Nā ʻenehana no ka hana ʻana i nā Histograms ma ka ʻikepili i hui pū ʻia
He mea hana hōʻike ʻikepili i hoʻohana pinepine ʻia ka histogram i nā helu helu, ʻoiai ke hana nei me ka ʻikepili i hui pū ʻia. ʻAʻole e like me ka pakuhi pā maʻamau, e hōʻike ana i nā māhele ʻokoʻa, hōʻike ka histogram i ka hoʻolaha pinepine ʻana o ka ʻikepili helu i hui pū ʻia i nā wā papa. Ma o ka histogram, hiki iā mākou ke nānā i nā ʻano hoʻolaha ʻikepili, nā ʻano (e.g., ke skewing i ka ʻākau a i ʻole hema), a hiki i kahi kuhi o ke ʻano hoʻolaha (maʻamau, skewed, bimodal, a pēlā aku). Kūkākūkā kēia ʻatikala i nā ʻano hana no ka hana ʻana i nā histograms no ka ʻikepili i hui pū ʻia, mai ke kūkulu ʻana i kahi papa hoʻolaha pinepine a hiki i ke kahakiʻi ʻana i kahi histogram pololei.
1. Ke Hoʻomaopopo ʻana i ka ʻIkepili i Hoʻohui ʻia a me nā Histograms
ʻO ka ʻikepili i hoʻohui ʻia he ʻikepili helu i hōʻuluʻulu ʻia i loko o kekahi mau wā papa. No ka laʻana, ʻaʻole hōʻike ʻia nā helu hoʻāʻo haumāna ma ke ʻano pākahi akā ua hoʻohui ʻia i loko o nā pae 40-49, 50-59, 60-69, a pēlā aku. Loaʻa i kēlā me kēia wā kahi alapine (frequency), ʻo ia ka helu o nā kiko ʻikepili e hāʻule ana i loko o kēlā wā.
He kiʻikuhi ka histogram i haku ʻia me nā kaola i hoʻokaʻawale ʻia me nā hakahaka ʻole (a i ʻole nā hakahaka liʻiliʻi loa), no ka mea, hōʻike ia i kahi pae mau o nā waiwai. Hōʻike ka laulā o ka kaola i ka lōʻihi o ka wā papa, ʻoiai ke kiʻekiʻe o ka kaola e hōʻike ana i ke alapine a i ʻole ka nui o ke alapine (ma muli o ka like a ʻokoʻa paha o nā laulā o ka papa).
2. Ke hōʻuluʻulu ʻana i kahi papa hoʻokaʻawale alapine (frequency distribution)
ʻO ka hana mua i ka hana ʻana i kahi histogram, ʻo ia ke kūkulu ʻana i kahi papa hoʻokaʻawale alapine. ʻO ka maʻamau, pili kēia kaʻina hana i kēia mau mea:
1. E hoʻoholo i nā waiwai liʻiliʻi a me nā waiwai kiʻekiʻe o ka ʻikepili.
2. E helu i ka laulā = maximum − minimum.
3. E hoʻoholo i ka helu o nā papa (k).
4. E hoʻoholo i ka lōʻihi o ka papa (p) = ka laulā / k (hoʻopuni ʻia e like me ka mea e pono ai).
5. E hoʻonohonoho i nā wā papa a e helu i ke alapine (pinepine) i kēlā me kēia wā.
Aia kekahi mau alakaʻi no ka hoʻoholo ʻana i ka helu o nā papa. ʻO kekahi mea kaulana ʻo ia ke ʻano Sturges:
k = 1 + 3,3 log10(n)
kahi ʻo n ka helu o nā kiko ʻikepili. Hoʻopuni ʻia ka hopena o k i ka helu piha kokoke loa.
Laʻana maʻalahi: inā ʻo n = 40, a laila k ≈ 1 + 3,3 log10(40) ≈ 1 + 3,3(1,602) ≈ 6,29 no laila hiki ke koho ʻia he 6 a 7 mau papa.
3. Ke hoʻoholo nei i nā palena papa a me nā lihi papa
ʻO kahi hewa maʻamau i ka wā e hana ai i nā histograms, ʻo ia ka huikau ʻana i nā palena papa me nā lihi papa.
