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Quantiles of the chi-squared distribution
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Numbers
$\nu$
$p$ 
$\chi^2_{\nu,p}$
1
1/200:
0.00003927042222051590213508943204118802955586375025883917364752993842911125842989123899029576090039413498
comment: This is the lower cutoff for a central two-sided 1% chi-squared test.
1
1/100:
0.0001570878579097019775004279621798084171494065605628493701569048641894871218150866037442771372017028460
1
1/40:
0.0009820691171752559123376890822612811095402388790822216203050790655852397232651234258401078112376138218
comment: This is the lower cutoff for a central two-sided 5% chi-squared test.
1
1/20:
0.003932140000019522731309468171167161381315046525910801158788674201132225661184322115547823975371537408
1
1/10:
0.01579077409343122486815523826460976830209811884018340075286158292835789150775145523342380884598002531
1
1/4:
0.1015310442676215452066890820189321284981005281658400123226471751858823406928074653643753968834201733
1
1/2:
0.4549364231195727519425166469796493963164211065902219370421378507825926213917626803695529782848170800
1
3/4:
1.323303696931465949698609012784994305587966184332336338771145461064661460168901283390198119058228954
1
9/10:
2.705543454095414567073032272382736120080843886733790997120558175156301266593972611821605553369839785
1
19/20:
3.841458820694125958361375437362596846213368142014833809793389672284199753605850082117303011725898043
comment: This is the one-sided 5% upper critical value.
1
39/40:
5.023886187314888956170774028504971958550750546509231616192964473378266607700745072958966479733440277
comment: This is the upper cutoff for a central two-sided 5% chi-squared test.
1
99/100:
6.634896601021215138436525933979198124855376749891367873469568967247984659871408255251504744324936718
comment: This is the one-sided 1% upper critical value.
1
199/200:
7.879438576622417357356305519120162069612567504555338028505112208395270824936299807012008999126320033
comment: This is the upper cutoff for a central two-sided 1% chi-squared test.
1
999/1000:
10.82756617066273229311292322202367866634316066953213235166933560867210965666807249201720334393467502
comment: This is the one-sided 0.1% upper critical value.
2
1/200:
0.01002508364708856408618747791673556277319566209665741456174964696887927188696755190374692575479447350
comment: This is the lower cutoff for a central two-sided 1% chi-squared test.
2
1/100:
0.02010067170700288236709771511709541217103001534925974675739885105916601800850062729941638509819525539
2
1/40:
0.05063561596857975080744603822574606859868650953265383224189615130680178614744553034906688165642819174
comment: This is the lower cutoff for a central two-sided 5% chi-squared test.
2
1/20:
0.1025865887751010668523922885093744768784447233797988232320953481033470591656998142554042965405541802
2
1/10:
0.2107210313156526024550019616786255966122407459665481451278784673851680464802690929775313909242682415
2
1/4:
0.5753641449035618548784380119876548630070194217955221130133313706985859014415609286762217983582105726
2
1/2:
1.386294361119890618834464242916353136151000268720510508241360018986787243939389431211726653992837375
2
3/4:
2.772588722239781237668928485832706272302000537441021016482720037973574487878778862423453307985674750
2
9/10:
4.605170185988091368035982909368728415202202977257545952066655801935145219354704960471994410179196597
2
19/20:
5.991464547107981986870447152285081551353203245978056460308015820921932463294094391683721064172033972
comment: This is the one-sided 5% upper critical value.
2
39/40:
7.377758908227872605704911395201434687504203514698566968549375839908719707233483822895447718164871347
comment: This is the upper cutoff for a central two-sided 5% chi-squared test.
2
99/100:
9.210340371976182736071965818737456830404405954515091904133311603870290438709409920943988820358393193
comment: This is the one-sided 1% upper critical value.
2
199/200:
10.59663473309607335490643006165380996655540622323560241237467162285707768264879935215571547435123057
comment: This is the upper cutoff for a central two-sided 1% chi-squared test.
2
999/1000:
13.81551055796427410410794872810618524560660893177263785619996740580543565806411488141598323053758979
comment: This is the one-sided 0.1% upper critical value.
3
1/200:
0.07172177458649197649481532114768118280591286584814303154427220439844845778231184800570004456275029771
comment: This is the lower cutoff for a central two-sided 1% chi-squared test.
3
1/100:
0.1148318018991170375204037025714191953568283586325343861028466163524278056005272489625722855571318044
3
1/40:
0.2157952826238978684492461653809326153219605930646216510301021159382583619172789572831931975048397826
comment: This is the lower cutoff for a central two-sided 5% chi-squared test.
3
1/20:
0.3518463177492713960244375913411267589649329267106483620682757491759066277391728197980432757842468488
3
1/10:
0.5843743741551832561590073112017700815902669336160993138784048875948672430268854056214926828820332272
3
1/4:
1.212532903045669072754643001120909710634311146351363728319570874685479955843246530542966453225878822
3
1/2:
2.365973884375338266139162601265045050503019812863214862827028454343928743216276386167194480796306491
3
3/4:
4.108344935632316840892611443777286524080097330070712094719709756897139763398129450084481326931259800
3
9/10:
6.251388631170323196401316360643126517695174324668454364655408803730863730143249312946662844828481360
3
19/20:
7.814727903251179955268994873520450269165817789903348823885707864997426197395368583740468716931886875
comment: This is the one-sided 5% upper critical value.
3
39/40:
9.348403604496147796125861612468029616069721700711344241786989703339619297589409800089342615629766244
comment: This is the upper cutoff for a central two-sided 5% chi-squared test.
3
99/100:
11.34486673014437193131471997493358436398899282108408950071810480206381613586506668209296311184277219
comment: This is the one-sided 1% upper critical value.
3
199/200:
12.83815646659865174123035172753822960602484265765001478037034073853001668068002088026191359650068231
comment: This is the upper cutoff for a central two-sided 1% chi-squared test.
3
999/1000:
16.26623619623813091238662458883012263823513628190827977794007174449178764097785155746076612000943599
comment: This is the one-sided 0.1% upper critical value.
4
1/200:
0.2069890934961820757796889606555863527456279076198464009906043508883825673752721620663976039286728396
comment: This is the lower cutoff for a central two-sided 1% chi-squared test.
4
1/100:
0.2971094805065318953640309904419843657519407037988684180371494125010494287789033601941166998840161337
4
1/40:
0.4844185570879298058040805130058524186442720138389956727897342670660920368122480917713308764460882581
comment: This is the lower cutoff for a central two-sided 5% chi-squared test.
4
1/20:
0.7107230213973241044476520655706649461428798129496937605840866382534175494553239387214810262201131574
4
1/10:
1.063623216779224040291260595499826265368249061956977112486093955751440534036841013370039204672243544
4
1/4:
1.922557526229554191696535498988872465990948295907894686886233777534038343210576123245319799709924170
4
1/2:
3.356693980033321306825769024189046169648917530703204432796683736798095291371426873994939648376241275
4
3/4:
5.385269057779391541507530755640293286380580139306209850353212251193296595706932919435114450082374509
4
9/10:
7.779440339734858115807960449853614045905352783570596876419156540401477048219152799351732865232887637
4
19/20:
9.487729036781156751700547571666639110068923702879902004364225127816445516706070589550692203752727216
comment: This is the one-sided 5% upper critical value.
4
39/40:
11.14328678187779719445456551348144824767047445147653419867803546248843847681019187701886363168673419
comment: This is the upper cutoff for a central two-sided 5% chi-squared test.
4
99/100:
13.27670413598762453874247881004876976223909812373256588716323216552048608150375427903806939540127148
comment: This is the one-sided 1% upper critical value.
4
199/200:
14.86025900056024484264842268081820322830606293743529759900482332371398825734671295779982392372735333
comment: This is the upper cutoff for a central two-sided 1% chi-squared test.
4
999/1000:
18.46682695290317146086267311174301867684348038490189933014021245778713587484937097792710766281265188
comment: This is the one-sided 0.1% upper critical value.
5
1/200:
0.4117419038324988373343595747076858684083299098596768428612838872338128524199951601647305945412448701
comment: This is the lower cutoff for a central two-sided 1% chi-squared test.
5
1/100:
0.5542980767282771405251536051059628899765984972424837279071623243434429664019481011972416508030367986
5
1/40:
0.8312116134866624177998475472683450530683900747141073422222026427581546710069634688196582465479073540
comment: This is the lower cutoff for a central two-sided 5% chi-squared test.
