based P-Value < 0.05.
Poor indicator. 21.2% of the rest have P-Value > 0.01.

Control Z-Score-Based P-Values
$VAR1 = '2.47890299632512e-05'; $VAR2 = '0.00407255533689989'; $VAR3 = '2.32963039884813e-08'; $VAR4 = '0.000285015778988536'; $VAR5 = '1.00435490576041e-08'; $VAR6 = '2.09118889671721e-06'; $VAR7 = '2.31519456283993e-05'; $VAR8 = '1.7777005202657e-05'; $VAR9 = '0.000386472696508642'; $VAR10 = '0.00266559311400637'; $VAR11 = '1.31199962038943e-10'; $VAR12 = '6.93803107800731e-06'; $VAR13 = '3.22042641904712e-10'; $VAR14 = '6.89007565475589e-13'; $VAR15 = '8.27082224310777e-07'; $VAR16 = '0.00104971659310742'; $VAR17 = '0.00306295331152457'; $VAR18 = '0.00976727387694273'; $VAR19 = '0.00162050210117427'; $VAR20 = '4.6667325940968e-09'; $VAR21 = '0.0230618269841854'; $VAR22 = '0.00347105450844604'; $VAR23 = '0.0339590106687758'; $VAR24 = '0.0225613685925604'; $VAR25 = '0.0316623405717912'; $VAR26 = '0.0382394870507127'; $VAR27 = '0.0139460708031967'; $VAR28 = '0.0384246023484281'; $VAR29 = '0.000694954198782519'; $VAR30 = '0.000874893857782245';

testsize: 2305


Bayesian Author Test: Posterior Probabilities from Equal Priors, Z-Score-Based Method
$VAR1 = '0.932889723826683'; $VAR2 = '3.09654520000773e-111'; $VAR3 = '0.00274235391042189'; $VAR4 = '0.0643679222628949';

Bayesian Comparison of Best Author to Best Control: from Equal Priors, Z-Score-Based Method
$VAR1 = 1; $VAR2 = '0.474979547561374'; $VAR3 = 26; $VAR4 = '0.525020452438626';

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
0.00588235294117647
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
0.994152046783626

Author Z-Score-Based P-Values
$VAR1 = '0.10610898312031'; $VAR2 = '3.52208041279636e-112'; $VAR3 = '0.000311921524440474'; $VAR4 = '0.00732135278419235';
Good compatibility. Z-Score-Based P-Value > 0.1.
Great indicator. 3% of the rest have P-Value > 0.1.

Control Z-Score-Based P-Values
$VAR1 = '0.000223265327866713'; $VAR2 = '0.00343856695842456'; $VAR3 = '2.84992089911655e-08'; $VAR4 = '0.0177150471647755'; $VAR5 = '4.40635607379384e-06'; $VAR6 = '0.0013564442527555'; $VAR7 = '0.000586574917239685'; $VAR8 = '0.00449893713847959'; $VAR9 = '0.00248332592352781'; $VAR10 = '0.0102961839476476'; $VAR11 = '1.85835000545774e-06'; $VAR12 = '2.91764459546261e-05'; $VAR13 = '2.2989156677516e-07'; $VAR14 = '5.13977745876045e-09'; $VAR15 = '0.000287212047180623'; $VAR16 = '0.00648870547028198'; $VAR17 = '0.00363569082424301'; $VAR18 = '0.00473029637399357'; $VAR19 = '0.0127098366790336'; $VAR20 = '2.49706539160265e-06'; $VAR21 = '0.0693010161730579'; $VAR22 = '0.00826699351717825'; $VAR23 = '0.0656842818330863'; $VAR24 = '0.0722572168263946'; $VAR25 = '0.0637857290699431'; $VAR26 = '0.117287968738125'; $VAR27 = '0.029207447795038'; $VAR28 = '0.0531462066855674'; $VAR29 = '0.00478237384322689'; $VAR30 = '0.00978204820544255';

Overall, then, it does look like the 'shorter' version of Romans fares better as the work of "Paul."

[Peter Kirby]

Now let's subtract Ephesians (Laodiceans?).

Things start going a little bit to "hell" for Romans. It's still possible/plausible that the 'shorter' epistle is authentic "Paul" (without Eph), as it still gets one match. However, the 'additions' and all three parts of the 'longer' Romans are now negatives.

This is starting to look like either "Romans" was written by a later "Paul" (along with some of the deutero-Paulines... which conclusion I might perhaps favor) or perhaps isn't authentic "Paul" at all (?!). Stay tuned for what happens next...

testsize: 2087


Bayesian Author Test: Posterior Probabilities from Equal Priors, Z-Score-Based Method
$VAR1 = '0.946196802032365'; $VAR2 = '2.55771663767978e-125'; $VAR3 = '7.63456630290293e-09'; $VAR4 = '0.0538031903330687';

Bayesian Comparison of Best Author to Best Control: from Equal Priors, Z-Score-Based Method
$VAR1 = 1; $VAR2 = '0.39178133319181'; $VAR3 = 26; $VAR4 = '0.60821866680819';

Percentage of Samples in the Best Author Candidate that Meet the P-Value>0.0273 Test, Z-Score-Based Method
1
Percentage of Samples outside the Best Author Candidate that Meet the P-Value>0.0273 Test, Z-Score-Based Method
0.100529100529101
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
0.908653846153846

Author Z-Score-Based P-Values
$VAR1 = '0.0273159800163317'; $VAR2 = '7.38393285754415e-127'; $VAR3 = '2.20404106329163e-10'; $VAR4 = '0.00155325706956122';
Poor compatibility. Z-Score-Based P-Value < 0.05.
Decent indicator. 18.1% of the rest have P-Value > 0.01.

Control Z-Score-Based P-Values
$VAR1 = '0.000166244341477038'; $VAR2 = '0.00437913190091121'; $VAR3 = '2.03077953606942e-13'; $VAR4 = '0.000633459346955809'; $VAR5 = '9.78636635354281e-07'; $VAR6 = '2.89966365511749e-05'; $VAR7 = '8.71296185737456e-05'; $VAR8 = '0.000278054759798847'; $VAR9 = '0.00033359391808579'; $VAR10 = '0.00459258691070026'; $VAR11 = '4.34853750525161e-08'; $VAR12 = '1.45398067566463e-05'; $VAR13 = '5.67076946287075e-10'; $VAR14 = '1.26447263599972e-10'; $VAR15 = '6.90393982003444e-07'; $VAR16 = '0.000906116076997264'; $VAR17 = '0.00226022174711581'; $VAR18 = '0.0046332973305112'; $VAR19 = '0.00196701290247792'; $VAR20 = '1.32313832126329e-08'; $VAR21 = '0.0387289866092177'; $VAR22 = '0.00297036433689476'; $VAR23 = '0.0309583198931813'; $VAR24 = '0.0269848428808084'; $VAR25 = '0.0393066649798417'; $VAR26 = '0.0424065353311726'; $VAR27 = '0.0057780627628984'; $VAR28 = '0.0225005589102237'; $VAR29 = '0.000965236767261804'; $VAR30 = '0.00116799725415307';

testsize: 2134


Bayesian Author Test: Posterior Probabilities from Equal Priors, Z-Score-Based Method
$VAR1 = '0.98712295006343'; $VAR2 = '2.30196365344979e-145'; $VAR3 = '1.41948207187393e-13'; $VAR4 = '0.0128770499364279';

Bayesian Comparison of Best Author to Best Control: from Equal Priors, Z-Score-Based Method
$VAR1 = 1; $VAR2 = '0.603476329746489'; $VAR3 = 26; $VAR4 = '0.396523670253511';

Percentage of Samples in the Best Author Candidate that Meet the P-Value>0.0715 Test, Z-Score-Based Method
1
Percentage of Samples outside the Best Author Candidate that Meet the P-Value>0.0715 Test, Z-Score-Based Method
0.00813008130081301
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
0.991935483870968

Author Z-Score-Based P-Values
$VAR1 = '0.0715740104690207'; $VAR2 = '1.66910080067263e-146'; $VAR3 = '1.02923374100829e-14'; $VAR4 = '0.000933685218139008';
Decent compatibility. Z-Score-Based P-Value > 0.05.
Excellent indicator. 0% of the rest have P-Value > 0.05.

Control Z-Score-Based P-Values
$VAR1 = '2.08749492558893e-07'; $VAR2 = '0.00195142078668819'; $VAR3 = '2.21129229233236e-10'; $VAR4 = '0.000878177089914076'; $VAR5 = '1.35523896475606e-08'; $VAR6 = '1.29709479109813e-05'; $VAR7 = '0.000229787412840667'; $VAR8 = '0.000653289031934515'; $VAR9 = '0.000735823997342405'; $VAR10 = '0.0071002486004269'; $VAR11 = '5.05459558008864e-09'; $VAR12 = '1.31837721632159e-05'; $VAR13 = '4.06332269131023e-07'; $VAR14 = '1.39116594397067e-08'; $VAR15 = '0.000359629019988651'; $VAR16 = '0.00253709454831398'; $VAR17 = '0.0049646388204307'; $VAR18 = '0.0176711164870606'; $VAR19 = '0.00517231954021418'; $VAR20 = '4.0125514009712e-06'; $VAR21 = '0.0294539930850406'; $VAR22 = '0.00544038486875767'; $VAR23 = '0.0452649525383539'; $VAR24 = '0.0452192802066773'; $VAR25 = '0.0419005974147993'; $VAR26 = '0.047028835974166'; $VAR27 = '0.0180258463400479'; $VAR28 = '0.0388667308202615'; $VAR29 = '0.00193596514587861'; $VAR30 = '0.00111234170467202';

The 'additions':

testsize: 2881


Bayesian Author Test: Posterior Probabilities from Equal Priors, Z-Score-Based Method
$VAR1 = '0.815467042833658'; $VAR2 = '2.11330395081461e-128'; $VAR3 = '5.10229814253998e-65'; $VAR4 = '0.184532957166342';

Bayesian Comparison of Best Author to Best Control: from Equal Priors, Z-Score-Based Method
$VAR1 = 1; $VAR2 = '0.361398515817917'; $VAR3 = 26; $VAR4 = '0.638601484182083';

Percentage of Samples in the Best Author Candidate that Meet the P-Value>0.0501 Test, Z-Score-Based Method
1
Percentage of Samples outside the Best Author Candidate that Meet the P-Value>0.0501 Test, Z-Score-Based Method
0.00371747211895911
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
0.996296296296296

Author Z-Score-Based P-Values
$VAR1 = '0.0501057642287938'; $VAR2 = '1.298503850448e-129'; $VAR3 = '3.1350690380662e-66'; $VAR4 = '0.0113384899187212';
Decent compatibility. Z-Score-Based P-Value > 0.05.
Decent indicator. 18.1% of the rest have P-Value > 0.05.