– ʻO nā palena papa he mau helu i kākau ʻia i nā wā waena, no ka laʻana 50–59.
– ʻO nā palena papa he mau palena hoʻomau e hoʻokaʻawale ana i nā papa i ʻole e loaʻa nā "ākea" ma waena o nā papa.
Inā he helu holoʻokoʻa ka ʻikepili, a laila hoʻoholo pinepine ʻia ka lihi papa ma ka hoʻohui ʻana a me ka unuhi ʻana i ka 0,5.
laʻana:
– ʻO ka wā ma waena o 50–59 he 49,5–59,5 nā lihi papa
– ʻO ka wā ma waena o 60–69 he 59,5–69,5 nā lihi papa
No laila, ua hui nā lihi o ka papa ma 59,5 i ʻike ʻia ai ka histogram ua hoʻokahi a hoʻomau maoli.
Eia nō naʻe, inā he ana hoʻomau ka ʻikepili (no ka laʻana, ke kiʻekiʻe ma ke kenimika a hiki ke loaʻa nā decimals), ʻo ka hoʻoholo ʻana i nā palena papa e pili ana i ka pololei o ke ana. ʻO ke kumumanaʻo ka hana ʻana i nā palena papa i ʻole e uhi a waiho ʻole i nā hakahaka.
4. E hoʻoholo i ka unahi ma ka X a me Y Axis
ʻElua mau koʻi nui o ka histogram:
– X axis (paepae): hōʻike i nā wā papa (e hoʻohana pinepine ana i nā lihi papa e hōʻoia i ka hoʻomau).
– Y axis (kū): hōʻike i ke alapine (frequency).
Inā like ka laulā o nā wā āpau o ka papa, a laila ana ʻia ke kiʻekiʻe o ka pā me ka hoʻohana ʻana i ke alapine (frequency). Eia nō naʻe, inā ʻokoʻa ka laulā o ka wā o ka papa, pono e ana ʻia ke kiʻekiʻe o ka pā me ka hoʻohana ʻana i ka nui o ke alapine (frequency density):
Ka nui o ke alapine (frequency density) = alapine (frequency) / laulā o ka papa
He mea nui ka hoʻohana ʻana i ka nui o ka paʻa i kūlike ka ʻāpana o ka pā me ke alapine maoli. A i ʻole, e ʻike ʻia nā papa ākea he "nui" ma muli wale nō o ko lākou laulā, ʻaʻole ma muli o ka nui o ka ʻikepili.
5. Ke kaha kiʻi ʻana i nā pā Histogram
Ke hoʻoholo ʻia ka unahi a me nā wā, ʻo ka hana aʻe e kahakiʻi i ke kaola.
ʻO ke ʻano hana kūpono no ke kaha kiʻi ʻana i kahi histogram:
1. E kaha i nā lihi o ka papa ma ke axis X ma ke kaʻina.
2. Ma kēlā me kēia wā, e kahakiʻi i kahi ʻāpana huinahā nona ka laulā e kūlike ana me kēlā wā.
3. Pili ke kiʻekiʻe o ka pā i ke alapine (a i ʻole ka nui o ke alapine inā ʻaʻole like ka laulā o ka papa).
4. E hōʻoia i ka pili pono ʻana o nā kumu (me ka ʻole o nā hakahaka).
5. E hāʻawi i ka histogram i kahi inoa, e lepili i nā koʻi X a me Y, a me nā anakahi inā pono.
Eia kekahi laʻana, inā he 40–49, 50–59, 60–69 nā wā papa, a ʻo ko lākou alapine (pinepine) he 5, 12, 18, a laila e ʻoi aku ke kiʻekiʻe o ke kaʻina no ka papa 60–69 ma mua o nā papa ʻē aʻe no ka mea ʻo kona alapine (pinepine) ka nui loa.
6. Ka Heluhelu ʻana a me ka Wehewehe ʻana i nā Histograms
ʻAʻole wale ka histogram he kiʻi, akā he mea hana loiloi. Mai kahi histogram, hiki iā mākou ke ʻike:
– Papa ʻano: papa me ke kaha kiʻekiʻe loa (alapine kiʻekiʻe loa).