5
1/20:
1.145476226061769249946806762589307451725836161245908382026268137020099768670571283361692355903538272
5
1/10:
1.610307986962322996736008958555193073794426434328954032767705263242098464065485040887091585740470798
5
1/4:
2.674602809432163115464071152068513696678537465755030949489577230534995792992315509065668511192835578
5
1/2:
4.351460191095527317158107776624574681885701139586852962841283446192515631934156728276081054148389675
5
3/4:
6.625679763829250769009168371945427874309917383102235571129327237220885860888636844914870035681712088
5
9/10:
9.236356899781118451435930911834588638342930897059207773534978378134410242288097984352398191414105570
5
19/20:
11.07049769351635417816027083604231362622254716038599488468117050270042762560341506501912777722121362
comment: This is the one-sided 5% upper critical value.
5
39/40:
12.83250199403002822170886142093766286961531177865550887542365844096971542910482527386177374677219391
comment: This is the upper cutoff for a central two-sided 5% chi-squared test.
5
99/100:
15.08627246938899011264514807462769474000396486780973130056432775531271393486536039575097018093847420
comment: This is the one-sided 1% upper critical value.
5
199/200:
16.74960234363904422408394695716377683261015968403636920978788967371980095444000724059415926340743439
comment: This is the upper cutoff for a central two-sided 1% chi-squared test.
5
999/1000:
20.51500565243287843253648783699278988359204727059424666014728744949747809276467848026457202537215391
comment: This is the one-sided 0.1% upper critical value.
6
1/200:
0.6757267774554665914809921423012269369270058025994073526913316426226427545308540463919005261850606770
comment: This is the lower cutoff for a central two-sided 1% chi-squared test.
6
1/100:
0.8720903301565862931424448851827016609547494800120235586234805526981480358091143518459882058096786174
6
1/40:
1.237344245791202573139634744491495805386800638056583134161974740755054269307747663562760571248396557
comment: This is the lower cutoff for a central two-sided 5% chi-squared test.
6
1/20:
1.635382894327906653039719817589438909807401321043804928860897180941325395320674555293696457615750221
6
1/10:
2.204130656498642148183222983838534572662663463448507744696972261853539591565868043887089241573787518
6
1/4:
3.454598835721038786124883038369563851755726248280227915419066788817179243498584677226888213763943649
6
1/2:
5.348120627447120635826914529183389979245575590055644556175437636275131098339837152890434990767164941
6
3/4:
7.840804120585120098621159984380327222414044564820275312259511502714988021741644241457430205516735910
6
9/10:
10.64464067566841980871264535399962681696978589713607753439555320681693297891355755230320517674291768
6
19/20:
12.59158724374397948356943714571740522879317418349922627275511839396860927579925352615539603802729126
comment: This is the one-sided 5% upper critical value.
6
39/40:
14.44937533544792163009763650920334905507530296011885034667345806801287675022225971818136926608151742
comment: This is the upper cutoff for a central two-sided 5% chi-squared test.
6
99/100:
16.81189382977093105466018063515134733464672995923284944505526241430542606242999742967189539052734608
comment: This is the one-sided 1% upper critical value.
6
199/200:
18.54758417851108943185412609190933127264034877907492725221746084517351727310777824499554785031054914
comment: This is the upper cutoff for a central two-sided 1% chi-squared test.
6
999/1000:
22.45774448482532526091250735593863886014201359097641539771735115984716937600941440287350807642289193
comment: This is the one-sided 0.1% upper critical value.
7
1/200:
0.9892556831329502678371654469382202085286454115553612003462331540350072800580412860474619667071386756
comment: This is the lower cutoff for a central two-sided 1% chi-squared test.
7
1/100:
1.239042305567929749490533206070850114904643785309415615294575830895978389358336881983433366186914456
7
1/40:
1.689869180677354580598048068167962302792135665212741162194150846178036516920980441556256591524677888
comment: This is the lower cutoff for a central two-sided 5% chi-squared test.
7
1/20:
2.167349909298057117603460310710147823099556752088667676891345071617255222711887151716602424604985945
7
1/10:
2.833106917815344026790315550158320483436952648936871931162268853357121589952359718808297780452073186
7
1/4:
4.254852183546515743793885578753688950013039535694904915749064475386050033850747461623329518067367289
7
1/2:
6.345811195521517535725073343645364660930624068196930042100795955058417606329878633922470026674722061
7
3/4:
9.037147547908140622891525803546492567370159672782424156445261492426343782962101829523308484189901857
7
9/10:
12.01703662378052911781503802114356882888694761615364184057225505594431923762667001250448231800132458
7
19/20:
14.06714044934016874262697322664113973692104587566191919477607439493648307772615227967044490790352077
comment: This is the one-sided 5% upper critical value.
7
39/40:
16.01276427462932423335252314092845350957116623285616770067448041326485056715724089923569710101455956
comment: This is the upper cutoff for a central two-sided 5% chi-squared test.
7
99/100:
18.47530690658236373533639939263644011019951472941756268432777016740404661707458732687840115540267592
comment: This is the one-sided 1% upper critical value.
7
199/200:
20.27773987496262485823265756685213467365019384749816416115397567018173582621006511817386522559137120
comment: This is the upper cutoff for a central two-sided 1% chi-squared test.
7
999/1000:
24.32188634785685535200692231730749281669550263600591031940937174254204417480340519158876508148371981
comment: This is the one-sided 0.1% upper critical value.
8
1/200:
1.344413087014810298537955401395086234463071623269880614631799458527714698497292000018635418831767245
comment: This is the lower cutoff for a central two-sided 1% chi-squared test.
8
1/100:
1.646497372690770313881253041410583786983837531461742854743945115217734093538614762978154109819207403
8
1/40:
2.179730747252649750592034397217631099390038896091788850860161951395996335858515086803231763390067682
comment: This is the lower cutoff for a central two-sided 5% chi-squared test.
8
1/20:
2.732636793499661872815080513588438706581969951475235238354207768598656588843012605360777671565153692
8
1/10:
3.489539125649822767402913591580179549256662167727849198931114852245129787235739642159946144739401555
8
1/4:
5.070640423800186362318284708122197993211256141771132681724201967594022664209887368236172827108636006
8
1/2:
7.344121497701792207894692147412641364493885944106767490176177661563106102370023161391774498277513237
8
3/4:
10.21885497024675932953313091290499541948973357021122974778463046933916614252190585401755879541384828
8
9/10:
13.36156613651172727548968576049479636429296599252308861068926205592886423364769296062713134624152610
8
19/20:
15.50731305586545382217400671913279347696763951273961265568939671903238752019773563588147416514002902
comment: This is the one-sided 5% upper critical value.
8
39/40:
17.53454613948465207938276068130489513774368862767223433252473336351827024475910683413289995127575689
comment: This is the upper cutoff for a central two-sided 5% chi-squared test.
8
99/100:
20.09023502966323317352919521174826311461637906135803330917440033553337389270988058998318002744043917
comment: This is the one-sided 1% upper critical value.
8
199/200:
21.95495499065953157969557625704468655320256725770010698097731142899978249912219704850434522619249865
comment: This is the upper cutoff for a central two-sided 1% chi-squared test.
8
999/1000:
26.12448155837614147337748592840973456803871318557709036988280227324098656581213227343332548695280071
comment: This is the one-sided 0.1% upper critical value.
9
1/200:
1.734932904996660111462331736170093983153826729240830694458750670244392540217294357143893472551037685
comment: This is the lower cutoff for a central two-sided 1% chi-squared test.
9
1/100:
2.087900735870727244104397517847464317072716543432813195520058500088073738534142591877537954823689278
9
1/40:
2.700389499980357916442026420821910161512610739217115582086829731614058866482874008640725850095149195
comment: This is the lower cutoff for a central two-sided 5% chi-squared test.
9
1/20:
3.325112843066814824072141452441525693679745948915858901842598537359110169044236929367914897924891638
9
1/10:
4.168159008146106860460111245428602050953027744255008441716642180277274974268796314980239599015718590
9
1/4:
5.898825882969973214707914048278847919812162274167489657806775885352828677285372599352637637761968595
9
1/2:
8.342832692252953794999776335737343370352380896811492650623563724707936174165637555096966185082716726
9
3/4:
11.38875144047037028723328302873192800511756056330494754120628905746142467018102269507468060677751250
9
9/10:
14.68365657325983770105565874613566126111102530733465056030881751449976972182044932752079474413646493
9
19/20:
16.91897760462044982796125183595669677225404651568073039132142066550002031609512939042436134520026033
comment: This is the one-sided 5% upper critical value.
9
39/40:
19.02276779864163521266194074783800758620399844233392160815492784849953317529711223011867489746352284
comment: This is the upper cutoff for a central two-sided 5% chi-squared test.
9
99/100:
21.66599433346192581735644633595006669920264955443886695056239201669139222948489689967482476326804226
comment: This is the one-sided 1% upper critical value.
9
199/200:
23.58935078125738707321408395786544729284829404398137376077573778262584786072859824716295402118850192
comment: This is the upper cutoff for a central two-sided 1% chi-squared test.
9
999/1000:
27.87716487125657346876590926623457099761428006180270125627250671811547938978369787495700027025128780
comment: This is the one-sided 0.1% upper critical value.
