John the Baptist in Josephus - A Statistical Analysis of Word Frequencies

This document was created in connection with a post regarding the authenticity of the John the Baptist passage in Josephus.

The moral of the story is that the attempt to demonstrate authenticity or inauthenticity from statistical features of word frequency in this snippet of text, which is only 163 words long, is futile.

The test sample fails to prove clear superiority as stemming from Josephus over four alternatives in a straight comparison (Acts, Clement of Alexandria, Origen, and Eusebius). The test sample also is edged out ever-so-slightly by one of the thirty control samples (Polybius).

The gist here is that there is no particular evidence, from word frequencies, that the author of the passage were one of the 35 authors considered here or someone else entirely. Using the Stouffer method for combining p-value statistics, 27 out of 35 authors are found to be minimally consistent at the (p-value > 0.05) level of the absence of statistically significant evidence otherwise. (Put it this way: the author himself might be expected to meet this standard 95% of the time, but 80% of every author considered here has met the same standard anyway. A thin reed, considered in Bayesian terms.)

Part of the trouble is the restrictive number of word features that can have their frequency measured in 163-word samples. It is important that the mean number of appearances of a word feature be somewhat substantial (at leaat 5 appearances per sample, average) in order to be able to make anything of the significance of the differences.

The word features settled upon were four cases of the 'definite article' (nominative, genetive, dative, and accusative) along with the third person pronoun (AUTOS), the most common conjunction (KAI), a list of five common conjunctions (MEN, DE, TE, GAR, ALLA), and a list of five common prepositions (EIS, PROS, EPI, PERI, KATA). The sample sizes are too small to test any more-subtle word frequency features (such as particular preposition frequencies).

The 5 author-candidate samples are from:
#1 Josephus, #2 Acts, #3 Clement of Alexandria, #4 Origen, #5 Eusebius

The 30 control samples are from:
#1 Mark, #2 John, #3 1Corinthians, #4 Hebrews, #5 Revelation,
#6 Apocalypse of Enoch, #7 Life of Adam and Eve, #8 2Baruch, #9 1Maccabees, #10 2Maccabees, #11 3Maccabees, #12 4Maccabees,
#13 Polybius, #14 Diodorus Siculus, #15 Dionysius Halicarnassus, #16 Strabo, #17 Plutarch, #18 Arrian,
#19 Herodian, #20 Herodotus, #21 Thucydides, #22 Xenophon, #23 Epictetus, #24 Galen, #25 Lucian, #26 Philostratus,
#27 Athanasius, #28 John Chrysostom, #29 Basil, #30 Gregory of Nyssa

The program that processed this data can currently be accessed here.

testsize: 163
testsample: TISI DE TWN IOUDAIWN EDOKEI OLWLENAI TON HRWDOU STRATON UPO TOU QEOU KAI MALA DIKAIWS TINUMENOU KATA POINHN IWANNOU TOU EPIKALOUMENOU BAPTISTOU KTEINEI GAR DH TOUTON HRWDHS AGAQON ANDRA KAI TOIS IOUDAIOIS KELEUONTA ARETHN EPASKOUSIN KAI TA PROS ALLHLOUS DIKAIOSUNHi KAI PROS TON QEON EUSEBEIAi XRWMENOIS BAPTISMWi SUNIENAI OUTW GAR DH KAI THN BAPTISIN APODEKTHN AUTWi FANEISQAI MH EPI TINWN AMARTADWN PARAITHSEI XRWMENWN ALL EF AGNEIAi TOU SWMATOS ATE DH KAI THS YUXHS DIKAIOSUNHi PROEKKEKAQARMENHS KAI TWN ALLWN SUSTREFOMENWN KAI GAR HSQHSAN EPI PLEISTON THi AKROASEI TWN LOGWN DEISAS HRWDHS TO EPI TOSONDE PIQANON AUTOU TOIS ANQRWPOIS MH EPI APOSTASEI TINI FEROI PANTA GAR EWiKESAN SUMBOULHi THi EKEINOU PRACONTES POLU KREITTON HGEITAI PRIN TI NEWTERON EC AUTOU GENESQAI PROLABWN ANELEIN TOU METABOLHS GENOMENHS MH EIS PRAGMATA EMPESWN METANOEIN KAI O MEN UPOYIAi THi HRWDOU DESMIOS EIS TON MAXAIROUNTA PEMFQEIS TO PROEIRHMENON FROURION TAUTHi KTINNUTAI TOIS DE IOUDAIOIS DOCAN EPI TIMWRIAi THi EKEINOU TON OLEQRON EPI TWi STRATEUMATI GENESQAI TOU QEOU KAKWSAI HRWDHN QELONTOS
$VAR1 = 4; $VAR2 = 9; $VAR3 = 8; $VAR4 = 5; $VAR5 = 3; $VAR6 = 9; $VAR7 = 8; $VAR8 = 11;