Control Z-Score-Based P-Values
$VAR1 = '1.19282132059614e-05'; $VAR2 = '0.00235643860331992'; $VAR3 = '2.27138216036957e-12'; $VAR4 = '0.000977837645150077'; $VAR5 = '9.51033104066922e-06'; $VAR6 = '0.000511432120049003'; $VAR7 = '0.000126373557161838'; $VAR8 = '0.00212916573070868'; $VAR9 = '0.00211281572427746'; $VAR10 = '0.00510017747566949'; $VAR11 = '4.52169218345977e-08'; $VAR12 = '2.32655001279504e-05'; $VAR13 = '1.08415952538465e-11'; $VAR14 = '4.87968967212497e-12'; $VAR15 = '3.36793206285858e-06'; $VAR16 = '0.00583167748893521'; $VAR17 = '0.000456855589688121'; $VAR18 = '0.00752908321264487'; $VAR19 = '0.00700552244248266'; $VAR20 = '5.45107165661332e-10'; $VAR21 = '0.0656965018662137'; $VAR22 = '0.00585574869544314'; $VAR23 = '0.0714791596423077'; $VAR24 = '0.053965793397119'; $VAR25 = '0.0672424095086243'; $VAR26 = '0.0885383143596155'; $VAR27 = '0.0173496096935468'; $VAR28 = '0.0501086419966099'; $VAR29 = '0.00357237379988016'; $VAR30 = '0.00486322419453579';

The 'longer' Romans

testsize: 2355


Bayesian Author Test: Posterior Probabilities from Equal Priors, Z-Score-Based Method
$VAR1 = '0.824141023025357'; $VAR2 = '3.31741627872532e-142'; $VAR3 = '3.00360819916289e-05'; $VAR4 = '0.175828940892652';

Bayesian Comparison of Best Author to Best Control: from Equal Priors, Z-Score-Based Method
$VAR1 = 1; $VAR2 = '0.329551722885788'; $VAR3 = 26; $VAR4 = '0.670448277114213';

Percentage of Samples in the Best Author Candidate that Meet the P-Value>0.0254 Test, Z-Score-Based Method
1
Percentage of Samples outside the Best Author Candidate that Meet the P-Value>0.0254 Test, Z-Score-Based Method
0.0725075528700906
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
0.932394366197183

Author Z-Score-Based P-Values
$VAR1 = '0.0254872574129309'; $VAR2 = '1.02593901140046e-143'; $VAR3 = '9.28891211586964e-07'; $VAR4 = '0.00543765854625605';
Poor compatibility. Z-Score-Based P-Value < 0.05.
Decent indicator. 18.1% of the rest have P-Value > 0.01.

Control Z-Score-Based P-Values
$VAR1 = '3.40309511570558e-06'; $VAR2 = '0.000902296985981737'; $VAR3 = '8.75576957998183e-08'; $VAR4 = '0.00195779138322629'; $VAR5 = '1.36526845316178e-05'; $VAR6 = '0.00022038808737756'; $VAR7 = '0.000348300424901637'; $VAR8 = '0.000742915283911426'; $VAR9 = '0.000413338057022147'; $VAR10 = '0.00477579650046178'; $VAR11 = '5.33164029841468e-09'; $VAR12 = '4.35843791286354e-05'; $VAR13 = '6.96860447425658e-10'; $VAR14 = '1.04124666403724e-10'; $VAR15 = '7.47727370396762e-07'; $VAR16 = '0.000749755322363956'; $VAR17 = '0.000412948650047284'; $VAR18 = '0.00294879675619189'; $VAR19 = '0.00249778012027658'; $VAR20 = '2.9062210288596e-09'; $VAR21 = '0.0406049786123009'; $VAR22 = '0.00304064200610611'; $VAR23 = '0.0399563686283354'; $VAR24 = '0.0472554039749862'; $VAR25 = '0.0468324942661113'; $VAR26 = '0.0518519146895436'; $VAR27 = '0.00394786212433269'; $VAR28 = '0.0287464988189576'; $VAR29 = '0.00207705828013908'; $VAR30 = '0.00175354484888247';

testsize: 2442


Bayesian Author Test: Posterior Probabilities from Equal Priors, Z-Score-Based Method
$VAR1 = '0.988100034458458'; $VAR2 = '2.02655593663864e-174'; $VAR3 = '3.20390470968676e-07'; $VAR4 = '0.0118996451510707';

Bayesian Comparison of Best Author to Best Control: from Equal Priors, Z-Score-Based Method
$VAR1 = 1; $VAR2 = '0.483486629592523'; $VAR3 = 28; $VAR4 = '0.516513370407477';

Percentage of Samples in the Best Author Candidate that Meet the P-Value>0.0359 Test, Z-Score-Based Method
1
Percentage of Samples outside the Best Author Candidate that Meet the P-Value>0.0359 Test, Z-Score-Based Method
0.025
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
0.975609756097561

Author Z-Score-Based P-Values
$VAR1 = '0.035967565794695'; $VAR2 = '7.3768122098719e-176'; $VAR3 = '1.1662448074779e-08'; $VAR4 = '0.000433155809107154';
Poor compatibility. Z-Score-Based P-Value < 0.05.
Poor indicator. 21.2% of the rest have P-Value > 0.01.

Control Z-Score-Based P-Values
$VAR1 = '2.48014344845566e-05'; $VAR2 = '0.004072532864687'; $VAR3 = '2.32964991412259e-08'; $VAR4 = '0.000285018664634318'; $VAR5 = '1.00429965034607e-08'; $VAR6 = '2.09120153969367e-06'; $VAR7 = '2.3151071764409e-05'; $VAR8 = '1.77770290070118e-05'; $VAR9 = '0.00038647316889781'; $VAR10 = '0.00266556448988364'; $VAR11 = '1.31201730790609e-10'; $VAR12 = '6.9381539670258e-06'; $VAR13 = '3.22031487987449e-10'; $VAR14 = '6.89097859322868e-13'; $VAR15 = '8.27082273313161e-07'; $VAR16 = '0.00104990927103249'; $VAR17 = '0.00306302474422022'; $VAR18 = '0.00976727469525028'; $VAR19 = '0.00162051522088455'; $VAR20 = '4.66673614574099e-09'; $VAR21 = '0.0230618193061809'; $VAR22 = '0.00347104558864142'; $VAR23 = '0.0339589343354812'; $VAR24 = '0.0225612824637426'; $VAR25 = '0.0316623401162928'; $VAR26 = '0.0382394202906799'; $VAR27 = '0.0139460830526618'; $VAR28 = '0.0384244930405369'; $VAR29 = '0.000694958135827385'; $VAR30 = '0.000874893396186955';

testsize: 2305


Bayesian Author Test: Posterior Probabilities from Equal Priors, Z-Score-Based Method
$VAR1 = '0.902016495241793'; $VAR2 = '1.57060935333887e-104'; $VAR3 = '0.00389795988412261'; $VAR4 = '0.0940855448740843';

Bayesian Comparison of Best Author to Best Control: from Equal Priors, Z-Score-Based Method
$VAR1 = 1; $VAR2 = '0.374754863990488'; $VAR3 = 26; $VAR4 = '0.625245136009512';

Percentage of Samples in the Best Author Candidate that Meet the P-Value>0.0702 Test, Z-Score-Based Method
1
Percentage of Samples outside the Best Author Candidate that Meet the P-Value>0.0702 Test, Z-Score-Based Method
0.00588235294117647
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
0.994152046783626

Author Z-Score-Based P-Values
$VAR1 = '0.0702991198512792'; $VAR2 = '1.22406248391624e-105'; $VAR3 = '0.000303789509964515'; $VAR4 = '0.00733260536837874';
Decent compatibility. Z-Score-Based P-Value > 0.05.
Decent indicator. 18.1% of the rest have P-Value > 0.05.

Control Z-Score-Based P-Values
$VAR1 = '0.000223261901704346'; $VAR2 = '0.00343856420868973'; $VAR3 = '2.84990687611617e-08'; $VAR4 = '0.0177150551805609'; $VAR5 = '4.40634771910659e-06'; $VAR6 = '0.0013564443430428'; $VAR7 = '0.000586574831381073'; $VAR8 = '0.00449893535786223'; $VAR9 = '0.00248332988844366'; $VAR10 = '0.0102961678600159'; $VAR11 = '1.85836169783893e-06'; $VAR12 = '2.91762809065291e-05'; $VAR13 = '2.29892644026533e-07'; $VAR14 = '5.1396521535738e-09'; $VAR15 = '0.000287213739729888'; $VAR16 = '0.00648881534973499'; $VAR17 = '0.00363574893645809'; $VAR18 = '0.00473030286350861'; $VAR19 = '0.0127098363878817'; $VAR20 = '2.4970646443017e-06'; $VAR21 = '0.0693010213672065'; $VAR22 = '0.0082669938663791'; $VAR23 = '0.065684256075521'; $VAR24 = '0.0722572178826292'; $VAR25 = '0.0637857290194388'; $VAR26 = '0.117287824592125'; $VAR27 = '0.0292074712843451'; $VAR28 = '0.0531462328579153'; $VAR29 = '0.00478237398703236'; $VAR30 = '0.00978203314398422';

[Peter Kirby]

Now let's subtract Colossians.