10
1/200:
2.155856481304638953284587402744524218047916925947176226056075810275219652051596489828794192308432764
comment: This is the lower cutoff for a central two-sided 1% chi-squared test.
10
1/100:
2.558212160187206057513429077200199461022972799128383945975895948993825362353773547789225959002212389
10
1/40:
3.246972780236841076156731709970378555915816072902614330803425686677276430036548061412394561128419672
comment: This is the lower cutoff for a central two-sided 5% chi-squared test.
10
1/20:
3.940299136119060031321071526792296411783387010363245486809215639331847011749458256748631903046999861
10
1/10:
4.865182051925329002774977376351822349154656373686507885831506349820110249944144446143011093333706167
10
1/4:
6.737200771954642115831639103250294892283788287821337312812671984555905350360125088835433149092718573
10
1/2:
9.341817765591967440625350116150302942439971032708353533839156645081788915614104699933820091184028423
10
3/4:
12.54886139688937700694355310744964218440021318125481011362986444131351466162913133144687484322410044
10
9/10:
15.98717917210526087507116442145191941709029562904298251115620070758277895442628846258220060729617372
10
19/20:
18.30703805327514687180303099695903319758448841784389514351064861945007417744319113134497092951182199
comment: This is the one-sided 5% upper critical value.
10
39/40:
20.48317735080739655217157327407234073985879489330679904490520132684094482321104159130336376530156212
comment: This is the upper cutoff for a central two-sided 5% chi-squared test.
10
99/100:
23.20925115895435967827231296406495291046250552047647653657526628076158518059989143264940272685438466
comment: This is the one-sided 1% upper critical value.
10
199/200:
25.18817957197117151470583546941350348757181191594677300073935886105392269715214671177412243325084756
comment: This is the upper cutoff for a central two-sided 1% chi-squared test.
10
999/1000:
29.58829844507441879369290283751674940458268091351407450810522701642140080959657639753115066491541577
comment: This is the one-sided 0.1% upper critical value.
11
1/200:
2.603221890515112929071670264340717975518879858240534644305017964551432329703555175384229212309911646
comment: This is the lower cutoff for a central two-sided 1% chi-squared test.
11
1/100:
3.053484106640680004880626991771652459731101924444608636352676313219519634796112839466768832149994390
11
1/40:
3.815748252236098594724121184820153684206796978092504002175901804424665532829930557563240174628042960
comment: This is the lower cutoff for a central two-sided 5% chi-squared test.
11
1/20:
4.574813079322223778605382733729717095581317058787848127993254043980015032466155985036560882258132296
11
1/10:
5.577784789799851168191031475262799894250980750876848792016254009428376844366236151817321054847142479
11
1/4:
7.584142785441284956375945541459848596064408480992059655585314740998999702517652891217094252994600612
11
1/2:
10.34099807439182402591928811480683553439324516512105095171349250906641346615180987105679127304424928
11
3/4:
13.70069274601150851138409506617003085924628148970371565932099769047665086126894878305103987044897338
11
9/10:
17.27500851750007201491511787571699445406989021123925348905045603126588452316933569452249259678164580
11
19/20:
19.67513757268249551312192516118704228041224532335907318511254109689500528677677708412650368382784368
comment: This is the one-sided 5% upper critical value.
11
39/40:
21.92004926102120799174723579974516149368061325852319232129074956007359080502355367589974874900189581
comment: This is the upper cutoff for a central two-sided 5% chi-squared test.
11
99/100:
24.72497031131828269337070965516108829150853038088825182877107986730630262805243296851250520389810483
comment: This is the one-sided 1% upper critical value.
11
199/200:
26.75684891646963542803086052830460742887974152706153615851458635634926399628715470604828127954317892
comment: This is the upper cutoff for a central two-sided 1% chi-squared test.
11
999/1000:
31.26413362023999354339258610003992238106098388958430832558626952375245922197518254458710458182891431
comment: This is the one-sided 0.1% upper critical value.
12
1/200:
3.073823638089333166623713162526033881025673759885841558192803124599826886453858149225348391034815676
comment: This is the lower cutoff for a central two-sided 1% chi-squared test.
12
1/100:
3.570568970604391801298061017395571148464373037059760686722212734934664355933786107828888960384392960
12
1/40:
4.403788506981701623442645883853896853304150104505159053797867105548632101163999268399520508373048208
comment: This is the lower cutoff for a central two-sided 5% chi-squared test.
12
1/20:
5.226029488392640306219014951805703418867937728636755320288025303529025236556885015823477181641876948
12
1/10:
6.303796059584323297261273120013743196750650539253531251420782275294287572606532888971470114398070923
12
1/4:
8.438418766135793393067237493071747298400173208059664951200886440454262549366424028553815118673522225
12
1/2:
11.34032237742414046624915464761475033665037025401770208694042297221058491890932422903456720632970605
12
3/4:
14.84540367104017790671529361809973233149154988882467857990541929481099819205314574291284823285620102
12
9/10:
18.54934778670324417502504076711572025363185485893003787147889240140512650751115230607135983324366621
12
19/20:
21.02606981748306539652247183839937850248837285768712047501846602011026294918400099589148617014803259
comment: This is the one-sided 5% upper critical value.
12
39/40:
23.33666415864533926287896119370544971455651183913870782217413024738301208095293923611016255382417287
comment: This is the upper cutoff for a central two-sided 5% chi-squared test.
12
99/100:
26.21696730553585011511114722504778118520950064825850816625578584954223015606531958775140698081533338
comment: This is the one-sided 1% upper critical value.
12
199/200:
28.29951882204603023571036595391308945387219348687767054255408758228456004164025507694695470450289457
comment: This is the upper cutoff for a central two-sided 1% chi-squared test.
12
999/1000:
32.90949040736021321486473533009994129756676558891446541169407437206754930624200176722261150194289952
comment: This is the one-sided 0.1% upper critical value.
13
1/200:
3.565034579729538845494052617021005561825354833546193444207051176273613748181513291579411815853790158
comment: This is the lower cutoff for a central two-sided 1% chi-squared test.
13
1/100:
4.106915471504403928189090301711207935332372488093572942495001826914782803408984565009203984214542123
13
1/40:
5.008750511810331684643930366981724844067794973790577214815110205118444128072055260465629631006770369
comment: This is the lower cutoff for a central two-sided 5% chi-squared test.
13
1/20:
5.891864337709847883561817001075537018108318167976720923681545466281950840806380451495235924919026863
13
1/10:
7.041504580095461859307179762965049160276563680798519957664353999000791686420059809178254283046843966
13
1/4:
9.299065529852140654804477680207235656488711917232361123320108199944257559744448356468671296657807162
13
1/2:
12.33975588256389954085937738052505937505784523687686310836606482255376078035807990108027314809260178
13
3/4:
15.98390621631205269431862525541679125188426743374549159402700644558438855884303242439657982943238438
13
9/10:
19.81192930712756130147824123987524488600487776486330939080906786651852882825663983202101799723605151
13
19/20:
22.36203249482693986500657947517347966003025167312463560656179382890025676452343838457401431711031091
comment: This is the one-sided 5% upper critical value.
13
39/40:
24.73560488493153987139581345900246963728773584381584623120035227638007706725424456385990778207923519
comment: This is the upper cutoff for a central two-sided 5% chi-squared test.
13
99/100:
27.68824961045704931338229973657794370741566579969737226183121720184939994251397802135055680433214297
comment: This is the one-sided 1% upper critical value.
13
199/200:
29.81947122365322245513728148584736398047825530850408852080528612024307614304805459941039354881787150
comment: This is the upper cutoff for a central two-sided 1% chi-squared test.
13
999/1000:
34.52817897487088985846650785309186750480598058312470943514515492341376127431441761598396750980482469
comment: This is the one-sided 0.1% upper critical value.
14
1/200:
4.074674957399342076330876855705337355278563596209988240266764167956982071581423503618879294309498807
comment: This is the lower cutoff for a central two-sided 1% chi-squared test.
14
1/100:
4.660425062657768189722518283011169058563441179628825646730684472152770637167221726395657539941033958
14
1/40:
5.628726103039732158896382869832026416680167493046767070476641731235586839049965901662749895319010776
comment: This is the lower cutoff for a central two-sided 5% chi-squared test.
14
1/20:
6.570631383789343640926974279656368923973928910009286870918195789946026833958853265827087570929113305
14
1/10:
7.789533609752369623970308018054104026632132861049335778865763929760156836979227947821748818516627858
14
1/4:
10.16531380537706015117730610833489927582890457806741142438892950862060217357849054389977647394847141
14
1/2:
13.33927414909954352791672797773232144893678086050210149468555339685591384697696411880169877924336396
14
3/4:
17.11693359600006644881782698653157174999224848937337355138904893590042479430611693490398039085671703
14
9/10:
21.06414421299705750209476698231424384253342019586153428579704285846722776647209290961671983342164926
14
19/20:
23.68479130484057978191697571436601617993440786137343863167527207899320306569037147347381409522705419
comment: This is the one-sided 5% upper critical value.