8 Words
$VAR1 = [ 'O', 'OI', 'H', 'AI', 'TO', 'TA' ]; $VAR2 = [ 'TOU', 'TWN', 'THS' ]; $VAR3 = [ 'TWi', 'TOIS', 'THi', 'TAIS' ]; $VAR4 = [ 'TON', 'TOUS', 'THN', 'TAS' ]; $VAR5 = [ 'AUTOS', 'AUTOU', 'AUTWi', 'AUTON', 'AUTOI', 'AUTWN', 'AUTOIS', 'AUTOUS', 'AUTH', 'AUTHS', 'AUTHi', 'AUTHN', 'AUTAI', 'AUTWN', 'AUTAIS', 'AUTAS', 'AUTO', 'AUTA' ]; $VAR6 = [ 'KAI' ]; $VAR7 = [ 'MEN', 'DE', 'D', 'TE', 'GAR', 'ALLA', 'ALL' ]; $VAR8 = [ 'EIS', 'PROS', 'EP', 'EPI', 'PERI', 'KATA', 'KAT', 'KAQ' ];

Author Stats - Mean, Standard Deviation
$VAR1 = [ [ '6.6865671641791', '2.82028343671331' ], [ '8.40671641791045', '2.62640716402141' ], [ '4.00746268656716', '2.04061838979923' ], [ '5.82462686567164', '2.52506647074217' ], [ '5.57835820895522', '2.3950777241088' ], [ '8.69402985074627', '2.77307849822501' ], [ '10.9962686567164', '3.0142672364274' ], [ '6.49626865671642', '2.3300408912054' ] ]; $VAR2 = [ [ '7.90265486725664', '2.7746150231881' ], [ '6.23008849557522', '2.43502775531608' ], [ '4', '2.39468437885586' ], [ '6.25663716814159', '2.54787352272872' ], [ '6.29203539823009', '2.80858801777944' ], [ '9.80530973451327', '3.47394450024611' ], [ '7.63716814159292', '2.93004559722488' ], [ '6.61946902654867', '2.91568411824039' ] ]; $VAR3 = [ [ '11.8153153153153', '3.44678197477841' ], [ '6.24324324324324', '2.94916759126593' ], [ '3.24774774774775', '2.05046014817447' ], [ '6.10810810810811', '2.86906881761392' ], [ '3.22972972972973', '2.37031546897232' ], [ '8.7027027027027', '3.51469141724578' ], [ '9.47747747747748', '3.00404186235046' ], [ '4.40990990990991', '2.30324702077971' ] ]; $VAR4 = [ [ '9.70748299319728', '4.16694293128283' ], [ '8.42857142857143', '3.53023866530488' ], [ '3.96598639455782', '2.04844379620468' ], [ '4.79591836734694', '2.37314560762056' ], [ '3.1156462585034', '2.1931154084076' ], [ '9.54421768707483', '3.74934242310216' ], [ '6.81632653061224', '2.53417567851328' ], [ '6.14965986394558', '2.92154497729806' ] ]; $VAR5 = [ [ '7.56213017751479', '3.50620551581742' ], [ '8.18934911242603', '3.42971769708103' ], [ '3.63313609467456', '2.24169002954887' ], [ '6.07100591715976', '3.16709032367379' ], [ '3.8698224852071', '2.57564387845192' ], [ '11.0236686390533', '3.97172352065441' ], [ '7.72189349112426', '3.24714621550507' ], [ '5.18934911242604', '2.5673655463402' ] ];

