{"id":512,"date":"2020-02-05T21:19:55","date_gmt":"2020-02-05T18:19:55","guid":{"rendered":"https:\/\/www.aciltipakademisi.org\/?p=512"},"modified":"2021-11-16T04:10:01","modified_gmt":"2021-11-16T01:10:01","slug":"p-degeri-ve-guven-araliklari-anlatilmaz-yasanir","status":"publish","type":"post","link":"https:\/\/tatd.org.tr\/atak\/2020\/02\/05\/p-degeri-ve-guven-araliklari-anlatilmaz-yasanir\/","title":{"rendered":"P de\u011feri ve G\u00fcven Aral\u0131klar\u0131: Anlat\u0131lmaz, ya\u015fan\u0131r"},"content":{"rendered":"\n

1920’lerde Fisher p degeri’ni tan\u0131mlad\u0131\u011f\u0131nda birg\u00fcn bu kadar yanl\u0131\u015f anla\u015f\u0131laca\u011f\u0131n\u0131 bilseydi herhalde matemati\u011fi b\u0131rak\u0131p inzivaya \u00e7ekilirdi. P de\u011feri ve anlam\u0131 g\u00fcn\u00fcm\u00fczde akademik d\u00fcnyan\u0131n a\u00e7\u0131k ara ile en b\u00fcy\u00fck ve en yayg\u0131n yanl\u0131\u015f anla\u015f\u0131lmas\u0131d\u0131r. Bu yanl\u0131\u015f anla\u015f\u0131lma hatta anla\u015f\u0131lamama durumunu bir nebze hafifletmek amac\u0131yla hayali bir \u00e7al\u0131\u015fma kurgulad\u0131m. Sizlerle beraber bu \u00e7al\u0131\u015fman\u0131n verileri \u00fczerinde oynayarak p de\u011feri ve g\u00fcven aral\u0131klar\u0131n\u0131n ger\u00e7ek hayatta neler ifade etti\u011fini anlamaya \u00e7al\u0131\u015faca\u011f\u0131z. Anla\u015f\u0131lmaz istatistiksel kavramlardan uzak durmaya gayret etsem de \u00e7ok ba\u015far\u0131l\u0131 olamad\u0131\u011f\u0131m yerler de oldu. Bu a\u00e7\u0131\u011f\u0131 deva eden yaz\u0131larla kapatmaya \u00e7al\u0131\u015faca\u011f\u0131z. E\u011fer yar\u0131m saatinizi vermeye haz\u0131rsan\u0131z, ba\u015flayal\u0131m…<\/p>\n\n\n\n

\u0130lk \u00e7al\u0131\u015fma: bir erke\u011fin anatomisi<\/h4>\n\n\n\n
\"Chris-Evans-Shirtless-Captain-America-Hairy-Chest-600x445\"<\/figure><\/div>\n\n\n\n