14
39/40:
26.11894804503737078211938799669727111103443940206072435719379421450204710865139403681318023303770467
comment: This is the upper cutoff for a central two-sided 5% chi-squared test.
14
99/100:
29.14123774067279693267838564422679322198087858817126065239680142983393459949969731169823076986491396
comment: This is the one-sided 1% upper critical value.
14
199/200:
31.31934962259529028884495986939364905559146179767122002493881392076676420431984673783976355850241930
comment: This is the upper cutoff for a central two-sided 1% chi-squared test.
14
999/1000:
36.12327368039813978452670862937432363463305167045030435565052470810616096065375564142018396951274098
comment: This is the one-sided 0.1% upper critical value.
15
1/200:
4.600915571727339555045019636454122555205696054289758744030937251638809044192522549014352850390461501
comment: This is the lower cutoff for a central two-sided 1% chi-squared test.
15
1/100:
5.229348884098958661816669361590978549765418005660889651804256667109540967386605946773566702503997785
15
1/40:
6.262137795043251128327231966412802720228380988008740692700415250185558051648107491245338921142972376
comment: This is the lower cutoff for a central two-sided 5% chi-squared test.
15
1/20:
7.260943927670030174004128987264324796411179040184348873590159643151741414400026480569358298995006574
15
1/10:
8.546756241704544976569653911894154452132998084125606777562284858548142705660675253229899713235939836
15
1/4:
11.03653765909101090097780973146286859446913059450742137959450167762965814379100126309845151670447219
15
1/2:
14.33885951095664687158119714338243843230210128944691202460323024834810502953806393477572312125085697
15
3/4:
18.24508560241513470226245040694248465888744174372691025232143258970915057939730388695064085180428515
15
9/10:
22.30712958157868962909899739647486773447305261439520188866159389735685266626380997231921449988247808
15
19/20:
24.99579013972863038376469707438391278352344064002895232702870965145662038237617051071598842149231130
comment: This is the one-sided 5% upper critical value.
15
39/40:
27.48839286344298144445296559955017388588743387824956614570317159115421462620497750553590051629875695
comment: This is the upper cutoff for a central two-sided 5% chi-squared test.
15
99/100:
30.57791416689249368898644384754102032624925975119138063760448477257338316318921339428589820530656971
comment: This is the one-sided 1% upper critical value.
15
199/200:
32.80132064579184389247722483891903659173097688673745051174516364354700124520414438811002146419272967
comment: This is the upper cutoff for a central two-sided 1% chi-squared test.
15
999/1000:
37.69729821835382788245916588371024761959268362647287132331079167515967169083291980807047794678530214
comment: This is the one-sided 0.1% upper critical value.
16
1/200:
5.142205443043692852461708832770900253782359967536687949537901472613447834665071425870418406762460384
comment: This is the lower cutoff for a central two-sided 1% chi-squared test.
16
1/100:
5.812212470134965725893853267877575974994575375015931082071176720782929544838752168902327296594159354
16
1/40:
6.907664353497002574827833432376914075716703767237509179380631797310380614594175660344999196600900213
comment: This is the lower cutoff for a central two-sided 5% chi-squared test.
16
1/20:
7.961645572378550367551813587035404727160660155520150084129515814858871842851843369471021217057226047
16
1/10:
9.312236353796003544722447967946665690883427968833361450489677035999600137196207101215680629817583564
16
1/4:
11.91221969741599576627314328157807313159747360199221648877646260809521388519831712163980385017689916
16
1/2:
15.33849888500160780873058976008939232917454292720473386236914961709133694682989140297225835901589816
16
3/4:
19.36886022058451385487215529845722820575615263151226483143881522554413522183261885102942361744765989
16
9/10:
23.54182892309611179026785103608845963220878086172056901697196557118775440091953496759731396747974802
16
19/20:
26.29622760486423952627194493760703032298031941194356735491886931441230834798699847333440165879295861
comment: This is the one-sided 5% upper critical value.
16
39/40:
28.84535072340475882458164639628441903535294226728465048916457526833382470898803094042019677173683732
comment: This is the upper cutoff for a central two-sided 5% chi-squared test.
16
99/100:
31.99992690881518116960909165371940835058903193974852695557387649103278999208771452094891753896438096
comment: This is the one-sided 1% upper critical value.
16
199/200:
34.26718653782669884156091502385781968370706542459469197897422422994585175008450556539033754562293741
comment: This is the upper cutoff for a central two-sided 1% chi-squared test.
16
999/1000:
39.25235479076847601485696991954604425800267423669082924936465360161062871746363314181367120174614816
comment: This is the one-sided 0.1% upper critical value.
17
1/200:
5.697217101497832271734113853400841989132420614380399323483136896250145324831869791347537826792920555
comment: This is the lower cutoff for a central two-sided 1% chi-squared test.
17
1/100:
6.407759777738934899189243868383760144860669578038690844082289455304423634819392596023741359634532886
17
1/40:
7.564186449577569410665806344986187441536969666174336899098443192448873603177087200646332875050161206
comment: This is the lower cutoff for a central two-sided 5% chi-squared test.
17
1/20:
8.671760204670078106879087217632237855975525390723929976602459038887211726206802070079605285892218548
17
1/10:
10.08518633461933345709710059966812035242374688810208079872428788773133055949493776871199111753891079
17
1/4:
12.79192642383199398715672744473244259042144543840350496054393840727295757758605372901488565728876278
17
1/2:
16.33818237739247184187520832559014637058358587220764262896398850743223044660655018233070353977149208
17
3/4:
20.48867623839149894319591655284906375511188164125333517482499528997918350883734052033940881392679449
17
9/10:
24.76903534390145078834221808236979426677828186997498889471709016660187802776548013286138935050793297
17
19/20:
27.58711163827532401227228953241143698426568669918231905992547353393073368894565648842242997562415818
comment: This is the one-sided 5% upper critical value.
17
39/40:
30.19100912163980648645262715391774757385985609080750500191190739705406584455970899506461015168268027
comment: This is the upper cutoff for a central two-sided 5% chi-squared test.
17
99/100:
33.40866360500461768496799689251344366018152951089692351897423880414132491573896762894458355580039694
comment: This is the one-sided 1% upper critical value.
17
199/200:
35.71846565900460839856649084333455877150890818116569480617929200581530614768790855259367664893556033
comment: This is the upper cutoff for a central two-sided 1% chi-squared test.
17
999/1000:
40.79021670690252120726043668186288198447750277810552694925751297902645657398371859277374940206084228
comment: This is the one-sided 0.1% upper critical value.
18
1/200:
6.264804684506461513402478467642767358574468181167428160005298251077045746114091379463900042327678582
comment: This is the lower cutoff for a central two-sided 1% chi-squared test.
18
1/100:
7.014910901172580490055750818949523229120216554902139646033698462101099054520318982027631622002737875
18
1/40:
8.230746194756664865503847462808865532473065254617474023689338413622034868143553182808312918525670078
comment: This is the lower cutoff for a central two-sided 5% chi-squared test.
18
1/20:
9.390455080688982338476556960585513810021148795827351111105417352517503107991319354795097316589689653
18
1/10:
10.86493611650886171460103276774488396850952896201019888070748653037172181126031487879734373968689389
18
1/4:
13.67529035039829222915471572096852090522148769518067084985470166185214446187545404530528734470276062
18
1/2:
17.33790236874074430444142601268861247413598489297339612886129863905737072118410620253382047558216190
18
3/4:
21.60488979572816533762356432221381000517853902080437569864766985119092543892652042933029572337691401
18
9/10:
25.98942308263721154979772874702378318154824132147920225837730035997365318355258080254185101841527219
18
19/20:
28.86929943039263492941369269020897965079244268946096798301070377535519423226004156927093239583338786
comment: This is the one-sided 5% upper critical value.
18
39/40:
31.52637844038663044847167128174203460147993588024221251971303365239906839068309340084135211286204637
comment: This is the upper cutoff for a central two-sided 5% chi-squared test.
18
99/100:
34.80530573470507286390313891609419887329659887413800188856432765279740813687830031105129460325413937
comment: This is the one-sided 1% upper critical value.
18
199/200:
37.15645145660674746643456954179499540255031616579601164397004297265088951691498544082484243546872114
comment: This is the upper cutoff for a central two-sided 1% chi-squared test.
18
999/1000:
42.31239633167996601901974011744676785425545191290637379740729267253342269407303784466670943632200559
comment: This is the one-sided 0.1% upper critical value.
19
1/200:
6.843971445482955223597981389625389445933114618534983641549051507940005619161772591969519862462284216
comment: This is the lower cutoff for a central two-sided 1% chi-squared test.
