Ka Hōʻike Haʻihelu Hoʻoili

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Pehea kākou e hoʻomaopopo ai i nā ʻikepili hōʻailona i hōʻiliʻili ʻia ma loko o kēia papahana nei? Hiki ke hoʻohana ʻia kekahi ʻano hana makemakika, ʻo ia hoʻi, ka hōʻike haʻihelu hoʻoili (Chi-Squared goodness of fit test).[1] I mea e hoʻomaopopo ai i ia hōʻike, eia kekahi laʻana nōhie: ʻEhā ou kākini, ʻo ia hoʻi, hoʻokahi ʻulaʻula, hoʻokahi polū, hoʻokahi ʻōmaʻomaʻo, hoʻokahi lenalena. Aia ia mau kākini ma loko o kekahi waihona. A laila, me ka nānā ʻole o ka maka, koho i hoʻokahi kākini mai ia waihona mai. Inā, e hoʻihoʻi ʻia ua kākini nei i ka waihona, a koho hou ʻia hoʻokahi kākini, e ʻokoʻa ana paha kona waihoʻoluʻu. Inā he pono koho ka hana, a he hoʻokahi haneli koho ʻana, hiki ke mahuʻi ʻia ka ʻikepili ma lalo iho nei: 

ʻUlaʻula:           25

Polu:                25

ʻŌmaʻomaʻo:   25

Lenalena:        25

 

Inā naʻe, ma hope o ka hana maoli ʻana, penei nā ʻikepili hāpana i loaʻa mai:

 

ʻUlaʻula:           15

Polu:                15

ʻŌmaʻomaʻo:    40

Lenalena:         30

 

Pehea kou manaʻo? He hana pono koho ia? He mea ʻokoʻa paha ko ke kākini ʻōmaʻomaʻo? He ʻokoʻa ʻano nui ko kēia mau ʻikepili hāpana a ʻokoʻa ka ʻikepili i mahuʻi ʻia? Hiki ke hoʻohana ʻia ia hōʻike haʻihelu hoʻoili ma ka ʻimi ʻana i ka hāʻina ʻana o ia mau nīnau. He aha ka mea o ia hōʻike e hoʻolako ai iā kākou? E ana ʻia ka ʻokoʻa o nā ʻikepili hāpana i ʻohi ʻia a me ka ʻokoʻa o nā ʻikepili i mahuʻi ʻia. Hana pinepine ʻia ia hōʻike no ka hoʻomaopopo ʻana i ka like a me ka ʻole o nā ʻikepili hāpana me nā ʻikepili mahuʻi. No laila, ʻo ka mea mua no ka hoʻohana ʻana i ia hōʻike, ʻo ia ka hoʻokumu ʻana i kahi kuhiakau kūpapa. Inā, he mau ʻikepili pono koho ʻoiaʻiʻo, a laila, eia ke kuhiakau kūpapa: ʻAʻole ʻokoʻa ka ʻikepili hāpana a ʻokoʻa ka ʻikepili mahuʻi. Nōhie paha ka haʻilula makemakika no kēia hōʻike, penei:

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                                                                         Eia nā hopena o kēia hōʻike:

            

 

 

 

 

 

 

 

 

Pehea kākou e hoʻomaopopo ai i ia mau hopena? ʻO ka mea ʻano nui loa, ʻo ia ka p-Pahiki. No ia laʻana, ʻo ka p-Pahiki = 0.001. He aha ka manaʻo nui o kēia p-Pakihi? Aia he 0.1% pahiki a ʻemi mai e like ana nā ʻikepili hāpana me ka ʻikepili mahuʻi. ʻO ia hoʻi, he 99.9% pahiki e ʻoi makemakika aku ana ka huina o kekahi mau waihoʻoluʻu kākini, a ʻoi aku ia ma mua o nā huina o nā waihoʻoluʻu kākini ʻē aʻe. No laila hōʻole ʻia ia kuhiakau kūpapa.ʻO ka waihoʻoluʻu kākini hea? ʻO ke kākini ʻōmaʻomaʻo paha no kēia laʻana. Hoʻopuka pinepine ʻia nā hopena o ka hōʻike haʻihelu hoʻoili, penei:

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χ2 (3, n = 100) = 18.00, p < 0.001

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df                                 Kēkelē o ke kūʻokoʻa

n                                  Ka huinanui hāpana

Chi Square                  Waiwai Chi Square

p-Pahiki                       Pahiki o ka ʻoiaʻiʻo o ke kuhiakau kūpapa

 

He kōkua paha ia wahi wehewehe ʻana i ia laʻana hana makemakika. Ke hoʻohana ʻia no ke kālailai ʻana i nā ʻikepili ānuenue ma loko o kēia papahana laeoʻo nei, hoihoi loa nā hopena.

Pākuʻina 2: Ke Kālaikūlohea Ānuenue

I kēia ʻōlelo pākuʻina nei, e wehewehe ʻia kekahi mau mea kālaikūlohea e pili ana i ke ānuenue.

Nā Waihoʻoluʻu Ao Kūmaka

 

ʻO ko ka lā malama a kākou e ʻike ai, ʻo ia wale nō kekahi ʻāpana liʻiliʻi o ka ʻauina mākēneki uila holoʻokoʻa. Aia ma loko o ia ʻauina ke kukuna gamma, ke kukuna X, UV, ka hawewe ʻulaʻula lalo, a me nā hawewe lekiō. ʻIke kākou i ka malama keʻokeʻo o ka lā, eia naʻe, aia ma loko o ka malama keʻokeʻo nā waihoʻoluʻu like ʻole. Hiki ke ʻike ʻia ka ʻauina mākēneki uila a me nā waihoʻoluʻu like ʻole o ka malama kūmaka ma ka Pakuhi ma lalo iho.[2] ʻAʻole hiki ke ʻike ʻia ia mau waihoʻoluʻu ke ʻole ka ʻapakau ʻia o ka malama keʻokeʻo e kekahi mea kālaʻe, e laʻa kahi ʻōpaka a i ʻole kahi huna wai. ʻO ia ʻapakau ʻia ʻana o ka malama keʻokeʻo e nā huna wai pūailewa, ʻo ia ka mea nāna e hoʻohua ke ānuenue.

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Ka ʻauina mākēneki uila

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Ko ka huna wai anawaena

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​Kaukaʻi ka ʻoi o nā ʻauina kala ānuenue i ke anawaena o nā huna wai ma ka lewa. Loli nō hoʻi ke ākea o nā ʻauina waihoʻoluʻu ma muli o ke anawaena o nā huna wai. Inā, nui ke anawaena, hāiki a ʻoi nā ʻauina waihoʻoluʻu. I ka manawa nui ka ua, kupu ke anawaena o nā huna wai i kekahi mau milimika.[3] Hiki ke ʻike ʻia kēia ʻano ʻauina waihoʻoluʻu nona ka ʻauina hāiki ma loko o ke Kiʻi o lalo.

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He ānuenue nona nā ʻauina hāiki (na Burt Johnson | Dreamstime.com)

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Inā, liʻiliʻi ke anawaena o nā huna wai, ʻōʻili ke ānuenue nona nā ʻauina waihoʻoluʻu ākea.[4] Hiki ke ʻike ʻia kēia ʻano ʻauina ma loko o ke Kiʻi o lalo.​

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He ānuenue nona nā ʻauina ākea (na R.B. Herkes | Dreamstime.com)

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Inā, kāwili ʻia ke anawaena o nā huna wai, poahi nā ʻauina makawalu. E aho ka ʻike maka ʻana i nā ʻauina makawalu i ka manawa o nā huna wai ʻuʻuku e kau ai i ka lewa. Eia naʻe, i ia manawa, poahi ka Piʻo Mōʻī. ʻO ia hoʻi, ʻoi aku ke anawaena o nā huna wai ma mua ka milimika he hoʻokahi, ʻaʻole ʻōʻili nā ʻauina makawalu. Eia kekahi, inā e ʻēmi ana ke anawaena a hiki i ka milimika he ʻole kiko ʻehā, ʻoi aku ana ke ākea a me ke ʻalohi o ka ʻauina makawalu. Inā he ʻuʻuku nō ka huna wai, ʻo ia hoʻi, he ʻohu, ʻōʻili paha kekahi ānuenue ma loko o ka ʻohu.[5]