Control Stats - Mean, Standard Deviation
$VAR1 = [ [ '9.89705882352941', '3.7735133647818' ], [ '4.60294117647059', '2.33980709286768' ], [ '2.83823529411765', '1.97491842063567' ], [ '5.36764705882353', '2.66736492444105' ], [ '11.1323529411765', '3.68184900705157' ], [ '15.8235294117647', '4.55664084370786' ], [ '4.01470588235294', '2.25240164020295' ], [ '5.29411764705882', '3.05854071090722' ] ]; $VAR2 = [ [ '11.563829787234', '3.81642171338963' ], [ '4.59574468085106', '2.4638628594407' ], [ '2.38297872340426', '1.53751929916082' ], [ '4.79787234042553', '2.43021664052266' ], [ '8.08510638297872', '3.20126163449857' ], [ '8.63829787234043', '2.95660480896221' ], [ '4.02127659574468', '2.01578200550247' ], [ '4.26595744680851', '2.19852722421989' ] ]; $VAR3 = [ [ '11.1463414634146', '3.96669657738795' ], [ '4.65853658536585', '2.95997491829816' ], [ '3.63414634146341', '2.91970678080886' ], [ '2.78048780487805', '2.03040540373341' ], [ '2.1219512195122', '2.15491635230357' ], [ '6.58536585365854', '2.5372888330359' ], [ '9.92682926829268', '3.18831895382794' ], [ '2.8780487804878', '2.07417479272871' ] ]; $VAR4 = [ [ '7.36666666666667', '2.63923389557568' ], [ '7.03333333333333', '2.58822118237389' ], [ '2.73333333333333', '2.09655802580219' ], [ '6', '1.91485421551268' ], [ '4.83333333333333', '3.57848509226398' ], [ '8.43333333333333', '2.85987567717355' ], [ '7.16666666666667', '2.25215945754785' ], [ '6.13333333333333', '2.53946626063212' ] ]; $VAR5 = [ [ '12.4833333333333', '4.66008464396184' ], [ '10.1833333333333', '4.31080683347741' ], [ '3.03333333333333', '1.94050394371038' ], [ '5.85', '3.37058353009287' ], [ '7.35', '3.85497514043001' ], [ '18.6', '4.87237108603193' ], [ '0.616666666666667', '0.877338145883457' ], [ '4.1', '1.9122412679018' ] ]; $VAR6 = [ [ '8.46', '3.28761311592468' ], [ '8.92', '4.23244610125162' ], [ '3.02', '1.79432438538855' ], [ '4.54', '3.08032465821381' ], [ '7.14', '3.40005882302057' ], [ '18.02', '4.2118404528187' ], [ '1.22', '1.28514590611339' ], [ '5.96', '2.18137571270976' ] ]; $VAR7 = [ [ '9.44444444444444', '3.71516744384455' ], [ '7.96296296296296', '2.86073652108556' ], [ '3.11111111111111', '1.91162783712058' ], [ '4.81481481481481', '2.29390556551141' ], [ '8', '3.55902608401044' ], [ '11.7037037037037', '4.10794005162734' ], [ '4.59259259259259', '1.79008088497697' ], [ '4.7037037037037', '2.55045115565731' ] ]; $VAR8 = [ [ '7.84810126582278', '2.46025936471015' ], [ '7.62025316455696', '3.48342839077097' ], [ '2.75949367088608', '1.89746793220792' ], [ '7.21518987341772', '2.84480822283464' ], [ '1.87341772151899', '1.6715572108226' ], [ '9.45569620253165', '4.17890261276182' ], [ '9.51898734177215', '3.06825625443472' ], [ '7.17721518987342', '2.84964796258333' ] ]; $VAR9 = [ [ '8.3206106870229', '3.65343543350037' ], [ '6.74045801526718', '3.21634135293799' ], [ '3.48091603053435', '2.21152824448507' ], [ '5.67175572519084', '2.56947063812318' ], [ '9.26717557251908', '4.2870734648287' ], [ '21.7709923664122', '4.42160705387454' ], [ '1.56488549618321', '1.68558883471424' ], [ '5.99236641221374', '2.96929884340854' ] ]; $VAR10 = [ [ '6.97260273972603', '2.90946778892412' ], [ '8.80821917808219', '3.21237988100819' ], [ '4.13698630136986', '2.216470528239' ], [ '10.0821917808219', '3.01935956494059' ], [ '3.20547945205479', '2.4936022472291' ], [ '9.91780821917808', '3.82405301969869' ], [ '8.42465753424658', '2.5098043815011' ], [ '6.84931506849315', '2.62585267496005' ] ]; $VAR11 = [ [ '6.48387096774194', '2.56365374016845' ], [ '7.12903225806452', '2.599527692633' ], [ '3.83870967741935', '1.91928706847013' ], [ '8.45161290322581', '2.58829511302162' ], [ '3.87096774193548', '1.86204770189185' ], [ '8.93548387096774', '3.31112965686615' ], [ '6.45161290322581', '2.64987777779521' ], [ '7.51612903225806', '2.74591741226199' ] ]; $VAR12 = [ [ '6.9375', '2.62524800415758' ], [ '9.0625', '3.41812722846883' ], [ '2.8125', '1.62860177759942' ], [ '8.45833333333333', '3.58793309426038' ], [ '3.35416666666667', '2.46212631118353' ], [ '10.5208333333333', '3.95805920103387' ], [ '6.58333333333333', '2.29885237068896' ], [ '4.5', '2.32737334062816' ] ]; $VAR13 = [ [ '6.59235668789809', '2.60806054307422' ], [ '9.47770700636943', '3.03815647098372' ], [ '4.13375796178344', '2.05061911235736' ], [ '10.6114649681529', '3.46161790075262' ], [ '2.80254777070064', '1.45610723709984' ], [ '8.05732484076433', '2.6667139974433' ], [ '11.2356687898089', '3.07887837834555' ], [ '7.84076433121019', '2.68638832232899' ] ]; $VAR14 = [ [ '5.6', '2.74135003237456' ], [ '10.95625', '3.33044080228128' ], [ '3.80625', '2.26245683660484' ], [ '10.55', '3.32565782966318' ], [ '1.64375', '1.35252945901374' ], [ '7.7125', '3.03188781949464' ], [ '11.94375', '2.77994351336497' ], [ '6.5625', '2.76967394290375' ] ]; $VAR15 = [ [ '6.90909090909091', '2.8237481684825' ], [ '7.56363636363636', '2.80970376760754' ], [ '3.09090909090909', '1.92532777789695' ], [ '6.26060606060606', '2.82391726571435' ], [ '3.24242424242424', '1.79949998156564' ], [ '7.47272727272727', '2.81675428165035' ], [ '11.0121212121212', '3.23051338220109' ], [ '4.83030303030303', '2.37824545060516' ] ]; $VAR16 = [ [ '9.19323671497585', '3.81724445433604' ], [ '8.06763285024155', '3.76293462676375' ], [ '3.05797101449275', '2.07969752053937' ], [ '7.44927536231884', '3.25800195972719' ], [ '1.90338164251208', '1.70827431195356' ], [ '10.024154589372', '4.20080463137497' ], [ '11.7487922705314', '3.52694061979961' ], [ '6.64734299516908', '2.9317980490185' ] ]; $VAR17 = [ [ '6.1044776119403', '2.93783516783692' ], [ '5.59701492537313', '2.27287510404404' ], [ '3.35820895522388', '1.55209528613202' ], [ '7.76119402985075', '2.84992564573762' ], [ '2.80597014925373', '1.51843208577431' ], [ '10.4626865671642', '3.40030006669278' ], [ '11.6417910447761', '2.7246880831331' ], [ '4.40298507462687', '1.95516691269407' ] ]; $VAR18 = [ [ '7.75177304964539', '3.44594741600675' ], [ '7.73758865248227', '3.09345084929991' ], [ '4.49645390070922', '2.08889028014513' ], [ '7.85106382978723', '3.27235610395676' ], [ '4.25531914893617', '1.99788631329187' ], [ '9.80141843971631', '2.99933765301993' ], [ '12.0212765957447', '2.76366517125609' ], [ '4.74468085106383', '2.34416207206963' ] ]; $VAR19 = [ [ '7.77464788732394', '2.63078836306304' ], [ '6.62676056338028', '2.89392066753635' ], [ '2.92957746478873', '1.75887242738926' ], [ '6.13380281690141', '2.70166582216231' ], [ '3.7112676056338', '2.06097538072062' ], [ '9.24647887323944', '2.72491534877771' ], [ '13.8661971830986', '2.84884180380214' ], [ '3.33802816901408', '1.75180922149139' ] ]; $VAR20 = [ [ '9.27450980392157', '3.28739977926741' ], [ '5.26470588235294', '2.67496186737796' ], [ '1.87745098039216', '1.45173370746876' ], [ '5.63235294117647', '2.84003803360013' ], [ '2.14705882352941', '1.53965274174641' ], [ '6.66176470588235', '2.72754806638501' ], [ '13.421568627451', '3.03391378149175' ], [ '2.93137254901961', '1.84582094983622' ] ]; $VAR21 = [ [ '8.26041666666667', '3.04221955591455' ], [ '5.54166666666667', '2.5856844140167' ], [ '3.09895833333333', '1.65063086371965' ], [ '5.06770833333333', '2.37183977429559' ], [ '3.66666666666667', '1.7950549357115' ], [ '10.65625', '2.97849278509002' ], [ '12.0520833333333', '2.78900292692369' ], [ '3.63541666666667', '1.89637698249115' ] ]; $VAR22 = [ [ '8.74358974358974', '3.20670730331373' ], [ '4.91282051282051', '2.56756689046559' ], [ '3.2974358974359', '1.69576957485947' ], [ '5.43589743589744', '2.62722308106596' ], [ '3.49230769230769', '1.9725532868412' ], [ '9.22564102564102', '3.09015956344453' ], [ '13.0717948717949', '2.92907167563365' ], [ '5.33846153846154', '2.78794248042562' ] ]; $VAR23 = [ [ '9.2962962962963', '3.49053197135805' ], [ '3.76543209876543', '2.08623711670505' ], [ '2.33333333333333', '1.72132593164774' ], [ '3.41975308641975', '2.2490832015903' ], [ '3.11111111111111', '1.94999208608714' ], [ '9.1358024691358', '4.27092694255426' ], [ '8.34567901234568', '2.816005812578' ], [ '4.64197530864198', '2.45104483629202' ] ]; $VAR24 = [ [ '9.16037735849057', '3.1923753280213' ], [ '8.28301886792453', '3.21480865060758' ], [ '3.28301886792453', '2.24766007040585' ], [ '4.58490566037736', '2.60937325131629' ], [ '3.0188679245283', '1.63095719131882' ], [ '8.52830188679245', '4.77060090192715' ], [ '11.7358490566038', '3.6141803705406' ], [ '5.16037735849057', '2.54446047383008' ] ]; $VAR25 = [ [ '8.05376344086022', '3.55105797168017' ], [ '5.52150537634409', '2.41902626203659' ], [ '2.76881720430108', '1.7212447667984' ], [ '5.39247311827957', '2.67640975048724' ], [ '3.8010752688172', '2.15730789142872' ], [ '11.8548387096774', '3.7653489786439' ], [ '10.3978494623656', '3.71755436126377' ], [ '3.65591397849462', '2.09707745256647' ] ]; $VAR26 = [ [ '8.75806451612903', '2.95496020316506' ], [ '5.14516129032258', '2.25412482738341' ], [ '3.10752688172043', '1.99171599214431' ], [ '5.44623655913978', '2.5101539660521' ], [ '3.74731182795699', '1.87960710821649' ], [ '9.43010752688172', '2.96900783348911' ], [ '13.9623655913978', '3.05921537408738' ], [ '2.62365591397849', '1.81933450254274' ] ]; $VAR27 = [ [ '8.5981308411215', '3.5503318604504' ], [ '7.67289719626168', '3.38709949781859' ], [ '2.78971962616822', '2.01111093953321' ], [ '6.45327102803738', '3.13037030913887' ], [ '4.47196261682243', '2.85909908013073' ], [ '12.6588785046729', '4.11181232687085' ], [ '8.17757009345794', '3.22899563132919' ], [ '4.77570093457944', '2.53317580299466' ] ]; $VAR28 = [ [ '7.01470588235294', '3.14280682152378' ], [ '7.25980392156863', '3.24281286164819' ], [ '2.54901960784314', '1.65758772861255' ], [ '5.98039215686275', '2.67332645893032' ], [ '3.38725490196078', '2.08919590351414' ], [ '11.6960784313725', '4.02879151755061' ], [ '9.74509803921569', '2.84117579398902' ], [ '3.39705882352941', '1.91336659886124' ] ]; $VAR29 = [ [ '10.5809523809524', '3.69756922052713' ], [ '10.3380952380952', '3.45652952712429' ], [ '4.36190476190476', '2.24084936925524' ], [ '6.35238095238095', '2.53351234598457' ], [ '2.51428571428571', '1.92286634116529' ], [ '8.43809523809524', '3.23352618823125' ], [ '7.31904761904762', '2.83819510850169' ], [ '5.12857142857143', '2.43146885983073' ] ]; $VAR30 = [ [ '11.4932126696833', '3.54367693784852' ], [ '9.38914027149321', '3.58764467074031' ], [ '4.1131221719457', '2.27734459334522' ], [ '5.7420814479638', '3.10035660081058' ], [ '2.31221719457014', '1.80679588599294' ], [ '8.13122171945701', '3.91261711844468' ], [ '7.64705882352941', '2.6350153375491' ], [ '5.25339366515837', '2.55775809882142' ] ];