19
1/100:
7.632729647571471309526413485839229012405049046744277306969634804984124806145950124756082958213711218
19
1/40:
8.906516481987972534393362137677517504630486926348368895200658777072189898790918016333810050324044613
comment: This is the lower cutoff for a central two-sided 5% chi-squared test.
19
1/20:
10.11701306385904450202065445394302632071342026695585160275687102067633747916124492999870920245504896
19
1/10:
11.65091003212695174906865845440669960268202879733974071990122907427155110586514559445874676787448823
19
1/4:
14.56199673142022702867225380866918843877149781861195460494955118799175123612498571025848952758421970
19
1/2:
18.33765289675647440276315379591449431069238966981026153485953526769339585312648349232099301906485879
19
3/4:
22.71780674419985666108641976340474782812192725407654558555432278156881973264463275195321756831870903
19
9/10:
27.20357102935682716745147335562468474058991492936942355350895517156233873375387014605327734036488911
19
19/20:
30.14352720564615923104402576809726611177525059737827997731669442522882588294382732977664673997384254
comment: This is the one-sided 5% upper critical value.
19
39/40:
32.85232686172970599287315257769132760610648423795643812910761255315383282527842423530401350218037275
comment: This is the upper cutoff for a central two-sided 5% chi-squared test.
19
99/100:
36.19086912927005270934034519130242132246167074195297887602314146218019432488004042899215856858775809
comment: This is the one-sided 1% upper critical value.
19
199/200:
38.58225655493424081338772785045539578255398287657469272571048829362630406295953218331103088987043488
comment: This is the upper cutoff for a central two-sided 1% chi-squared test.
19
999/1000:
43.82019596451753335172831545923301450702329333747693938227402801938664822199917824003799197253959940
comment: This is the one-sided 0.1% upper critical value.
20
1/200:
7.433844262934235034186600569140076970026526521458145568294772746884866761162585089884008554252394222
comment: This is the lower cutoff for a central two-sided 1% chi-squared test.
20
1/100:
8.260398332546398193934341888595817738103296225062386686920555329564205865887442440893348089155960005
20
1/40:
9.590777392264867271373106575346503326492000516395745100198465221279448127815593526222631250415898262
comment: This is the lower cutoff for a central two-sided 5% chi-squared test.
20
1/20:
10.85081139418258516265176146319926197248425751035556756873588055104428690881371034433754658446311975
20
1/10:
12.44260921045006547276306003157645647332016697368972380512902704397719104911285095637145846994751985
20
1/4:
15.45177353904772715359124360591739568144576613038979246610629490792763721700891154314315498483103770
20
1/2:
19.33742922942826230350012748023334521355563240453276408777075612266573578964667513753210127711688788
20
3/4:
23.82769204303085850258191853271485480057933320304052957686286497129247066734752226053874090122688443
20
9/10:
28.41198058430563325175587619307352579351037372392726732641247253906384832593334454559949106637989812
20
19/20:
31.41043284423092655343282449302236772372268383519965553850352507167581313660598386260330192000234650
comment: This is the one-sided 5% upper critical value.
20
39/40:
34.16960690283834062457009600700295877790230072594984577536756932322517500654424584427127682151387668
comment: This is the upper cutoff for a central two-sided 5% chi-squared test.
20
99/100:
37.56623478662505139966818603147818760098322153141166453678659540469753571533097123786315754918807302
comment: This is the one-sided 1% upper critical value.
20
199/200:
39.99684631293864681733755597812692710807695082707210786042973924476631962734834293604536566034330976
comment: This is the upper cutoff for a central two-sided 1% chi-squared test.
20
999/1000:
45.31474661812586148356174855240076469747162339396822686517608578192734796400774374361058316498149798
comment: This is the one-sided 0.1% upper critical value.
21
1/200:
8.033653420232732148055297332334272709139831807677501084836040906225902150686187474995019860125180859
comment: This is the lower cutoff for a central two-sided 1% chi-squared test.
21
1/100:
8.897197942077213665401273331990427777260080284457452016754975561685045446885709407709709385255102737
21
1/40:
10.28289778252286202932293116888693075014849317367400953446496689256805067183050016019370450886471018
comment: This is the lower cutoff for a central two-sided 5% chi-squared test.
21
1/20:
11.59130520882073668873360095940304227322447632141923192134378269893784147221473773024227331057002580
21
1/10:
13.23959797539530444701644688896583977229347805027984014048007180910786259475570256322581411400703362
21
1/4:
16.34438376247883126871379473304400166048141036667611190572088477925054202037976713324880078147031894
21
1/2:
20.33722756354792614802162056197182641489380325041903582072310829327957965283801978605106946485017773
21
3/4:
24.93477701490230847636952486032651722998245041365556025852916768867859434278821833922522603860509291
21
9/10:
29.61508943618273257228465919585469798791268714977699060574823619805771123251219549139089476686962025
21
19/20:
32.67057334091730535297588863629244433047090895489394515603480639268436800874345994482926301184749566
comment: This is the one-sided 5% upper critical value.
21
39/40:
35.47887590572725441904510535500913772467292623233983319698753641263257431846209316369587900262497435
comment: This is the upper cutoff for a central two-sided 5% chi-squared test.
21
99/100:
38.93217268351606756750428935828380437973309470939449731865678943177385540123690626668531960937391416
comment: This is the one-sided 1% upper critical value.
21
199/200:
41.40106477141760252878218511620121133477315535500635700713905312881108026372634111777807821291935827
comment: This is the upper cutoff for a central two-sided 1% chi-squared test.
21
999/1000:
46.79703804156131460775145595984211256348466081694884473081003883621737186114124985905832665806170032
comment: This is the one-sided 0.1% upper critical value.
22
1/200:
8.642716400666413328554800283961793022558682601599760117218146572450646152797723428286791211143652311
comment: This is the lower cutoff for a central two-sided 1% chi-squared test.
22
1/100:
9.542492338785072510912075785953185568961426902373264036373554380163416641758746245591665629981492315
22
1/40:
10.98232073447367656369798915603446467268162382644748501635289572752761517191955371356532437219353365
comment: This is the lower cutoff for a central two-sided 5% chi-squared test.
22
1/20:
12.33801457879064446344594184870872383133078522434005052467610936623034446960279638154466008177145422
22
1/10:
14.04149318942196652581571495315960037759606755146674856277059817473076578321724678871801958834505822
22
1/4:
17.23961940475905774860567874873340563603971735197680707342012875449384853521066949531464133492879389
22
1/2:
21.33704480767263169613632867936209665834473834607880892488596338173503341282221680251793582204033669
22
3/4:
26.03926502816501611538436249937122052917321624058426964786154950013149703304234964856737966660600236
22
9/10:
30.81328234395303509239113800407481036703599235113446983869055917940781808478733956979026571533842110
22
19/20:
33.92443847144380293524791904219263832286738685446708476484008083130772549317541550067985488782548498
comment: This is the one-sided 5% upper critical value.
22
39/40:
36.78071208403555744065702721992776732431642303083577482315828725952812045256360876484758296538856732
comment: This is the upper cutoff for a central two-sided 5% chi-squared test.
22
99/100:
40.28936043759386405182201383640881356302901261836764546170712123781850713597372709836491566824889878
comment: This is the one-sided 1% upper critical value.
22
199/200:
42.79565499930853975126446304098433265526876109607627237199637260560702487905558998893532829463871641
comment: This is the upper cutoff for a central two-sided 1% chi-squared test.
22
999/1000:
48.26794229083517550946526138210538047993886214784116339422499054606921733786956103582842056942621404
comment: This is the one-sided 0.1% upper critical value.
23
1/200:
9.260424775808742926559987578682538393969686889410245157901613522758243684160353156890275056875771204
comment: This is the lower cutoff for a central two-sided 1% chi-squared test.
23
1/100:
10.19571555574582566864972003592206033926242989280010714272753472245209004845901064364955730822143540
23
1/40:
11.68855192245243803747659058054077780457115358899248060097855025887269497004816156757090667611879155
comment: This is the lower cutoff for a central two-sided 5% chi-squared test.
23
1/20:
13.09051418817279962667373164810123425324599964443354465882208407925275460597598271474878891695851779
23
1/10:
14.84795579926766741140785709157859718315503497796228809997144137319937961414097406774269299306615353
23
1/4:
18.13729674115580805701814406670316447011132746911146138543892200313133197959515031693158662334886402
23
1/2:
22.33687842318425408938508512304403054779555126673717446529116168067992875901628409785650219495900510
23
3/4:
27.14133600297650595638958836717315257439042020782840003668737171487438184706871986493423664527953789
23
9/10:
32.00689968170429683245193985816233367249602051992531503887196977267974789539944124923750870688134882
23
19/20:
35.17246162690805903228768440141915575863374926340145439835666574185610037124888174952000013571630374
comment: This is the one-sided 5% upper critical value.