Bir grup ara\u015ft\u0131rmac\u0131, erkek asistanlar\u0131n kad\u0131n asistanlar taraf\u0131ndan be\u011fenilmelerinde yeni trend olan sakal b\u0131rakman\u0131n etkisini incelemek \u00fczere bir ara\u015ft\u0131rma planlarlar (konu \u00fczerinde fazla d\u00fc\u015f\u00fcnmeme gerek kalmad\u0131, \u00e7\u00fcnk\u00fc t\u00fcm asistanlar\u0131n birden 2 kar\u0131\u015f sakalla gezmeye ba\u015flamas\u0131nda 20’li ya\u015f grubu i\u00e7in ilk hipotez daima kar\u015f\u0131 cinsle ilgili olmak durumundad\u0131r. Mesela durduk yere n\u00f6bet de\u011fi\u015fmek, rotasyona \u00e7\u0131kmak i\u00e7in a\u015f\u0131r\u0131 heveslenmek, n\u00f6beti yokken hastanede g\u00f6r\u00fcnmek gibi). Farkl\u0131 hastanelerde farkl\u0131 ihtisas dallar\u0131nda asistanl\u0131k yapan erkekler ya\u015f, boy, kilo gibi fakt\u00f6rler a\u00e7\u0131s\u0131ndan stratifiye edilmi\u015f gruplar i\u00e7ine kurumlar ve ihtisas dallar\u0131 aras\u0131nda fark olmayacak \u015fekilde \u00f6rneklendikten sonra (226 erkek asistan) sakal b\u0131rakan (n=112) ve her g\u00fcn t\u0131ra\u015f olan (n=114) gruplar\u0131na randomize edilirler (dolay\u0131s\u0131yla “sakal bana yak\u0131\u015f\u0131yor abi” diyenlerle eskik\u0131z arkada\u015f\u0131 be\u011fendi diye b\u0131rak\u0131p sonra vazge\u00e7emeyenlerden kaynaklanan bias\u0131 minimize etmeye \u00e7al\u0131\u015f\u0131yoruz). S\u0131f\u0131r hipotezimiz sakall\u0131lar ile sinekkayd\u0131lar aras\u0131nda fark olmad\u0131\u011f\u0131, alternatif hipotezimiz ise birinin daha \u00e7ekici oldu\u011fu \u015feklinde. \u00c7al\u0131\u015fman\u0131n birincil sonlan\u0131m noktas\u0131 (hedefimiz) ayn\u0131 \u015fekilde \u00f6rneklenmi\u015f kad\u0131n asistanlar taraf\u0131ndan 10 \u00fczerinden bu erkek asistanlar\u0131n \u00e7ekiciliklerinin puanlanmas\u0131, toplu ortalamalar\u0131n\u0131n al\u0131nmas\u0131 ve her erkek asistan\u0131n buna g\u00f6re \u00e7ekici ya da de\u011fil olarak s\u0131n\u0131fland\u0131r\u0131lmas\u0131 sonras\u0131nda sakal gruplar\u0131 aras\u0131ndaki fark\u0131n incelenmesidir (bu de\u011ferlendirme elbette subjektif bir \u00f6l\u00e7\u00fcm\u00fcn kantitatif veriye d\u00f6n\u00fc\u015ft\u00fcr\u00fclmesi oldu\u011fundan kendi i\u00e7inde yan\u0131lg\u0131 pay\u0131 var. Ancak sosyologlar \u00e7ekicili\u011fin asl\u0131nda subjektif olmad\u0131\u011f\u0131n\u0131, \u00e7ekici olan ki\u015filer \u00fczerinde herkesin hemfikir oldu\u011funu, e\u011fer hemfikir de\u011fillerse o ki\u015finin \u00e7ekici olmad\u0131\u011f\u0131n\u0131 belirten \u00e7al\u0131\u015fmalar yapm\u0131\u015flar). Sonu\u00e7 olarak her g\u00fcn t\u0131ra\u015f olan asistanlar i\u00e7erisinde \u00e7ekici olarak tan\u0131mlananlar\u0131n say\u0131s\u0131 daha fazla olsa da aradaki fark istatistiksel olarak anlaml\u0131 bulunmam\u0131\u015ft\u0131r (sakal b\u0131rakanlar: 33\/112 (%29,4) \u2013 t\u0131ra\u015f olanlar: 41\/114 (%35,9); P=0,32) (Burada da asl\u0131nda bir bias var, \u00e7ekici olan sakal b\u0131raksa da b\u0131rakmasa da \u00e7ekicidir. Ama zaten bu sebeple gruplar\u0131 randomize ettik, iki gruba da e\u015fit say\u0131da Brad Pitt d\u00fc\u015fs\u00fcn diye).<\/p>\n\n\n\n

Buradaki p de\u011ferini a\u015fa\u011f\u0131dakilerden hangisi en iyi tan\u0131mlar?<\/strong><\/p>\n\n\n\n

a) S\u0131f\u0131r hipotezinin (sakal makal farketmez, \u00f6nce bakar\u0131m adam m\u0131 diye) do\u011fru olma olas\u0131l\u0131\u011f\u0131d\u0131r.<\/p>\n\n\n\n

b) Alternatif hipotezin do\u011fru olma olas\u0131l\u0131\u011f\u0131d\u0131r.<\/p>\n\n\n\n

c) Ara\u015ft\u0131rma yap\u0131lan gruplar aras\u0131nda fark olmad\u0131\u011f\u0131 s\u00fcrece sonlan\u0131m \u00f6l\u00e7\u00fct\u00fcnde g\u00f6zlenen fark (%35,9-%29,4=%6,5) ya da daha fazlas\u0131n\u0131 elde etme ihtimalidir.<\/p>\n\n\n\n

d) G\u00f6zlenen fark (%6,5) ya da daha fazlas\u0131n\u0131n \u015fans eseri olma ihtimalidir.<\/p>\n\n\n\n

[toggle title=”Cevap i\u00e7in t\u0131klay\u0131n” state=”close”]En iyi yan\u0131t C se\u00e7ene\u011fidir.[\/toggle]<\/p>\n\n\n\n

\"1\"<\/a>
B\u00f6yle \u00e7al\u0131\u015fma m\u0131 olur diyenler i\u00e7in yay\u0131nlanm\u0131\u015f\u0131n\u0131 buradan ispat ediyoruz<\/figcaption><\/figure><\/div>\n\n\n\n

\u00c7al\u0131\u015fman\u0131n s\u0131f\u0131r hipotezi \u00f6rneklemin al\u0131nd\u0131\u011f\u0131 erkek asistanlar pop\u00fclasyonunda sakal b\u0131rakan ya da her g\u00fcn t\u0131ra\u015f olan erkek asistanlar i\u00e7inde, kad\u0131n asistanlar\u0131n puanlamas\u0131nda \u00e7ekici olarak belirlenen erkek asistan oran\u0131 a\u00e7\u0131s\u0131ndan fark olmad\u0131\u011f\u0131d\u0131r (sakal makal farketmez). Alternatif hipotez ise iki y\u00f6nl\u00fcd\u00fcr. Ya sakal b\u0131rakanlarda ya da her g\u00fcn t\u0131ra\u015f olanlarda \u00e7ekici olarak belirlenen erkek asistan oran\u0131 daha fazlad\u0131r.<\/p>\n\n\n\n