Author Q-Values
$VAR1 = [ '0.829600386516814', '0.410642815874354', '0.02520122391008', '0.628005925481149', '0.859153462384132', '0.456071610482331', '0.839895524664025', '0.026624416685359' ]; $VAR2 = [ '0.920220768673111', '0.127658841625186', '0.0474234563290143', '0.689068048246243', '0.879427992227455', '0.591658862100467', '0.450724469416908', '0.066496501292399' ]; $VAR3 = [ '0.988317822426907', '0.17495672649812', '0.0102341326168838', '0.650335368548968', '0.5386047002331', '0.466294986545382', '0.688580276585676', '0.00211008882683007' ]; $VAR4 = [ '0.914610642369393', '0.435705432391805', '0.024458978948163', '0.465734827450756', '0.521026964051219', '0.5577037529647', '0.320219705193699', '0.0484374061696361' ]; $VAR5 = [ '0.845173393559871', '0.406576324113773', '0.0257061303693003', '0.632381503607582', '0.632209510109612', '0.694805839285391', '0.465873870664808', '0.0118094132988428' ];

Control Q-Values
$VAR1 = [ '0.940944391078621', '0.0301059807162676', '0.00447891037164284', '0.55481312757411', '0.986404631571464', '0.932867351106002', '0.0384175301206517', '0.0310517811258784' ]; $VAR2 = [ '0.976255694114219', '0.036925131603041', '0.000129445064602091', '0.466857243066703', '0.943909946002032', '0.451316184020364', '0.0242030327968343', '0.00109572746694748' ]; $VAR3 = [ '0.964194571868393', '0.0712255923095668', '0.067417259688473', '0.137166723703525', '0.341833836236635', '0.170635030056586', '0.727191245907909', '4.50616853856517e-05' ]; $VAR4 = [ '0.898955650017703', '0.223671456971361', '0.00600153868085872', '0.699245999985', '0.695786916719588', '0.421466300431611', '0.355685437597578', '0.0276562998803315' ]; $VAR5 = [ '0.965652741391927', '0.608151368729057', '0.00524155613798989', '0.599549791189419', '0.870427036597789', '0.97559759186688', '1.95432265080086e-17', '0.00015408640732417' ]; $VAR6 = [ '0.912547121452516', '0.492459858270169', '0.00275654093921954', '0.440644773935107', '0.888317020709472', '0.983886411938499', '6.61375636828601e-08', '0.0104311147145156' ]; $VAR7 = [ '0.928602941616071', '0.358486467295979', '0.00527216539668135', '0.467828782735177', '0.919971454857036', '0.744783994511633', '0.0284881314921426', '0.00678026114476906' ]; $VAR8 = [ '0.941103484212772', '0.346019644592176', '0.00287381567538207', '0.781915198536984', '0.250164715128544', '0.543417214902532', '0.689723090863468', '0.0898799772920887' ]; $VAR9 = [ '0.881519354220241', '0.241177761248786', '0.0205053866112115', '0.603122445013391', '0.928112703209664', '0.998063438813863', '6.73439886137409e-05', '0.0458526555890988' ]; $VAR10 = [ '0.846538453492274', '0.476197190468215', '0.0406784525947511', '0.953831989623246', '0.532836608719612', '0.594838497956994', '0.567180056349987', '0.0569732813725855' ]; $VAR11 = [ '0.833697200489002', '0.235844577032947', '0.0150738782858431', '0.908823928444112', '0.68001744230006', '0.492227307799255', '0.279501173375569', '0.102265774447215' ]; $VAR12 = [ '0.868417559904734', '0.507294145031635', '0.000723150881484355', '0.832446613214082', '0.557188809972536', '0.649598781883472', '0.268864943271587', '0.00261231173292181' ]; $VAR13 = [ '0.839883317601069', '0.56247041897682', '0.0296878804785333', '0.947496864461115', '0.446067745557922', '0.361857848522104', '0.853353342787473', '0.119794177768551' ]; $VAR14 = [ '0.720273462270738', '0.721527328055604', '0.0318964037770804', '0.952425731950007', '0.157990619252408', '0.335544731201906', '0.921998700620286', '0.0545585051273901' ]; $VAR15 = [ '0.84854733807248', '0.304600066831685', '0.0053901187849178', '0.672347152033614', '0.553582301168125', '0.293836826063384', '0.824434216172819', '0.00474026079358554' ]; $VAR16 = [ '0.913159101858587', '0.402153592288389', '0.00874312116052933', '0.773905860902511', '0.260454449084309', '0.596307027345741', '0.856086784138162', '0.0688198451329073' ]; $VAR17 = [ '0.763108007701617', '0.0671684234096718', '0.00139187110293942', '0.833693711486085', '0.449160450294275', '0.666461938030674', '0.909321887294487', '0.000370227961923897' ]; $VAR18 = [ '0.86186778574824', '0.341603079727888', '0.0467489146423834', '0.808193008319177', '0.735103988656283', '0.605341884322004', '0.927172687395486', '0.00380991313392766' ]; $VAR19 = [ '0.924327680660234', '0.206086072895373', '0.00197098333344035', '0.662636140875682', '0.634995083611723', '0.536036556698047', '0.98026013068323', '6.10657168843021e-06' ]; $VAR20 = [ '0.945693978138935', '0.0812981819696328', '1.23564931552485e-05', '0.588098578219685', '0.289795260205602', '0.195648966545929', '0.963030248322442', '6.17559581198282e-06' ]; $VAR21 = [ '0.919307888462351', '0.0905308476750052', '0.00149291481604745', '0.511386883573506', '0.644826843893881', '0.710918480898483', '0.92687141938622', '5.14813949189956e-05' ]; $VAR22 = [ '0.930466185296132', '0.0557092346719651', '0.00277612451274991', '0.565888267318915', '0.598543533845517', '0.529104458545457', '0.958321915352803', '0.0211415730785755' ]; $VAR23 = [ '0.935408668005705', '0.00605204008645429', '0.000497324668511658', '0.241146928513077', '0.522719432872571', '0.512682927820886', '0.548849362158464', '0.00474324345225836' ]; $VAR24 = [ '0.947003617156614', '0.411758207698042', '0.0179252771090724', '0.436803717781167', '0.504615072051647', '0.460618475086394', '0.849353383554262', '0.0108655965967626' ]; $VAR25 = [ '0.873182595846068', '0.0752207254786443', '0.00118609219395312', '0.558292466748528', '0.644804617968847', '0.775830367827506', '0.740538708477446', '0.000230839902353635' ]; $VAR26 = [ '0.946322483336695', '0.0436212590299125', '0.00701662772429716', '0.570549157233995', '0.654533685473931', '0.557591469904858', '0.9743513768804', '2.07156177031988e-06' ]; $VAR27 = [ '0.902361917335784', '0.347598807404928', '0.00478838839977221', '0.678765399565096', '0.696665707919491', '0.813225506137542', '0.521927608523651', '0.00700293248374122' ]; $VAR28 = [ '0.831280971758915', '0.295760977138973', '0.000503610526340607', '0.643090352920345', '0.573526907163606', '0.748316866361385', '0.730463963075407', '3.53981667269682e-05' ]; $VAR29 = [ '0.962446001554752', '0.65066682183642', '0.0522376122483446', '0.703259016543464', '0.400288973337398', '0.431021357078873', '0.405194387317574', '0.00787265902624026' ]; $VAR30 = [ '0.982764998644814', '0.543187161957487', '0.043933470151048', '0.594584316308716', '0.35172602809409', '0.412139300334433', '0.446724030413039', '0.0123284647989544' ];

