anova - usu opencoursewareocw.usu.ac.id/.../his127_slide_anova.pdf · uji 2 arah zkemaknaan 5% z...
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![Page 1: Anova - USU OpenCourseWareocw.usu.ac.id/.../his127_slide_anova.pdf · Uji 2 arah zKemaknaan 5% z Penentuan uji : > 2 klpk = anova. ... ANOVA A 140.150 3 46.717 23.070 .000 32.400](https://reader031.vdocuments.net/reader031/viewer/2022012310/5ca9d49588c99371398d546a/html5/thumbnails/1.jpg)
AnovaAnova
Dr. Arlinda Sari Wahyuni, Mkes
Topik :Prinsip anovaSyaratSyaratAplikasi
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AnovaAnova
Anova = uji beda > 2 mean
Tidak dianjurkan menggunakan uji t ok inflasi nilai alpha1-(1-a)Dianjurkan uji F
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AnovaAnova
anovaanova
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PrinsipPrinsip
Melakukan telaah variabilitas data menjadi 2 sumber variasidata menjadi 2 sumber variasiyaitu variasi within (dlm kelompok) dan variasi antar kelompok) dan variasi antar kelompok (between)
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Asumsi/syaratAsumsi/syarat
Varian homogenSampel/kelompok independenSampel/kelompok independenData berdistribusi normalJenis data yg dihubungkan adalah numerik dengan kategori
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PerhitunganPerhitungan
F = Sb2F = Sb2
Sw2
df = k-1 utk pembilangn-k utk penyebutn k utk penyebut
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AnovaAnova
Sw2 = (n1-1)S2 + (n2-1)S2 + … (nk-1)Sk2
N-k
Sb2 = (n1(X1-X) 2 +n2(X2-X) 2+ ….n(Xk-X) 2
K-1
X 1X1 2X2 k XkX = n1X1 + n2X2 + … nk XkN
N = jumlah seluruh data (n1+n2+ nK)N = jumlah seluruh data (n1+n2+…nK)
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AplikasiAplikasi
Suatu penelitian ingin mengetahui perbedaan kadar mengetahui perbedaan kadar folat sel darah pada 3 zat pembius (anestesi) yang pembius (anestesi) yang berbeda. Data yang berhasil dikumpulkan :dikumpulkan :
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AplikasiAplikasi
Klpk I: 243 251 275 291 347 254 280 392
Klpk II: 206 210 226 249 255 273 285 295 309
Klpk III: 241 258 270 293 328
Coba buktikan apakah ada perbedaan kadar folat sel darah merah pada kelompok p ptsb dengan alpha 5%
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Jawab:Jawab:
Hipotesis : Ho : m1 = m2= m3Ho : m1 = m2= m3Ha : m1 ≠ m2 ≠ m3Uji 2 arah
Kemaknaan 5%Kemaknaan 5%Penentuan uji : > 2 klpk = anova
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Perhitungan :Perhitungan :
Klpk I : mean = 316,62 sd 58,72klpk II : mean = 256 44 sd 37 12klpk II : mean = 256,44 sd 37,12klpk iii: mean = 278,00 sd 33,76Sw2 = (n1-1)S2 + (n2-1)S2 + … (nk-1)Sk2
N-k(8 1)(58 72) 2 + (9 1)(37 12) 2 + (5 1)(33 76) 2 (8-1)(58,72) 2 + (9-1)(37,12) 2 + (5-1)(33,76) 2
22-3= 2090= 2090
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Sb2 = (n1(X1-X) 2 +n2(X2-X) 2+ ….n(Xk-X) 2
K-1X = n1X1 + n2X2 + … nk Xk
NX = 8(316,62)+9(256,44)+5(278)
22X = 283,22
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Sb2 = n1(X1-X) 2 +n2(X2-X) 2+ ….n(Xk-X) 2
K-18 (316,62-283,22) 2 + 9(256,4-283,22) 2 + 5(278,00 -283,22) 2
3-1
Sb 2 = 7758
F = 7758/ 2090 = 3,71numerator = df 1 = K-1 = 3-1 =2denunerator = df 2 = N-K = 22-3 = 19
![Page 14: Anova - USU OpenCourseWareocw.usu.ac.id/.../his127_slide_anova.pdf · Uji 2 arah zKemaknaan 5% z Penentuan uji : > 2 klpk = anova. ... ANOVA A 140.150 3 46.717 23.070 .000 32.400](https://reader031.vdocuments.net/reader031/viewer/2022012310/5ca9d49588c99371398d546a/html5/thumbnails/14.jpg)
F = 3,71Numerator = 2Numerator = 2denumerator = 19Lihat tabel F 3,523,71> 3,52 3,71 3,52 Kesimpulan : Ho ditolak
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Latihan :Latihan :
Dari 4 jenis obat sakit kepala yg diberikan kepada 20 orang dicatat diberikan kepada 20 orang dicatat berapa lama obat itu dapat mengurangi rasa sakit (menit). Ke 20 orang itu dibagi secara random kedalam 4 kelompok dan masing-masing kelompok diberi 1 jenis obatmasing kelompok diberi 1 jenis obat.Ujilah dengan alpha 5% apakah ada perbedaan lama mengurangi rasa perbedaan lama mengurangi rasa sakit?
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Lama hilang rasa sakit:A B C DA B C D10 8 7 812 7 4 913 7 3 913 7 3 99 9 3 1013 7 4 1113 7 4 11
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Descriptives
A
Std L U
95% ConfidenceInterval for Mean
5 11.4000 1.8166 .8124 9.1444 13.6556 9.00 13.005 7.6000 .8944 .4000 6.4894 8.7106 7.00 9.00
1.002.00
N MeanStd.
Deviation Std. ErrorLowerBound
UpperBound Minimum Maximum
5 4.2000 1.6432 .7348 2.1597 6.2403 3.00 7.005 9.4000 1.1402 .5099 7.9843 10.8157 8.00 11.00
20 8.1500 3.0136 .6739 6.7396 9.5604 3.00 13.00
3.004.00Total
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ANOVA
A
140.150 3 46.717 23.070 .00032.400 16 2.025
Between GroupsWithin Groups
Sum ofSquares df
MeanSquare F Sig.
172.550 19Total
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Posthoc TestPosthoc Test
Apabila pada uji anova terdapat perbedaan maka selanjutnya perbedaan, maka selanjutnya dapat dilakukan analisis multiple comparison (Posthoc multiple comparison (Posthoc test) untuk menentukan kelompok mana yang berbedakelompok mana yang berbeda
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Jenis Posthoc TestJenis Posthoc Test
BonferoniHonestly Significant DifferenceHonestly Significant DifferenceScheffedll
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Rumus BonferoniRumus Bonferoni
x1 - x2T12 = -----------------
√ SW² (1/n1 +1/n2)
Apha (α) = α---------- k/2 = 3!---------- k/2 = 3!(k 2!(3-2)!
2))
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Suatu penelitian ingin membedakan rerata td pada 3 kelompok anti hipertensi. Adapun data sbbdata sbbKlp 1 : 144 154 176 158 162 124 143 133 139Klp 2 : 130 132 132 128 129 133 131 130 125Klp 3 : 144 142 141 139 138 142Klp 3 : 144 142 141 139 138 142140 138 133Ujilah apakah ada perbedaanKelompok mana yang cendrung berbeda?