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Uji Lanjut dengan Uji t
Hipotesis :
𝐻0: 𝜇𝑖𝑗(𝑎𝑑𝑗) = 𝜇𝑖𝑗′(𝑎𝑑𝑗)
1. 𝐻1: 𝜇𝑖𝑗(𝑎𝑑𝑗) ≠ 𝜇𝑖𝑗′(𝑎𝑑𝑗)
2. 𝐻1: 𝜇𝑖𝑗(𝑎𝑑𝑗) > 𝜇𝑖𝑗′(𝑎𝑑𝑗)
3. 𝐻1: 𝜇𝑖𝑗(𝑎𝑑𝑗) < 𝜇𝑖𝑗′ (𝑎𝑑𝑗)
Statistik uji ∶
𝑡 =
𝑌𝑖𝑗(𝑎𝑑𝑗) − 𝑌𝑖𝑗′(𝑎𝑑𝑗)
𝑀𝑆𝑆 𝑎𝑑𝑗
1
𝑛𝑗
+
1
𝑛𝑗′
+
𝑋𝑗 − 𝑋𝑗′
2
𝐸 𝑥𝑥
Dengan
𝑌𝑖𝑗(𝑎𝑑𝑗) = 𝑌𝑖𝑗 − 𝛽 𝑊 𝑋𝑗 − 𝑋 , 𝛽 𝑊 =
𝐸 𝑥𝑦
𝐸 𝑥𝑥
𝑀𝑆𝑆 𝑎𝑑𝑗 =
𝑆𝑆 𝑎𝑑𝑗
𝑛1 + 𝑛2 + ⋯ + 𝑛 𝐾 − 𝐾 − 1
𝑆𝑆 𝑎𝑑𝑗 = 𝐸 𝑌𝑌 −
𝐸 𝑋𝑌
2
𝐸 𝑋𝑋
Kriteria :𝐻0 ditolak jika
1. 𝑡 >𝑡 𝛼
2
,𝑛1+𝑛2+⋯+𝑛 𝐾−𝐾−1
2. 𝑡 > 𝑡 𝛼,𝑛1+𝑛2+⋯+𝑛 𝐾−𝐾−1
3. 𝑡 < −𝑡 𝛼,𝑛1+𝑛2+⋯+𝑛 𝐾−𝐾−1
Untuk t Bonferroni nilai 𝑡 𝛼/2,𝑛1+𝑛2+⋯+𝑛 𝐾−𝐾−1 diganti
𝑡 𝛼
𝑝𝐾(𝐾−1)
,𝑛1+𝑛2+⋯+𝑛 𝐾−𝐾−1.

• Uji Fisher Hayter: q𝐹𝐻 =
𝑌 𝑖𝑗(𝑎𝑑𝑗)− 𝑌 𝑖𝑗′(𝑎𝑑𝑗)
1
𝑛 𝑗
+
1
𝑛 𝑗′
+
𝑋 𝑗− 𝑋 𝑗′
2
𝐸 𝑥𝑥
2
Kriteria :𝐻0 ditolak jika 𝑞𝐹𝐻 >𝑞 𝛼,𝐾−1,𝑛1+𝑛2+⋯+𝑛 𝐾−𝐾−1
• Uji Bryant-Paulson : B𝑃 =
1
𝑛 𝑗
+
1
𝑛 𝑗′
+
𝑋 𝑗− 𝑋 𝑗′
2
𝐸 𝑥𝑥
2
Kriteria :𝐻0 ditolak jika 𝐵𝑃 >𝑞 𝛼,𝑞,𝐾,𝑛1+𝑛2+⋯+𝑛 𝐾−𝐾−1
• Uji Scheffe :
• 𝐹𝑆 =
𝑌 𝑖𝑗 𝑎𝑑𝑗 − 𝑌 𝑖𝑗′ 𝑎𝑑𝑗
2
1
𝑛 𝑗
+
1
𝑛
𝑗′
+
𝑋 𝑗− 𝑋
𝑗′
2
𝐸 𝑥𝑥
• Kriteria :𝐻0 ditolak jika 𝐹𝑆 >(𝐾 − 1)𝐹𝛼,𝐾−1,𝑛1+𝑛2+⋯+𝑛 𝐾−𝐾−1