We're now using the most common scholarly definition of the rest of Paul--the letters 1 Cor, 2 Cor, Gal (albeit shorter), 1 Thess, Phillipians, and Philemon.

We still see the same thing happening with 'shorter' Romans: one match. Possibly the first half has not removed all the 'additions'. Also, when we remove all three of the major deutero-Paulilnes, the 'additions' take a major dive from where they were; they are no longer even really borderline.

So there are a couple more-likely options here:
(1) The 'shorter' Romans isn't short enough, and the deutero-Paulines really are all deutero.
(2) The 'shorter' Romans is the right size, and Colossians/Laodiceans are part of "Paul."

This is a question that is very thorny and will require detailed analysis of all the issues involved. But it's important to note what's going on here with the stylometry: (a) with Colossians & Laodiceans, the 'shorter' Romans is a full match; (b) without them, the 'shorter' Romans matches only in the latter half; (c) the 'longer' Romans matches poorly regardless.

testsize: 2087


Bayesian Author Test: Posterior Probabilities from Equal Priors, Z-Score-Based Method
$VAR1 = '0.946932804190891'; $VAR2 = '5.44426644799202e-116'; $VAR3 = '7.24147483674015e-09'; $VAR4 = '0.0530671885676345';

Bayesian Comparison of Best Author to Best Control: from Equal Priors, Z-Score-Based Method
$VAR1 = 1; $VAR2 = '0.386486542115042'; $VAR3 = 26; $VAR4 = '0.613513457884958';

Percentage of Samples in the Best Author Candidate that Meet the P-Value>0.0267 Test, Z-Score-Based Method
1
Percentage of Samples outside the Best Author Candidate that Meet the P-Value>0.0267 Test, Z-Score-Based Method
0.103174603174603
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
0.906474820143885

Author Z-Score-Based P-Values
$VAR1 = '0.0267142809563642'; $VAR2 = '1.53590268337189e-117'; $VAR3 = '2.04291996719253e-10'; $VAR4 = '0.00149709861004495';
Poor compatibility. Z-Score-Based P-Value < 0.05.
Decent indicator. 18.1% of the rest have P-Value > 0.01.

Control Z-Score-Based P-Values
$VAR1 = '0.000166246366901465'; $VAR2 = '0.00437919043924937'; $VAR3 = '2.03073488065149e-13'; $VAR4 = '0.000633494219857476'; $VAR5 = '9.78681925424055e-07'; $VAR6 = '2.89968708550538e-05'; $VAR7 = '8.71348642243178e-05'; $VAR8 = '0.000278067015963692'; $VAR9 = '0.00033359510651018'; $VAR10 = '0.00459260376428523'; $VAR11 = '4.34829571332107e-08'; $VAR12 = '1.45396868780938e-05'; $VAR13 = '5.67024933619946e-10'; $VAR14 = '1.26446674288433e-10'; $VAR15 = '6.90484950993302e-07'; $VAR16 = '0.000906131834769118'; $VAR17 = '0.00226027326429607'; $VAR18 = '0.00463330339199074'; $VAR19 = '0.00196703089403656'; $VAR20 = '1.3232795747577e-08'; $VAR21 = '0.038728989196897'; $VAR22 = '0.00297041811640494'; $VAR23 = '0.0309582908247654'; $VAR24 = '0.0269848657663113'; $VAR25 = '0.0393066706141335'; $VAR26 = '0.0424065759049659'; $VAR27 = '0.00577803818842705'; $VAR28 = '0.0225005840879898'; $VAR29 = '0.000965230641326902'; $VAR30 = '0.00116798923968634';

testsize: 2134


Bayesian Author Test: Posterior Probabilities from Equal Priors, Z-Score-Based Method
$VAR1 = '0.983968193064514'; $VAR2 = '5.34713215594743e-151'; $VAR3 = '1.71947533842401e-13'; $VAR4 = '0.0160318069353143';

Bayesian Comparison of Best Author to Best Control: from Equal Priors, Z-Score-Based Method
$VAR1 = 1; $VAR2 = '0.552439263996036'; $VAR3 = 26; $VAR4 = '0.447560736003964';

Percentage of Samples in the Best Author Candidate that Meet the P-Value>0.058 Test, Z-Score-Based Method
1
Percentage of Samples outside the Best Author Candidate that Meet the P-Value>0.058 Test, Z-Score-Based Method
0.00542005420054201
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
0.994609164420485

Author Z-Score-Based P-Values
$VAR1 = '0.058049273853508'; $VAR2 = '3.15454443588036e-152'; $VAR3 = '1.01440570445334e-14'; $VAR4 = '0.000945797595607452';
Decent compatibility. Z-Score-Based P-Value > 0.05.
Excellent indicator. 0% of the rest have P-Value > 0.05.

Control Z-Score-Based P-Values
$VAR1 = '2.08752434931054e-07'; $VAR2 = '0.00195144492811163'; $VAR3 = '2.2111309248219e-10'; $VAR4 = '0.000878187572017662'; $VAR5 = '1.35522082480704e-08'; $VAR6 = '1.29709978596245e-05'; $VAR7 = '0.000229786128574886'; $VAR8 = '0.000653286814897789'; $VAR9 = '0.00073581842984939'; $VAR10 = '0.00710021031901619'; $VAR11 = '5.05425714304034e-09'; $VAR12 = '1.31834511026935e-05'; $VAR13 = '4.06303879262641e-07'; $VAR14 = '1.39103202473137e-08'; $VAR15 = '0.000359627316776662'; $VAR16 = '0.00253709362017898'; $VAR17 = '0.00496464923075697'; $VAR18 = '0.0176711222743586'; $VAR19 = '0.00517231859130472'; $VAR20 = '4.01255736020212e-06'; $VAR21 = '0.0294539968926761'; $VAR22 = '0.00544039101499244'; $VAR23 = '0.0452649457441296'; $VAR24 = '0.0452192792525636'; $VAR25 = '0.0419006030613515'; $VAR26 = '0.0470288363329623'; $VAR27 = '0.0180258454861494'; $VAR28 = '0.0388667210598459'; $VAR29 = '0.00193596498255139'; $VAR30 = '0.00111234276116118';

The 'additions' fare very poorly when measured against the other 6 of 7 'undisputed' epistles.

testsize: 2881 ['additions']


Bayesian Author Test: Posterior Probabilities from Equal Priors, Z-Score-Based Method
$VAR1 = '0.639839255345178'; $VAR2 = '6.16896811756038e-137'; $VAR3 = '3.35921773173724e-66'; $VAR4 = '0.360160744654822';

Bayesian Comparison of Best Author to Best Control: from Equal Priors, Z-Score-Based Method
$VAR1 = 1; $VAR2 = '0.197409374701012'; $VAR3 = 26; $VAR4 = '0.802590625298988';

Percentage of Samples in the Best Author Candidate that Meet the P-Value>0.0217 Test, Z-Score-Based Method
1
Percentage of Samples outside the Best Author Candidate that Meet the P-Value>0.0217 Test, Z-Score-Based Method
0.00371747211895911
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
0.996296296296296

Author Z-Score-Based P-Values
$VAR1 = '0.0217773303626886'; $VAR2 = '2.09964699056375e-138'; $VAR3 = '1.1433308240017e-67'; $VAR4 = '0.0122582968370528';
Poor compatibility. Z-Score-Based P-Value < 0.05.
Poor indicator. 24.2% of the rest have P-Value > 0.01.

Control Z-Score-Based P-Values
$VAR1 = '9.18077415105891e-06'; $VAR2 = '0.00213561104183092'; $VAR3 = '2.88942215093662e-12'; $VAR4 = '0.000977947668835678'; $VAR5 = '9.51025185685483e-06'; $VAR6 = '0.000511442808364768'; $VAR7 = '0.000126376278417155'; $VAR8 = '0.00212922402790513'; $VAR9 = '0.00211280613167044'; $VAR10 = '0.00510009725875773'; $VAR11 = '4.52195181552781e-08'; $VAR12 = '2.32656199887884e-05'; $VAR13 = '1.08423798795975e-11'; $VAR14 = '4.88027732471944e-12'; $VAR15 = '3.36802154027238e-06'; $VAR16 = '0.00583175352189663'; $VAR17 = '0.000456861538484269'; $VAR18 = '0.00752909018165899'; $VAR19 = '0.00700477611317188'; $VAR20 = '5.45248104182134e-10'; $VAR21 = '0.0656965016325962'; $VAR22 = '0.00585568318181788'; $VAR23 = '0.0714788602778323'; $VAR24 = '0.0539657866848624'; $VAR25 = '0.0672421900643954'; $VAR26 = '0.088538253158467'; $VAR27 = '0.0173496966030275'; $VAR28 = '0.0501087010898713'; $VAR29 = '0.00357238653873936'; $VAR30 = '0.00486327663998154';

The 'longer' Romans is completely rejected when measured against the other 6 of 7 'undisputed' epistles.

testsize: 2355


Bayesian Author Test: Posterior Probabilities from Equal Priors, Z-Score-Based Method
$VAR1 = '0.823089342199655'; $VAR2 = '7.24671537437145e-146'; $VAR3 = '3.31995374424953e-05'; $VAR4 = '0.176877458262903';

Bayesian Comparison of Best Author to Best Control: from Equal Priors, Z-Score-Based Method
$VAR1 = 1; $VAR2 = '0.327946715937498'; $VAR3 = 26; $VAR4 = '0.672053284062502';

Percentage of Samples in the Best Author Candidate that Meet the P-Value>0.0253 Test, Z-Score-Based Method
1
Percentage of Samples outside the Best Author Candidate that Meet the P-Value>0.0253 Test, Z-Score-Based Method
0.0725075528700906
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
0.932394366197183

Author Z-Score-Based P-Values
$VAR1 = '0.0253027671115757'; $VAR2 = '2.22772841343775e-147'; $VAR3 = '1.02059414580019e-06'; $VAR4 = '0.00543742811898548';
Poor compatibility. Z-Score-Based P-Value < 0.05.
Decent indicator. 18.1% of the rest have P-Value > 0.01.

