Paul -- A Basic Stylometric Study

[Peter Kirby]

For slogging through that Origen thread, I believe that we all deserve an interesting trip through the letters attributed to Paul.

A few questions (at least) hold our interest here:

(1) Are there any subgroups of letters that were likely written by the same author?
(2) Do any of the long letters (1 Corinthians, Romans) seem likely or unlikely to have composite authorship?
(3) If so, does a shorter version of them (such as a shorter Romans) have a better claim to be written by the same author as other epistles?

Some of this work is based on my post identifying "shorter readings" of Paul in the text preserved by Marcion, discerned primarily through references:
http://peterkirby.com/marcions-shorter- ... -paul.html

Based on current stylometric techniques surveyed so far, most of the letters cannot be subdivided, but three of them are long enough that they can: 1 Corinthians (3 subdivisions), Romans (3 subdivisions), and 2 Corinthians (2 subdivisions). We will look at the longer letters first, in order to see whether they are likely to be of singular authorship or composite and to see whether they are likely to have a common author. Then we'll look at the other texts attributed to Paul in the New Testament.

The "author candidates" generally speaking are:

#1 an appropriately-changing subset of the text of the 10 non-pastoral letters attributed to Paul, not including the sample

#2 The Pastoral Epistles

#3 Hebrews

#4 Acts

The use of #2 to #4 is to determine whether any samples from the 10 non-pastoral letters attributed to Paul match with the Pastorals, with Hebrews, or with Acts. This is an ongoing test of the claims that "Paul" may have authored the pastorals, that "Paul" may have written Hebrews, or that the author of Acts may have had some hand in the non-pastoral letters of "Paul."

The "controls" are:

#1 Mark
#2 John
#3 Revelation
#4 Aristeas
#5 1 Macc
#6 2 Macc
#7 Polybius
#8 Diodorus Siculus
#9 Dionysius Halicarnassus
#10 Strabo
#11 Plutarch
#12 Arrian
#13 Herodian
#14 Herodotus
#15 Thucydides
#16 Xenophon
#17 Epictetus
#18 Galen
#19 Lucian
#20 Philostratus
#21 Athanasius
#22 John Chrysostom
#23 Basil of Caesarea
#24 Gregory Nyssenus
#25 Justin Martyr
#26 Theophilus of Antioch
#27 Origen
#28 Eusebius
#29 Cyril
#30 Clement of Alexandria

For the purposes of this study, "Paul" is defined as "the author of 1 Corinthians," if it is (mostly) not a composite text (the first thing tested), without prejudice for when or why this "Paul" may have written the text of (most of) 1 Corinthians. Stylometry has no need for assumptions or analysis of when or why; it operates purely on the level of an analysis of the style of text as observed by the frequency/co-incidence of certain features of that text (here, the frequency of some common words).

To avoid any accusations of 'cooking' the results, a full list of 40 common 'words' (features defined by one or several word tokens) is used throughout:

o oi h ai to ta
tou twn ths
tou twn ths
ton tous thn tas to ta
autos [etc.]
outos [etc.]
ode [etc.]
ekeinos [etc.]
tis [etc.]
ekeinos [etc.]
ekeinos [etc.]
gignomai [etc.]
kai ka
te t
oute out' ouq' eite eit' eiq' mhte mht' mhq'
de d
mh
oude oud' mhde mhd'
men
alla all
gar
eis
en
dia di
ek ec
kata kat' kaq'
pros
oun
ina in'
oti ot oq
apo ap
peri
polus [etc.]
pas [etc.]
an ean
meta met meq me m
oun
ou ouk oux
epi ep
dh

Let's begin!

[Tenorikuma]

Can't wait.

[Peter Kirby]

The first question that concerns us, then, is whether 1 Corinthians is more likely to be (mostly) singular or is discernibly a composite text.

The text of 1 Corinthians all on its own isn't necessarily enough to provide enough material both for a sample and for a training set (which should be a minimum of approximately 4-5 times the size of the sample). At a minimum we will need to throw one other letter into the mix, in order to establish a baseline for training the computer to calculate the tendencies of 'Pauline' style.

Because it is the longest, Romans is chosen. Because there is controversy over the extent of Romans, the test is repeated with a pared-down version of Romans, after first performing the test with the full version of Romans. (The sample from 1 Corinthians is left out of the training set for 1 Corinthians.)

The results actually make my jaw drop. Based on my experience so far, this is a very strong confirmation of the hypothesis that each sample taken from 1 Corinthians was written by the author of the rest of 1 Corinthians. This can be taken as established, and the text of 1 Corinthians can be treated as a good basis on which to discover whether any other text probably belongs to "Paul," defined as the author of 1 Corinthians.

Naturally this doesn't prove that there aren't any short interpolations into 1 Corinthians (comprising only a couple verses), or that letter fragments from a single author couldn't have been pasted together to make 1 Corinthians, but it does make it much less likely that it isn't substantially the work of one author. The author of the substance of 1 Corinthians will be called "Paul" for the purposes of this stylometric study.

testsize: 2328


Bayesian Author Test: Posterior Probabilities from Equal Priors, Z-Score-Based Method
$VAR1 = '0.992442550113856'; $VAR2 = '6.13024475229415e-83'; $VAR3 = '2.61256036580405e-13'; $VAR4 = '0.00755744988588292';

Bayesian Comparison of Best Author to Best Control: from Equal Priors, Z-Score-Based Method
$VAR1 = 1; $VAR2 = '0.721199494527033'; $VAR3 = 24; $VAR4 = '0.278800505472967';

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 = '0.157073376776262'; $VAR2 = '9.70230713704625e-84'; $VAR3 = '4.13488598046901e-14'; $VAR4 = '0.00119611374306435';
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 = '1.97696058251512e-06'; $VAR2 = '0.00379750270375588'; $VAR3 = '1.5204008956441e-08'; $VAR4 = '0.00279002935967186'; $VAR5 = '3.60150004243592e-10'; $VAR6 = '4.01485306384629e-06'; $VAR7 = '1.67631289694981e-05'; $VAR8 = '0.00112289743041003'; $VAR9 = '0.0010923967231662'; $VAR10 = '0.00295359746717212'; $VAR11 = '3.20346993603285e-10'; $VAR12 = '3.44633930245054e-05'; $VAR13 = '1.00292821621375e-05'; $VAR14 = '1.59513065652164e-05'; $VAR15 = '0.00389528936518744'; $VAR16 = '0.000970661449778316'; $VAR17 = '0.00649401714008736'; $VAR18 = '0.00325431189240362'; $VAR19 = '0.0100848641146296'; $VAR20 = '0.00011794261985524'; $VAR21 = '0.042137874638314'; $VAR22 = '0.0146528542908138'; $VAR23 = '0.0271622789174538'; $VAR24 = '0.0607212528210199'; $VAR25 = '0.0399873629626321'; $VAR26 = '0.0385987035361995'; $VAR27 = '0.0236766370627787'; $VAR28 = '0.0317817869427112'; $VAR29 = '0.0013860563088484'; $VAR30 = '0.00552957488705145';


