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Analisis of Varians (Anova) Uji F uji beda mean tiga atau lebih sampel Oleh: Roni Saputra, M.Si

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Analisis of Varians (Anova) Uji F uji beda mean tiga atau lebih sampel Oleh: Roni Saputra, M.Si. Kegunaan. Menguji perbedaan mean dari beberapa kelompok (lebih dari dua kelompok) dengan menggunakan analisis variansi. Ringkasan Anava. Keterangan : F=Nilai F X=Nilai observasi - PowerPoint PPT Presentation
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Analisis Varians (Anava) uji beda tiga tau lebih sampel

Analisis of Varians (Anova) Uji F uji beda mean tiga atau lebih sampel

Oleh: Roni Saputra, M.Si KegunaanMenguji perbedaan mean dari beberapa kelompok (lebih dari dua kelompok) dengan menggunakan analisis variansi.

SUMBER VARIASIDERAJAT KEBEBASAN(db)JUMLAH KUADRAT (JK)MEAN KUADRAT (MK)FKelompok (K)dbK = K - 1Dalam (d)dbd = N KJKd = JKT - JKKTotal (T)dbT = N 1MKTRingkasan AnavaKeterangan :F=Nilai FX=Nilai observasinK=Banyaknya objek pada kelompok kK=Banyaknya kelompokN=Banyaknya seluruh objekKetentuan aplikasiData berskala interval atau rasio.Varians masing-masing kelompok tidak berbeda, alternatif uji bila varians data pada masing-masing kelompok berbeda adalah uji non parametrik Kruskal Wallis.Signifikansi, nilai hasil hitung F dibandingkan dengan nilai tabel F, derajat bebas v1=(k-1) dan v2=(N-k). Bila Ho ditolak, maka untuk melihat rincian perbedaan dilanjutkan dengan uji HSD atau LSD atau t test.NOMORDESA ARJODESA BARUDESA CITADESA DUKU1.2,583,152,402,752.2,542,882,852,823.2,482,763,002,674.2,653,083,022,595.2,503,102,952,846.2,462,982,747.2,902,588.2,892,909.3,00Di bawah ini data berat badan (satuan kg) bayi lahir di empat desa yang dicatat petugas desa masing-masing. Selidikilah dengan = 5%, apakah ada perbedaan berat badan bayi lahir di masing-masing desa?Contoh Aplikasi 1Penyelesaian :

HipotesisHo : BDA = BDB = BDC = BDD tidak ada perbedaan berat badan bayi baru lahir di Desa Arjo, Desa Baru, Desa Cita, Desa DukuHa : BDA BDB BDC BDD ada perbedaan berat badan bayi baru lahir di Desa Arjo, Desa Baru, Desa Cita, Desa Duku

Level signifikansi = 5%Ringkasan Anava

SUMBER VARIASIDERAJAT KEBEBASAN(db)JUMLAH KUADRAT (JK)MEAN KUADRAT (MK)FKelompok (K)dbK = K - 1Dalam (d)dbd = N KJKd = JKT - JKKTotal (T)dbT = N 1MKTNODESA ARJODESA BARUDESA CITADESA DUKUJUMLAH1.2,583,152,402,752.2,542,882,852,823.2,482,763,002,674.2,653,083,022,595.2,503,102,952,846.2,462,982,747.2,902,588.2,892,909.3,00XK15,2126,7414,2221,8978,06(XT)nK695828(N)Mean2,542,972,842,74XK238,5879,5740,7159,99218,85(XT2)

JKd = JKT - JKKJKd = 1,230 - 0,724JKd = 0,506

dbK = K 1 = 4 1 = 3dbd = N K = 28 4 = 24dbT = N 1 = 28 1 = 27

Df/db/dkdbK = K 1 = 4 1 = 3 V1dbd = N K= 28 4 = 24 V2

Nilai tabelNilai tabel F, = 5%, df = 3 ; 24, Nilai tabel F = 3,01

Daerah penolakanMenggunakan gambarMenggunakan rumus 11,476 > 3,01 ; berarti Ho ditolak, Ha diterima

SimpulanAda perbedaan berat badan bayi baru lahir di Desa Arjo, Desa Baru, Desa Cita, Desa Duku, pada = 5%.Karena Ho ditolak, maka dicari kelompok desa yang berbeda dan tidak beda.