Author Fisher Chi-Square Stat
$VAR1 = '0.223824619077403'; $VAR2 = '0.246175264071738'; $VAR3 = '0.0215803752301491'; $VAR4 = '0.156787359156108'; $VAR5 = '0.129970897564168';

Control Fisher Chi-Square Stat
$VAR1 = '0.00797010499147885'; $VAR2 = '3.48252254091085e-05'; $VAR3 = '0.000544260892192801'; $VAR4 = '0.0561486867527354'; $VAR5 = '1.38412590127888e-15'; $VAR6 = '1.38060304383322e-06'; $VAR7 = '0.00979213239479129'; $VAR8 = '0.0896643074555557'; $VAR9 = '0.00183476309997838'; $VAR10 = '0.355323420852068'; $VAR11 = '0.173473939247785'; $VAR12 = '0.00733473154924831'; $VAR13 = '0.395340014415993'; $VAR14 = '0.213502954905526'; $VAR15 = '0.026274042370201'; $VAR16 = '0.16425148600283'; $VAR17 = '0.00158186741139972'; $VAR18 = '0.146177331588006'; $VAR19 = '0.000298941756287377'; $VAR20 = '8.99126004726074e-07'; $VAR21 = '0.000596690968465798'; $VAR22 = '0.0244172542353317'; $VAR23 = '0.000285219473362224'; $VAR24 = '0.0923302977779948'; $VAR25 = '0.00115482086869474'; $VAR26 = '0.000109937463631632'; $VAR27 = '0.0521352495884949'; $VAR28 = '0.000438249568822137'; $VAR29 = '0.126191170635842'; $VAR30 = '0.118874797205066';