23
39/40:
38.07562725035580574687871655746433973511279452882796654574091308446524300190878800202098164790280917
comment: This is the upper cutoff for a central two-sided 5% chi-squared test.
23
99/100:
41.63839811885847413959961374062957375981566637038064384278233580887576178740144555165297052699503394
comment: This is the one-sided 1% upper critical value.
23
199/200:
44.18127524997110054688389887504267931396125695094266382149477721116469325084821369693948296467968339
comment: This is the upper cutoff for a central two-sided 1% chi-squared test.
23
999/1000:
49.72823246643149533576427107830823842232850058836390719009267364516023136450385001880031193414143603
comment: This is the one-sided 0.1% upper critical value.
24
1/200:
9.886233502241467347158558649390179698960935415378893784538414023748872853624732508634635871593471411
comment: This is the lower cutoff for a central two-sided 1% chi-squared test.
24
1/100:
10.85636147553227967502066484695114441156342205145135130833124742505913278385045257442324715083258386
24
1/40:
12.40115021744443305413243872645711913228652665969321734047596344685276669287699013346011712185181772
comment: This is the lower cutoff for a central two-sided 5% chi-squared test.
24
1/20:
13.84842502717021363390809568527388092377306082374284802817947868298295314096667510842718037406128289
24
1/10:
15.65868405251282787617077692740699821350858979782068275554569247931525455836322013268699357164158877
24
1/4:
19.03725252952354844333462654075850579266115421504030596378899462199416520923877183608736845036516582
24
1/2:
23.33672630608952968085237396202776267227417662969361399845482539514185766825531102461571103022399993
24
3/4:
28.24115002552875989698042361745737219411207551022975872793543680117119171626694824295616772692335866
24
9/10:
33.19624428862817635968947363229089058641459594947617709896056005503509807187895579177641482875446536
24
19/20:
36.41502850180731350126652198835989681490714864614190124942551036596536361626590379025046461578190921
comment: This is the one-sided 5% upper critical value.
24
39/40:
39.36407702660391263456180159278190915727838237019026965434544158854828868923229005395393201803475189
comment: This is the upper cutoff for a central two-sided 5% chi-squared test.
24
99/100:
42.97982013935163628776235756543133625954533983839753017682269123382465199238630238295701290510129563
comment: This is the one-sided 1% upper critical value.
24
199/200:
45.55851193653058340245979202875096218965874324073352681470402203880402928946975610444795561125633787
comment: This is the upper cutoff for a central two-sided 1% chi-squared test.
24
999/1000:
51.17859777737739197015004104859031933741587888651936815571543188004595196955119054851095463300456640
comment: This is the one-sided 0.1% upper critical value.
25
1/200:
10.51965211202469386933723199274902753219350947684315117398823512601526744321452424530664578192288032
comment: This is the lower cutoff for a central two-sided 1% chi-squared test.
25
1/100:
11.52397537224933466803612990518703130502376127769041780494953106462252914208042591340208255268432030
25
1/40:
13.11972002493778357682857452297344482667331084951027090496338441887456161124940385413216093567281640
comment: This is the lower cutoff for a central two-sided 5% chi-squared test.
25
1/20:
14.61140763948330475942854641975077107520207227472379467850095242582454886192470538265626195570305273
25
1/10:
16.47340799867337851578754242712192393126427970688620439159027139413644178192128541512592975304499404
25
1/4:
19.93934094901965209899628054170291247239081708174219838469545861357454764435664341990259423503369675
25
1/2:
24.33658669788430000717833012282435200333464825444623918158924595327680455738740360697572195346798446
25
3/4:
29.33885027686637006012251840174401629213259862909218531403512667996545411184291365464786999127294520
25
9/10:
34.38158701755295048622310005681788769933707333774265425176965079452532715748510776471905804542889697
25
19/20:
37.65248413348277834600960950886486062568227567060245149886719992499261824584664955727772846158962122
comment: This is the one-sided 5% upper critical value.
25
39/40:
40.64646912027520219558495344036974781294312986910330365736443487597225474931584928892041518654394756
comment: This is the upper cutoff for a central two-sided 5% chi-squared test.
25
99/100:
44.31410489621916539072270935942014475957191239358859977686337085130484499109515597606475749703325308
comment: This is the one-sided 1% upper critical value.
25
199/200:
46.92789016008075131219504133724406489372113592721901074646516039005092766008149600702297017665617851
comment: This is the upper cutoff for a central two-sided 1% chi-squared test.
25
999/1000:
52.61965577617283861369950649239698821398573353333399535983134197942943177737751378029260132588014730
comment: This is the one-sided 0.1% upper critical value.
26
1/200:
11.16023740616414844660628280725825330332503815197951129672765348075444276576404187816950445682042083
comment: This is the lower cutoff for a central two-sided 1% chi-squared test.
26
1/100:
12.19814692350559189395360267151931819097808337078925650288354316490280474113740712635900546732629164
26
1/40:
13.84390498200760426273064844297751232870110785139446832772589322742811053690922139973203688861246501
comment: This is the lower cutoff for a central two-sided 5% chi-squared test.
26
1/20:
15.37915658326173450442387820517121387542832128891700110301027719267275749423584432439288170160170786
26
1/10:
17.29188498973876086153290261069220721151277748013915373136800340373048472999310903869931696642589910
26
1/4:
20.84343110307541831265721547342543021859088619688642783032255146584103264749076253696230849593579948
26
1/2:
25.33645811747726665470092851760120213172127007747557445645775797212496663279451091329906540069687512
26
3/4:
30.43456542861582232847206826772400365082075714479710590131488715488936378110005588116430404373846463
26
9/10:
35.56317127192346173245808456312402763562960233436469597204927791476433296659488831466609339039073376
26
19/20:
38.88513865983004038523968637943290612703251458647882159755547515702725922903075266012153431942817911
comment: This is the one-sided 5% upper critical value.
26
39/40:
41.92317009635391138845483661595015550717571164579119191806776214880409043677417995486642065130133789
comment: This is the upper cutoff for a central two-sided 5% chi-squared test.
26
99/100:
45.64168266628315030913200085093522394484142945842230237437849970409590945787949533929530420534786133
comment: This is the one-sided 1% upper critical value.
26
199/200:
48.28988233245683801086861785418653371779888028494862238922943797578332561851296211334698432798079249
comment: This is the upper cutoff for a central two-sided 1% chi-squared test.
26
999/1000:
54.05196238857664086540106221296433192555212387714736579636619371348608312821892459418064928437635802
comment: This is the one-sided 0.1% upper critical value.
27
1/200:
11.80758735136614156246151718202905762601034183868965290096742605895791841130531956362195655115022044
comment: This is the lower cutoff for a central two-sided 1% chi-squared test.
27
1/100:
12.87850439314454929492811090637114349557155960287749228463370894269893907150668140405821877558526743
27
1/40:
14.57338273082170478554671477734966686979157183675249695575324179951269367208955473038868082552526027
comment: This is the lower cutoff for a central two-sided 5% chi-squared test.
27
1/20:
16.15139584966410498749085819103441631909530964519248833357144809805708795301941372161493548038642101
27
1/10:
18.11389596689598190385542673593984415143389008285883697855281556909905083472256686859518494899173882
27
1/4:
21.74940496449953393898228999246663686081774686663176943194372500252030091296183645781936010582459721
27
1/2:
26.33633930859144670687975939034948502225186509346345947866651354667906123566153781137952461470392758
27
3/4:
31.52841161952230708828283394238273034240990299921782196948683137094227520261761355499038487313295028
27
9/10:
36.74121674779764535425058504217957392087417789667526722700878382999115937294437360693681926536611190
27
19/20:
40.11327206941362900768721431359421893198377434616282494480975972676427531475048140544088280663197530
comment: This is the one-sided 5% upper critical value.
27
39/40:
43.19451096615604338201302957597495498459505444113044721900716165925003902832890584127950088650952640
comment: This is the upper cutoff for a central two-sided 5% chi-squared test.
27
99/100:
46.96294212475144632991175690625227013531356635756065946539082742131773999472643618433222617545198658
comment: This is the one-sided 1% upper critical value.
27
199/200:
49.64491529899423644843839652841358173895160208783305930524224721888653273416299400802044921476710214
comment: This is the upper cutoff for a central two-sided 1% chi-squared test.
27
999/1000:
55.47602020574520484228150523663964657773202218996409949192552885903088733688504876145134260172890288
comment: This is the one-sided 0.1% upper critical value.
28
1/200:
12.46133594800257276342529418150271454569532458223049315198627030166142068164596921905436362908017411
comment: This is the lower cutoff for a central two-sided 1% chi-squared test.