Uji Lanjut Mancova 2 kovariat dengan Uji t
Hipotesis :
𝐻0: 𝜇𝑖𝑗(𝑎𝑑𝑗) = 𝜇𝑖𝑗′(𝑎𝑑𝑗)
1. 𝐻1: 𝜇𝑖𝑗(𝑎𝑑𝑗) ≠ 𝜇𝑖𝑗′(𝑎𝑑𝑗)
2. 𝐻1: 𝜇𝑖𝑗(𝑎𝑑𝑗) > 𝜇𝑖𝑗′(𝑎𝑑𝑗)
3. 𝐻1: 𝜇𝑖𝑗(𝑎𝑑𝑗) < 𝜇𝑖𝑗′ (𝑎𝑑𝑗)
Statistik uji ∶
𝑡 =
𝑌𝑖𝑗(𝑎𝑑𝑗) − 𝑌𝑖𝑗′(𝑎𝑑𝑗)
1
𝑛𝑗
+
1
𝑛𝑗′
+ 𝑑′ 𝑊−1 𝑑
Dengan 𝛽 𝑊𝑦 𝑖 𝑥1
=
𝐸 𝑥2𝑥2 𝐸 𝑦𝑖𝑥1−𝐸 𝑥1𝑥2 𝐸 𝑦𝑖𝑥2
𝐸 𝑥2𝑥2 𝐸 𝑥1𝑥1−𝐸 𝑥1𝑥2
2
𝛽 𝑊𝑦 𝑖 𝑥2
=
𝐸 𝑥1𝑥1 𝐸 𝑦𝑖𝑥2 − 𝐸 𝑥1𝑥2 𝐸 𝑦𝑖𝑥1
𝐸 𝑥2𝑥2 𝐸 𝑥1𝑥1 − 𝐸 𝑥1𝑥2
2
𝑀𝑆𝑆 𝑎𝑑𝑗 =
𝑆𝑆 𝑎𝑑𝑗
𝑛1 + 𝑛2 + ⋯ + 𝑛 𝐾 − 𝐾 − 2
𝑆𝑆 𝑎𝑑𝑗 = 𝐸 𝑦𝑖𝑦𝑖 − 𝛽 𝑊𝑦 𝑖 𝑥1
𝐸 𝑥1𝑦𝑖 − 𝛽 𝑊𝑦 𝑖 𝑥2
𝐸 𝑥2𝑦𝑖
𝑑 =
𝑋1𝑗 − 𝑋2𝑗′
𝑋2𝑗 − 𝑋2𝑗′
, 𝑊 =
𝐸 𝑥1𝑥1 𝐸 𝑥1𝑥2
𝐸 𝑥1𝑥2 𝐸 𝑥2𝑥2
Kriteria :𝐻0 ditolak jika
1. 𝑡 >𝑡 𝛼
2
,𝑛1+𝑛2+⋯+𝑛 𝐾−𝐾−1
2. 𝑡 > 𝑡 𝛼,𝑛1+𝑛2+⋯+𝑛 𝐾−𝐾−1
3. 𝑡 < −𝑡 𝛼,𝑛1+𝑛2+⋯+𝑛 𝐾−𝐾−1

• Untuk t Bonferroni nilai 𝑡 𝛼/2,𝑛1+𝑛2+⋯+𝑛 𝐾−𝐾−2 diganti
𝑡 𝛼
𝑝𝐾(𝐾−1)
,𝑛1+𝑛2+⋯+𝑛 𝐾−𝐾−2.
• Uji Fisher Hayter : q𝐹𝐻 =
1
𝑛 𝑗
+
1
𝑛 𝑗′
+𝑑′ 𝑊−1 𝑑 2
• Kriteria :𝐻0 ditolak jika 𝑞𝐹𝐻 >𝑞 𝛼,𝐾−1,𝑛1+𝑛2+⋯+𝑛 𝐾−𝐾−2
• Uji Bryant-Paulson : B𝑃 =
1
𝑛 𝑗
+
1
𝑛 𝑗′
+𝑑′ 𝑊−1 𝑑 2
• Kriteria :𝐻0 ditolak jika 𝐵𝑃 >𝑞 𝛼,𝑞,𝐾,𝑛1+𝑛2+⋯+𝑛 𝐾−𝐾−2
• Uji Scheffe :
• 𝐹𝑆 =
𝑌 𝑖𝑗 𝑎𝑑𝑗 − 𝑌 𝑖𝑗′ 𝑎𝑑𝑗
2
1
𝑛 𝑗
+
1
𝑛 𝑗′
+𝑑′ 𝑊−1 𝑑
• Kriteria :𝐻0 ditolak jika 𝐹𝑆 >(𝐾 − 1)𝐹𝛼,𝐾−1,𝑛1+𝑛2+⋯+𝑛 𝐾−𝐾−2

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