40 Words
$VAR1 = [ 'O', 'OI', 'H', 'AI', 'TO', 'TA' ]; $VAR2 = [ 'TOU', 'TWN', 'THS' ]; $VAR3 = [ 'TWi', 'TOIS', 'THi', 'TAIS' ]; $VAR4 = [ 'TON', 'TOUS', 'THN', 'TAS', 'TO', 'TA' ]; $VAR5 = [ 'AUTOS', 'AUTOU', 'AUTWi', 'AUTON', 'AUTOI', 'AUTWN', 'AUTOIS', 'AUTOUS', 'AUTH', 'AUTHS', 'AUTHi', 'AUTHN', 'AUTAI', 'AUTWN', 'AUTAIS', 'AUTAS', 'AUTO', 'AUTA' ]; $VAR6 = [ 'OUTOS', 'TOUTOU', 'TOUTWi', 'TOUTON', 'AUTOI', 'TOUTWN', 'TOUTOIS', 'TOUTOUS', 'AUTH', 'TAUTHS', 'TAUTHi', 'TAUTHN', 'AUTAI', 'TAUTAIS', 'TAUTAS', 'TOUTO', 'TOUTO', 'TAUTA' ]; $VAR7 = [ 'ODE', 'TOUDE', 'TWiDE', 'TONDE', 'OIDE', 'TWNDE', 'TOISDE', 'TOUSDE', 'HDE', 'THSDE', 'THiDE', 'THNDE', 'AIDE', 'TWNDE', 'TAISDE', 'TASDE', 'TODE', 'TOUDE', 'TODE', 'TADE' ]; $VAR8 = [ 'EKEINOS', 'EKEINOU', 'EKEINWi', 'EKEINON', 'EKEINOI', 'EKEINWN', 'EKEINOIS', 'EKEINOUS', 'EKEINH', 'EKEINHS', 'EKEINHi', 'EKEINHN', 'EKEINAI', 'EKEINAIS', 'EKEINAS', 'EKEINO', 'EKEINOU', 'EKEINWi', 'EKEINO', 'EKEINA', 'EKEINWN', 'EKEINOIS', 'EKEINA' ]; $VAR9 = [ 'TIS', 'TINOS', 'TINI', 'TINA', 'TINES', 'TINWN', 'TISI', 'TISIN', 'TINAS', 'TI', 'TINA' ]; $VAR10 = [ 'EIMI', 'EI', 'ESTI', 'ESTIN', 'ESMEN', 'ESTE', 'EISI', 'EISIN', 'HN', 'HSQA', 'HN', 'HMEN', 'HTE', 'HSAN', 'ESOMAI', 'ESHi', 'ESEI', 'ESTAI', 'ESOMEQA', 'ESESQE', 'ESONTAI', 'W', 'HiS', 'Hi', 'WMEN', 'HTE', 'WSI', 'EIHN', 'EIHS', 'EIH', 'EIHMEN', 'EIMEN', 'EIHTE', 'EITE', 'EIHSAN', 'EIEN', 'ESOIMHN', 'ESOIO', 'ESOITO', 'ESOIMEQA', 'ESOISQE', 'ESOINTO', 'ISQI', 'ESTW', 'ESTE', 'ESTWN', 'ONTWN', 'ESTWSAN', 'EINAI', 'ESESQAI', 'WN', 'OUSA', 'ON', 'ESOMENOS', 'ESOMENH', 'ESOMENON' ]; $VAR11 = [ 'EXW', 'EXEIS', 'EXEI', 'EXOMEN', 'EXETE', 'EXOUSIN', 'EXEIN', 'EIXON', 'EIXES', 'EIXE', 'EIXOMEN', 'EIXETE', 'EIXON', 'ECW', 'ECEIS', 'ECEI', 'ECOMEN', 'ECETE', 'ECOUSI', 'ECOUSIN', 'ECEIN', 'ESXON', 'ESXES', 'ESXE', 'ESXEN', 'ESXOMEN', 'ESXETE', 'ESXON', 'SXESEIN', 'ESXHKA', 'ESXHKAS', 'ESXHKE', 'ESXHKEN', 'ESXHKAMEN', 'ESXHKATE', 'ESXHKASI', 'ESXHKASIN', 'ESXHKENAI', 'ESXHKEIN', 'ESXHKEIS', 'ESXHKEI', 'ESXHKEIMEN', 'ESXHKEITE', 'ESXHKEISAN', 'ECOMAI', 'ECEI', 'ECETAI', 'ECOMEQA', 'ECESQE', 'ECONTAI', 'ECESQAI', 'ESXON', 'ESXOU', 'ESXOMEQA', 'ESXESQE', 'ESXONTO', 'ESXHMAI', 'ESXHSAI', 'ESXHTAI', 'ESXHMEQA', 'ESXHSQE', 'ESXHNTAI', 'ESXHSQAI', 'HSXHMHN', 'HSXHSO', 'HSXHTO', 'HSXHMEQA', 'HSXHSQE', 'HSXHNTO', 'SXEQHSOMAI', 'SXEQHSH', 'SXEQHSETAI', 'SXEQHSOMEQA', 'SXEQHSESQE', 'SXEQHSONTAI', 'SXEQHSESQAI', 'ESXEQHN', 'ESXEQHS', 'ESXEQH', 'ESXEQHMEN', 'ESXEQHTE', 'ESXEQHSAN', 'SXEQHNAI', 'ESXHSO', 'ESXHSQW', 'ESXHSQE', 'ESXHSQWN', 'ESXHSQAI', 'HSXHMHN', 'HSXHSO', 'HSXHTO', 'HSXHMEQA', 'HSXHSQE', 'HSXHNTO', 'EXW', 'EXHS', 'EXH', 'EXWMEN', 'EXHTE', 'EXWSI', 'EXWSIN', 'SXESQ', 'SXESHS', 'SXESH', 'SXESWM' ]; $VAR12 = [ 'GIGNOMAI', 'GIGNWMAI', 'GIGNOIMHN', 'GIGESQAI', 'EGIGNOMHN', 'GENHSOMAI', 'GENHSOIMEHN', 'GENHQHSOMAI', 'GENHQHSOIMHN', 'GENHSESQAI', 'GENHSOMENOS', 'GENHSOMENH', 'GENHSOMENON', 'GEGONA', 'GEGONWS', 'GEGONW', 'GEGONWS', 'GEGONW', 'GEGONWS', 'GEGONOIMI', 'GEGONOIHN', 'GEGENHMAI', 'GEGENHMAI', 'GEGENHMENOS', 'GEGONENAI', 'GEGONWS', 'GEGONUIA', 'GEGONOS', 'EGEGONEIN', 'EGEGONH', 'EGEGENHMHN', 'GIGNEI', 'GIGNHi', 'GIGNOIO', 'GIGNOU', 'EGIGNOU', 'GENHSEI', 'GENHSHi', 'GENHSOIO', 'GENHQHSEI', 'GENHQHSHi', 'GENHQHSOIO', 'EGENOU', 'GENHi', 'GENOIO', 'GENOU', 'EGENHQHS', 'GENHQHiS', 'GENHQEIHS', 'GENHQHTI', 'GEGONAS', 'GEGONWS', 'GEGONHS', 'GEGONWS', 'GEGONOIS', 'GEGONOIHS', 'GEGONWS', 'GEGENHSAI', 'GEGENHMENOS', 'GEGENHSO', 'EGEGONEIS', 'EGEGONHS', 'EGEGENHSO', 'GIGNETAI', 'GIGNHTAI', 'GIGNOITO', 'GIGNESQW', 'EGIGNETO', 'GENHSETAI', 'GENHSOITO', 'GENHQHSETAI', 'GENHQHSOITO', 'EGENETO', 'GENHTAI', 'GENOITO', 'GENESQW', 'EGENHQH', 'GENHQHi', 'GENHQEIN', 'GENHQHTW', 'GEGONE', 'GEGONWS', 'GEGONHi', 'GEGONWS', 'GEGONOI', 'GEGONOIN', 'GEGONWS', 'GEGENHTAI', 'GE' ]; $VAR13 = [ 'KAI', 'KA' ]; $VAR14 = [ 'TE', 'T' ]; $VAR15 = [ 'OUTE', 'OUT', 'OUQ', 'EITE', 'EIT', 'EIQ', 'MHTE', 'MHT', 'MHQ' ]; $VAR16 = [ 'DE', 'D' ]; $VAR17 = [ 'MH' ]; $VAR18 = [ 'OUDE', 'OUD', 'MHDE', 'MHD' ]; $VAR19 = [ 'MEN' ]; $VAR20 = [ 'ALLA', 'ALL' ]; $VAR21 = [ 'GAR' ]; $VAR22 = [ 'EIS' ]; $VAR23 = [ 'EN' ]; $VAR24 = [ 'DIA', 'DI' ]; $VAR25 = [ 'EK', 'EC' ]; $VAR26 = [ 'KATA', 'KAT', 'KAQ' ]; $VAR27 = [ 'PROS' ]; $VAR28 = [ 'OUN' ]; $VAR29 = [ 'INA', 'IN' ]; $VAR30 = [ 'OTI', 'OT', 'OQ' ]; $VAR31 = [ 'APO', 'AP' ]; $VAR32 = [ 'PERI' ]; $VAR33 = [ 'POLUS', 'POLLOU', 'POLLWi', 'POLUN', 'POLLH', 'POLLHS', 'POLLHi', 'POLLHN', 'POLU', 'POLLOU', 'POLLWi', 'POLU', 'POLLOI', 'POLLWN', 'POLLOIS', 'POLLOUS', 'POLLAI', 'POLLWN', 'POLLAIS', 'POLLAS', 'POLLA', 'POLLWN', 'POLLOIS', 'POLLA' ]; $VAR34 = [ 'PAS', 'PANTOS', 'PANTI', 'PANTA', 'PAS', 'PASA', 'PASHS', 'PASHi', 'PASAN', 'PASA', 'PAN', 'PANTOS', 'PANTI', 'PAN', 'PANTES', 'PANTWN', 'PASI', 'PASIN', 'PANTAS', 'PANTES', 'PASAI', 'PASWN', 'PASAIS', 'PASAS', 'PASAI', 'PANTA', 'PANTWN' ]; $VAR35 = [ 'AN', 'EAN' ]; $VAR36 = [ 'META', 'MET', 'MEQ', 'ME', 'M' ]; $VAR37 = [ 'OUN' ]; $VAR38 = [ 'OU', 'OUK', 'OUX' ]; $VAR39 = [ 'EPI', 'EP' ]; $VAR40 = [ 'DH' ];

$VAR1 = 142; $VAR2 = 84; $VAR3 = 55; $VAR4 = 97; $VAR5 = 25; $VAR6 = 25; $VAR7 = 0; $VAR8 = 0; $VAR9 = 33; $VAR10 = 85; $VAR11 = 12; $VAR12 = 7; $VAR13 = 93; $VAR14 = 3; $VAR15 = 17; $VAR16 = 64; $VAR17 = 30; $VAR18 = 6; $VAR19 = 8; $VAR20 = 31; $VAR21 = 37; $VAR22 = 10; $VAR23 = 75; $VAR24 = 17; $VAR25 = 7; $VAR26 = 8; $VAR27 = 8; $VAR28 = 5; $VAR29 = 20; $VAR30 = 20; $VAR31 = 5; $VAR32 = 3; $VAR33 = 5; $VAR34 = 19; $VAR35 = 10; $VAR36 = 6; $VAR37 = 5; $VAR38 = 56; $VAR39 = 7; $VAR40 = 1;

testsize: 2265


Bayesian Author Test: Posterior Probabilities from Equal Priors, Z-Score-Based Method
$VAR1 = '0.996255294610424'; $VAR2 = '1.67263109198622e-116'; $VAR3 = '6.34804973451174e-10'; $VAR4 = '0.00374470475477142';