Bayesian Author Test: Posterior Probabilities from Equal Priors, Fisher Method
$VAR1 = '0.287567189256684'; $VAR2 = '0.316283030193163'; $VAR3 = '0.0277262075709931'; $VAR4 = '0.201438520790728'; $VAR5 = '0.166985052188432';

Author Z-Scores
$VAR1 = [ '-0.952587647470627', '0.225891701110482', '1.95653304576249', '-0.326576300159444', '-1.07652381507353', '0.110335913480118', '-0.994028870601296', '1.93289798487342' ]; $VAR2 = [ '-1.40655724655177', '1.13752769280662', '1.67036626426366', '-0.493210183681236', '-1.17213182474263', '-0.231814219961264', '0.123831471684511', '1.50240245369755' ]; $VAR3 = [ '-2.26742375134353', '0.934757578687965', '2.31765160443776', '-0.386225698493239', '-0.0969194745327852', '0.0845870268549117', '-0.491829856299489', '2.8612172427164' ]; $VAR4 = [ '-1.36970510211432', '0.161866838365508', '1.96930646225995', '0.0859962540847563', '-0.0527314969654838', '-0.145150169192749', '0.467084219702629', '1.66019697582756' ]; $VAR5 = [ '-1.01595019500285', '0.236360820094288', '1.94802307534207', '-0.338167152718716', '-0.33771069536597', '-0.509519010708937', '0.0856464385705166', '2.2632736876356' ];

Control Z-Scores
$VAR1 = [ '-1.562750215374', '1.879239889875', '2.61365970966078', '-0.137831556325413', '-2.20876872614851', '-1.49749116636812', '1.76935323013172', '1.86555710459996' ]; $VAR2 = [ '-1.98191666311323', '1.7875407725204', '3.65330131443652', '0.0831726917691572', '-1.58846947346596', '0.122336988211331', '1.9737865470545', '3.06297892471217' ]; $VAR3 = [ '-1.80158510337094', '1.46672304140005', '1.49530551740099', '1.09313745473728', '0.407463045862167', '0.951659154804352', '-0.604340185595079', '3.91575061464672' ]; $VAR4 = [ '-1.2756226995684', '0.759852627766094', '2.51205385295813', '-0.522232967867094', '-0.512321076115884', '0.198143811351516', '0.370015244942144', '1.9164132015108' ]; $VAR5 = [ '-1.8204247307665', '-0.274503910531006', '2.55947259615976', '-0.252181852907997', '-1.12841194600149', '-1.9702932782606', '8.41560733222024', '3.60833128947741' ]; $VAR6 = [ '-1.35660731440584', '0.0189015992374581', '2.77541789018356', '0.149334908180341', '-1.21762599281211', '-2.14158159622678', '5.27566556275658', '2.31046855919157' ]; $VAR7 = [ '-1.46546408115872', '0.362507008035649', '2.55744805236402', '0.0807292104650783', '-1.40487871737254', '-0.658165326106121', '1.90349354378545', '2.46869903088719' ]; $VAR8 = [ '-1.56410389937735', '0.396088761031676', '2.76184184204683', '-0.778678104076362', '0.673971714032212', '-0.109046858651362', '-0.495065345202728', '1.34149370740555' ]; $VAR9 = [ '-1.18261585996699', '0.702519333860142', '2.04342132221687', '-0.261437400849815', '-1.4618773445184', '-2.8883146355625', '3.81772492276134', '1.68647005635777' ]; $VAR10 = [ '-1.02169982807242', '0.0597005425951114', '1.74286716173904', '-1.68320190805825', '-0.0824026575541966', '-0.240009281892854', '-0.169199455294834', '1.58069985079037' ]; $VAR11 = [ '-0.968879271339788', '0.719733722105658', '2.16814378158533', '-1.33354689187522', '-0.467747276855785', '0.019484627821346', '0.58432396759918', '1.26874572126044' ]; $VAR12 = [ '-1.11894190390695', '-0.018284866484621', '3.18524765928135', '-0.963878991741967', '-0.143845855940843', '-0.384237136457202', '0.616249518555251', '2.79284800875379' ]; $VAR13 = [ '-0.993978722918133', '-0.157235814195821', '1.88540232309256', '-1.62105267797836', '0.135602807450249', '0.353496910482135', '-1.05092452256838', '1.17601600726543' ]; $VAR14 = [ '-0.583654032175555', '-0.587384708552697', '1.85362652323275', '-1.66884276262483', '1.0027508021814', '0.424652914834626', '-1.41864393324536', '1.60217415171538' ]; $VAR15 = [ '-1.03022321238167', '0.511215329147207', '2.54974294011026', '-0.44640332629829', '-0.134717557603598', '0.542210137824976', '-0.932397069987965', '2.59422212628518' ]; $VAR16 = [ '-1.36046742017709', '0.247776600509353', '2.37632104510348', '-0.751772218861382', '0.641945119594901', '-0.24379962393937', '-1.06290200903479', '1.4846373904533' ]; $VAR17 = [ '-0.716336176712662', '1.49721604525126', '2.99066113160097', '-0.968865287408608', '0.127783028667577', '-0.430163967436799', '-1.33659007330793', '3.37414411145234' ]; $VAR18 = [ '-1.08874936170472', '0.408091613223281', '1.67722839853866', '-0.871257204049364', '-0.628323614103852', '-0.267198472605907', '-1.45505202206424', '2.66846700723787' ]; $VAR19 = [ '-1.43479724189182', '0.820077572700049', '2.88276878769282', '-0.419668046136792', '-0.345112131026576', '-0.0904537725731541', '-2.05915160865352', '4.3737478584928' ]; $VAR20 = [ '-1.60446254124194', '1.3963915385861', '4.21740501588483', '-0.222656504488737', '0.553982825700753', '0.857266393554948', '-1.78698836483918', '4.37129476274301' ]; $VAR21 = [ '-1.40043037274669', '1.33749243124416', '2.9691930366686', '-0.0285467568539454', '-0.371390676354103', '-0.556069837835763', '-1.45287883860446', '3.88350175167121' ]; $VAR22 = [ '-1.47927119468866', '1.59184927269347', '2.7731150341896', '-0.165915654075548', '-0.249578906482199', '-0.0730192150302776', '-1.73153662096633', '2.0307228363887' ]; $VAR23 = [ '-1.51733212580651', '2.50909537526679', '3.29203584427631', '0.702618254612758', '-0.056980288229819', '-0.031796954376041', '-0.122755077706752', '2.59400586934041' ]; $VAR24 = [ '-1.616469502566', '0.223024512497801', '2.09861855632989', '0.15907817688146', '-0.0115686203345688', '0.0988760374017029', '-1.03366425401867', '2.29503374156144' ]; $VAR25 = [ '-1.1415649851929', '1.43797307133299', '3.03918588256868', '-0.14664164117924', '-0.371330987106656', '-0.758187016892548', '-0.645007235765195', '3.50205759568749' ]; $VAR26 = [ '-1.61019580264826', '1.71012654793928', '2.45641102324647', '-0.177772584938928', '-0.397589381679927', '-0.144865743374031', '-1.94898523389401', '4.60407037535678' ]; $VAR27 = [ '-1.29512705342936', '0.391810988898619', '2.59074736823873', '-0.464248917706212', '-0.514834420063235', '-0.889845696692425', '-0.0549923610100549', '2.45711294812715' ]; $VAR28 = [ '-0.9592399576412', '0.536631669071062', '3.28850189830948', '-0.366731176279545', '-0.18536074157019', '-0.669202767040099', '-0.614216847443137', '3.97359355023525' ]; $VAR29 = [ '-1.77980505257835', '-0.38712102054817', '1.62353404383641', '-0.533796866837604', '0.252599088826909', '0.173774612975108', '0.239924443147907', '2.41476609815078' ]; $VAR30 = [ '-2.11453041603522', '-0.108466781748738', '1.70675875728794', '-0.239353578801156', '0.380664363230985', '0.222045309889238', '0.133942740841451', '2.24673566178505' ];