Untuk memerinci perbedaan masing-masing kelompok dapat dilakukan dengan menggunakan :Uji dengan menggunakan Higly Significance Difference (HSD)Uji dengan menggunakan Leat Significance Difference (LSD)T test untuk dua kelompok sampel yang berbeda (independent)HSD=Higly Significance Difference

HSD0,05 antara rerata X1 dan X2 =

Beda signifikan jika X1 X2 HSD0,05X1 =mean kelompok 1X2 =mean kelompok 2MKd=Mean kuadrat dalamN1=banyaknya anggota sampel 1N2=banyaknya anggota sampel 2q=nilai tabel q

BEDA KETA vs B4,17 = 0,3182,54 2,97= 0,43signifikanA vs C4,17 = 0,3662,54 2,84= 0,30tidak signifikanA vs D4,17 = 0,3262,54 2,74= 0,20tidak signifikanB vs C4,17 = 0,3372,97 2,84= 0,13tidak signifikanB vs D4,17 = 0,2942,97 2,74= 0,23tidak signifikanC vs D4,17 = 0,3442,84 2,74= 0,10tidak signifikan

LSD=Leat Significance Difference

LSD0,05 antara X1 dan X2 =

Beda signifikan jika X1 X2 LSD0,05X1 =mean kelompok 1X2 =mean kelompok 2MKd=kuadrat dalamN1=banyaknya anggota sampel 1N2=banyaknya anggota sampel 2t=nilai tabel t

BEDAKETA vs B2,064 = 0,1582,54 2,97=0,43signifikanA vs C2,064 = 0,1812,54 2,84=0,30signifikanA vs D2,064 = 0,1622,54 2,74=0,20signifikanB vs C2,064 = 0,1672,97 2,84=0,13tidak signifikanB vs D 2,064 = 0,1452,97 2,74=0,23signifikanC vs D2,064 = 0,1712,84 2,74= 0,10tidak signifikan

Contoh aplikasi 2BLOK MBLOK OBLOK PBLOK ABLOK D5666785668606070557049707548656555695068596870557070655765687665Hasil pengukuran pencahayaan alami rumah ruang keluarga pada deret blok perumahan didapatkan data sebagai berikut:Selidikilah dengan = 5%, apakah ada perbedaan pencahayaan rumah blok M, blok O, blok P, blok A dan blok D?Penyelesaian :

HipotesisHo : Pm = Po = Pp = Pa = Pd tidak terdapat perbedaan pencahayaan alami ruang keluarga antara rumah pada blok M, blok O, blok P, blok A dan blok D.Ha : Pm Po Pp Pa Pd ada perbedaan pencahayaan alami ruang keluarga antara rumah pada blok M, blok O, blok P, blok A dan blok D

Level signifikansi = 5%Ringkasan Anava

SUMBER VARIASIDERAJAT KEBEBASAN(db)JUMLAH KUADRAT (JK)MEAN KUADRAT (MK)FKelompok (K)dbK = K - 1Dalam (d)dbd = N KJKd = JKT - JKKTotal (T)dbT = N 1MKTNOBLOK MBLOK OBLOK PBLOK ABLOK DJUMLAH1.56667856682.60607055703.49707548654.65556950685.59687055706.706557657.687665XK2894575033214712041(XT)nK5776732(N)Mean57,8065,2971,8653,5067,29XK21684330029362711723931723132105(XT2)

JKd = JKT - JKKJKd = 1927,47 1371,45JKd = 556,02

dbK = K 1 = 5 1 = 4dbd = N K = 32 5 = 27dbT = N 1 = 32 1 = 31

Df/db/dkdbK = K 1 = 5 1 = 4 V1dbd = N K= 32 5 = 27 V2

Nilai tabelNilai tabel F, = 5%, df = 4 ; 27, Nilai tabel F = 2,73

Daerah penolakanMenggunakan gambarMenggunakan rumus 4,80 > 2,73 ; berarti Ho ditolak, Ha diterima

SimpulanAda perbedaan pencahayaan alami ruang keluarga antara rumah pada blok M, blok O, blok P, blok A dan blok D, pada = 5%.Karena Ho ditolak, maka dicari kelompok blok rumah yang berbeda dan tidak beda.