Bayesian Comparison of Best Author to Best Control: from Equal Priors, Z-Score-Based Method
$VAR1 = 1; $VAR2 = '0.706527970473288'; $VAR3 = 21; $VAR4 = '0.293472029526713';

Percentage of Samples in the Best Author Candidate that Meet the P-Value>0.13 Test, Z-Score-Based Method
1
Percentage of Samples outside the Best Author Candidate that Meet the P-Value>0.13 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 = '0.139207659660239'; $VAR2 = '2.33718265840084e-117'; $VAR3 = '8.87018770920298e-11'; $VAR4 = '0.000523251005892162';
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 = '2.64325688938784e-05'; $VAR2 = '0.00992046238110366'; $VAR3 = '4.98594446717481e-09'; $VAR4 = '0.00454100644732211'; $VAR5 = '5.03695591824844e-09'; $VAR6 = '6.32319359939892e-06'; $VAR7 = '4.81035522296213e-06'; $VAR8 = '0.000241952255740368'; $VAR9 = '0.000395677752162933'; $VAR10 = '0.0025406681207344'; $VAR11 = '4.85858994363731e-10'; $VAR12 = '3.13215188435879e-06'; $VAR13 = '4.53944040425992e-07'; $VAR14 = '4.17609835836359e-07'; $VAR15 = '0.000174018577047181'; $VAR16 = '0.000911813232359711'; $VAR17 = '0.00514221869033238'; $VAR18 = '0.00283947625734649'; $VAR19 = '0.00519256984500339'; $VAR20 = '2.80541378303437e-05'; $VAR21 = '0.0578229824061844'; $VAR22 = '0.0080877370881594'; $VAR23 = '0.0175539538711101'; $VAR24 = '0.053697199473005'; $VAR25 = '0.0404925566075996'; $VAR26 = '0.0323340261121566'; $VAR27 = '0.0120226566806298'; $VAR28 = '0.0334306653243073'; $VAR29 = '0.00066374529788219'; $VAR30 = '0.00154745381765037'

testsize: 2233


Bayesian Author Test: Posterior Probabilities from Equal Priors, Z-Score-Based Method
$VAR1 = '0.993047573027366'; $VAR2 = '5.52871291496e-115'; $VAR3 = '1.32689491488088e-20'; $VAR4 = '0.00695242697263452';

Bayesian Comparison of Best Author to Best Control: from Equal Priors, Z-Score-Based Method
$VAR1 = 1; $VAR2 = '0.785360855600842'; $VAR3 = 24; $VAR4 = '0.214639144399158';

Percentage of Samples in the Best Author Candidate that Meet the P-Value>0.13 Test, Z-Score-Based Method
1
Percentage of Samples outside the Best Author Candidate that Meet the P-Value>0.13 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 = '0.134341263148362'; $VAR2 = '7.47934234727667e-116'; $VAR3 = '1.79504732474004e-21'; $VAR4 = '0.000940536835111651';
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 = '1.98537077807307e-05'; $VAR2 = '0.0035469860611535'; $VAR3 = '6.54166709827733e-08'; $VAR4 = '0.00521548871001579'; $VAR5 = '1.26415380429968e-07'; $VAR6 = '1.16055943986945e-05'; $VAR7 = '7.42264393887536e-06'; $VAR8 = '0.000303233532364961'; $VAR9 = '0.000399601503364975'; $VAR10 = '0.0025816517736103'; $VAR11 = '8.34440827340123e-11'; $VAR12 = '1.96504166522351e-05'; $VAR13 = '4.28163025198601e-06'; $VAR14 = '6.15361839047362e-06'; $VAR15 = '0.000530146787129181'; $VAR16 = '0.00163920744890275'; $VAR17 = '0.00361678154053708'; $VAR18 = '0.000901494783089076'; $VAR19 = '0.00434696386074594'; $VAR20 = '5.3011606671982e-05'; $VAR21 = '0.0352923154895603'; $VAR22 = '0.00396468370719806'; $VAR23 = '0.0158890890246912'; $VAR24 = '0.0367154710780772'; $VAR25 = '0.0214765244959266'; $VAR26 = '0.0315242920426677'; $VAR27 = '0.00892066618142467'; $VAR28 = '0.0274591416803003'; $VAR29 = '0.000703051689068664'; $VAR30 = '0.00102564205052343';

But since we're also considering the hypothesis that a shorter form of Romans is original, we should also try this using the shorter form of Romans instead. (This is not completely apples-to-apples with the previous, since there is less text in the "Paul" author candidate, meaning that there is less data from which to compute a range of style. It should be considered only confirmation of the hypothesis that 1 Corinthians has basically one author for most of it.)

testsize: 2328


Bayesian Author Test: Posterior Probabilities from Equal Priors, Z-Score-Based Method
$VAR1 = '0.981425427400352'; $VAR2 = '1.53111125190042e-82'; $VAR3 = '6.70176351599564e-13'; $VAR4 = '0.0185745725989773';

Bayesian Comparison of Best Author to Best Control: from Equal Priors, Z-Score-Based Method
$VAR1 = 1; $VAR2 = '0.511302129966119'; $VAR3 = 24; $VAR4 = '0.48869787003388';

Percentage of Samples in the Best Author Candidate that Meet the P-Value>0.0635 Test, Z-Score-Based Method
1
Percentage of Samples outside the Best Author Candidate that Meet the P-Value>0.0635 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 = '0.0635298184518451'; $VAR2 = '9.91121863639378e-84'; $VAR3 = '4.33819837546069e-14'; $VAR4 = '0.00120237278563221';
Decent compatibility. Z-Score-Based P-Value > 0.05.
Great indicator. 3% of the rest have P-Value > 0.05.

Control Z-Score-Based P-Values
$VAR1 = '1.97692007389422e-06'; $VAR2 = '0.00379750480079746'; $VAR3 = '1.52025970575235e-08'; $VAR4 = '0.00278998486870617'; $VAR5 = '3.60160631958269e-10'; $VAR6 = '4.01474669952036e-06'; $VAR7 = '1.67630028812664e-05'; $VAR8 = '0.00112288450139574'; $VAR9 = '0.00109239356893885'; $VAR10 = '0.00295358058249759'; $VAR11 = '3.20294313200905e-10'; $VAR12 = '3.44632412087791e-05'; $VAR13 = '1.00290901917263e-05'; $VAR14 = '1.59500379310899e-05'; $VAR15 = '0.00389486112441875'; $VAR16 = '0.000970725894572284'; $VAR17 = '0.0064940348311954'; $VAR18 = '0.00325430878573428'; $VAR19 = '0.0100848626428909'; $VAR20 = '0.000117942075219656'; $VAR21 = '0.0421379262627592'; $VAR22 = '0.0146528510366637'; $VAR23 = '0.0271622842582459'; $VAR24 = '0.0607212157772804'; $VAR25 = '0.0399873704696034'; $VAR26 = '0.0385987480017356'; $VAR27 = '0.0236766360454202'; $VAR28 = '0.0317817846617093'; $VAR29 = '0.00138602140596832'; $VAR30 = '0.00552957237072887';

testsize: 2265


Bayesian Author Test: Posterior Probabilities from Equal Priors, Z-Score-Based Method
$VAR1 = '0.992290074239128'; $VAR2 = '3.45324057388621e-116'; $VAR3 = '1.31073925824725e-09'; $VAR4 = '0.00770992445013282';

Bayesian Comparison of Best Author to Best Control: from Equal Priors, Z-Score-Based Method
$VAR1 = 1; $VAR2 = '0.537396488936964'; $VAR3 = 21; $VAR4 = '0.462603511063036';

Percentage of Samples in the Best Author Candidate that Meet the P-Value>0.0671 Test, Z-Score-Based Method
1
Percentage of Samples outside the Best Author Candidate that Meet the P-Value>0.0671 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 = '0.0671715343087158'; $VAR2 = '2.33761753449877e-117'; $VAR3 = '8.87284568704841e-11'; $VAR4 = '0.000521911352501245';
Decent compatibility. Z-Score-Based P-Value > 0.05.
Good indicator. 6% of the rest have P-Value > 0.05.

