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ANAVA ANALISIS VARIANSI

ANAVA ANALISIS VARIANSI. Klasifikasi satu arah Pendekatan yang memungkinkan digunakannya data sampel untuk menguji apakah nilai dari dua atau lebih rata-rata adalah sama . Hipotesis-nol yang digunakan dalam analisis sampel adalah :

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ANAVA ANALISIS VARIANSI

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  1. ANAVAANALISIS VARIANSI Klasifikasisatuarah Pendekatanyang memungkinkandigunakannya data sampeluntukmengujiapakahnilaidariduaataulebih rata-rata adalahsama. Hipotesis-nol yang digunakandalamanalisissampeladalah : Ho : 1 = 2 = 3…………..=k, sedanghipotesis-alternatifnya : HI : seluruhpopulasitidakmempunyairerata yang sama. Dalamanalisisini, bilahipotesis-alternatif yang diterima, makapaling tidakakanterdapatsebuahreratapopulasi yang berbeda. Tetapianalisisinitidakakanmemberikaninformasi, berapabanyak yang berbedaataupopulasimanasaja yang berbeda.

  2. Prosedurpengujian : RK = RJA / RJD = [JA/(k-1)] / [JD / (k) (n – 1)] Dimana ; JK = ∑ ∑ X ij2 - C JA = [(∑ T i2 ) / ( n ) ] – C C = T2 / kn JD = JK – JA Bilasampeltidaksama : JA = [(∑ T i2 ) / ( ni ) ] – C C = T2 / ∑n JA = Jumlahkuadratantarsampel JD = Jumlahkuadratdalamsebuahsampel JK = Jumlahkuadratkeseluruhan C = koreksi Ti = Jumlah n observasidalamsampelke-I T = Jumlahknobservasi

  3. Rekapitulasi ANAVA _____________________________________________________________________ SumberDerajat ∑ Kuadrat Rata kuadrat RK VariasikebebasanDf ===================================================================== Perlakuan k – 1 JA RJA = JA/(k-1) RJA/RJD Galat k(n -1) JD RJD= JD/(k)(n-1) ===================================================================== Jumlah nk-1 JK Bandingkannilai RK dengantabeldistribusi F denganα 1% atau 5% Penerimaan HO Penolakan HO α = 5% atau 1 % 0 F Contoh ; Df1 = Degree of freedom for numerator = k – 1 Df2 = Degree of freedom for denumerator = k (n – 1)

  4. Contoh : Lakukananalisisvariansiuntukmengetahui, apakahadaperbedaan yang berartiantaraklastersebutdalamhalperolehannilai, denganα 5% (Jumlahsampelsama) ============================================================= Klas A Klas B klas C Klas D ============================================================= 80 90 70 85 70 85 80 90 80 70 90 85 90 65 80 70 80 80 60 75 60 75 80 90 80 70 75 75 75 95 85 80 80 90 75 65 60 75 90 70 =============================================================

  5. Penyelesaian : Ho µA = µB = µC=µD H1 µA ≠ µB ≠ µC≠µD HitungNilai : Ti, T2, C, JK, JD, JA ============================================================= Klas A Klas B klas C Klas D ============================================================= 80 90 70 85 70 85 80 90 80 70 90 85 90 65 80 70 80 80 60 75 60 75 80 90 80 70 75 75 75 95 85 80 80 90 75 65 60 75 90 70 ============================================================= TA= TB = TC = TD = T = TA + TB +TC + TD

  6. T total = 3120 C = (T total) 2 / [(k)(n)] = 243360 JA = [[(TA)2 + (TB)2+(TC)2+(TD)2] / (n) ] - C = 90 JK = (80)2 + (70)2 + …….. + (65)2+ (70)2 ] - C = 3290 JD = JK - JA = 3200 RJA = JA/(k - 1) = 30 RJD = JD/[(k)(n - 1)] = 88.889 RK = RJA / RJD = 0.3375 BerdasarkantabelDistribusi F : α = 5% Df1 = (k - 1) = 3 Df2 = k (n - 1) = 36 Diperolehnilai F adalah 2.88 RK Penerimaan HO Penolakan HO α =5% 0 F =2.88 Ternyata RK jatuhdidaerahpenerimaan, jadi HO diterima. Artinyabahwanilaidiklastersebuttidakadaperbedaan yang berarti.

  7. Sampeltidaksama Diketahui data sebagaiberikut : Kelompok A Kelompok B Kelompok C 90 105 83 82 89 89 79 93 80 98 104 94 83 89 91 95 86 Lakukananalisisvariansiuntukmengetahui, apakahadaperbedaan yang berartiantarakelompoktersebut , denganα 5% Penyelesaian : Ho µA = µB = µC H1 µA ≠ µB ≠ µC

  8. TA =523 , TB = 661 , TC =346 T total =1530 C (T total) 2 / [n] = 137700 JA = [[(TA)2 /6+ (TB)2/7+(TC)2/4] ] - C = 234.452 JK = (90)2 + (82)2 + …….. + (80)2+ (94)2 ] - C = 938 JD = JK - JA = 703.548 RJA = JA/(k - 1) = 117.226 RJD = JD/[n - k)] = 50.2534 RK = RJA / RJD = 2.3327 BerdasarkantabelDistribusi F : α = 5% Df1 = (k - 1) = 2 Df2 = (n - k) = 14 Diperolehnilai F adalah 3.74 RK Penerimaan HO Penolakan HO α = 5% 0 F = 3.74 Ternyata RK jatuhdidaerahpenerimaan, jadi HO diterima. Artinyabahwatidakadaperbedaan yang berartiantaraketigakelompoktersebut.

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