Untuk memerinci perbedaan masing-masing kelompok dapat dilakukan dengan menggunakan :Uji dengan menggunakan Higly Significance Difference (HSD)Uji dengan menggunakan Leat Significance Difference (LSD)T test untuk dua kelompok sampel yang berbeda (independent)HSD=Higly Significance Difference

HSD0,05 antara rerata X1 dan X2 =

Beda signifikan jika X1 X2 HSD0,05X1 =mean kelompok 1X2 =mean kelompok 2MKd=Mean kuadrat dalamN1=banyaknya anggota sampel 1N2=banyaknya anggota sampel 2q=nilai tabel q

BEDA KETM vs O4,30 = 21,2757,8065,29=7,49tidak signifikanM vs P4,30 = 21,2757,8071,86=14,06tidak signifikanM vs A4,30 =22,00 57,8053,50= 4,30tidak signifikanM vs D4,30 = 21,2757,8067,29= 9,49tidak signifikanO vs P4,30 = 19,4265,2971,86= 6,57tidak signifikanO vs A 4,30 = 20,2165,2953,50=11,79tidak signifikanO vs D4,30 = 19,4265,2967,29= 2,00tidak signifikanP vs A4,30 = 20,2171,8653,50=18,36tidak signifikanP vs D4,30 = 19,4271,8667,29= 4,57tidak signifikanA vs D4,30 = 20,2153,50 67,29=13,79tidak signifikan

LSD=Leat Significance Difference

LSD0,05 antara X1 dan X2 =

Beda signifikan jika X1 X2 LSD0,05X1 =mean kelompok 1X2 =mean kelompok 2MKd=kuadrat dalamN1=banyaknya anggota sampel 1N2=banyaknya anggota sampel 2t=nilai tabel t

BEDA KETM vs O2,052 = 10,1557,8065,29=7,49tidak signifikanM vs P2,052 = 10,1557,8071,86=14,06SignifikanM vs A2,052 = 10,5057,8053,50= 4,30tidak signifikanM vs D2,052 = 10,1557,8067,29= 9,49tidak signifikanO vs P2,052 = 9,2765,2971,86= 6,57tidak signifikanO vs A 2,052 = 9,6565,2953,50=11,79SignifikanO vs D2,052 = 9,2765,2967,29= 2,00tidak signifikanP vs A2,052 = 9,6571,8653,50=18,36SignifikanP vs D2,052 = 9,27, 71,8667,29= 4,57tidak signifikanA vs D2,052 = 9,6553,50 67,29=13,79signifikan