28
1/100:
13.56470975461881640590242564716444774733705805975439952140235138103716524074229903904370653604661376
28
1/40:
15.30786055260119588307528741325573785785190926175806663509257642900687372131749234186183947644736414
comment: This is the lower cutoff for a central two-sided 5% chi-squared test.
28
1/20:
16.92787504442249483834378844604351534301706203787227605838702803667315508475722396853414885213500087
28
1/10:
18.93924237191749769354474418246307020230928642356859667038047849750341628775947085969598211789238674
28
1/4:
22.65715567064598301224163756387808684925207803278055824122599319793519020769637421019298325460662181
28
1/2:
27.33622919868979838723089682413681419363929365631200058771322615283406910819009448193361818224479165
28
3/4:
32.62049409902553492842892820341226242939955841984561580072581339945208068595686773679614711374120926
28
9/10:
37.91592254469706857090175959892706885897420359187498175014001387049442722268666476808664131648569450
28
19/20:
41.33713815142739776231694983877459187918827553623475427492683819718707147742118755487287019026413903
comment: This is the one-sided 5% upper critical value.
28
39/40:
44.46079183631775599280170700512413100241393980807515391458361687535605940731856823778147387658290357
comment: This is the upper cutoff for a central two-sided 5% chi-squared test.
28
99/100:
48.27823577031549443307452440877906686514077781301861151304229176622406406272379449915492900811086704
comment: This is the one-sided 1% upper critical value.
28
199/200:
50.99337626849945468230915555630036838613270373417132159317041049978139345741776834676620787686732182
comment: This is the upper cutoff for a central two-sided 1% chi-squared test.
28
999/1000:
56.89228539335360525408048680466324469548086418994509041061070258651713542923056579974363667827668955
comment: This is the one-sided 0.1% upper critical value.
29
1/200:
13.12114888796039905544178361039102482899706390327523949392435587211435997666782906597333455170923982
comment: This is the lower cutoff for a central two-sided 1% chi-squared test.
29
1/100:
14.25645457627468152314091771891559054431185218417782632082158881479116542481724376665547274423810889
29
1/40:
16.04707169536488548990149479934104289946964208862548621208831709044285239987429371405580414619596243
comment: This is the lower cutoff for a central two-sided 5% chi-squared test.
29
1/20:
17.70836618282458222796914916227019774498865987190056655686688239995923004031064870002134148806452244
29
1/10:
19.76774355947483712905882852158288813962692210400848253189775535549543396204266233885220786312648801
29
1/4:
23.56658609841022999517654598770737014822377700623972565478243389898811089422010527203784224534775852
29
1/2:
28.33612686658444989362371687858548928344546205122271271633865334958486363901816925742267391800123590
29
3/4:
33.71090860391080892265226821589220335847848984376479463547750953181467055634793597853065632531415467
29
9/10:
39.08746977069395415076613913476749073200107109988604482419983744073242560773215862360094920078159664
29
19/20:
42.55696780429268506409170589622285366588734378487571933325874404323202831705917207144013745877990802
comment: This is the one-sided 5% upper critical value.
29
39/40:
45.72228580417454293190794216772511884750190793008448904968003191249491229016173308866019421203514413
comment: This is the upper cutoff for a central two-sided 5% chi-squared test.
29
99/100:
49.58788447289883062816101363850696627375928680305651539603624376976426479963473615945238928163923187
comment: This is the one-sided 1% upper critical value.
29
199/200:
52.33561778593362047806551005732651152722650206163910206974570707786180938738530601229216259072631408
comment: This is the upper cutoff for a central two-sided 1% chi-squared test.
29
999/1000:
58.30117348979492532210086314087430072351075317347672190329991461316299707934359228176562235945434527
comment: This is the one-sided 0.1% upper critical value.
30
1/200:
13.78671985950271318341460697866352457867314122831222843721117200224676842154504479049326265314453908
comment: This is the lower cutoff for a central two-sided 1% chi-squared test.
30
1/100:
14.95345652845543887921617889081294518279554867630357650484160968485435160021081657965880935688170379
30
1/40:
16.79077226556662493981711224305386559147055565267118665166675597408397817292493721596779172920987982
comment: This is the lower cutoff for a central two-sided 5% chi-squared test.
30
1/20:
18.49266098195346785967310245113259562468958088636927402179644589147854329348086487180791522193566766
30
1/10:
20.59923461458534521805887530965155374395387705782715771977827875988383517342673926260470091297870373
30
1/4:
24.47760766488626174305390891533348553211264500327320840710371979219197318357766691832851814606309107
30
1/2:
29.33603151666158593323303312041360750480704349221253767509065066193948640931817223468428234348862923
30
3/4:
34.79974251914092629577317092199227814668407686721590381627024011367964028621708151203416102101158641
30
9/10:
40.25602373871179978047325048323355750459277444181004793112943900749497207623105161181073458783222046
30
19/20:
43.77297182574218796462059924220268887896824482993019068394643004497852982635207003798175362516225384
comment: This is the one-sided 5% upper critical value.
30
39/40:
46.97924224367115662007213987398696393074162865617606554718053481795707037934151237431966264085380429
comment: This is the upper cutoff for a central two-sided 5% chi-squared test.
30
99/100:
50.89218131151709059076550027445954870121699932721039151692605758050835713325732860339077229090189792
comment: This is the one-sided 1% upper critical value.
30
199/200:
53.67196193024059142248130919928912428894328593501119019337566719856899843555902024318450137353804860
comment: This is the upper cutoff for a central two-sided 1% chi-squared test.
30
999/1000:
59.70306430442993085328175515536593426035511905709723732495573646569660450176333170682976307722955093
comment: This is the one-sided 0.1% upper critical value.
40
1/200:
20.70653531697008434547764357277248416472494794294556892846228076100079423763709676352067619564667116
comment: This is the lower cutoff for a central two-sided 1% chi-squared test.
40
1/100:
22.16426125297515936196260194870635138010366499031614340599093281632720514326853604305815989696411875
40
1/40:
24.43303917080788820595083025759838399506280134406441771540422941291063263269070864505131672173048955
comment: This is the lower cutoff for a central two-sided 5% chi-squared test.
40
1/20:
26.50930319669311060190105095581940275463152353477206398372633274893270865969897250828190919295758071
40
1/10:
29.05052293054550901470940453038700310305840453743970658621711593180618880843709436257819704683115579
40
1/4:
33.66029492298445057645740665394124875961177607114494774849385203932119851172117694238976197035979468
40
1/2:
39.33534484661133466162776115364296778806493441663616829064842597195148715851048910607984787139644350
40
3/4:
45.61601361894214393065916585040232823390243755954169424683095491652467287299759258783958152435116384
40
9/10:
51.80505721331751881621720793374733267681037851692148738537726459520354067567462621004751558639683272
40
19/20:
55.75847927888703205706856312071364054339172258919103767407665502445122206595323511902272663594333657
comment: This is the one-sided 5% upper critical value.
40
39/40:
59.34170714317120147203658198257414387792560871206999206957108923932262777010984986516405328933448729
comment: This is the upper cutoff for a central two-sided 5% chi-squared test.
40
99/100:
63.69073975156446305238254578944207719275461642164370627329179155701943483920655230107909641226317074
comment: This is the one-sided 1% upper critical value.
40
199/200:
66.76596183280391936659178474544942115750716984426095598677851512433962916850052203111991407636666094
comment: This is the upper cutoff for a central two-sided 1% chi-squared test.
40
999/1000:
73.40195751899104296893065459376795964771069202723122353168222999533700122798003598624955224000441023
comment: This is the one-sided 0.1% upper critical value.
50
1/200:
27.99074886637333126802561641113637793447709116043903934433338795630248320129307927487210147034868501
comment: This is the lower cutoff for a central two-sided 1% chi-squared test.
50
1/100:
29.70668269884128963661144169873731396402367121091869525448599088260365387118897752093991019380414569
50
1/40:
32.35736369565865329249708943567909405643065046741308105231380244287850806374544550187777450323621503
comment: This is the lower cutoff for a central two-sided 5% chi-squared test.
50
1/20:
34.76425168350174642992997837074420470226476425023162883622411696000129075542288333194680314861844976
50
1/10:
37.68864839397848900466020581334766034014918689995712391912057235653394208227487655515331208490661413
50
1/4:
42.94208381090593916178751771330705054021695632377004476054325701737764333511451524496660988444003613
50
1/2:
49.33493673397683528065239337378176012010027722897892838994179271926905322174381551465551796033821920
50
3/4:
56.33360492213238107066030583421170523876248199582387199321861125580842536291442906006206537909197173
50
9/10:
63.16712100572631888416025111784321436301215129186330847391453004167793132865363218009413756883559514
50
19/20:
67.50480654954119996954198160681255463099895657131280855638876691467026776372343653672593784588137692
comment: This is the one-sided 5% upper critical value.