P de\u011feri, sakal b\u0131rakan ve her g\u00fcn t\u0131ra\u015f olan erkek asistan gruplar\u0131nda kad\u0131n asistanlar taraf\u0131ndan \u00e7ekici olarak tan\u0131mlanan asistan oranlar\u0131 aras\u0131nda g\u00f6zlenen en az %6,5\u2019lik fark\u0131n, asl\u0131nda hi\u00e7 fark olmamas\u0131na ra\u011fmen g\u00f6r\u00fclebilme ihtimalidir. Yani bu say\u0131da asistan kulland\u0131\u011f\u0131mda %32 ihtimalle arada fark olmamas\u0131na ra\u011fmen en az %6,5 fark varm\u0131\u015f gibi sonu\u00e7 alabilece\u011fimizi belirtir. Ki-kare testi kullanarak buldu\u011fumuz p de\u011feri tam olarak bu olas\u0131l\u0131\u011f\u0131 ifade eder.<\/p>\n\n\n\n

Verilerimizi hesaplama sitesinde yerlerine koyduk ve a\u015fa\u011f\u0131da yer alan ilk hesap tablosunu olu\u015fturduk. Bu hesap tablosunun biraz ayr\u0131nt\u0131s\u0131na inelim: Her g\u00fcn t\u0131ra\u015f olanlar\u0131n 41 tanesi \u00e7ekici iken (%35,9) sakal b\u0131rakanlar\u0131n 33\u2019\u00fc \u00e7ekicidir (%29,4). Yani \u00e7ekici olanlar\u0131n say\u0131s\u0131 her g\u00fcn t\u0131ra\u015f olanlarda 1,22 kat (%35,9\/29,4) daha fazlad\u0131r. Her g\u00fcn t\u0131ra\u015f olan asistanlar\u0131n \u00e7ekici olma odds\u2019u (\u00e7ekici olanlar\u0131n olmayanlara oran\u0131) 0,56; sakal b\u0131rakanlar\u0131n \u00e7ekici olma odds\u2019u 0,41\u2019dir. Bu iki odds aras\u0131ndaki orana odds oran\u0131 denilir ve 1,34\u2019d\u00fcr (0,56\/0,46). Bu ise her g\u00fcn t\u0131ra\u015f olanlar\u0131n \u00e7ekici olma olas\u0131l\u0131\u011f\u0131n\u0131n sakall\u0131 gezenlerin \u00e7ekici olma olas\u0131l\u0131\u011f\u0131n\u0131n 1,34 kat\u0131 (ya da %34 daha fazla) oldu\u011funu g\u00f6sterir. Bu de\u011ferin hemen beraberinde bir de %95 g\u00fcven aral\u0131\u011f\u0131 gelir genellikle (otomatik olarak yaz\u0131l\u0131m hesaplar bunu). %95 g\u00fcven aral\u0131\u011f\u0131, e\u011fer biz ayn\u0131 k\u0131staslar\u0131 kullanarak ayn\u0131 asistan evreninden 20 \u00f6rneklem se\u00e7seydik 19\u2019unda elde edece\u011fimiz sonu\u00e7lar\u0131n yer alaca\u011f\u0131 aral\u0131\u011f\u0131n \u00fcst ve alt s\u0131n\u0131rlar\u0131d\u0131r (95\/100=19\/20). Ayn\u0131 veriye g\u00f6re 20 farkl\u0131 erkek asistan grubunu de\u011ferlendirirsek 19\u2019unda \u00e7ekici olma olas\u0131l\u0131klar\u0131 oran\u0131 0,77 ile 2,35 kat aras\u0131nda iken, 1\u2019inde bu aral\u0131\u011f\u0131n d\u0131\u015f\u0131ndad\u0131r (ilk tabloya bakal\u0131m). Yani 20\u2019de 19 ihtimalle sinekkayd\u0131lar\u0131n 1,34 kat olan \u00e7ekici olma olas\u0131l\u0131k oran\u0131, farkl\u0131 bir \u00f6rneklem al\u0131n\u0131rsa 2,35 kat\u2019a \u00e7\u0131kabilirken, tam tersine bir ba\u015fka grupta sakalla gezenlerin \u00e7ekici olma olas\u0131l\u0131\u011f\u0131 1,29 kat daha fazla \u00e7\u0131kabilir (0,77 \u2013 100\/77=1,29). Sonu\u00e7 olarak, elde etti\u011fimiz veriye g\u00f6re sakall\u0131lar ya da sinekkayd\u0131lar daha fazla \u00e7ekici olma olas\u0131l\u0131\u011f\u0131na sahip demek m\u00fcmk\u00fcn de\u011fildir (matematiksel olarak odds oran\u0131n\u0131n %95 g\u00fcven aral\u0131\u011f\u0131 i\u00e7inde 1 yer al\u0131r, ya da s\u0131n\u0131rlardan biri 1’den k\u00fc\u00e7\u00fckken di\u011feri b\u00fcy\u00fckt\u00fcr, yani oranlar\u0131n\u0131n 1 olma ihtimali s\u00f6z konusudur). \u00c7al\u0131\u015fma sonunda sakal kesmek ya da kesmemenin erkek asistanlar\u0131n \u00e7ekicili\u011fine bir katk\u0131 sa\u011flamad\u0131\u011f\u0131, \u00f6nemli olan\u0131n i\u00e7 g\u00fczellikleri olduklar\u0131 yorumu yap\u0131larak \u00e7al\u0131\u015fma yay\u0131nlan\u0131r, \u00e7al\u0131\u015fmaya istinaden de herkesin sakallar\u0131n\u0131 kesmesi istenir.<\/p>\n\n\n\n