Control Z-Score-Based P-Values
$VAR1 = '3.40303591273326e-06'; $VAR2 = '0.000902296912145533'; $VAR3 = '8.75573381708066e-08'; $VAR4 = '0.00195774725595257'; $VAR5 = '1.36526955081773e-05'; $VAR6 = '0.000220386953484047'; $VAR7 = '0.000348291125196146'; $VAR8 = '0.000742912605211161'; $VAR9 = '0.000413334344568832'; $VAR10 = '0.00477579334001751'; $VAR11 = '5.33162958898869e-09'; $VAR12 = '4.35838787254247e-05'; $VAR13 = '6.96842369315304e-10'; $VAR14 = '1.04143521929492e-10'; $VAR15 = '7.47630970171136e-07'; $VAR16 = '0.000749644334209328'; $VAR17 = '0.000412937851989638'; $VAR18 = '0.00294877913476463'; $VAR19 = '0.00249778551888358'; $VAR20 = '2.9062095656735e-09'; $VAR21 = '0.0406048692075456'; $VAR22 = '0.00304057178645032'; $VAR23 = '0.0399564903467594'; $VAR24 = '0.0472553357636731'; $VAR25 = '0.0468324909157914'; $VAR26 = '0.0518523495031552'; $VAR27 = '0.0039478452323898'; $VAR28 = '0.028746616957941'; $VAR29 = '0.00207705797043628'; $VAR30 = '0.00175355237215191';

testsize: 2442


Bayesian Author Test: Posterior Probabilities from Equal Priors, Z-Score-Based Method
$VAR1 = '0.984604520155947'; $VAR2 = '8.99630464342334e-181'; $VAR3 = '2.83686952343005e-07'; $VAR4 = '0.0153951961571004';

Bayesian Comparison of Best Author to Best Control: from Equal Priors, Z-Score-Based Method
$VAR1 = 1; $VAR2 = '0.418911178345924'; $VAR3 = 28; $VAR4 = '0.581088821654076';

Percentage of Samples in the Best Author Candidate that Meet the P-Value>0.0277 Test, Z-Score-Based Method
1
Percentage of Samples outside the Best Author Candidate that Meet the P-Value>0.0277 Test, Z-Score-Based Method
0.00625
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
0.993788819875776

Author Z-Score-Based P-Values
$VAR1 = '0.0277006429436506'; $VAR2 = '2.5310001898052e-182'; $VAR3 = '7.98118514973034e-09'; $VAR4 = '0.000433124998987163';
Poor compatibility. Z-Score-Based P-Value < 0.05.
Poor indicator. 21.2% of the rest have P-Value > 0.01.

Control Z-Score-Based P-Values
$VAR1 = '2.47993044566514e-05'; $VAR2 = '0.00407256615522923'; $VAR3 = '2.32985437596923e-08'; $VAR4 = '0.000285018761794428'; $VAR5 = '1.00429058974286e-08'; $VAR6 = '2.0911399158043e-06'; $VAR7 = '2.3151953211684e-05'; $VAR8 = '1.77771106592001e-05'; $VAR9 = '0.000386469634841151'; $VAR10 = '0.00266553679325011'; $VAR11 = '1.31202136974818e-10'; $VAR12 = '6.93796376241379e-06'; $VAR13 = '3.21950302063144e-10'; $VAR14 = '6.89086398429834e-13'; $VAR15 = '8.27062339073398e-07'; $VAR16 = '0.00104995901162946'; $VAR17 = '0.00306301428284113'; $VAR18 = '0.00976727200756357'; $VAR19 = '0.0016205262949613'; $VAR20 = '4.66672324333768e-09'; $VAR21 = '0.0230618887649023'; $VAR22 = '0.00347105108488047'; $VAR23 = '0.0339589357637501'; $VAR24 = '0.0225612777315286'; $VAR25 = '0.0316623384387877'; $VAR26 = '0.0382392263455067'; $VAR27 = '0.0139460770336831'; $VAR28 = '0.0384246943009342'; $VAR29 = '0.000694959302649693'; $VAR30 = '0.000874886568353141';

testsize: 2305


Bayesian Author Test: Posterior Probabilities from Equal Priors, Z-Score-Based Method
$VAR1 = '0.902225441250518'; $VAR2 = '3.30732481814126e-106'; $VAR3 = '0.00384711364524323'; $VAR4 = '0.0939274451042385';

Bayesian Comparison of Best Author to Best Control: from Equal Priors, Z-Score-Based Method
$VAR1 = 1; $VAR2 = '0.375211809038791'; $VAR3 = 26; $VAR4 = '0.624788190961209';

Percentage of Samples in the Best Author Candidate that Meet the P-Value>0.0704 Test, Z-Score-Based Method
1
Percentage of Samples outside the Best Author Candidate that Meet the P-Value>0.0704 Test, Z-Score-Based Method
0.00588235294117647
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
0.994152046783626

Author Z-Score-Based P-Values
$VAR1 = '0.0704361744362267'; $VAR2 = '2.58200774614574e-107'; $VAR3 = '0.000300341749858835'; $VAR4 = '0.00733285673982035';
Decent compatibility. Z-Score-Based P-Value > 0.05.
Decent indicator. 18.1% of the rest have P-Value > 0.05.

Control Z-Score-Based P-Values
$VAR1 = '0.000223260215326579'; $VAR2 = '0.00343853773259207'; $VAR3 = '2.8499687588806e-08'; $VAR4 = '0.0177150528480727'; $VAR5 = '4.40625143835013e-06'; $VAR6 = '0.00135647765370478'; $VAR7 = '0.000586577465937439'; $VAR8 = '0.00449893881626202'; $VAR9 = '0.00248328196473088'; $VAR10 = '0.010296150320704'; $VAR11 = '1.85834617261273e-06'; $VAR12 = '2.91777281323087e-05'; $VAR13 = '2.29862285227591e-07'; $VAR14 = '5.13982022453665e-09'; $VAR15 = '0.000287280584481268'; $VAR16 = '0.00648939121142012'; $VAR17 = '0.00363576037700491'; $VAR18 = '0.00473035079595806'; $VAR19 = '0.012709835061453'; $VAR20 = '2.49715314774512e-06'; $VAR21 = '0.0693011357459522'; $VAR22 = '0.00826705149344466'; $VAR23 = '0.0656841048582596'; $VAR24 = '0.0722572084894644'; $VAR25 = '0.0637857820523424'; $VAR26 = '0.117287593151655'; $VAR27 = '0.0292074713096256'; $VAR28 = '0.0531460866910006'; $VAR29 = '0.00478236069966389'; $VAR30 = '0.00978203023223525';

[Peter Kirby]

Lastly, we'll subtract Philemon and Philippians.

The corpus of "Paul" used for training is thus reduced to 1 Cor, 2 Cor, Gal (shorter), and 1 Thess.

In this context, even that second half of the 'shorter' letter of Romans is getting to be a very narrow match.

There might seem to be something to this theory that the later epistles of Paul have a slightly different style than the earlier ones.

testsize: 2087


Bayesian Author Test: Posterior Probabilities from Equal Priors, Z-Score-Based Method
$VAR1 = '0.949148522044989'; $VAR2 = '2.43076290474127e-114'; $VAR3 = '7.78011077239281e-09'; $VAR4 = '0.0508514701749';

Bayesian Comparison of Best Author to Best Control: from Equal Priors, Z-Score-Based Method
$VAR1 = 1; $VAR2 = '0.386686560080334'; $VAR3 = 26; $VAR4 = '0.613313439919666';

Percentage of Samples in the Best Author Candidate that Meet the P-Value>0.0267 Test, Z-Score-Based Method
1
Percentage of Samples outside the Best Author Candidate that Meet the P-Value>0.0267 Test, Z-Score-Based Method
0.0502645502645503
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
0.952141057934509

Author Z-Score-Based P-Values
$VAR1 = '0.0267368197766548'; $VAR2 = '6.8472813468454e-116'; $VAR3 = '2.19160031051513e-10'; $VAR4 = '0.00143244872837698';
Poor compatibility. Z-Score-Based P-Value < 0.05.
Decent indicator. 18.1% of the rest have P-Value > 0.01.