Control Z-Score-Based P-Values
$VAR1 = '2.64336388229147e-05'; $VAR2 = '0.00992044397658488'; $VAR3 = '4.98591546396335e-09'; $VAR4 = '0.00454101260559033'; $VAR5 = '5.03695070971544e-09'; $VAR6 = '6.3231623955956e-06'; $VAR7 = '4.81028275928233e-06'; $VAR8 = '0.000241952248955164'; $VAR9 = '0.000395674966926965'; $VAR10 = '0.00254068369889427'; $VAR11 = '4.85785869052687e-10'; $VAR12 = '3.13212519886451e-06'; $VAR13 = '4.53969783011282e-07'; $VAR14 = '4.17584630574987e-07'; $VAR15 = '0.000174041295529479'; $VAR16 = '0.00091176453699552'; $VAR17 = '0.00514221531729652'; $VAR18 = '0.00283948903185406'; $VAR19 = '0.00519256746724404'; $VAR20 = '2.80540927074421e-05'; $VAR21 = '0.0578228333351617'; $VAR22 = '0.00808769493334684'; $VAR23 = '0.0175538857069647'; $VAR24 = '0.0536971951816816'; $VAR25 = '0.0404925563025511'; $VAR26 = '0.0323340061354673'; $VAR27 = '0.0120226617444294'; $VAR28 = '0.0334305400828155'; $VAR29 = '0.000663747750375433'; $VAR30 = '0.00154745109073763';

testsize: 2233


Bayesian Author Test: Posterior Probabilities from Equal Priors, Z-Score-Based Method
$VAR1 = '0.993044788307362'; $VAR2 = '3.89891346992266e-115'; $VAR3 = '9.72519794379028e-21'; $VAR4 = '0.00695521169263843';

Bayesian Comparison of Best Author to Best Control: from Equal Priors, Z-Score-Based Method
$VAR1 = 1; $VAR2 = '0.781093539543617'; $VAR3 = 24; $VAR4 = '0.218906460456383';

Percentage of Samples in the Best Author Candidate that Meet the P-Value>0.13 Test, Z-Score-Based Method
1
Percentage of Samples outside the Best Author Candidate that Meet the P-Value>0.13 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 = '0.131006701484105'; $VAR2 = '5.14361284688017e-116'; $VAR3 = '1.28298956794044e-21'; $VAR4 = '0.000917561174183633';
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 = '1.98541496897153e-05'; $VAR2 = '0.00354700737388277'; $VAR3 = '6.54119679535863e-08'; $VAR4 = '0.00521551892192294'; $VAR5 = '1.26404678964212e-07'; $VAR6 = '1.16053845681933e-05'; $VAR7 = '7.4225312503309e-06'; $VAR8 = '0.000303234992364118'; $VAR9 = '0.0003995958210476'; $VAR10 = '0.00258175066507105'; $VAR11 = '8.34488961329525e-11'; $VAR12 = '1.96501646044395e-05'; $VAR13 = '4.28158539108854e-06'; $VAR14 = '6.15325959253068e-06'; $VAR15 = '0.000530235095783289'; $VAR16 = '0.00163920923425382'; $VAR17 = '0.00361678206541656'; $VAR18 = '0.000901500930933551'; $VAR19 = '0.00434695847123273'; $VAR20 = '5.30114213520383e-05'; $VAR21 = '0.0352923247043413'; $VAR22 = '0.00396467641874296'; $VAR23 = '0.0158890560563779'; $VAR24 = '0.0367154660307493'; $VAR25 = '0.0214765123334276'; $VAR26 = '0.0315243076207949'; $VAR27 = '0.00892066774343245'; $VAR28 = '0.0274590731772661'; $VAR29 = '0.000703053703474061'; $VAR30 = '0.00102561841690983';

This demonstrates that it is reasonable to start with the assumption that "Paul" (whenever and for whatever reason "Paul" wrote) can be identified with the author of 1 Corinthians and invites us to ask whether this "Paul" actually did write (part of or all of) Romans itself, as well. We will do this by taking test samples from Romans.

PS -- 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

[Peter Kirby]

Next we want to know whether Romans is just as like to be by the author of the rest of Romans and by the author of the Corinthians.

We first have to try to do this with the entire text of Romans, to see how that works out (ofc, leaving the sample out).

We get a negative result for the first part of Romans (1:1-7:17) and a positive result for the other two (7:18-12:14, 12:15-16:27). This is insufficient to establish that "Paul" is the author of the entire thing or that "Paul" is not (but it does seem like "Paul" wrote some of it).

testsize: 2355


Bayesian Author Test: Posterior Probabilities from Equal Priors, Z-Score-Based Method
$VAR1 = '0.772577175447618'; $VAR2 = '2.7415925093792e-141'; $VAR3 = '4.05558250518987e-05'; $VAR4 = '0.22738226872733';

Bayesian Comparison of Best Author to Best Control: from Equal Priors, Z-Score-Based Method
$VAR1 = 1; $VAR2 = '0.260685888223824'; $VAR3 = 26; $VAR4 = '0.739314111776176';

Percentage of Samples in the Best Author Candidate that Meet the P-Value>0.0182 Test, Z-Score-Based Method
1
Percentage of Samples outside the Best Author Candidate that Meet the P-Value>0.0182 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 = '0.0182833359703126'; $VAR2 = '6.48808410805439e-143'; $VAR3 = '9.59769196582174e-07'; $VAR4 = '0.00538108883481448';
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 = '3.40302803820894e-06'; $VAR2 = '0.000902293667385392'; $VAR3 = '8.75683515779075e-08'; $VAR4 = '0.00195774615884925'; $VAR5 = '1.36523593909393e-05'; $VAR6 = '0.000220388121566216'; $VAR7 = '0.000348301685017604'; $VAR8 = '0.000742914241862054'; $VAR9 = '0.000413338040735248'; $VAR10 = '0.00477579811358395'; $VAR11 = '5.33189438181506e-09'; $VAR12 = '4.3584517157267e-05'; $VAR13 = '6.96819491577765e-10'; $VAR14 = '1.04131480951483e-10'; $VAR15 = '7.47572878856206e-07'; $VAR16 = '0.000749618104049088'; $VAR17 = '0.000412977119723566'; $VAR18 = '0.00294880290287246'; $VAR19 = '0.00249778694391597'; $VAR20 = '2.90621982693089e-09'; $VAR21 = '0.0406050206346067'; $VAR22 = '0.00304066660342711'; $VAR23 = '0.0399564326195422'; $VAR24 = '0.0472553342096208'; $VAR25 = '0.0468324932277252'; $VAR26 = '0.0518521673163655'; $VAR27 = '0.00394784132798323'; $VAR28 = '0.0287465725568304'; $VAR29 = '0.00207705083798647'; $VAR30 = '0.00175355365122852';

testsize: 2442


Bayesian Author Test: Posterior Probabilities from Equal Priors, Z-Score-Based Method
$VAR1 = '0.993006298536278'; $VAR2 = '1.79033684545193e-174'; $VAR3 = '1.73354169905197e-07'; $VAR4 = '0.00699352810955216';

Bayesian Comparison of Best Author to Best Control: from Equal Priors, Z-Score-Based Method
$VAR1 = 1; $VAR2 = '0.614321464516803'; $VAR3 = 28; $VAR4 = '0.385678535483197';

Percentage of Samples in the Best Author Candidate that Meet the P-Value>0.0612 Test, Z-Score-Based Method
1
Percentage of Samples outside the Best Author Candidate that Meet the P-Value>0.0612 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 = '0.0612041356164863'; $VAR2 = '1.10347758367445e-175'; $VAR3 = '1.06847178514382e-08'; $VAR4 = '0.000431047460107426';
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 = '2.48013845894791e-05'; $VAR2 = '0.00407255993562114'; $VAR3 = '2.32974181440622e-08'; $VAR4 = '0.000285015296892861'; $VAR5 = '1.00425425006204e-08'; $VAR6 = '2.09120511609193e-06'; $VAR7 = '2.31528460559292e-05'; $VAR8 = '1.7777288781171e-05'; $VAR9 = '0.000386470726585197'; $VAR10 = '0.00266555909331225'; $VAR11 = '1.31209130599911e-10'; $VAR12 = '6.93812658643627e-06'; $VAR13 = '3.22000282234719e-10'; $VAR14 = '6.8919719220318e-13'; $VAR15 = '8.27068233284892e-07'; $VAR16 = '0.00104999117001875'; $VAR17 = '0.00306309132402'; $VAR18 = '0.00976726304888324'; $VAR19 = '0.00162053132699968'; $VAR20 = '4.66674213847195e-09'; $VAR21 = '0.0230618988914888'; $VAR22 = '0.0034710671889592'; $VAR23 = '0.0339589345518519'; $VAR24 = '0.0225613324374361'; $VAR25 = '0.0316623408884044'; $VAR26 = '0.038239357145434'; $VAR27 = '0.0139460335084201'; $VAR28 = '0.0384247055548485'; $VAR29 = '0.000694943243167888'; $VAR30 = '0.000874893326615366';

testsize: 2305


Bayesian Author Test: Posterior Probabilities from Equal Priors, Z-Score-Based Method
$VAR1 = '0.952271123641623'; $VAR2 = '8.41281884137384e-104'; $VAR3 = '0.00189919556841045'; $VAR4 = '0.0458296807899664';

Bayesian Comparison of Best Author to Best Control: from Equal Priors, Z-Score-Based Method
$VAR1 = 1; $VAR2 = '0.563104754171063'; $VAR3 = 26; $VAR4 = '0.436895245828937';

Percentage of Samples in the Best Author Candidate that Meet the P-Value>0.15 Test, Z-Score-Based Method
0.8
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 = '0.151169366224017'; $VAR2 = '1.33550252741525e-104'; $VAR3 = '0.000301489967808911'; $VAR4 = '0.00727528497637769';
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 = '0.000223275807265531'; $VAR2 = '0.00343858513382626'; $VAR3 = '2.84997191660751e-08'; $VAR4 = '0.0177151151796679'; $VAR5 = '4.40639105170587e-06'; $VAR6 = '0.00135643840001729'; $VAR7 = '0.000586569124900336'; $VAR8 = '0.00449893311798016'; $VAR9 = '0.00248326055515807'; $VAR10 = '0.0102961108320819'; $VAR11 = '1.85836458618153e-06'; $VAR12 = '2.91768665935006e-05'; $VAR13 = '2.29860427081295e-07'; $VAR14 = '5.13949050022085e-09'; $VAR15 = '0.000287236934640351'; $VAR16 = '0.00648921777154882'; $VAR17 = '0.00363574914893766'; $VAR18 = '0.00473032447578366'; $VAR19 = '0.0127098232815032'; $VAR20 = '2.49706535999372e-06'; $VAR21 = '0.0693012331038409'; $VAR22 = '0.00826702257448337'; $VAR23 = '0.0656840999249195'; $VAR24 = '0.072257216362939'; $VAR25 = '0.0637857284293271'; $VAR26 = '0.117287550724856'; $VAR27 = '0.0292074684770376'; $VAR28 = '0.05314608064025'; $VAR29 = '0.00478243431455014'; $VAR30 = '0.00978199750632829';

Okay so that went well but not as well as we might like. What about the division according to the "shorter" Romans hypothesis?