\"Ekran<\/a>
Sakals\u0131z asistan cand\u0131r<\/figcaption><\/figure><\/div>\n\n\n\n

Big Shave: \u015eeytani t\u0131ra\u015f makinasi firma \u00e7al\u0131\u015fmas\u0131<\/h4>\n\n\n\n
\"2\"<\/a>
\u0130svi\u00e7reli bilimadamlar\u0131 laboratuvardaki tek yak\u0131\u015f\u0131kl\u0131 teknisyeni denek olarak kullanm\u0131\u015flar<\/figcaption><\/figure><\/div>\n\n\n\n

Ard\u0131ndan bir t\u0131ra\u015f makinesi firmas\u0131 az buz erkek asistan olmad\u0131\u011f\u0131, i\u015f-g\u00fc\u00e7 y\u00fcz\u00fcnden 30\u2019lu ya\u015flar\u0131na kadar bekar gezdikleri ve e\u011fer erkek asistanlar\u0131n t\u0131ra\u015f olduklar\u0131nda daha \u00e7ekici olduklar\u0131 y\u00f6n\u00fcnde g\u00fc\u00e7l\u00fc bir veri sa\u011flayabilirse makine sat\u0131\u015flar\u0131n\u0131 patlatabilece\u011fi yarg\u0131s\u0131na var\u0131r. A cihaz\u0131yla t\u0131ra\u015f olmak (giri\u015fim-intervention) ya da t\u0131ra\u015f olmamak (kontrol) gruplar\u0131na tamamen ayn\u0131 demografik oranlarla erkek asistanlar\u0131 randomize ederler. Ama yat\u0131r\u0131m g\u00fc\u00e7leri daha fazla oldu\u011fundan 226 erkek asistan de\u011fil de 2260 erkek asistan\u0131 \u00e7al\u0131\u015fmaya al\u0131rlar. \u015eansa bak\u0131n ki \u00e7al\u0131\u015fman\u0131n t\u00fcm verileri birebir ayn\u0131 \u00e7\u0131kar. Aradaki fark yine %6,5\u2019dir. \u00c7ekici olanlar\u0131n olmayanlara oran\u0131 (odds) ve t\u0131ra\u015f olanlarla olmayanlar\u0131n \u00e7ekici olma olas\u0131l\u0131klar\u0131n\u0131n oran\u0131 (odds oran\u0131) da do\u011fal olarak birebir ayn\u0131d\u0131r. Ancak bu sefer g\u00fcven aral\u0131\u011f\u0131 \u00e7ok daha dard\u0131r. 20 farkl\u0131 2260 ki\u015filik \u00f6rneklemler alsayd\u0131m 19\u2019unda \u00e7ekici olma olas\u0131l\u0131klar\u0131 oran\u0131 1,13 ile 1,60 kat aras\u0131nda de\u011fi\u015fecek, ancak 1 seferinde ise bu aral\u0131\u011f\u0131nda da d\u0131\u015f\u0131nda olabilecekti (%95 g\u00fcven aral\u0131\u011f\u0131, %5 ihtimalle yan\u0131laca\u011f\u0131m anlam\u0131na gelir). Yani 20 seferin 19\u2019unda \u00f6yle ya da b\u00f6yle sinekkayd\u0131 ekibin i\u00e7inde yer alan bir asistan\u0131n \u00e7ekici olma olas\u0131l\u0131\u011f\u0131 daha fazla diyebiliriz. Bu 20’de 1 tamamen yan\u0131lma durumuna (ki biz bu miktarda yan\u0131lmay\u0131 kabulleniyor ve %95 g\u00fcven aral\u0131\u011f\u0131 se\u00e7iyoruz ba\u015fta, \u00f6rnekleme hatas\u0131 da denir. E\u011fer %5 size fazla geliyorsa %1 (%99 g\u00fcven aral\u0131\u011f\u0131) yan\u0131lma pay\u0131 da b\u0131rakabilirsiniz, ancak o zaman daha geni\u015f bir aral\u0131k bulacaks\u0131n\u0131z). Hesaplad\u0131\u011f\u0131m\u0131z bir di\u011fer de\u011fer ise P de\u011feri olup 0,0012\u2019dir. Ayn\u0131 say\u0131da asistan kulland\u0131\u011f\u0131mda arada fark olmamas\u0131na ra\u011fmen %0,12 ihtimalle en az %6,5 fark varm\u0131\u015f gibi sonu\u00e7 alabilece\u011fimizi belirtir. Arada fark yokken hata yap\u0131p en az %6,5 fark varm\u0131\u015f gibi bulma ihtimalimiz neredeyse yoktur. Arada buldu\u011fumuz fark\u0131n ger\u00e7ekli\u011fine g\u00fcvenebilece\u011fimiz anlam\u0131na gelir. Bu hesaplamay\u0131 da a\u015fa\u011f\u0131daki tabloda g\u00f6rebilirsiniz.<\/p>\n\n\n\n