Control Z-Score-Based P-Values
$VAR1 = '0.000166246715689931'; $VAR2 = '0.00437918666385531'; $VAR3 = '2.03056535655346e-13'; $VAR4 = '0.000633491209481881'; $VAR5 = '9.78683356197226e-07'; $VAR6 = '2.89962557807356e-05'; $VAR7 = '8.71345337377548e-05'; $VAR8 = '0.000278064873667177'; $VAR9 = '0.000333593327946422'; $VAR10 = '0.00459256996625536'; $VAR11 = '4.34812186526793e-08'; $VAR12 = '1.45391357382145e-05'; $VAR13 = '5.67059629318253e-10'; $VAR14 = '1.26350592084816e-10'; $VAR15 = '6.90474238514994e-07'; $VAR16 = '0.000906131420187756'; $VAR17 = '0.00226027775634156'; $VAR18 = '0.00463330313902615'; $VAR19 = '0.00196703537070166'; $VAR20 = '1.32328355529849e-08'; $VAR21 = '0.0387289876606812'; $VAR22 = '0.00297040785152256'; $VAR23 = '0.0309582861645683'; $VAR24 = '0.0269849019111958'; $VAR25 = '0.0393066688775728'; $VAR26 = '0.042406570599003'; $VAR27 = '0.00577803664489483'; $VAR28 = '0.0225006118752867'; $VAR29 = '0.000965232885073504'; $VAR30 = '0.0011679912251851';

testsize: 2134


Bayesian Author Test: Posterior Probabilities from Equal Priors, Z-Score-Based Method
$VAR1 = '0.980942565546059'; $VAR2 = '1.62572573735515e-142'; $VAR3 = '2.05714742089258e-13'; $VAR4 = '0.0190574344537351';

Bayesian Comparison of Best Author to Best Control: from Equal Priors, Z-Score-Based Method
$VAR1 = 1; $VAR2 = '0.506939907230916'; $VAR3 = 26; $VAR4 = '0.493060092769084';

Percentage of Samples in the Best Author Candidate that Meet the P-Value>0.0483 Test, Z-Score-Based Method
1
Percentage of Samples outside the Best Author Candidate that Meet the P-Value>0.0483 Test, Z-Score-Based Method
0.00542005420054201
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
0.994609164420485

Author Z-Score-Based P-Values
$VAR1 = '0.0483527212744828'; $VAR2 = '8.01354393295474e-144'; $VAR3 = '1.01401121081507e-14'; $VAR4 = '0.00093938100834193';
Poor compatibility. Z-Score-Based P-Value < 0.05.
Poor indicator. 24.2% of the rest have P-Value > 0.01.

Control Z-Score-Based P-Values
$VAR1 = '2.0874045159434e-07'; $VAR2 = '0.00195143313608465'; $VAR3 = '2.21114261777439e-10'; $VAR4 = '0.000878146655219055'; $VAR5 = '1.35529388333459e-08'; $VAR6 = '1.2970581785581e-05'; $VAR7 = '0.000229787531729499'; $VAR8 = '0.000653283487689552'; $VAR9 = '0.00073582802756521'; $VAR10 = '0.007100237329612'; $VAR11 = '5.05413179156186e-09'; $VAR12 = '1.31839015683994e-05'; $VAR13 = '4.06409015381491e-07'; $VAR14 = '1.39212824732789e-08'; $VAR15 = '0.000359646905563858'; $VAR16 = '0.00253709638011355'; $VAR17 = '0.004964563763453'; $VAR18 = '0.0176710882120225'; $VAR19 = '0.00517231940106821'; $VAR20 = '4.01247062946397e-06'; $VAR21 = '0.0294539802639748'; $VAR22 = '0.00544035520118123'; $VAR23 = '0.0452650259641693'; $VAR24 = '0.0452192800761564'; $VAR25 = '0.0419005800601524'; $VAR26 = '0.0470288428612001'; $VAR27 = '0.0180258457049128'; $VAR28 = '0.0388667684995952'; $VAR29 = '0.00193599384485358'; $VAR30 = '0.00111233848976721';

testsize: 2881


Bayesian Author Test: Posterior Probabilities from Equal Priors, Z-Score-Based Method
$VAR1 = '0.655040703699367'; $VAR2 = '1.55861930776719e-129'; $VAR3 = '3.09683028139174e-65'; $VAR4 = '0.344959296300633';

Bayesian Comparison of Best Author to Best Control: from Equal Priors, Z-Score-Based Method
$VAR1 = 1; $VAR2 = '0.20016670314603'; $VAR3 = 26; $VAR4 = '0.79983329685397';

Percentage of Samples in the Best Author Candidate that Meet the P-Value>0.0221 Test, Z-Score-Based Method
1
Percentage of Samples outside the Best Author Candidate that Meet the P-Value>0.0221 Test, Z-Score-Based Method
0.00371747211895911
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
0.996296296296296

Author Z-Score-Based P-Values
$VAR1 = '0.0221576468882694'; $VAR2 = '5.27224278731148e-131'; $VAR3 = '1.04754515956723e-66'; $VAR4 = '0.011668719569774';
Poor compatibility. Z-Score-Based P-Value < 0.05.
Poor indicator. 24.2% of the rest have P-Value > 0.01.

Control Z-Score-Based P-Values
$VAR1 = '8.76914226343202e-06'; $VAR2 = '0.00208389827511333'; $VAR3 = '2.88676406110988e-12'; $VAR4 = '0.000977903147466056'; $VAR5 = '9.51068003541424e-06'; $VAR6 = '0.000511435918655553'; $VAR7 = '0.000126374669178547'; $VAR8 = '0.00212917897387773'; $VAR9 = '0.00211281664177407'; $VAR10 = '0.00510009282965351'; $VAR11 = '4.52199653742613e-08'; $VAR12 = '2.3266017071992e-05'; $VAR13 = '1.08421931161665e-11'; $VAR14 = '4.88017228442364e-12'; $VAR15 = '3.36806887319705e-06'; $VAR16 = '0.00583147791671241'; $VAR17 = '0.00045688352219959'; $VAR18 = '0.00752909135911655'; $VAR19 = '0.0070055217492714'; $VAR20 = '5.45099230530363e-10'; $VAR21 = '0.0656965032182236'; $VAR22 = '0.005855749512911'; $VAR23 = '0.0714790957590671'; $VAR24 = '0.0539657806493942'; $VAR25 = '0.0672423924711331'; $VAR26 = '0.0885383207228096'; $VAR27 = '0.017349616490731'; $VAR28 = '0.0501087011077161'; $VAR29 = '0.00357237437922244'; $VAR30 = '0.00486324488119398';

testsize: 2355


Bayesian Author Test: Posterior Probabilities from Equal Priors, Z-Score-Based Method
$VAR1 = '0.821886006903757'; $VAR2 = '1.50928530898819e-140'; $VAR3 = '3.31553990298667e-05'; $VAR4 = '0.178080837697213';

Bayesian Comparison of Best Author to Best Control: from Equal Priors, Z-Score-Based Method
$VAR1 = 1; $VAR2 = '0.321575258205437'; $VAR3 = 26; $VAR4 = '0.678424741794563';

Percentage of Samples in the Best Author Candidate that Meet the P-Value>0.0245 Test, Z-Score-Based Method
1
Percentage of Samples outside the Best Author Candidate that Meet the P-Value>0.0245 Test, Z-Score-Based Method
0.00604229607250755
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
0.993993993993994

Author Z-Score-Based P-Values
$VAR1 = '0.0245779500272137'; $VAR2 = '4.51341653094519e-142'; $VAR3 = '9.91489979928345e-07'; $VAR4 = '0.00532538806228757';
Poor compatibility. Z-Score-Based P-Value < 0.05.
Decent indicator. 18.1% of the rest have P-Value > 0.01.

Control Z-Score-Based P-Values
$VAR1 = '3.40307575179092e-06'; $VAR2 = '0.000902306785415303'; $VAR3 = '8.75502825227684e-08'; $VAR4 = '0.00195779362785885'; $VAR5 = '1.36529155819345e-05'; $VAR6 = '0.000220383329319875'; $VAR7 = '0.000348301136255064'; $VAR8 = '0.000742914139247185'; $VAR9 = '0.0004133346607769'; $VAR10 = '0.00477577178649037'; $VAR11 = '5.33168527633636e-09'; $VAR12 = '4.35847704737767e-05'; $VAR13 = '6.96807153417806e-10'; $VAR14 = '1.04124459307894e-10'; $VAR15 = '7.47831848835488e-07'; $VAR16 = '0.000749777025665676'; $VAR17 = '0.000412949259967083'; $VAR18 = '0.00294879636350676'; $VAR19 = '0.00249777795676177'; $VAR20 = '2.90621302031396e-09'; $VAR21 = '0.0406049619774091'; $VAR22 = '0.00304063613351408'; $VAR23 = '0.0399563741131749'; $VAR24 = '0.047255452688404'; $VAR25 = '0.0468324915034299'; $VAR26 = '0.0518519039496497'; $VAR27 = '0.00394786045981302'; $VAR28 = '0.028746495885275'; $VAR29 = '0.00207704545475246'; $VAR30 = '0.00175355332929954';

testsize: 2442


Bayesian Author Test: Posterior Probabilities from Equal Priors, Z-Score-Based Method
$VAR1 = '0.984470799297584'; $VAR2 = '1.94150967472097e-176'; $VAR3 = '3.63612965886731e-07'; $VAR4 = '0.0155288370894504';

Bayesian Comparison of Best Author to Best Control: from Equal Priors, Z-Score-Based Method
$VAR1 = 1; $VAR2 = '0.416815570851444'; $VAR3 = 28; $VAR4 = '0.583184429148556';

Percentage of Samples in the Best Author Candidate that Meet the P-Value>0.0274 Test, Z-Score-Based Method
1
Percentage of Samples outside the Best Author Candidate that Meet the P-Value>0.0274 Test, Z-Score-Based Method
0.00625
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
0.993788819875776

Author Z-Score-Based P-Values
$VAR1 = '0.0274630088034376'; $VAR2 = '5.41607707682796e-178'; $VAR3 = '1.01434253715969e-08'; $VAR4 = '0.000433195773809654';
Poor compatibility. Z-Score-Based P-Value < 0.05.
Poor indicator. 21.2% of the rest have P-Value > 0.01.