That gives us two positive results (for the two sections of the "shorter" Romans). It also gives us a negative result for the "additions" to Romans.

testsize: 2087 ['shorter' Romans sample 1]


Bayesian Author Test: Posterior Probabilities from Equal Priors, Z-Score-Based Method
$VAR1 = '0.966545716117898'; $VAR2 = '3.93486901837129e-116'; $VAR3 = '3.14751964585212e-09'; $VAR4 = '0.0334542807345826';

Bayesian Comparison of Best Author to Best Control: from Equal Priors, Z-Score-Based Method
$VAR1 = 1; $VAR2 = '0.507600092043161'; $VAR3 = 26; $VAR4 = '0.492399907956839';

Percentage of Samples in the Best Author Candidate that Meet the P-Value>0.0437 Test, Z-Score-Based Method
1
Percentage of Samples outside the Best Author Candidate that Meet the P-Value>0.0437 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 = '0.0437156414120409'; $VAR2 = '1.77969153597166e-117'; $VAR3 = '1.42358336373446e-10'; $VAR4 = '0.00151309484476818';
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 = '0.000166243404330356'; $VAR2 = '0.00437921513803946'; $VAR3 = '2.03025419625198e-13'; $VAR4 = '0.00063348538964468'; $VAR5 = '9.78673689013227e-07'; $VAR6 = '2.89960721895361e-05'; $VAR7 = '8.71310132213092e-05'; $VAR8 = '0.000278063508554145'; $VAR9 = '0.000333596859298723'; $VAR10 = '0.00459245282285456'; $VAR11 = '4.34821808908444e-08'; $VAR12 = '1.45388579244598e-05'; $VAR13 = '5.67044924265751e-10'; $VAR14 = '1.26458580319628e-10'; $VAR15 = '6.90402750929825e-07'; $VAR16 = '0.00090612994991791'; $VAR17 = '0.0022602557821681'; $VAR18 = '0.00463329797132295'; $VAR19 = '0.00196701284841635'; $VAR20 = '1.32326396306982e-08'; $VAR21 = '0.0387289877369509'; $VAR22 = '0.00297040319686633'; $VAR23 = '0.0309583360910784'; $VAR24 = '0.0269848410370945'; $VAR25 = '0.039306679028784'; $VAR26 = '0.0424065679754306'; $VAR27 = '0.00577797227536189'; $VAR28 = '0.0225005797812019'; $VAR29 = '0.000965227113827221'; $VAR30 = '0.00116797990854335';

testsize: 2134 ['shorter' Romans sample 2]


Bayesian Author Test: Posterior Probabilities from Equal Priors, Z-Score-Based Method
$VAR1 = '0.99088198655657'; $VAR2 = '3.17028717097389e-145'; $VAR3 = '1.00492162423624e-13'; $VAR4 = '0.00911801344333008';

Bayesian Comparison of Best Author to Best Control: from Equal Priors, Z-Score-Based Method
$VAR1 = 1; $VAR2 = '0.685006933729239'; $VAR3 = 26; $VAR4 = '0.314993066270761';

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
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 = '0.102272343794587'; $VAR2 = '3.27216261750964e-146'; $VAR3 = '1.03721423171351e-14'; $VAR4 = '0.000941101582480609';
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 = '2.08750869860324e-07'; $VAR2 = '0.00195143092980322'; $VAR3 = '2.21115897847691e-10'; $VAR4 = '0.000878172719470051'; $VAR5 = '1.355244404406e-08'; $VAR6 = '1.29712640526285e-05'; $VAR7 = '0.000229787582902859'; $VAR8 = '0.000653290100049269'; $VAR9 = '0.000735816441490847'; $VAR10 = '0.00710012305687503'; $VAR11 = '5.05495361857137e-09'; $VAR12 = '1.31832589409891e-05'; $VAR13 = '4.06317690801489e-07'; $VAR14 = '1.39140637836016e-08'; $VAR15 = '0.000359630147796435'; $VAR16 = '0.00253709966378578'; $VAR17 = '0.00496463500470759'; $VAR18 = '0.0176711172828776'; $VAR19 = '0.0051723194043775'; $VAR20 = '4.01257343794987e-06'; $VAR21 = '0.0294539934873268'; $VAR22 = '0.00544039518782499'; $VAR23 = '0.0452650349136477'; $VAR24 = '0.0452192800287768'; $VAR25 = '0.0419005779501987'; $VAR26 = '0.0470288366150873'; $VAR27 = '0.018025846224115'; $VAR28 = '0.0388667070593343'; $VAR29 = '0.00193596512370383'; $VAR30 = '0.00111234159765411';

testsize: 2881 [the 'additions']


Bayesian Author Test: Posterior Probabilities from Equal Priors, Z-Score-Based Method
$VAR1 = '0.681939204340396'; $VAR2 = '3.59446461010958e-125'; $VAR3 = '8.44094768476372e-66'; $VAR4 = '0.318060795659604';

Bayesian Comparison of Best Author to Best Control: from Equal Priors, Z-Score-Based Method
$VAR1 = 1; $VAR2 = '0.220845320063438'; $VAR3 = 26; $VAR4 = '0.779154679936562';

Percentage of Samples in the Best Author Candidate that Meet the P-Value>0.025 Test, Z-Score-Based Method
1
Percentage of Samples outside the Best Author Candidate that Meet the P-Value>0.025 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 = '0.0250954968945519'; $VAR2 = '1.32277004880269e-126'; $VAR3 = '3.10628535596446e-67'; $VAR4 = '0.011704699860268';
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 = '3.20257887412289e-06'; $VAR2 = '0.00175550408524153'; $VAR3 = '2.89805765782585e-12'; $VAR4 = '0.000977909803165766'; $VAR5 = '9.51073740716551e-06'; $VAR6 = '0.000511435110044118'; $VAR7 = '0.000126375012573185'; $VAR8 = '0.00212918121073401'; $VAR9 = '0.00211281643074345'; $VAR10 = '0.0051001469257945'; $VAR11 = '4.52193132170391e-08'; $VAR12 = '2.32659874375615e-05'; $VAR13 = '1.08436273201201e-11'; $VAR14 = '4.8801670858291e-12'; $VAR15 = '3.36806708728316e-06'; $VAR16 = '0.00583142866626513'; $VAR17 = '0.000456874552348669'; $VAR18 = '0.00752909143806294'; $VAR19 = '0.00700551174096493'; $VAR20 = '5.4511830566745e-10'; $VAR21 = '0.0656965310857933'; $VAR22 = '0.00585574948924853'; $VAR23 = '0.0714790976082512'; $VAR24 = '0.0539657810183953'; $VAR25 = '0.067242418009275'; $VAR26 = '0.0885383210525219'; $VAR27 = '0.0173496162937232'; $VAR28 = '0.0501086561831812'; $VAR29 = '0.00357237436245224'; $VAR30 = '0.00486322919233695';

Based on the stylometric evidence, the "shorter" Romans has a better claim of being the work of "Paul" than the longer, canonical Romans. This can't be stated with complete confidence, however, only to a degree of probability.

We will attempt to verify this result again stylometrically before we start treating the "shorter" Romans as being the actual work of "Paul."

[Ben C. Smith]

This is getting pretty interesting.

[Peter Kirby]

Next we'd like to know whether 2 Corinthians were by "Paul." We will have to do this study twice--once with the longer Romans, and again with the shorter Romans. In each case we will use the full text of 1 Corinthians and the full text of the version of Romans selected in order to establish the stylistic range of "Paul." We don't need to include any samples from 2 Corinthians in the training set (like we did before), since that is now large enough.