\"Ekran
Al\u00e7ak t\u0131ra\u015f makinas\u0131 firmas\u0131 \u00e7al\u0131\u015fmas\u0131 – kalabal\u0131klar\u0131n g\u00fcc\u00fcn\u00fc k\u00fc\u00e7\u00fcmsemeyin<\/figcaption><\/figure><\/div>\n\n\n\n

\u00d6rneklemimiz k\u00fc\u00e7\u00fck oldu\u011fundan fark bulamad\u0131k, biri paraya k\u0131y\u0131p daha geni\u015f \u00f6rneklem ile anlaml\u0131 fark bulacak ama fikir benden \u00e7\u0131kt\u0131 \u00e7al\u0131\u015fmas\u0131<\/h4>\n\n\n\n
\"hugh1\"<\/a>
Allame-i cihan da olsan\u0131z \u015fans\u0131n\u0131z\u0131 fazla zorlamayacaks\u0131n\u0131z<\/figcaption><\/figure><\/div>\n\n\n\n

\u015eimdi i\u015fleri biraz kar\u0131\u015ft\u0131ral\u0131m. \u00c7ekici olarak tespit edilen asistan oranlar\u0131 \u015fu \u015fekilde olmu\u015f olsun: sakal b\u0131rakanlar: 33\/112 (%29,4) \u2013 t\u0131ra\u015f olanlar: 33\/114 (%28,9). Yani her iki grupta da ayn\u0131 say\u0131da \u00e7ekici asistan\u0131m\u0131z var ve oranlar da neredeyse ayn\u0131. P de\u011ferini hesaplad\u0131\u011f\u0131m\u0131zda tam 1 oldu\u011funu g\u00f6r\u00fcyoruz (Yine a\u015fa\u011f\u0131daki tablodan takip edelim). Peki bu ne demekti? Ayn\u0131 say\u0131da asistan kulland\u0131\u011f\u0131mda arada fark olmamas\u0131na ra\u011fmen %100 ihtimalle en az %0,5 fark varm\u0131\u015f gibi sonu\u00e7 alaca\u011f\u0131z demek (%29,4-%28,9=%0,5). Odds oran\u0131 1,02 %95 g\u00fcven aral\u0131\u011f\u0131 ise 0,58 ile 1,82 aras\u0131nda. Bu sonu\u00e7 ise ayn\u0131 say\u0131da asistan i\u00e7eren t\u0131pat\u0131p benzer ama farkl\u0131 20 \u00f6rneklem alsam 19\u2019unda bir grubun di\u011ferinden daha \u00e7ekici olma miktar\u0131n\u0131n y\u00fczdesel olarak b\u00fcy\u00fckl\u00fc\u011f\u00fcn\u00fcn ters y\u00f6nlerde %82 ile %72 (100\/58) aras\u0131nda de\u011fi\u015febilece\u011fini g\u00f6steriyor (1,82 odds birinin di\u011ferine g\u00f6re \u00e7ekici olma olas\u0131l\u0131\u011f\u0131n\u0131n %82 daha fazla olmas\u0131 demek, 0,58 ise tam tersine az olmas\u0131. 58 say\u0131s\u0131 100’den %42 daha azd\u0131r, ama 100 say\u0131s\u0131 58’den %72 daha fazlad\u0131r. Tamamen ak\u0131l kar\u0131\u015ft\u0131r\u0131c\u0131 matematik.). P de\u011feri arada buldu\u011fum farka g\u00fcvenmemem gerekti\u011fini belirtirken, odds oran\u0131 ise bu fark\u0131n anlaml\u0131l\u0131\u011f\u0131n\u0131 d\u00fc\u015f\u00fcnmemi sa\u011fl\u0131yor.<\/p>\n\n\n\n