Author Stouffer Z-Sum Stat
$VAR1 = '0.378397391725781'; $VAR2 = '0.344702668871137'; $VAR3 = '0.14800266767106'; $VAR4 = '0.163106742403646'; $VAR5 = '0.20483604023716';

Control Stouffer Z-Sum Stat
$VAR1 = '0.168022992872066'; $VAR2 = '0.00595617550879792'; $VAR3 = '0.00718170961673434'; $VAR4 = '0.111526086579875'; $VAR5 = '0.00061759320093317'; $VAR6 = '0.019912962718673'; $VAR7 = '0.0870431288331792'; $VAR8 = '0.21558624995552'; $VAR9 = '0.192618368327413'; $VAR10 = '0.473678026906035'; $VAR11 = '0.24082154639102'; $VAR12 = '0.0804732481182634'; $VAR13 = '0.538400294885502'; $VAR14 = '0.41260174480624'; $VAR15 = '0.0982199965238923'; $VAR16 = '0.318877109423758'; $VAR17 = '0.0543160122260218'; $VAR18 = '0.437741863875048'; $VAR19 = '0.0937786591354858'; $VAR20 = '0.00296674054310105'; $VAR21 = '0.0607062045076397'; $VAR22 = '0.170216813938258'; $VAR23 = '0.00458974117441872'; $VAR24 = '0.216993290394936'; $VAR25 = '0.0410843209792094'; $VAR26 = '0.0561568292099433'; $VAR27 = '0.216195032279433'; $VAR28 = '0.0384325991193168'; $VAR29 = '0.239324659602512'; $VAR30 = '0.215452361608467';

Bayesian Author Test: Posterior Probabilities from Equal Priors, Stouffer Method
$VAR1 = '0.305394263886436'; $VAR2 = '0.27820016765834'; $VAR3 = '0.119448935788086'; $VAR4 = '0.131639024529466'; $VAR5 = '0.165317608137672';

Bayesian Comparison of Best Author to Best Control: from Equal Priors, Stouffer Method
$VAR1 = 1; $VAR2 = '0.412738161594227'; $VAR3 = 13; $VAR4 = '0.587261838405773';