Recall what we said about 1 Corinthians--a positive result doesn't mean that there aren't minor interpolations or that the letter isn't built up from fragments drawn from the actual writings of "Paul."

testsize: 2244 [i.e., 2 Corinthians 1:1-7:12]


Bayesian Author Test: Posterior Probabilities from Equal Priors, Z-Score-Based Method
$VAR1 = '0.992301310471938'; $VAR2 = '2.06740694454893e-71'; $VAR3 = '9.40272999261886e-11'; $VAR4 = '0.0076986894340347';

Bayesian Comparison of Best Author to Best Control: from Equal Priors, Z-Score-Based Method
$VAR1 = 1; $VAR2 = '0.676045086970408'; $VAR3 = 21; $VAR4 = '0.323954913029592';

Percentage of Samples in the Best Author Candidate that Meet the P-Value>0.0928 Test, Z-Score-Based Method
1
Percentage of Samples outside the Best Author Candidate that Meet the P-Value>0.0928 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 = '0.0928135470049473'; $VAR2 = '1.9337208325865e-72'; $VAR3 = '8.79471500173372e-12'; $VAR4 = '0.000720086395252703';
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 = '6.31414328279277e-05'; $VAR2 = '0.00422801823683856'; $VAR3 = '4.33494941090155e-07'; $VAR4 = '0.00130988384402407'; $VAR5 = '3.84888244859751e-06'; $VAR6 = '2.96029220819513e-05'; $VAR7 = '1.46761104758149e-05'; $VAR8 = '0.000602085980610502'; $VAR9 = '0.000404131535822397'; $VAR10 = '0.00240380999447438'; $VAR11 = '6.7896853560622e-10'; $VAR12 = '1.63271709823649e-05'; $VAR13 = '7.77268514107204e-09'; $VAR14 = '1.6960751826892e-08'; $VAR15 = '3.65383812928646e-05'; $VAR16 = '0.000855152910608329'; $VAR17 = '0.000328911986454457'; $VAR18 = '0.00112348066162488'; $VAR19 = '0.00189560631343284'; $VAR20 = '2.69701515992145e-07'; $VAR21 = '0.0444754427292685'; $VAR22 = '0.00716190306152792'; $VAR23 = '0.0293720073677527'; $VAR24 = '0.0274086025003886'; $VAR25 = '0.0365401191625884'; $VAR26 = '0.0221767898577678'; $VAR27 = '0.00801564555348839'; $VAR28 = '0.014487302829976'; $VAR29 = '0.000197413844367013'; $VAR30 = '0.0004217918482984';

testsize: 2229 [i.e., 2 Cor 7:13-13:13]


Bayesian Author Test: Posterior Probabilities from Equal Priors, Z-Score-Based Method
$VAR1 = '0.969122337934396'; $VAR2 = '3.12707353291163e-52'; $VAR3 = '3.39162604610173e-08'; $VAR4 = '0.0308776281493431';

Bayesian Comparison of Best Author to Best Control: from Equal Priors, Z-Score-Based Method
$VAR1 = 1; $VAR2 = '0.678197094636046'; $VAR3 = 21; $VAR4 = '0.321802905363953';

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 = '0.12351025184503'; $VAR2 = '3.98531356124811e-53'; $VAR3 = '4.32247375507862e-09'; $VAR4 = '0.00393521383196175';
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 = '9.01474397611666e-05'; $VAR2 = '0.00311526448058668'; $VAR3 = '4.0674488384421e-08'; $VAR4 = '0.0042826502049976'; $VAR5 = '4.16457993032461e-06'; $VAR6 = '7.43838708033869e-05'; $VAR7 = '2.32027831541466e-05'; $VAR8 = '0.000545156784507239'; $VAR9 = '0.00158498622303388'; $VAR10 = '0.00271866442147968'; $VAR11 = '1.34285956926167e-10'; $VAR12 = '3.70892549515652e-05'; $VAR13 = '1.64116715905184e-10'; $VAR14 = '1.7692832967552e-08'; $VAR15 = '3.6369819204266e-06'; $VAR16 = '0.00251251835736796'; $VAR17 = '0.00326214982642029'; $VAR18 = '0.00178877927225169'; $VAR19 = '0.00389861761078689'; $VAR20 = '6.56200214645917e-08'; $VAR21 = '0.0586053201942626'; $VAR22 = '0.00781289665705838'; $VAR23 = '0.0329558047453527'; $VAR24 = '0.0353171002333594'; $VAR25 = '0.0561026628126037'; $VAR26 = '0.0298639874700537'; $VAR27 = '0.0161844704869947'; $VAR28 = '0.022464082197395'; $VAR29 = '0.00134798883122187'; $VAR30 = '0.00149299625040972';

These are positive results. It's looking good for the hypothesis that 2 Corinthians is substantially by "Paul."

The same tests, using the "shorter" version of Romans, also provide positive results.

testsize: 2244


Bayesian Author Test: Posterior Probabilities from Equal Priors, Z-Score-Based Method
$VAR1 = '0.989581270127504'; $VAR2 = '9.97827425040438e-72'; $VAR3 = '1.37740541633533e-10'; $VAR4 = '0.0104187297347552';

Bayesian Comparison of Best Author to Best Control: from Equal Priors, Z-Score-Based Method
$VAR1 = 1; $VAR2 = '0.599040784986152'; $VAR3 = 21; $VAR4 = '0.400959215013848';

Percentage of Samples in the Best Author Candidate that Meet the P-Value>0.0664 Test, Z-Score-Based Method
1
Percentage of Samples outside the Best Author Candidate that Meet the P-Value>0.0664 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 = '0.066447146924485'; $VAR2 = '6.70008492666799e-73'; $VAR3 = '9.24882703792713e-12'; $VAR4 = '0.000699583638403524';
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 = '6.31423108051113e-05'; $VAR2 = '0.00422802841677036'; $VAR3 = '4.33487666390419e-07'; $VAR4 = '0.00130990605808341'; $VAR5 = '3.8485304057719e-06'; $VAR6 = '2.96027403158402e-05'; $VAR7 = '1.46766724082774e-05'; $VAR8 = '0.000602089384221667'; $VAR9 = '0.000404112373479885'; $VAR10 = '0.00240377110367594'; $VAR11 = '6.7900991657677e-10'; $VAR12 = '1.63274960109991e-05'; $VAR13 = '7.77353699191298e-09'; $VAR14 = '1.69629824040894e-08'; $VAR15 = '3.65409032265514e-05'; $VAR16 = '0.000855201833470584'; $VAR17 = '0.000328912042967616'; $VAR18 = '0.00112349256659145'; $VAR19 = '0.00189560137112414'; $VAR20 = '2.69711444436853e-07'; $VAR21 = '0.0444754289499124'; $VAR22 = '0.00716198310407444'; $VAR23 = '0.029372137676836'; $VAR24 = '0.0274086323485174'; $VAR25 = '0.0365402253815946'; $VAR26 = '0.0221768957900098'; $VAR27 = '0.00801564562456847'; $VAR28 = '0.0144874628769909'; $VAR29 = '0.000197412642566855'; $VAR30 = '0.000421796629426054';

testsize: 2229


Bayesian Author Test: Posterior Probabilities from Equal Priors, Z-Score-Based Method
$VAR1 = '0.967858287723147'; $VAR2 = '3.25604853140619e-52'; $VAR3 = '3.52595698854082e-08'; $VAR4 = '0.0321416770172831';

Bayesian Comparison of Best Author to Best Control: from Equal Priors, Z-Score-Based Method
$VAR1 = 1; $VAR2 = '0.66913470392139'; $VAR3 = 21; $VAR4 = '0.33086529607861';

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 = '0.118522092649916'; $VAR2 = '3.98729535725519e-53'; $VAR3 = '4.31782014140271e-09'; $VAR4 = '0.00393600888651563';
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 = '9.0148813056066e-05'; $VAR2 = '0.00311518378643082'; $VAR3 = '4.06742199092862e-08'; $VAR4 = '0.00428265221704282'; $VAR5 = '4.16488724732795e-06'; $VAR6 = '7.43786265841311e-05'; $VAR7 = '2.32031940248791e-05'; $VAR8 = '0.000545170352732385'; $VAR9 = '0.00158494034137695'; $VAR10 = '0.00271853407221791'; $VAR11 = '1.34290765683397e-10'; $VAR12 = '3.70894930352583e-05'; $VAR13 = '1.64108836824933e-10'; $VAR14 = '1.76916825844359e-08'; $VAR15 = '3.63862577765591e-06'; $VAR16 = '0.00251249542785842'; $VAR17 = '0.00326214997600057'; $VAR18 = '0.00178877811771298'; $VAR19 = '0.00389862426526844'; $VAR20 = '6.56180199626009e-08'; $VAR21 = '0.0586053107792147'; $VAR22 = '0.00781282247902811'; $VAR23 = '0.0329557138933259'; $VAR24 = '0.0353170477626063'; $VAR25 = '0.0561026199279731'; $VAR26 = '0.029863938094894'; $VAR27 = '0.0161844669467667'; $VAR28 = '0.0224638154883819'; $VAR29 = '0.00134798726427216'; $VAR30 = '0.00149296191494441';

I have a pet hypothesis that chapters 10-13 and 6:14-7:1a might not be by the author "Paul." So I plug that in and...

testsize: 1557 [2 Cor 10-13 and 2 Cor 6:14-7:1a, compared against 1 Cor and 'shorter' Romans]


Bayesian Author Test: Posterior Probabilities from Equal Priors, Z-Score-Based Method
$VAR1 = '0.894103620516519'; $VAR2 = '0.000143753861562443'; $VAR3 = '0.032435372291308'; $VAR4 = '0.0733172533306102';

Bayesian Comparison of Best Author to Best Control: from Equal Priors, Z-Score-Based Method
$VAR1 = 1; $VAR2 = '0.708848254761637'; $VAR3 = 21; $VAR4 = '0.291151745238363';