– ʻAno hoʻolaha: likelike, skewed i ka ʻākau (positive skew), skewed i ka hema (negative skew), a i ʻole he ʻelua piko (bimodal).
– Ka hoʻolaha ʻikepili: inā paha ua kālele ʻia ka ʻikepili ma kahi manawa kikoʻī a i ʻole ua hoʻolaha nui ʻia.
– Hōʻike ʻokoʻa: inā aia kahi papa ma ka hopena me kahi alapine liʻiliʻi a ua hoʻokaʻawale ʻia mai ka hui nui.
ʻO ka wehewehe maikaʻi e hele pū me kahi hopena pōkole. Eia kekahi laʻana: "ʻO ka hapa nui o ka ʻikepili e hāʻule ana ma ka pae 60-79, e hōʻike ana he maʻamau nā helu o ka poʻe komo ma ka māhele waena."
7. Nā hewa maʻamau
Eia kekahi mau hewa e pale aku ai:
1. E hāʻawi i kahi hakahaka ma waena o nā kaola i mea e like ai me ka pakuhi kaola.
2. Ke hoʻohana nei i nā palena papa, ʻaʻole nā lihi papa, no laila aia nā hakahaka i ka laulā ʻikepili.
3. ʻAʻole e hoʻoponopono i ke kiʻekiʻe o ka pā i ka wā e ʻokoʻa ai ka laulā o ka papa, i lilo ai ka hoʻohālikelike alapine i mea hoʻopilikia.
4. Kūlike ʻole nā unahi axis a ʻaʻole hoʻomaka ma ka ʻole ma ke axis alapine (hiki ke alakaʻi hewa i ka ʻike maka).
5. ʻAʻole pili pono a pili pū paha nā wā papa, no ka laʻana 50–60 a me 60–70 me ka ʻole o ka wehewehe ʻana i nā lihi papa.
8. Nā Manaʻo Kūpono no ka Hoʻolilo ʻana i nā Histograms i mea ʻIke Hou aku
I mea e maʻalahi ai ke hoʻomaopopo ʻana i ka histogram:
– E hoʻohana i kahi helu kūpono o nā papa (ma ke ʻano maʻamau he 5-12 mau papa, ma muli o ka nui o ka ʻikepili).
– E hōʻalo i nā wā haiki loa (nui loa nā papa) no ka mea e lilo ka histogram i "walaʻau".
– E pale i nā wā ākea loa (kakaikahi nā papa) no ka mea e nalowale paha ke ʻano hoʻolaha.
– E hoʻokomo i nā kumu ʻikepili, ka nui o ka laʻana (n), a me nā ʻike ʻē aʻe inā pono i loko o ka hōʻike.
Inā ʻoe e hoʻohana ana i nā polokalamu e like me Excel, Google Sheets, a i ʻole nā polokalamu helu, e hoʻomaopopo mau i ke kumumanaʻo o ka lihi papa a me ka laulā o ka papa i ʻole e hewa nā hopena histogram.
Pani
ʻO ke ʻano hana o ka hana ʻana i kahi histogram no ka ʻikepili i hui pū ʻia e pono ai ka pololei i ke kūkulu ʻana i nā wā papa, ka hoʻoholo ʻana i nā palena papa, a me ka hoʻoholo ʻana i nā kiʻekiʻe kūpono o ka pā. Inā like nā wā papa, e hoʻohana wale i ke alapine (frequency) ma ke ʻano he kiʻekiʻe o ka pā. Inā ʻaʻole like nā wā, e hoʻohana i ka nui o ke alapine (frequency density) e mālama i kahi ʻike kūpono a pololei. Me kahi histogram i kūkulu pono ʻia, hiki iā mākou ke loaʻa koke i kahi ʻike o ke ʻano hoʻolaha ʻikepili a hana i nā wehewehe pololei i ka loiloi helu.
Inā makemake ʻoe, hiki iaʻu ke hoʻohui i ka ʻikepili laʻana a hoʻopau i nā ʻanuʻu helu a hiki i ka pau ʻana o ka histogram (ma ka lima a i ʻole me Excel/Sheets).