\"Ekran
Fark\u0131n anlams\u0131zl\u0131\u011f\u0131 fark\u0131n yoklu\u011fu anlam\u0131na gelmez<\/figcaption><\/figure><\/div>\n\n\n\n

RAZ-R: Biggest Shave \u00c7al\u0131\u015fmas\u0131: \u00c7ok merkezli, 10 y\u0131ll\u0131k \u00e7al\u0131\u015fma. Art\u0131k g\u00f6n\u00fcl rahatl\u0131\u011f\u0131yla hepimiz t\u0131ra\u015f makinas\u0131 alabiliriz<\/h4>\n\n\n\n
\"hugh-jackman-ftr\"<\/a>
Bu g\u00f6r\u00fcnt\u00fcn\u00fcn alt\u0131nda bir volverine sakl\u0131<\/figcaption><\/figure><\/div>\n\n\n\n

Yine t\u0131ra\u015f makinas\u0131 firmas\u0131n\u0131n yapt\u0131\u011f\u0131 bir hit \u00e7al\u0131\u015fma sayesinde i\u015fler biraz daha kar\u0131\u015f\u0131yor. Bu sefer o kadar azimliler ki bir\u00e7ok \u00fclkede bir\u00e7ok asistan\u0131 \u00e7al\u0131\u015fmaya al\u0131yor ve d\u00fcnya \u00e7ap\u0131nda birka\u00e7 y\u0131l s\u00fcren bir \u00e7al\u0131\u015fma yap\u0131lmas\u0131na \u00f6n ayak oluyorlar. Sonu\u00e7ta tam 226000 asistanl\u0131k dev bir \u00e7al\u0131\u015fma elde ediliyor (ilk \u00e7al\u0131\u015fmam\u0131z\u0131n tam 1000 kat\u0131). 33000\/112000 (%29,4) \u2013 t\u0131ra\u015f olanlar: 33000\/114000 (%28,9). P de\u011feri tam 0,006973! Ayn\u0131 say\u0131da asistan kulland\u0131\u011f\u0131mda arada fark olmamas\u0131na ra\u011fmen sadece %0,6 ihtimalle en az %0,5 fark varm\u0131\u015f gibi sonu\u00e7 alabilece\u011fimiz g\u00f6r\u00fcl\u00fcyor. Verilerimiz \u00e7ok keskin, aradaki fark\u0131 \u00e7ok b\u00fcy\u00fck ihtimalle do\u011fru olarak tespit etmi\u015f durumday\u0131z. Peki ama esas \u00f6nemli soruyu atlamayal\u0131m. Fark ne kadar? Sinekkayd\u0131 t\u0131ra\u015f olan asistanlar, sakalla gezenlerden \u00e7ekici olma olas\u0131l\u0131\u011f\u0131 a\u00e7\u0131s\u0131ndan tam 1,02 kat daha \u015fansl\u0131 ve bu \u00fcst\u00fcnl\u00fck istatistiksel olarak da 20 farkl\u0131 \u00f6rneklemin 19\u2019unda ge\u00e7erli! G\u00fcven aral\u0131\u011f\u0131 da olduk\u00e7a dar, olsa olsa bu odds oran\u0131 1,0069 kat ile 1,0441 aras\u0131nda de\u011fi\u015febilir. Peki bu ne demek? Son derece anlaml\u0131 bir \u015fekilde %0,69 ile %4 aras\u0131nda de\u011fi\u015fen miktarda \u00e7ekici olma ihtimaliniz var demek. \u0130lk \u00e7al\u0131\u015fmada %6,5 fark\u0131 bile anlaml\u0131 bulmazken \u015fimdi %0,69 kadar az bir fark\u0131 anlaml\u0131 bulup buna g\u00f6re karar vermek demek. Haydi hep beraber t\u0131ra\u015f makinas\u0131 almaya… (m\u0131 acaba?)<\/p>\n\n\n\n

\"Ekran
Yeterince b\u00fcy\u00fck \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc al\u0131nd\u0131\u011f\u0131nda anlams\u0131z \u00e7\u0131kmayacak hi\u00e7bir fark yoktur<\/figcaption><\/figure><\/div>\n\n\n\n