Control Z-Score-Based P-Values
$VAR1 = '2.47961997101556e-05'; $VAR2 = '0.0040725528286737'; $VAR3 = '2.32975812057325e-08'; $VAR4 = '0.000285013595365126'; $VAR5 = '1.00427646392864e-08'; $VAR6 = '2.09123350604134e-06'; $VAR7 = '2.31528337112309e-05'; $VAR8 = '1.7777204561901e-05'; $VAR9 = '0.000386473255669232'; $VAR10 = '0.00266559789944647'; $VAR11 = '1.31206412787209e-10'; $VAR12 = '6.93814513014839e-06'; $VAR13 = '3.21923842464961e-10'; $VAR14 = '6.88493694642216e-13'; $VAR15 = '8.27083737536963e-07'; $VAR16 = '0.00104989295931053'; $VAR17 = '0.00306322362689092'; $VAR18 = '0.0097672186284944'; $VAR19 = '0.00162052849993143'; $VAR20 = '4.66674842209323e-09'; $VAR21 = '0.0230618520779007'; $VAR22 = '0.00347108556828742'; $VAR23 = '0.0339590002119894'; $VAR24 = '0.0225613540086259'; $VAR25 = '0.0316623411777529'; $VAR26 = '0.0382393583808683'; $VAR27 = '0.0139460593058132'; $VAR28 = '0.0384246660435887'; $VAR29 = '0.000694945145209309'; $VAR30 = '0.000874893567635288';

testsize: 2305


Bayesian Author Test: Posterior Probabilities from Equal Priors, Z-Score-Based Method
$VAR1 = '0.862920425338603'; $VAR2 = '2.47760607324049e-103'; $VAR3 = '0.00545445851101437'; $VAR4 = '0.131625116150382';

Bayesian Comparison of Best Author to Best Control: from Equal Priors, Z-Score-Based Method
$VAR1 = 1; $VAR2 = '0.28907305139074'; $VAR3 = 26; $VAR4 = '0.71092694860926';

Percentage of Samples in the Best Author Candidate that Meet the P-Value>0.0476 Test, Z-Score-Based Method
1
Percentage of Samples outside the Best Author Candidate that Meet the P-Value>0.0476 Test, Z-Score-Based Method
0.00294117647058824
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
0.997067448680352

Author Z-Score-Based P-Values
$VAR1 = '0.0476907501255594'; $VAR2 = '1.36929070953577e-104'; $VAR3 = '0.000301449832777971'; $VAR4 = '0.00727448364907165';
Poor compatibility. Z-Score-Based P-Value < 0.05.
Poor indicator. 30.3% of the rest have P-Value > 0.01.

Control Z-Score-Based P-Values
$VAR1 = '0.000223268226087813'; $VAR2 = '0.00343857255984129'; $VAR3 = '2.84976026223797e-08'; $VAR4 = '0.0177150695340684'; $VAR5 = '4.40620672300269e-06'; $VAR6 = '0.00135644718031074'; $VAR7 = '0.000586574230701933'; $VAR8 = '0.00449893303441137'; $VAR9 = '0.00248332115406778'; $VAR10 = '0.0102961563605413'; $VAR11 = '1.85839909785407e-06'; $VAR12 = '2.91740953321891e-05'; $VAR13 = '2.29871420972055e-07'; $VAR14 = '5.13920347208715e-09'; $VAR15 = '0.000287281207171404'; $VAR16 = '0.00648928546863754'; $VAR17 = '0.00363574918217332'; $VAR18 = '0.00473032321978191'; $VAR19 = '0.0127098259843404'; $VAR20 = '2.49706861698e-06'; $VAR21 = '0.0693012505041972'; $VAR22 = '0.00826701636064617'; $VAR23 = '0.065684069089056'; $VAR24 = '0.0722572777228162'; $VAR25 = '0.0637857272392853'; $VAR26 = '0.117287444473064'; $VAR27 = '0.0292074713597436'; $VAR28 = '0.0531460374251962'; $VAR29 = '0.00478238899709036'; $VAR30 = '0.0097820305615645';

The next task, however, is to test a different claim/idea -- if we start with the so-called later epistles of "Paul," could they be a self-contained body of writing by a different author? Let's call that author "Deutero-Paul" and see how far we can run with the idea.

From now on, we'll let author candidate #5 represent "Paul" (1 Cor, 2 Cor, shorter Galatians, and 1 Thessalonians).

We want to know whether any of the deutero-Pauline samples match this "Paul" better or whether they all will be a closer match for the rest of "Deutero-Paul."

The 'shorter' Romans will be used as the basis of "Deutero-Paul," as the more-conservative option. But let's test the so-called 'additions' first!

[Peter Kirby]

Author Candidate #1 is what we are for now calling "Deutero-Paul" and currently consists of (somewhat-arbitrarily):

Philippians, Philemon, Colossians, Ephesians, and 2 Thessalonians

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

The test material is:

The "additions" to Romans

testsize: 2881


Bayesian Author Test: Posterior Probabilities from Equal Priors, Z-Score-Based Method
$VAR1 = '3.96351183150659e-06'; $VAR2 = '1.26009062753545e-128'; $VAR3 = '1.4002645702773e-66'; $VAR4 = '0.345392942414064'; $VAR5 = '0.654603094074104';

Bayesian Comparison of Best Author to Best Control: from Equal Priors, Z-Score-Based Method
$VAR1 = 5; $VAR2 = '0.200177937793203'; $VAR3 = 26; $VAR4 = '0.799822062206797';

Percentage of Samples in the Best Author Candidate that Meet the P-Value>0.0221 Test, Z-Score-Based Method
1
Percentage of Samples outside the Best Author Candidate that Meet the P-Value>0.0221 Test, Z-Score-Based Method
0.00738007380073801
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
0.992673992673993

Author Z-Score-Based P-Values
$VAR1 = '1.34170249285383e-07'; $VAR2 = '4.26557761918783e-130'; $VAR3 = '4.74008542036274e-68'; $VAR4 = '0.0116920193896563'; $VAR5 = '0.0221592022551175';
Poor compatibility. Z-Score-Based P-Value < 0.05.
Poor indicator. 23.5% of the rest have P-Value > 0.01.

Control Z-Score-Based P-Values
$VAR1 = '3.20237259754731e-06'; $VAR2 = '0.00175198241428289'; $VAR3 = '2.90172234761022e-12'; $VAR4 = '0.000977925810678382'; $VAR5 = '9.51074185516765e-06'; $VAR6 = '0.000511450731247394'; $VAR7 = '0.000126377484825414'; $VAR8 = '0.00212918034824098'; $VAR9 = '0.00211281350794316'; $VAR10 = '0.0051001575559904'; $VAR11 = '4.52196318897884e-08'; $VAR12 = '2.32662764678529e-05'; $VAR13 = '1.08437352338531e-11'; $VAR14 = '4.8801141570482e-12'; $VAR15 = '3.36799563507345e-06'; $VAR16 = '0.00583175923384894'; $VAR17 = '0.000456872963639088'; $VAR18 = '0.00752908133883504'; $VAR19 = '0.00700557757187242'; $VAR20 = '5.4525065010718e-10'; $VAR21 = '0.065696553354477'; $VAR22 = '0.00585575556716383'; $VAR23 = '0.0714789877334433'; $VAR24 = '0.0539657592421215'; $VAR25 = '0.0672424396065923'; $VAR26 = '0.088538322653993'; $VAR27 = '0.0173495550332673'; $VAR28 = '0.050108757487604'; $VAR29 = '0.00357237179169791'; $VAR30 = '0.00486326859226086';

Once again, it looks like the so-called "additions" to Romans are not very likely to come from either "Paul" ... or even from "deutero-Paul."

[Peter Kirby]

The 'shorter' Romans is more ambiguous: half gets a match, and the other half doesn't, to "Paul."

testsize: 2087


Bayesian Author Test: Posterior Probabilities from Equal Priors, Z-Score-Based Method
$VAR1 = '1.18245538815305e-05'; $VAR2 = '8.65271785464805e-118'; $VAR3 = '6.86373424276438e-09'; $VAR4 = '0.0446101046689166'; $VAR5 = '0.955378063913468';

Bayesian Comparison of Best Author to Best Control: from Equal Priors, Z-Score-Based Method
$VAR1 = 5; $VAR2 = '0.401128531735124'; $VAR3 = 26; $VAR4 = '0.598871468264876';

Percentage of Samples in the Best Author Candidate that Meet the P-Value>0.0284 Test, Z-Score-Based Method
1
Percentage of Samples outside the Best Author Candidate that Meet the P-Value>0.0284 Test, Z-Score-Based Method
0.0446194225721785
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
0.957286432160804

Author Z-Score-Based P-Values
$VAR1 = '3.51554672890387e-07'; $VAR2 = '2.57253121384557e-119'; $VAR3 = '2.04065021877109e-10'; $VAR4 = '0.0013262987264985'; $VAR5 = '0.028404253226869';
Poor compatibility. Z-Score-Based P-Value < 0.05.
Decent indicator. 17.6% of the rest have P-Value > 0.01.