 

Ka pilina o ke anawaena huna wai me nā hiʻohiʻona ānuenue

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Kaukaʻi ʻia nā waihoʻoluʻu i mea e ʻike ai i ke anawaena o nā huna wai i ka lewa. Inā, nui ke anawaena huna wai (1mm a ʻoi ke anawaena), a laila, ʻalohi nō ke ānuenue nona ka nui aʻe o nā waihoʻoluʻu ʻaʻai. Ke emi ke anawaena huna wai, ʻāweʻaweʻa ka waihoʻoluʻu ʻulaʻula. I ka noe, nalowale paha nā waihoʻoluʻu like ʻole koe ka waioleka. I ka lilinoe (0.05mm a emi mai ke anawaena huna wai), kauhapa nā waihoʻolulu a pau kekahi i kekahi, a keʻokeʻo ke ānuenue ke nānā aku. Hiki ke ʻike ʻia ka pilina o ke anawaena huna wai me nā hiʻohiʻona o ke ānuenue i ka Pakuhi o luna aʻe.[6]

 

Inā aia kekahi mau anawaena huna wai he ʻelua ma loko o kekahi mau kuāua he ʻelua i kahi manawa hoʻokahi, ʻōʻili paha ʻelua ānuenue e hoʻohihi ʻia. ʻŌʻili nā ānuenue e hoʻohihi ʻia ma muli o nā anawaena huna wai he ʻelua. Pipiʻo ia mau ānuenue i kekahi mau ala he ʻelua, eia naʻe, pili pū ia mau ānuenue he ʻelua i ko lāua mau kumu. ʻO ke koina mua no ka ʻōʻili ʻana o ia ʻano ānuenue, ʻo ia kekahi mau huna wai he ʻelua i ʻokoʻa ko lāua anawaena ʻiʻo. Inā, lolilua nō nā anawaena huna wai ma loko o nā kuāua he ʻelua, kāwili pū ʻia ia mau ānuenue he ʻelua, a ʻōʻili mai he hoʻokahi wale nō ānuenue.[7] Kākaʻikahi ia ʻano ānuenue. Hiki ke ʻike ʻia ma loko o ke Kiʻi o lalo.

 

ʻElua ānuenue e hoʻohihi ʻia (na Jacobs School of Engineering)

 

 

 

 

 

 

 

 

 

 

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[1] Frederick J. Gravetter and Larry B Wallnau. 2013. Essentials of Statistics for the Behavioral Sciences. 8. Wadsworth Cenegage Learning. ʻaoʻao 518.

[2] Judith Donnelly, Nicholas Massa. 2018. LIGHT: Introduction to Optics and Photonics. Pittsfield: Photonics Media Press; Laurin Publishing Co. Inc.

[3] 2003. The Effect of a Water Drop on a Rainbow. Craig Ryomoto. Apelila 28. Accessed Apelila 2024. https://personal.math.ubc.ca/~cass/courses/m309-03a/m309-projects/ryomoto/project.html.

[4] n.d. Effect of drop size on primary rainbow. Accessed 4 2024. https://atoptics.co.uk/blog/effect-of-drop-size-on-primary-rainbow/.

[5] k.l.

[6] 2003. The Effect of a Water Drop on a Rainbow. Craig Ryomoto. Apelila 28. Accessed Apelila 2024. https://personal.math.ubc.ca/~cass/courses/m309-03a/m309-projects/ryomoto/project.html.

[7] Katherine Wright.  n.d. Think You Know Rainbows? Look Again. Accessed Apelila 2024. https://www.scientificamerican.com/article/think-you-know-rainbows-look-again-slide-show1/.​​​​​