D\u00fc\u015fman karde\u015fler: Fisher, Neyman ve Pearson<\/h4>\n\n\n\n

Yukar\u0131da ironi ve abart\u0131 ile verdi\u011fimiz 4 \u00f6rnek san\u0131r\u0131m bir noktaya a\u00e7\u0131kl\u0131k getirmi\u015ftir. P de\u011ferinin bakt\u0131\u011f\u0131m\u0131z kar\u015f\u0131la\u015ft\u0131rman\u0131n anlaml\u0131 olup olmamas\u0131yla ilgili bir s\u00f6yleyece\u011fi yoktur. P de\u011feri buldu\u011funuz fark\u0131n rastlant\u0131sal olarak ger\u00e7ekle\u015fme olas\u0131l\u0131\u011f\u0131n\u0131 size belirtir. Teorik olarak belirlenen p=0.05 s\u0131n\u0131r\u0131, fark olmamas\u0131na ra\u011fmen \u00f6rneklemimizin fark varl\u0131\u011f\u0131n\u0131 g\u00f6stermesini (\u00f6rnekleme hatas\u0131) %5 ihtimali a\u015fmad\u0131\u011f\u0131 s\u00fcrece makul kar\u015f\u0131lad\u0131\u011f\u0131m\u0131z anlam\u0131na gelir. Tip I hata olarak da tan\u0131mlan\u0131r (her ne kadar tip I hata her zaman \u00f6rnekleme hatas\u0131na e\u015fit olmasa da \u015fimdilik genel kan\u0131y\u0131 kabul edelim).<\/p>\n\n\n\n

\"Fisher<\/a>
Fisher da \u00e7ekicili\u011fini sakal\u0131na bor\u00e7lu olanlardand\u0131<\/figcaption><\/figure><\/div>\n\n\n\n

Ronald Fisher 1920\u2019ler p de\u011ferini ilk ortaya att\u0131\u011f\u0131nda bunun definitif bir test olarak alg\u0131lanaca\u011f\u0131n\u0131 hi\u00e7 d\u00fc\u015f\u00fcnmemi\u015fti. 20\u2019lerin sonunda, Fisher\u2019in en az\u0131l\u0131 rakipleri olan Polonyal\u0131 matematik\u00e7i Jerzy Neyman ve \u0130ngiliz istatistik\u00e7i Egon Pearson, veri analizi i\u00e7in g\u00fc\u00e7 (power), yanl\u0131\u015f pozitif, yanl\u0131\u015f negatif ve di\u011fer konseptleri ortaya at\u0131p \u00f6zellikle p de\u011ferine kar\u015f\u0131 \u00e7\u0131kt\u0131lar. Neyman, Fisher\u2019in baz\u0131 \u00e7al\u0131\u015fmalar\u0131n\u0131 metamatiksel a\u00e7\u0131dan \u201ck\u00f6t\u00fcden de beter\u201d olarak tan\u0131mlarken, Fisher da Neyman\u2019\u0131n yakla\u015f\u0131m\u0131n\u0131 \u201c\u00e7ocuk\u00e7a\u201d ve “Bat\u0131\u2019daki entellekt\u00fcel \u00f6zg\u00fcrl\u00fck ad\u0131na korkun\u00e7\u201d olarak nitelendirdi. Bu kavga, istatistik\u00e7i olmayan klinisyenlerin her iki konsepti birbirine yakla\u015ft\u0131r\u0131p beraber kullanarak yazd\u0131klar\u0131 kitaplar ve uygulamalar sayesinde bir kar\u0131\u015f\u0131k sisteme d\u00f6n\u00fc\u015ft\u00fc. Tamamen bir kabul olarak ba\u015flayan s\u0131f\u0131r hipotezinin %5 ihtimalle rastlant\u0131sal olarak elenmesi ihtimali birden fark\u0131n anlaml\u0131l\u0131\u011f\u0131 kavram\u0131na d\u00f6n\u00fc\u015ferek en az\u0131ndan istatistik\u00e7i olmayan klinisyenler i\u00e7in anla\u015f\u0131lmas\u0131 ve i\u00e7inden \u00e7\u0131k\u0131lmas\u0131 imkans\u0131z bir hale geldi.<\/p>\n\n\n\n

\"Pearson_Egon_4\"<\/a>
Egon Pearson: Fisher’in top sakal\u0131na uyuz oldu\u011fundan p de\u011ferine \u0131s\u0131namad\u0131\u011f\u0131 s\u00f6ylenir<\/figcaption><\/figure><\/div>\n\n\n\n