Control Z-Score-Based P-Values
$VAR1 = '0.000166249072316491'; $VAR2 = '0.00437919890120142'; $VAR3 = '2.03076724974005e-13'; $VAR4 = '0.000633506851822505'; $VAR5 = '9.78639153443217e-07'; $VAR6 = '2.89960828782277e-05'; $VAR7 = '8.71260228448773e-05'; $VAR8 = '0.000278070661344713'; $VAR9 = '0.00033358177759962'; $VAR10 = '0.00459255014254193'; $VAR11 = '4.3484933663268e-08'; $VAR12 = '1.45400389481316e-05'; $VAR13 = '5.67224220159262e-10'; $VAR14 = '1.26374753259826e-10'; $VAR15 = '6.90378779013818e-07'; $VAR16 = '0.000906113237281334'; $VAR17 = '0.00226027225928387'; $VAR18 = '0.0046332799321267'; $VAR19 = '0.00196701277798349'; $VAR20 = '1.32328408266287e-08'; $VAR21 = '0.0387289716915664'; $VAR22 = '0.00297039653711281'; $VAR23 = '0.0309583011881753'; $VAR24 = '0.0269848424296817'; $VAR25 = '0.0393066693644923'; $VAR26 = '0.0424065991051838'; $VAR27 = '0.00577803289967633'; $VAR28 = '0.0225006264250395'; $VAR29 = '0.000965233618623708'; $VAR30 = '0.00116799625212652';

testsize: 2134


Bayesian Author Test: Posterior Probabilities from Equal Priors, Z-Score-Based Method
$VAR1 = '1.60727084822215e-06'; $VAR2 = '9.49299740268812e-146'; $VAR3 = '2.06246722173648e-13'; $VAR4 = '0.0175198433059701'; $VAR5 = '0.982478549422975';

Bayesian Comparison of Best Author to Best Control: from Equal Priors, Z-Score-Based Method
$VAR1 = 5; $VAR2 = '0.506899357948393'; $VAR3 = 26; $VAR4 = '0.493100642051607';

Percentage of Samples in the Best Author Candidate that Meet the P-Value>0.0483 Test, Z-Score-Based Method
1
Percentage of Samples outside the Best Author Candidate that Meet the P-Value>0.0483 Test, Z-Score-Based Method
0.00806451612903226
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
0.992

Author Z-Score-Based P-Values
$VAR1 = '7.90890684787039e-08'; $VAR2 = '4.67122465687617e-147'; $VAR3 = '1.01487942443197e-14'; $VAR4 = '0.000862099930758226'; $VAR5 = '0.0483448781268703';
Poor compatibility. Z-Score-Based P-Value < 0.05.
Poor indicator. 23.5% of the rest have P-Value > 0.01.

Control Z-Score-Based P-Values
$VAR1 = '2.08737062871018e-07'; $VAR2 = '0.0019514161348242'; $VAR3 = '2.21103642497885e-10'; $VAR4 = '0.000878152384625247'; $VAR5 = '1.35544040425698e-08'; $VAR6 = '1.2970984617574e-05'; $VAR7 = '0.000229786662551214'; $VAR8 = '0.000653278450415608'; $VAR9 = '0.000735827422914809'; $VAR10 = '0.00710020376791064'; $VAR11 = '5.05497288695705e-09'; $VAR12 = '1.31829989115188e-05'; $VAR13 = '4.06385601774152e-07'; $VAR14 = '1.39168867971041e-08'; $VAR15 = '0.000359637316087677'; $VAR16 = '0.00253710899276376'; $VAR17 = '0.00496459385096349'; $VAR18 = '0.0176710563827563'; $VAR19 = '0.0051723124395305'; $VAR20 = '4.01246493629408e-06'; $VAR21 = '0.0294540080646972'; $VAR22 = '0.00544033675517199'; $VAR23 = '0.0452650172356279'; $VAR24 = '0.0452192371738883'; $VAR25 = '0.0419005800236023'; $VAR26 = '0.0470288432416863'; $VAR27 = '0.0180258032549473'; $VAR28 = '0.0388667623019988'; $VAR29 = '0.00193597512984032'; $VAR30 = '0.00111234438956121';

The interesting here is that it doesn't seem to be an especially-good match to the so-called "Deutero-Paul."

Next we'll look at how closely "Deutero-Paul" matches itself.

[Peter Kirby]

"Deutero-Paul" here is defined as the text of Philippians, Philemon, Colossians, Ephesians, and 2 Thessalonians.

Philemon is too short to be left out as a test sample, while Ephesians is too large relative to the rest of the text.

Leaving one out (Philippians), we find that Philippians matches "Paul" much better than the rest of "Deutero-Paul."

testsize: 1627


Bayesian Author Test: Posterior Probabilities from Equal Priors, Z-Score-Based Method
$VAR1 = '0.0892011858526865'; $VAR2 = '0.00498287972841087'; $VAR3 = '0.0526689006982505'; $VAR4 = '0.19107016609468'; $VAR5 = '0.662076867625972';

Bayesian Comparison of Best Author to Best Control: from Equal Priors, Z-Score-Based Method
$VAR1 = 5; $VAR2 = '0.565883369224097'; $VAR3 = 25; $VAR4 = '0.434116630775903';

Percentage of Samples in the Best Author Candidate that Meet the P-Value>0.15 Test, Z-Score-Based Method
0.888888888888889
Percentage of Samples outside the Best Author Candidate that Meet the P-Value>0.15 Test, Z-Score-Based Method
0.00203252032520325
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
0.997718631178707

Author Z-Score-Based P-Values
$VAR1 = '0.0209885247976527'; $VAR2 = '0.00117244287442758'; $VAR3 = '0.0123926887047886'; $VAR4 = '0.0449577085868868'; $VAR5 = '0.155782870163507';
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 = '0.0105693511358958'; $VAR2 = '0.023673906684863'; $VAR3 = '0.000633069096713582'; $VAR4 = '0.0120394025162931'; $VAR5 = '0.0010732464228018'; $VAR6 = '0.00873360652811379'; $VAR7 = '0.00088273849709854'; $VAR8 = '0.00422170608881027'; $VAR9 = '0.0104961846402595'; $VAR10 = '0.0110784903157345'; $VAR11 = '6.85254381142563e-05'; $VAR12 = '0.00204803318689515'; $VAR13 = '1.81481833371401e-05'; $VAR14 = '6.10905266530226e-06'; $VAR15 = '0.000788861909676932'; $VAR16 = '0.0142172158896558'; $VAR17 = '0.012500067142404'; $VAR18 = '0.012700916489731'; $VAR19 = '0.0200405288714838'; $VAR20 = '2.40967549116655e-05'; $VAR21 = '0.0935765210025299'; $VAR22 = '0.0237986391968933'; $VAR23 = '0.0877209130847959'; $VAR24 = '0.066779714836068'; $VAR25 = '0.119508609734738'; $VAR26 = '0.118165427032857'; $VAR27 = '0.04177680890205'; $VAR28 = '0.0703029854958946'; $VAR29 = '0.0095101765560775'; $VAR30 = '0.00959766463027938';

Leaving one out (Colossians), we find that it matches "Paul" slightly better than "Deutero-Paul" but not enough for a positive result.

testsize: 1581


Bayesian Author Test: Posterior Probabilities from Equal Priors, Z-Score-Based Method
$VAR1 = '0.373673005466334'; $VAR2 = '1.77738327886745e-09'; $VAR3 = '0.0263967893066493'; $VAR4 = '0.180641753485'; $VAR5 = '0.419288449964634';

Bayesian Comparison of Best Author to Best Control: from Equal Priors, Z-Score-Based Method
$VAR1 = 5; $VAR2 = '0.471617597201695'; $VAR3 = 25; $VAR4 = '0.528382402798305';

Percentage of Samples in the Best Author Candidate that Meet the P-Value>0.0735 Test, Z-Score-Based Method
1
Percentage of Samples outside the Best Author Candidate that Meet the P-Value>0.0735 Test, Z-Score-Based Method
0.0197628458498024
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
0.98062015503876

Author Z-Score-Based P-Values
$VAR1 = '0.0655569776593936'; $VAR2 = '3.11823102553206e-10'; $VAR3 = '0.00463103756905351'; $VAR4 = '0.0316916855762458'; $VAR5 = '0.0735597250672948';
Decent compatibility. Z-Score-Based P-Value > 0.05.
Decent indicator. 17.6% of the rest have P-Value > 0.05.

Control Z-Score-Based P-Values
$VAR1 = '0.00893186545232079'; $VAR2 = '0.012669123378462'; $VAR3 = '0.00663816392804151'; $VAR4 = '0.00271175040954301'; $VAR5 = '0.0040390610041461'; $VAR6 = '0.00653628704968908'; $VAR7 = '0.000910586910468114'; $VAR8 = '0.00925412638802891'; $VAR9 = '0.0050188228953195'; $VAR10 = '0.00790091113912834'; $VAR11 = '6.21622936909499e-06'; $VAR12 = '0.00230951706070595'; $VAR13 = '2.37104471441032e-05'; $VAR14 = '3.96140066510835e-05'; $VAR15 = '0.000253466200171512'; $VAR16 = '0.00544701839006307'; $VAR17 = '0.00046393840313928'; $VAR18 = '0.00368466979167238'; $VAR19 = '0.00779701486044745'; $VAR20 = '1.36946118993814e-05'; $VAR21 = '0.0584395414582921'; $VAR22 = '0.00722081944894727'; $VAR23 = '0.0530913717818954'; $VAR24 = '0.05583482171975'; $VAR25 = '0.0824135157611974'; $VAR26 = '0.0741485126786656'; $VAR27 = '0.0148588182512339'; $VAR28 = '0.0454386444047562'; $VAR29 = '0.00580428486568474'; $VAR30 = '0.00679949575420408';

Leaving one out (2 Thessalonians), it doesn't even come closer to "Paul." It is closer to "Deutero-Paul," and yet still not a match to that.

testsize: 820


Bayesian Author Test: Posterior Probabilities from Equal Priors, Z-Score-Based Method
$VAR1 = '0.286515700590479'; $VAR2 = '0.142140087629156'; $VAR3 = '0.166122677366155'; $VAR4 = '0.127200179239546'; $VAR5 = '0.278021355174665';

Bayesian Comparison of Best Author to Best Control: from Equal Priors, Z-Score-Based Method
$VAR1 = 1; $VAR2 = '0.494627379956467'; $VAR3 = 25; $VAR4 = '0.505372620043533';

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
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 = '0.147632665747328'; $VAR2 = '0.0732403843943077'; $VAR3 = '0.0855978700298277'; $VAR4 = '0.0655423123618383'; $VAR5 = '0.143255792665222';

Control Z-Score-Based P-Values
$VAR1 = '0.0687589451798484'; $VAR2 = '0.0620618509443492'; $VAR3 = '0.00780222112666957'; $VAR4 = '0.021837353498468'; $VAR5 = '0.0246657617847624'; $VAR6 = '0.0280833677839434'; $VAR7 = '0.00579117101370208'; $VAR8 = '0.0139502664011113'; $VAR9 = '0.0236180215092794'; $VAR10 = '0.0269079869663319'; $VAR11 = '0.00315344585835241'; $VAR12 = '0.0112564765200636'; $VAR13 = '0.000383483606053092'; $VAR14 = '0.000574621172191821'; $VAR15 = '0.0017849305327949'; $VAR16 = '0.0251152637795993'; $VAR17 = '0.0335347898442551'; $VAR18 = '0.0242636853602586'; $VAR19 = '0.027055297047465'; $VAR20 = '0.000594018667213684'; $VAR21 = '0.112735199139375'; $VAR22 = '0.0486158647751834'; $VAR23 = '0.0946150524417857'; $VAR24 = '0.064479915310459'; $VAR25 = '0.150839824312404'; $VAR26 = '0.121923503134581'; $VAR27 = '0.0979587984539918'; $VAR28 = '0.073851442173496'; $VAR29 = '0.0178398338350161'; $VAR30 = '0.0169580154847809';

There appears to be no good reason for believing in a single "Deutero-Paul" author. We will discard the concept, then.