Percentage of Samples in the Best Author Candidate that Meet the P-Value>0.13 Test, Z-Score-Based Method
1
Percentage of Samples outside the Best Author Candidate that Meet the P-Value>0.13 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 = '0.139834086585629'; $VAR2 = '2.24825059014171e-05'; $VAR3 = '0.00507275728824326'; $VAR4 = '0.0114665134053817';
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 = '0.0083243881636233'; $VAR2 = '0.02777250758828'; $VAR3 = '2.97978728074139e-05'; $VAR4 = '0.00480432648843007'; $VAR5 = '3.43221977884812e-05'; $VAR6 = '0.000630359875391725'; $VAR7 = '0.000240308034185146'; $VAR8 = '0.00132952109797505'; $VAR9 = '0.00185903130603507'; $VAR10 = '0.00541642881153415'; $VAR11 = '1.2594314903837e-05'; $VAR12 = '0.000248982274863876'; $VAR13 = '2.90384955935834e-07'; $VAR14 = '1.07121146337105e-05'; $VAR15 = '5.1599427757572e-05'; $VAR16 = '0.00606405875858365'; $VAR17 = '0.0103933217038868'; $VAR18 = '0.00651979748146781'; $VAR19 = '0.0119746499198108'; $VAR20 = '1.02881911028526e-06'; $VAR21 = '0.0574353369423312'; $VAR22 = '0.0172090381976755'; $VAR23 = '0.0339293045900348'; $VAR24 = '0.0471190818045169'; $VAR25 = '0.0559695647436378'; $VAR26 = '0.0480165228064549'; $VAR27 = '0.0219716027836115'; $VAR28 = '0.0363282100719464'; $VAR29 = '0.00427374197066986'; $VAR30 = '0.00644199152556627';

Darn. Pet hypothesis shot down. Let's try again with "longer" Romans.

testsize: 1557


Bayesian Author Test: Posterior Probabilities from Equal Priors, Z-Score-Based Method
$VAR1 = '0.897798377403126'; $VAR2 = '0.000135042841896297'; $VAR3 = '0.0319949509364112'; $VAR4 = '0.0700716288185661';

Bayesian Comparison of Best Author to Best Control: from Equal Priors, Z-Score-Based Method
$VAR1 = 1; $VAR2 = '0.71675643471227'; $VAR3 = 21; $VAR4 = '0.28324356528773';

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 = '0.145341867796922'; $VAR2 = '2.18616778196729e-05'; $VAR3 = '0.00517956597629364'; $VAR4 = '0.0113436843598683';
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 = '0.00832439617152879'; $VAR2 = '0.0277725753691281'; $VAR3 = '2.97970680352816e-05'; $VAR4 = '0.00480430960798635'; $VAR5 = '3.43218018054889e-05'; $VAR6 = '0.00063036729235676'; $VAR7 = '0.000240297468364332'; $VAR8 = '0.00132955510403777'; $VAR9 = '0.00185898216391935'; $VAR10 = '0.00541641959022276'; $VAR11 = '1.25959393598391e-05'; $VAR12 = '0.000248973335141352'; $VAR13 = '2.9038508026158e-07'; $VAR14 = '1.07122297909986e-05'; $VAR15 = '5.15997466741595e-05'; $VAR16 = '0.00606412216288315'; $VAR17 = '0.0103934090003857'; $VAR18 = '0.00651979848454687'; $VAR19 = '0.0119747505110488'; $VAR20 = '1.0288198406181e-06'; $VAR21 = '0.0574353390170874'; $VAR22 = '0.0172091202201858'; $VAR23 = '0.0339293049813956'; $VAR24 = '0.0471192475722587'; $VAR25 = '0.0559695663467421'; $VAR26 = '0.0480163737188381'; $VAR27 = '0.0219715185004091'; $VAR28 = '0.0363282131398736'; $VAR29 = '0.00427375318991777'; $VAR30 = '0.00644202504618784';

Darn. Pet hypothesis shot down.

For the rest of this study, both 1 Corinthians and 2 Corinthians will be treated as substantially the work of the author "Paul." (The short section 6:14-7:1a might still be an interpolation, but the last three chapters as an entirety seem unlikely to be. Naturally, it may be pasted together.)

[Peter Kirby]

Next let's compare the style of 1 Corinthians and 2 Corinthians (taken to be "Paul") to the style of Galatians (both "shorter" and "longer").

testsize: 2228 ['longer']


Bayesian Author Test: Posterior Probabilities from Equal Priors, Z-Score-Based Method
$VAR1 = '0.976067544275196'; $VAR2 = '3.45788570830365e-74'; $VAR3 = '1.21393436916633e-12'; $VAR4 = '0.0239324557235899';

Bayesian Comparison of Best Author to Best Control: from Equal Priors, Z-Score-Based Method
$VAR1 = 1; $VAR2 = '0.587983080251002'; $VAR3 = 25; $VAR4 = '0.412016919748998';

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
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 = '0.100284941110155'; $VAR2 = '3.55276503820627e-75'; $VAR3 = '1.24724295400928e-13'; $VAR4 = '0.00245891273297467';
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 = '0.000199421292299884'; $VAR2 = '0.00553613542559138'; $VAR3 = '3.98274503503422e-06'; $VAR4 = '0.00427808505197463'; $VAR5 = '9.2401417689559e-06'; $VAR6 = '0.000102672021865501'; $VAR7 = '0.000100510262532845'; $VAR8 = '0.00133375083509701'; $VAR9 = '0.00142311214028271'; $VAR10 = '0.00605720269808379'; $VAR11 = '1.79313773972302e-09'; $VAR12 = '0.000124144165118152'; $VAR13 = '1.70318258170373e-08'; $VAR14 = '4.12882529021678e-07'; $VAR15 = '8.44077648276701e-05'; $VAR16 = '0.00533810674408319'; $VAR17 = '0.0054339067200165'; $VAR18 = '0.00569570314032493'; $VAR19 = '0.00546784301980498'; $VAR20 = '1.70710781760016e-06'; $VAR21 = '0.0691928666510192'; $VAR22 = '0.00700693775882247'; $VAR23 = '0.0326278037511965'; $VAR24 = '0.0353641747983817'; $VAR25 = '0.0702725876325846'; $VAR26 = '0.0580605505160437'; $VAR27 = '0.019765575114447'; $VAR28 = '0.0391711520417562'; $VAR29 = '0.00136891336659962'; $VAR30 = '0.00122972999007745';

testsize: 1966 ['shorter']


Bayesian Author Test: Posterior Probabilities from Equal Priors, Z-Score-Based Method
$VAR1 = '0.947933920984785'; $VAR2 = '3.85194376186263e-61'; $VAR3 = '6.53233712871345e-06'; $VAR4 = '0.0520595466780865';

Bayesian Comparison of Best Author to Best Control: from Equal Priors, Z-Score-Based Method
$VAR1 = 1; $VAR2 = '0.540053991248601'; $VAR3 = 21; $VAR4 = '0.459946008751399';

Percentage of Samples in the Best Author Candidate that Meet the P-Value>0.0871 Test, Z-Score-Based Method
1
Percentage of Samples outside the Best Author Candidate that Meet the P-Value>0.0871 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 = '0.08715809321692'; $VAR2 = '3.54168224209106e-62'; $VAR3 = '6.00617865639068e-07'; $VAR4 = '0.00478663198114638';
Decent compatibility. Z-Score-Based P-Value > 0.05.
Decent indicator. 12.1% of the rest have P-Value > 0.05.

Control Z-Score-Based P-Values
$VAR1 = '0.00387900316291587'; $VAR2 = '0.0206542084330708'; $VAR3 = '5.6447704513807e-06'; $VAR4 = '0.00456328769022403'; $VAR5 = '1.02709000025416e-05'; $VAR6 = '0.000237353701230053'; $VAR7 = '0.000225562355400832'; $VAR8 = '0.00201643970535752'; $VAR9 = '0.00287728989225602'; $VAR10 = '0.00799961122895536'; $VAR11 = '6.12085534906551e-07'; $VAR12 = '0.000306694281083874'; $VAR13 = '2.30227437415096e-07'; $VAR14 = '2.35486292011424e-06'; $VAR15 = '9.90561176477666e-05'; $VAR16 = '0.00492071120677738'; $VAR17 = '0.00722347453826441'; $VAR18 = '0.00979192145198923'; $VAR19 = '0.00594116497380141'; $VAR20 = '1.58501361848615e-06'; $VAR21 = '0.0742296469521899'; $VAR22 = '0.0110601201522113'; $VAR23 = '0.036356722151492'; $VAR24 = '0.0482613929940739'; $VAR25 = '0.0738653106913569'; $VAR26 = '0.0598703553545825'; $VAR27 = '0.0255157929245509'; $VAR28 = '0.0532750846772714'; $VAR29 = '0.000911451968305292'; $VAR30 = '0.00315047974439641';

There is no very solid basis on which to declare either of these results better.

All that we can say from the stylometry is that the "Paul" (of 1-2 Cor) wrote Galatians ('shorter' or 'longer').

The omissions from the 'shorter' / additions to the 'longer' are:

Gal 1:18-24
Gal 2:7-8
Gal 3:6-9
Gal 3:16
Gal 3:29
Gal 4:1-2
Gal 4:4b

As the more-conservative of the two positions, the "shorter" Galatians (at a minimum) will be joined with "1 Cor" and "2 Cor" to represent the text of "Paul."

[Peter Kirby]

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.)