P de\u011feri, g\u00f6zlenen sonucun ne d\u00fczeyde rastlant\u0131sal \u015fansa ba\u011flanabilece\u011fini g\u00f6steren ihtimal olarak tan\u0131mlan\u0131p, aradaki fark\u0131n anlaml\u0131l\u0131\u011f\u0131na do\u011fru evrilince bu hatay\u0131 daha net belirtmek i\u00e7in \u201cMuhtemel Sebep\u201d kavram\u0131 (probable cause) ortaya \u00e7\u0131kt\u0131. \u00c7\u00fcnk\u00fc, P de\u011feri ara\u015ft\u0131rmac\u0131n\u0131n esas akl\u0131ndaki sorunun yan\u0131t\u0131n\u0131 vermekten \u00e7ok uzakt\u0131. O soru ise hipotezimin do\u011fru olma ihtimali nedir sorusudur. Ancak bu noktada \u00e7ok \u00f6nemli bir basamak hep atlan\u0131r. O da hipotezin daha \u00e7al\u0131\u015fma yap\u0131lmadan \u00f6nce ne derece ihtimal dahilinde oldu\u011fudur. \u00d6rne\u011fin, %5 ihtimalle do\u011fru olabilecek ekstrem bir hipotezi test eden bir \u00e7al\u0131\u015fma yap\u0131yorsan\u0131z, p de\u011feriniz 0,05 d\u00fczeyinde \u201cistatistiksel olarak anlaml\u0131\u201d fark g\u00f6sterse bile hipotezinizin ger\u00e7ek hayatta do\u011fru olmas\u0131 ve fark\u0131n ger\u00e7ek olma olas\u0131l\u0131\u011f\u0131 sadece %11\u2019dir. Bu muhtemel sebep kavram\u0131na ilerdeki yaz\u0131larda tekrar de\u011finece\u011fiz.<\/p>\n\n\n\n

\"Ekran
Elde etti\u011finiz sonu\u00e7 ancak sordu\u011funuz soru kadar anlaml\u0131d\u0131r<\/figcaption><\/figure><\/div>\n\n\n\n

Sonu\u00e7<\/h4>\n\n\n\n

Sonu\u00e7 olarak, p de\u011feri hepimizin i\u00e7ine i\u015flemi\u015f olan \u201canlam\u201d kelimesinin kar\u015f\u0131l\u0131\u011f\u0131 kesinlikle de\u011fildir. Amac\u0131, hedefi farkl\u0131 olan bir konsept olarak son derece yanl\u0131\u015f ifadelerle kullanmaya devam etmekteyiz. Bir faydan\u0131n ya da bir fark\u0131n ne kadar oldu\u011fu sorusuna yan\u0131t vermez, sadece \u015fansa ba\u011fl\u0131 olarak o sonu\u00e7la kar\u015f\u0131la\u015fma ihtimalimizin bir g\u00f6stergesidir. P de\u011feri yerine %95 g\u00fcven aral\u0131klar\u0131n\u0131, Odds ve Likelihood Ratio\u2019lar\u0131 kullanaca\u011f\u0131n\u0131z g\u00fcnler umar\u0131m ki bu yaz\u0131dan sonra daha yak\u0131n olsun.<\/p>\n\n\n\n

Referanslar<\/h3>\n\n\n\n
  • Doll, H. (2005). Statistical approaches to uncertainty: p values and confidence intervals unpacked. Evidence-Based Medicine<\/em>, 10(5), pp.133-134.<\/li>
  • Sedgwick, P. (2012). What is a P value?. BMJ<\/em>, 345(nov21 1), pp.e7767-e7767.<\/li>
  • Sedgwick, P. (2010). P values. BMJ<\/em>, 340(apr28 1), pp.c2203-c2203.<\/li>
  • Nuzzo, R. (2014). Scientific method: Statistical errors. Nature<\/em>, 506(7487), pp.150-152.<\/li><\/ul>\n","protected":false},"excerpt":{"rendered":"

    1920’lerde Fisher p degeri’ni tan\u0131mlad\u0131\u011f\u0131nda birg\u00fcn bu kadar yanl\u0131\u015f anla\u015f\u0131laca\u011f\u0131n\u0131 bilseydi herhalde matemati\u011fi b\u0131rak\u0131p inzivaya \u00e7ekilirdi. P de\u011feri ve anlam\u0131 g\u00fcn\u00fcm\u00fczde akademik d\u00fcnyan\u0131n…<\/p>\n","protected":false},"author":1561,"featured_media":514,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"inline_featured_image":false,"_lmt_disableupdate":"","_lmt_disable":"","footnotes":""},"categories":[21,10014],"tags":[],"class_list":["post-512","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-istatistik-yazilari","category-akademik-blog-yazisi"],"acf":[],"_links":{"self":[{"href":"https:\/\/tatd.org.tr\/atak\/wp-json\/wp\/v2\/posts\/512","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/tatd.org.tr\/atak\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/tatd.org.tr\/atak\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/tatd.org.tr\/atak\/wp-json\/wp\/v2\/users\/1561"}],"replies":[{"embeddable":true,"href":"https:\/\/tatd.org.tr\/atak\/wp-json\/wp\/v2\/comments?post=512"}],"version-history":[{"count":0,"href":"https:\/\/tatd.org.tr\/atak\/wp-json\/wp\/v2\/posts\/512\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/tatd.org.tr\/atak\/wp-json\/wp\/v2\/media\/514"}],"wp:attachment":[{"href":"https:\/\/tatd.org.tr\/atak\/wp-json\/wp\/v2\/media?parent=512"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/tatd.org.tr\/atak\/wp-json\/wp\/v2\/categories?post=512"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/tatd.org.tr\/atak\/wp-json\/wp\/v2\/tags?post=512"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}