[Peter Kirby]

One of the issues still outstanding regards the relationship of the author of Colossians to the author of 1 Corinthians (i.e., "Paul").

The most-common approach to pseudonymity for Colossians is to posit that the author of Colossians reworked bits of Philemon and Philippians.

What better way, then, to be able to confirm (potentially) or fail to confirm authenticity, than by leaving out all but those two, which are said to have been used by the author of Colossians? Any stylistic similarity that remains, if it existed, would be more difficult to explain as a result of copying.

We will then treat as the training set for "Paul" the following:

1 Corinthians, 2 Corinthians, 'shorter' Romans, 'shorter' Galatians, 1 Thessalonians

And here is the result for Colossians:

testsize: 1581


Bayesian Author Test: Posterior Probabilities from Equal Priors, Z-Score-Based Method
$VAR1 = '0.703278256046037'; $VAR2 = '3.8579748011221e-09'; $VAR3 = '0.0374164472167192'; $VAR4 = '0.259305292879269';

Bayesian Comparison of Best Author to Best Control: from Equal Priors, Z-Score-Based Method
$VAR1 = 1; $VAR2 = '0.511686671513998'; $VAR3 = 25; $VAR4 = '0.488313328486002';

Percentage of Samples in the Best Author Candidate that Meet the P-Value>0.0863 Test, Z-Score-Based Method
1
Percentage of Samples outside the Best Author Candidate that Meet the P-Value>0.0863 Test, Z-Score-Based Method
0.0238568588469185
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
0.976699029126214

Author Z-Score-Based P-Values
$VAR1 = '0.0863583100153252'; $VAR2 = '4.73735937436413e-10'; $VAR3 = '0.00459451308302922'; $VAR4 = '0.031841119327336';
Decent compatibility. Z-Score-Based P-Value > 0.05.
Decent indicator. 15.1% of the rest have P-Value > 0.05.

Control Z-Score-Based P-Values
$VAR1 = '0.00893186325227254'; $VAR2 = '0.0126691502243515'; $VAR3 = '0.00663817942229942'; $VAR4 = '0.00271168715217845'; $VAR5 = '0.00403889250214233'; $VAR6 = '0.0065362600436967'; $VAR7 = '0.00091056642758233'; $VAR8 = '0.00925426599245974'; $VAR9 = '0.00501868961626175'; $VAR10 = '0.00790086855948678'; $VAR11 = '6.21647779607875e-06'; $VAR12 = '0.00230947423135397'; $VAR13 = '2.37112799016556e-05'; $VAR14 = '3.96128767099528e-05'; $VAR15 = '0.000253474213623057'; $VAR16 = '0.00544704454536568'; $VAR17 = '0.000463941687760249'; $VAR18 = '0.00368463821361355'; $VAR19 = '0.00779705841095192'; $VAR20 = '1.36943370412167e-05'; $VAR21 = '0.0584394160199737'; $VAR22 = '0.00722085200784237'; $VAR23 = '0.053091369472589'; $VAR24 = '0.0558348970160497'; $VAR25 = '0.0824135474962353'; $VAR26 = '0.0741485449087943'; $VAR27 = '0.0148587571008382'; $VAR28 = '0.045438859405049'; $VAR29 = '0.0058042758685333'; $VAR30 = '0.00679950810442295';

Even after Philippians and Philemon are removed from the training set, Colossians appears to be a good match for "Paul."

Once again stylometry can be said to speak in favor of the hypothesis that the author of 1 Corinthians and of Colossians are the same author ("Paul").

[Peter Kirby]

Another one of the issues still outstanding regards the relationship of the author of Ephesians to the author of 1 Corinthians (i.e., "Paul").

The most-common approach to pseudonymity for Ephesians is to posit that the author of Ephesians reworked Colossians. Likewise, it is frequently stated that Colossians itself is pseudepigraphic and has been constructed using bits of Philemon and Philippians.

What better way, then, to be able to confirm (potentially) or fail to confirm authenticity, than by leaving out all but those three (Colossians, Philemon, and Philippians), which are said to have been used by the author of Colossians? Any stylistic similarity that remains, if it existed, would be more difficult to explain as a result of copying.

We will then treat as the training set for "Paul" the following:

1 Corinthians, 2 Corinthians, 'shorter' Romans, 'shorter' Galatians, 1 Thessalonians

And here is the result for Ephesians (aka the Apostolikon's Laodiceans):

testsize: 2421


Bayesian Author Test: Posterior Probabilities from Equal Priors, Z-Score-Based Method
$VAR1 = '0.773458451655571'; $VAR2 = '3.83692888820772e-157'; $VAR3 = '1.63252410442008e-10'; $VAR4 = '0.226541548181176';

Bayesian Comparison of Best Author to Best Control: from Equal Priors, Z-Score-Based Method
$VAR1 = 1; $VAR2 = '0.525136846147602'; $VAR3 = 25; $VAR4 = '0.474863153852398';

Percentage of Samples in the Best Author Candidate that Meet the P-Value>0.043 Test, Z-Score-Based Method
1
Percentage of Samples outside the Best Author Candidate that Meet the P-Value>0.043 Test, Z-Score-Based Method
0.0279503105590062
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
0.972809667673716

Author Z-Score-Based P-Values
$VAR1 = '0.0430523489939931'; $VAR2 = '2.13571654956603e-158'; $VAR3 = '9.08697775997638e-12'; $VAR4 = '0.0126097863085717';
Poor compatibility. Z-Score-Based P-Value < 0.05.
Poor indicator. 21.2% of the rest have P-Value > 0.01.

Control Z-Score-Based P-Values
$VAR1 = '0.00106043947223793'; $VAR2 = '0.00266538892050876'; $VAR3 = '0.000211823977658538'; $VAR4 = '4.31124667247622e-05'; $VAR5 = '0.00104128655529343'; $VAR6 = '0.00220153813825086'; $VAR7 = '0.000118793985074662'; $VAR8 = '0.00101103096421342'; $VAR9 = '0.00107069810908773'; $VAR10 = '0.000585655320908642'; $VAR11 = '1.2810418826443e-08'; $VAR12 = '0.000391118127865787'; $VAR13 = '4.82938947185816e-08'; $VAR14 = '9.88852677978061e-10'; $VAR15 = '3.04215251978726e-07'; $VAR16 = '0.00037654731372621'; $VAR17 = '2.99697378758136e-06'; $VAR18 = '0.000480492188355303'; $VAR19 = '0.00144544735466695'; $VAR20 = '1.26560093207273e-09'; $VAR21 = '0.0372443037433892'; $VAR22 = '0.00139765911707033'; $VAR23 = '0.0329575252092404'; $VAR24 = '0.028923993319096'; $VAR25 = '0.0389307556192608'; $VAR26 = '0.0187829512069839'; $VAR27 = '0.00559124007502281'; $VAR28 = '0.0189627344457085'; $VAR29 = '0.000859376229641134'; $VAR30 = '0.00127576356162657';

Even without Philippians and without Philemon and without Colossians, Ephesians appears to be a good match for "Paul." (!)

This actually removes most of the ambiguity that we were talking about earlier: Colossians and Laodiceans (aka Ephesians) are probably "Paul." At least, that is the most likely stylometric conclusion.

So what changed?

Simple: the addition of 'shorter' Romans to the training material. When this material was added to the rest of "Paul," then (I am assuming) there was adequate information there about the stylistic habits about Paul in his later life to be able for the computer to conclude that "Paul" was the closest match for Ephesians.

Not only does this tend to provide support for Ephesians/Laodiceans and Colossians as part of the works created by the author "Paul," but it also provides some surprising incidental support for the hypothesis of this author's growth and maturation as a writer over a longer period of time, given the way that the letters tend to (often) require samples of the later work in authenticate the later work of "Paul." (Maybe it's time to remove the scare quotes?)

It looks like we can regard these as the stylometrically-probable works of "Paul" (with speculative assignments to 'earlier' or 'later'):

Galatians ('shorter' or 'longer') - earlier
1 Corinthians - earlier
2 Corinthians - earlier
1 Thessalonians - earlier
Romans ('shorter') - later
Philippians - later(?)
Ephesians (Laodiceans) - later
Colossians - later

And, since they are so short, simply with a question mark (no stylometric decision):

Philemon (?) - only about 350 words
2 Thessalonians (?) - only 820 words

There are still some questions outstanding, however.

[perseusomega9]

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

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