Simpsonen paradoxa

Puntu urdin nahiz gorrien multzoetarako x eta y aldagaien arteko korrelazioa positiboa da (x aldagaiak gora egitean, y aldagaiak ere gora egiten du) baina puntu guztiak bateratzean, x eta y aldagaien arteko korrelazioa negatiboa da, marra etenak erakusten duen bezala.

Probabilitatean eta estatistikan, Simpsonen paradoxa multzo zenbaitetan dagoen bi aldagaien arteko erlazio estatistikoa multzo horiek bateratzean norabidez aldatzearen paradoxa da. Paradoxa, aldagaien arteko kausa-ondorio erlazioen bitartez burutzen da, multzoak bereizten dituen aldagaia benetan erabakiorra den aztertuz. Bestalde, estatistika jendarteratzean maiz azaltzen den paradoxa da, publikoak emaitza estatistikoak kontuz interpretatu beharra nabarmentzeko.

Adibidea

Ikastetxe batean matematika eta hizkuntza frogak egin zaizkie zenbait ikasleei, datuak sexuaren arabera sailkatuz:

MATEMATIKA neska mutil GUZTIRA
gainditu 1 2 3
ez gainditu 4 6 10
GUZTIRA 5 8 13
HIZKUNTZA neska mutil GUZTIRA
gainditu 6 4 10
ez gainditu 2 1 3
GUZTIRA 8 5 13


Matematikan, 1/5<2/8 betetzen da; beraz, mutilek matematika gainditzeko joera nabarmenagoa dute. Hizkuntzan berriz, 6/8 < 4/5 betetzen da; beraz, horretan ere mutilek gainditzeko joera handiagoa dute. Bi frogak bateratzean:


BI FROGAK neska mutil GUZTIRA
gainditu 7 6 13
ez gainditu 6 7 13
GUZTIRA 13 13 26


Bi frogak bateraturik, 7/13>6/13; beraz, neskek, oro har, gainditzeko joera nabarmenagoa dute.

Taula bateratu gabe eta bateratuta sortzen den kontraesana irakasgai mota benetan kontuan hartu behar den aldagaia ote den aztertuz ebatzten da. Kasu horretan, nahiko garbi dago irakasgai mota kontuan hartu behar dela eta beraz, bi jakintza-arloetan mutilek neskek baino emaitza hobeak izaten dituztela ondorioztatu behar da.

Kanpo estekak

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