"Paul" now is represented by 1 Cor, 2 Cor, and a 'shorter' Galatians.

testsize: 1478


Bayesian Author Test: Posterior Probabilities from Equal Priors, Z-Score-Based Method
$VAR1 = '0.678262158288346'; $VAR2 = '0.00167521776264334'; $VAR3 = '0.118077565052731'; $VAR4 = '0.20198505889628';

Bayesian Comparison of Best Author to Best Control: from Equal Priors, Z-Score-Based Method
$VAR1 = 1; $VAR2 = '0.554434659661292'; $VAR3 = 21; $VAR4 = '0.445565340338708';

Percentage of Samples in the Best Author Candidate that Meet the P-Value>0.13 Test, Z-Score-Based Method
1
Percentage of Samples outside the Best Author Candidate that Meet the P-Value>0.13 Test, Z-Score-Based Method
0.00185873605947955
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
0.998144712430427

Author Z-Score-Based P-Values
$VAR1 = '0.137828531036281'; $VAR2 = '0.00034041822998602'; $VAR3 = '0.0239943466411701'; $VAR4 = '0.0410450496445295';

Control Z-Score-Based P-Values
$VAR1 = '0.0410951436988192'; $VAR2 = '0.0546417282271676'; $VAR3 = '0.000781049471071238'; $VAR4 = '0.0108377529677987'; $VAR5 = '0.00707271212274762'; $VAR6 = '0.0110662420414526'; $VAR7 = '0.00504343149286514'; $VAR8 = '0.013633353163661'; $VAR9 = '0.0141051983637701'; $VAR10 = '0.0239116958263161'; $VAR11 = '0.00243172672015498'; $VAR12 = '0.00329998353502375'; $VAR13 = '1.04955345665399e-05'; $VAR14 = '9.14730254133832e-05'; $VAR15 = '0.000304895674462606'; $VAR16 = '0.0209821364760245'; $VAR17 = '0.0186126034722808'; $VAR18 = '0.0248678522222467'; $VAR19 = '0.0282209373014592'; $VAR20 = '3.85412315765426e-05'; $VAR21 = '0.110764389039245'; $VAR22 = '0.0411553722678735'; $VAR23 = '0.0764306419789761'; $VAR24 = '0.0635461804253728'; $VAR25 = '0.11068629796465'; $VAR26 = '0.0955440558601551'; $VAR27 = '0.0341995013839847'; $VAR28 = '0.0820827972464417'; $VAR29 = '0.019845347762871'; $VAR30 = '0.0182877390440734';

This is a positive result, and it seems that "Paul" is also the author of 1 Thessalonians.

[Peter Kirby]

The next text to be tested is the one called Philippians, in full.

"Paul" is still being represented by 1 Cor, 2 Cor, and a 'shorter' Galatians.

testsize: 1627


Bayesian Author Test: Posterior Probabilities from Equal Priors, Z-Score-Based Method
$VAR1 = '0.702965883818766'; $VAR2 = '0.00669730285767142'; $VAR3 = '0.0652340739400614'; $VAR4 = '0.225102739383501';

Bayesian Comparison of Best Author to Best Control: from Equal Priors, Z-Score-Based Method
$VAR1 = 1; $VAR2 = '0.527164830725408'; $VAR3 = 25; $VAR4 = '0.472835169274592';

Percentage of Samples in the Best Author Candidate that Meet the P-Value>0.13 Test, Z-Score-Based Method
1
Percentage of Samples outside the Best Author Candidate that Meet the P-Value>0.13 Test, Z-Score-Based Method
0.00204498977505112
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
0.997959183673469

Author Z-Score-Based P-Values
$VAR1 = '0.133240376634749'; $VAR2 = '0.0012694089083606'; $VAR3 = '0.0123644870700919'; $VAR4 = '0.0426660446365333';
Good compatibility. Z-Score-Based P-Value > 0.1.
Good indicator. 6% of the rest have P-Value > 0.1.

Control Z-Score-Based P-Values
$VAR1 = '0.0105693447749743'; $VAR2 = '0.0236740630597205'; $VAR3 = '0.000633061152495319'; $VAR4 = '0.0120397910604154'; $VAR5 = '0.00107324373491938'; $VAR6 = '0.00873358955591716'; $VAR7 = '0.000882716165950419'; $VAR8 = '0.00422173550896562'; $VAR9 = '0.0104961164408355'; $VAR10 = '0.0110785156338442'; $VAR11 = '6.85392271283222e-05'; $VAR12 = '0.00204789200572219'; $VAR13 = '1.81492065365133e-05'; $VAR14 = '6.10905476195609e-06'; $VAR15 = '0.000788873042579296'; $VAR16 = '0.0142172300847673'; $VAR17 = '0.012499976427208'; $VAR18 = '0.0127010658156257'; $VAR19 = '0.0200405277486288'; $VAR20 = '2.40951942577647e-05'; $VAR21 = '0.0935768923621985'; $VAR22 = '0.0237982774945232'; $VAR23 = '0.0877208964649714'; $VAR24 = '0.0667796842464594'; $VAR25 = '0.119508609771273'; $VAR26 = '0.118165430367594'; $VAR27 = '0.0417767491980822'; $VAR28 = '0.0703024031341374'; $VAR29 = '0.00951024992681941'; $VAR30 = '0.0095976386313686';

And now "Paul" is being represented by 1 Cor, 2 Cor, 'shorter' Galatians, and by 1 Thessalonians.

testsize: 1627


Bayesian Author Test: Posterior Probabilities from Equal Priors, Z-Score-Based Method
$VAR1 = '0.726282430523061'; $VAR2 = '0.00606033127154167'; $VAR3 = '0.059021871863448'; $VAR4 = '0.20863536634195';

Bayesian Comparison of Best Author to Best Control: from Equal Priors, Z-Score-Based Method
$VAR1 = 1; $VAR2 = '0.565728596008469'; $VAR3 = 25; $VAR4 = '0.434271403991531';

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
0.00204498977505112
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
0.997704667176741

Author Z-Score-Based P-Values
$VAR1 = '0.15568472179843'; $VAR2 = '0.00129908276500203'; $VAR3 = '0.0126518325583972'; $VAR4 = '0.0447227381541741';
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 = '0.0105694202778059'; $VAR2 = '0.0236739421622763'; $VAR3 = '0.000633061577984205'; $VAR4 = '0.0120398084517254'; $VAR5 = '0.00107329561638053'; $VAR6 = '0.00873389865883823'; $VAR7 = '0.000882684363138996'; $VAR8 = '0.00422184694511021'; $VAR9 = '0.0104958726862348'; $VAR10 = '0.0110783260762975'; $VAR11 = '6.85453049279882e-05'; $VAR12 = '0.00204799599685807'; $VAR13 = '1.81491467799956e-05'; $VAR14 = '6.10912983892133e-06'; $VAR15 = '0.000788900157895745'; $VAR16 = '0.0142174269389207'; $VAR17 = '0.012500108612046'; $VAR18 = '0.0127010207624139'; $VAR19 = '0.0200405349797589'; $VAR20 = '2.4096490390704e-05'; $VAR21 = '0.0935768997561437'; $VAR22 = '0.0237985656613338'; $VAR23 = '0.0877208995366153'; $VAR24 = '0.0667797152074301'; $VAR25 = '0.119508582724044'; $VAR26 = '0.118165428847503'; $VAR27 = '0.0417766134244342'; $VAR28 = '0.0703028889883055'; $VAR29 = '0.00951025712159654'; $VAR30 = '0.00959756279774368';

Either way, it looks as though the author of Philippians is "Paul." Let's add it, in full, to the text representing "Paul."

[Peter Kirby]

Next up, a frequently-debated possible epistle of Paul: Colossians.

The basis for comparison to "Paul" is 1 Corinthians, 2 Corinthians, 'shorter' Galatians, 1 Thessalonians, and Philippians.

testsize: 1581


Bayesian Author Test: Posterior Probabilities from Equal Priors, Z-Score-Based Method
$VAR1 = '0.718780059365324'; $VAR2 = '2.81849384749191e-09'; $VAR3 = '0.0359741034451113'; $VAR4 = '0.245245834371071';

Bayesian Comparison of Best Author to Best Control: from Equal Priors, Z-Score-Based Method
$VAR1 = 1; $VAR2 = '0.530942538156256'; $VAR3 = 25; $VAR4 = '0.469057461843744';

Percentage of Samples in the Best Author Candidate that Meet the P-Value>0.0932 Test, Z-Score-Based Method
1
Percentage of Samples outside the Best Author Candidate that Meet the P-Value>0.0932 Test, Z-Score-Based Method
0.0099403578528827
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
0.990157480314961

Author Z-Score-Based P-Values
$VAR1 = '0.0932867697492297'; $VAR2 = '3.65797830872995e-10'; $VAR3 = '0.00466889399795301'; $VAR4 = '0.0318291964069413';
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 = '0.00893189319118513'; $VAR2 = '0.01266917526504'; $VAR3 = '0.00663820030291991'; $VAR4 = '0.00271179810395527'; $VAR5 = '0.00403895480719969'; $VAR6 = '0.00653639474544105'; $VAR7 = '0.00091058317503737'; $VAR8 = '0.00925423570351274'; $VAR9 = '0.00501883376135153'; $VAR10 = '0.0079008523192368'; $VAR11 = '6.2169307293712e-06'; $VAR12 = '0.00230949791501568'; $VAR13 = '2.37112857820229e-05'; $VAR14 = '3.96138127484607e-05'; $VAR15 = '0.000253474156982259'; $VAR16 = '0.00544701448591267'; $VAR17 = '0.000463931663444301'; $VAR18 = '0.00368464989651186'; $VAR19 = '0.00779694341094471'; $VAR20 = '1.3694327920947e-05'; $VAR21 = '0.0584392773608055'; $VAR22 = '0.00722074342025299'; $VAR23 = '0.0530913691964373'; $VAR24 = '0.0558349614038286'; $VAR25 = '0.082413542516531'; $VAR26 = '0.074148681433277'; $VAR27 = '0.0148587573418621'; $VAR28 = '0.0454386801103707'; $VAR29 = '0.00580434675993175'; $VAR30 = '0.00679951515830743';

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