V2(N-k)degree fredom of greater mean square (V1) derajat kebebasan untuk pembilang 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72,392,322,272,222,182,152,102,051,991,951,901,851,821,781,761,721,701,697,725,834,644,143,823,593,423,293,173,093,022,962,862,772,662,582,502,412,362,282,252,192,152,13274,213,352,962,732,572,462,372,302,252,202,162,132,082,031,971,931,881,841,801,761,741,711,681,677,685,494,604,113,793,563,393,263,143,062,982,932,832,742,632,552,472,382,332,252,212,162,122,10284,203,342,952,712,562,442,362,292,242,192,152,122,062,021,961,911,871,811,781,751,721,691,671,657,645,544,574,073,763,533,363,233,113,032,952,902,802,712,602,522,442,352,302,222,182,132,092,06294,183,332,932,702,542,432,352,282,222,182,142,102,052,001,941,901,851,801,771,731,711,681,651,647,605,424,544,043,733,503,333,203,083,002,922,872,772,682,572,492,412,322,272,192,152,102,062,03304,173,322,922,692,532,422,342,272,212,162,122,092,041,991,931,891,841,791,761,721,691,661,641,627,565,394,514,023,703,473,303,173,062,982,902,842,742,662,552,472,382,292,242,162,132,072,032,02Tingkat Signifikansi untuk tes satu sisi0,400,250,100,050,0250,010,0050,00250,0010,0005Tingkat Signifikansi untuk tes dua sisiDf0,800,500,200,100,050,020,010,0050,0020,00110,3251,0003,0786,31412,70631,82163,657127,32318,31636,6220,2890,8161,8862,9204,3036,9659,92514,08922,32731,59830,2770,7651,6382,3533,1824,5415,8417,45310,21412,92440,2710,7411,5332,1322,7763,7474,6045,5987,1738,61050,2670,7271,4762,0152,5713,3654,0324,7735,8936,86960,2650,7181,4401,9432,4473,1433,7074,3175,2085,95970,2630,7111,4151,8952,3652,9983,4994,0294,7855,40880,2620,7061,3971,8602,3062,8963,3553,8334,5015,04190,2610,7031,3831,8332,2622,8213,2503,6904,2974,781100,2600,7001,3721,8122,2282,7643,1693,5814,1444,587110,2600,6971,3631,7962,2012,7183,1063,4974,0254,437120,2590,6951,3561,7822,1792,6813,0553,4283,9304,318130,2590,6941,3501,7712,1602,6503,0123,3723,8524,221140,2580,6921,3451,7612,1452,6242,9773,3263,7874,140150,2580,6911,3411,7532,1312,6022,9473,2863,7334,073160,2580,6901,3371,7462,1202,5832,9213,2523,6864,015170,2570,6891,3331,7402,1102,5672,8983,2223,6463,965180,2570,6881,3301,7342,1012,5522,8783,1973,6103,922190,2570,6881,3281,7292,0932,5392,8613,1743,5793,883200,2570,6871,3251,7252,0862,5282,8453,1533,5523,850210,2570,6861,3231,7212,0802,5182,8313,1353,5273,819220,2560,6861,3211,7172,0742,5082,8193,1193,5053,792230,2560,6851,3191,7142,0692,5002,8073,1043,4853,767240,2560,6851,3181,7112,0642,4922,7973,0913,4673,745250,2560,6841,3161,7082,0602,4852,7873,0783,4503,725260,2560,6841,3151,7062,0562,4792,7793,0673,4353,707270,2560,6841,3141,7032,0522,4732,7713,0573,4213,690280,2560,6831,3131,7012,0482,4672,7633,0473,4083,674290,2560,6831,3111,6992,0452,4622,7563,0383,3963,659300,2560,6831,3101,6972,0422,4572,7503,0303,3853,646400,2550,6811,3031,6842,0212,4232,7042,9713,3073,551600,2540,6791,2961,6712,0002,3902,6602,9153,2323,4601200,2540,6771,2891,6581,9802,3582,6172,8603,1603,3730,2530,6741,2821,6451,9602,3262,5762,8073,0903,291Tabel Nilai qdfJumlah Perlakuan2345678910111213141516126,7032,8037,2040,5043,1045,4047,3049,1050,6051,9053,2054,3055,4056,3026,7028,289,8010,8911,7312,4313,0313,5413,9914,3914,7515,0815,3815,6515,918,2835,886,837,518,048,478,359,189,469,729,9510,1610,3510,5210,695,8845,005,766,316,737,067,357,607,838,038,218,378,528,678,805,0054,545,185,645,996,286,526,746,937,107,257,397,527,647,754,5464,344,905,315,635,896,126,326,496,656,796,927,047,147,244,3474,164,685,065,355,595,805,996,156,296,426,546,656,756,844,1684,044,534,895,175,405,605,775,926,056,186,296,396,486,574,0493,954,424,765,025,245,435,605,745,875,986,096,196,286,363,95103,884,334,664,915,125,305,465,605,725,835,936,036,126,203,88113,824,264,584,825,035,205,355,495,615,715,815,905,986,063,82123,774,204,514,754,955,125,275,405,515,615,715,805,885,953,77133,734,154,464,694,885,055,195,325,435,535,635,715,795,863,73143,704,114,414,644,834,995,135,255,365,465,565,645,725,793,70153,674,084,374,594,784,945,085,205,315,405,495,575,655,723,67163,654,054,344,564,744,905,035,155,265,355,445,525,595,663,65173,624,024,314,524,704,864,995,115,215,315,395,475,555,613,62183,614,004,284,494,674,834,965,075,175,275,355,435,505,573,61193,593,984,264,474,644,794,935,045,145,235,325,395,465,533,59203,583,964,244,454,624,774,905,015,115,205,285,365,435,503,58243,353,904,174,374,544,684,814,925,015,105,185,255,325,383,35303,483,844,114,304,464,604,724,834,925,005,085,155,215,273,48403,443,794,044,234,394,524,634,744,824,904,985,055,115,173,44603,403,743,984,164,314,444,554,654,734,814,884,945,005,063,401203,363,693,924,104,244,364,474,564,644,714,784,844,904,953,363,323,633,864,034,174,294,394,474,554,624,684,744,804,843,32

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Analisis of Varians (Anova) Uji F uji beda mean tiga atau lebih sampel Oleh: Roni Saputra, M.Si
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