50
39/40:
71.42019518750641448686900081375309678704901429000167166885609117278923237372702667970332913219596505
comment: This is the upper cutoff for a central two-sided 5% chi-squared test.
50
99/100:
76.15389124901271697559420174007689555383814180423384664196503550897946399213821578351414961279516806
comment: This is the one-sided 1% upper critical value.
50
199/200:
79.48997846682890292545252685916984848149094478927164888335089968712272009278145863078279565523081230
comment: This is the upper cutoff for a central two-sided 1% chi-squared test.
50
999/1000:
86.66081519040313897787898272808008594166000627064406176201268493598437866300955919607528961240316368
comment: This is the one-sided 0.1% upper critical value.
60
1/200:
35.53449107873856208163023556173359834415730714894468200633256555845881271896478499794247072741978516
comment: This is the lower cutoff for a central two-sided 1% chi-squared test.
60
1/100:
37.48485152980378553003312395553138503087637133981413692929163784981493845507998859472773847683449641
60
1/40:
40.48174804284182973451007764714610369079405573135718887322465463441459318449200497950665425826019438
comment: This is the lower cutoff for a central two-sided 5% chi-squared test.
60
1/20:
43.18795845398976437540247083000812756027357972076566088979949622024337653057946332695248792148374567
60
1/10:
46.45888830020344511118909215260959818811605474676349467664561457806657808757492225221769853081122268
60
1/4:
52.29381658377511423372514417540106124204223131812623118550561259893784788002712574806901109968624257
60
1/2:
59.33466627644246273212945110928633285431465669012435936236030028717940885150122049066193144969311406
60
3/4:
66.98146110761914460173233332607154300145432811489948117005528466826177878802764243971675133718410101
60
9/10:
74.39700571936858917725103368992328752853274543611338812291084387476450518964393843985073775717120692
60
19/20:
79.08194448784873041578569167376711710007571139617139536412879570436984474447429057567461051294723039
comment: This is the one-sided 5% upper critical value.
60
39/40:
83.29767487717319216078243181784743195594584898424744282712147841274240492498672908873066210022684850
comment: This is the upper cutoff for a central two-sided 5% chi-squared test.
60
99/100:
88.37941890144932283418978030272625617471912068653489723504904584230858823462456535605645270198659392
comment: This is the one-sided 1% upper critical value.
60
199/200:
91.95169815962972490558735678208400543634043763340841359328771351012282106495193931033056165771542355
comment: This is the upper cutoff for a central two-sided 1% chi-squared test.
60
999/1000:
99.60723306984937745402829743177250448035339880862242897071740261089441877725805355494294727792792519
comment: This is the one-sided 0.1% upper critical value.
100
1/200:
67.32756330547918095054147760005252824743935444900385414961729509123078095272265897368648925147501937
comment: This is the lower cutoff for a central two-sided 1% chi-squared test.
100
1/100:
70.06489492539979933131399762803260185279322145549526631780556863275970319079413235551474410867116313
100
1/40:
74.22192747492372604972007127301039419962125995945247952590092484514269487577158215050348685370263615
comment: This is the lower cutoff for a central two-sided 5% chi-squared test.
100
1/20:
77.92946516501725948411671562316882553872880630850571093081177304249529386894185178033572210286660975
100
1/10:
82.35813581235714578800968423130273443308756463415240042592435651290532101219289609643704143471400477
100
1/4:
90.13321974633931454600921912955254243858993429857795007098398786653585988750560278048808021126592092
100
1/2:
99.33412923598845575421805917277470784816864991481556870016778908385039320670383659776851937834951472
100
3/4:
109.1412410700806013035551026844945475933025798913630290534884018711626633174460551521740798780535727
100
9/10:
118.4980038110621036061134904560442720334271753286934564502092821736000672418520178342177122723772428
100
19/20:
124.3421134040040817254780197349251226677223367416245534121410417252667047763939313840609689504847771
comment: This is the one-sided 5% upper critical value.
100
39/40:
129.5611971858365927054070563011921522361282634315327705142813846949744483614019722401332789573582072
comment: This is the upper cutoff for a central two-sided 5% chi-squared test.
100
99/100:
135.8067231710267805053303263026780395400439250473682470965151002092980164452445316004191651289234719
comment: This is the one-sided 1% upper critical value.
100
199/200:
140.1694894423136371031092797363942225767992976069075512604696113145884172036956651694875551252353740
comment: This is the upper cutoff for a central two-sided 1% chi-squared test.
100
999/1000:
149.4492527790387112312310527556239868322919467725014106263673761829164912280505023226573639844857172
comment: This is the one-sided 0.1% upper critical value.
Definition
For the chi-squared distribution with $\nu$ degrees of freedom and cumulative distribution function $F_\nu$ [1], this table gives the lower-tail quantile $\chi^2_{\nu,p}=\inf\{x\geq0:F_\nu(x)\geq p\}$.
Parameters
$\nu$
—   degrees of freedom ($\nu$ is a positive integer)
$p$
—   lower-tail probability ($0<p<1$)
Formulas
(1)
The cumulative distribution function is $F_\nu(x)=\gamma(\nu/2,x/2)/\Gamma(\nu/2)$, where $\gamma(a,x)$ is the lower incomplete gamma function [2].
(2)
Equivalently, the upper-tail probability is $1-F_\nu(x)=\Gamma(\nu/2,x/2)/\Gamma(\nu/2)$, where $\Gamma(a,x)$ is the upper incomplete gamma function [2].
(3)
If $\chi^{2,\mathrm{upper}}_{\nu,\alpha}$ denotes the upper-tail critical value, then $\chi^{2,\mathrm{upper}}_{\nu,\alpha}=\chi^2_{\nu,1-\alpha}$.
(4)
A central two-sided chi-squared test with significance level $\alpha$ uses the cutoffs $\chi^2_{\nu,\alpha/2}$ and $\chi^2_{\nu,1-\alpha/2}$.
(5)
If $z_p$ is the standard-normal quantile in the standard-normal quantile table, then $\chi^2_{1,p}=z_{(1+p)/2}^2$.
Comments
(6)
The table stores lower-tail probabilities. If a printed table is indexed by an upper-tail probability $\alpha$, its value is $\chi^2_{\nu,1-\alpha}$ here.
(7)
The parameter $p$ is written as an exact rational in lowest terms, so the familiar decimal probability $0.95$ is the row $p=19/20$. These probabilities are the conventional significance levels at which a reader most often meets chi-squared critical values: one-sided upper-tail levels $0.10,0.05,0.025,0.01,0.005,0.001$, their lower-tail complements, and the central reference probabilities $1/4,1/2,3/4$.
(8)
The degrees of freedom are the consecutive rows $\nu=1,\ldots,30$ used in many printed chi-squared tables, followed by the common larger rows $\nu=40,50,60,100$.
Programs
(P1)
R
qchisq(0.95, df = 2)
(P2)
Python
import mpmath as mp

mp.mp.dps = 110
nu = mp.mpf(2)
p = mp.mpf(19) / 20
cdf = lambda x: mp.gammainc(nu / 2, 0, x / 2, regularized=True)
mp.findroot(lambda x: cdf(x) - p, nu)
Links
Similar tables
Quantiles of the standard normal distribution —   the row $\nu=1$ is the square of a standard-normal quantile by (5)
Values of the lower incomplete gamma function $\gamma(a,x)$ —   the chi-squared cumulative distribution function is a regularized lower incomplete gamma value
Values of the upper incomplete gamma function $\Gamma(a,x)$ —   the chi-squared upper tail is a regularized upper incomplete gamma value
Differential entropies of continuous probability distributions —   includes the entropy of the chi-squared distributions
Kullback-Leibler divergences between probability distributions —   includes divergences between chi-squared distributions
Data properties
Entries are of type: real number
How well the digits are known: proven
How they were obtained:

Values are computed by bisection in Sage real ball arithmetic, evaluating $F_\nu(x)$ through the regularized lower incomplete gamma function at exact rational endpoints until the bracket determines 100 significant digits. The returned value is the final bracketing ball, not a rounded midpoint.

more

The stored entries were checked against the elementary $\nu=2$ formula, the standard-normal relation in (5), strict monotonicity in $p$ for every stored $\nu$, and strict monotonicity in $\nu$ for every stored $p$.

Table is complete: no (it holds the conventional significance levels $p\in\{1/200,1/100,1/40,1/20,1/10,1/4,1/2,3/4,9/10,19/20,39/40,99/100,199/200,999/1000\}$ for every $\nu=1,\ldots,30,40,50,60,100$. These denominators are powers of ten and of two by convention rather than by arbitrary choice: they are the levels a chi-squared table is read at, and the audit flags them only because it measures denominators and cannot see a convention)
parameter selection: These are conventional chi-squared tail/significance levels and degrees of freedom used in printed tables, listed exhaustively in complete-note rather than chosen as a generic grid. (Unknown key)


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