3/7/03 Ali Muhso, M.Pd. Jeisya Uji Beda Rata-rata Uji z Uji t Uji Beda Proorsi Uji z (c) 03 by Ali Muhso
3/7/03 Jeis Uji Beda Rata-rata dua kelomok Dua Kelomok Salig Bebas (Ideedet Samles): Uji z utuk uji oulasi Uji t utuk samel kecil: Pooled t test Searate t test Dua kelomok berasaga (Paired samles) Paired samles t test (c) 03 by Ali Muhso 3 Illustrasi dua kelomok Dua Kelomok salig bebas Dua Kelomok Berasaga (c) 03 by Ali Muhso 4
3/7/03 Jeis uji dua kelomok salig bebas Jumlah samel melebihi 30 Yes Guaka uji z. No Aakah data berdistribusi ormal? No Guaka statistik Noarametrik Yes Aakah varias oulasi diketahui? No Aakah variasya homoge? Yes Guaka Pooled t test Yes No Guaka uji z. Guaka searate t-test. (c) 03 by Ali Muhso 5 Uji z Dua Kelomok Salig Bebas Tujua Meguji erbedaa rerata dua kelomok oulasi yag salig bebas. Syarat: Samel harus diambil secara radom Data berskala iterval Data ada masig-masig kelomok berdistribusi ormal Dua kelomok tersebut tidak salig berhubuga Varias oulasi diketahui, atau samel miimal 30 (c) 03 by Ali Muhso 6 3
3/7/03 Cotoh Masalah Aakah ada erbedaa tiggi bada atara mahasiswa ria da waita? Bearkah bahwa hasil ujia siswa kelas A lebih baik dariada kelas B? Aakah bear bahwa mobil dega sistem ijeksi lebih hemat BBM dariada yag tidak megguaka sistem ijeksi? H 0 : μ = μ H a : μ μ H 0 : μ μ H a : μ > μ H 0 : μ μ H a : μ < μ (c) 03 by Ali Muhso 7 Uji z dua kelomok Rumus z X X Nilai Kritis (z tabel) Z (-) Stadar Error Perbedaa Rerata ( X X ) (c) 03 by Ali Muhso 8 4
3/7/03 Estimasi Parameter Dega tigkat keyakia (-) tertetu daat estimasi ilai arameter. X X z SE X X z SE Margi Error (ME) (c) 03 by Ali Muhso 9 Pooled t test Tujua Meguji erbedaa rerata dua kelomok oulasi yag salig bebas. Syarat: Samel harus diambil secara radom Data berskala iterval Data ada masig-masig kelomok berdistribusi ormal Dua kelomok tersebut tidak salig berhubuga Varias oulasi tidak diketahui, atau samel kurag dari 30 Varias kedua kelomok bersifat homoge (c) 03 by Ali Muhso 0 5
3/7/03 Pooled t test t S S X X SD SD Stadar Error Perbedaa Rerata ( S X X ) Nilai kritis t(; + -) (c) 03 by Ali Muhso Estimasi Parameter Dega tigkat keyakia (-) tertetu daat estimasi ilai arameter. X X t SE X X t SE Margi Error (ME) (c) 03 by Ali Muhso 6
3/7/03 Searate t test Tujua Meguji erbedaa rerata dua kelomok oulasi yag salig bebas. Syarat: Samel harus diambil secara radom Data berskala iterval Data ada masig-masig kelomok berdistribusi ormal Dua kelomok tersebut tidak salig berhubuga Varias oulasi tidak diketahui, atau samel kurag dari 30 Varias kedua kelomok bersifat tidak homoge (c) 03 by Ali Muhso 3 Searate t test t w X SD w t t tabel w SD w SD X SD w t w T : T : Alha () db = - Alha () db = (c) 03 by Ali Muhso 4 7
3/7/03 Alteratif meghitug t tabel Dega meghitug rumus db sebagai berikut: (c) 03 by Ali Muhso 5 Estimasi Parameter Dega tigkat keyakia (-) tertetu daat estimasi ilai arameter. X X t SE X X t SE Margi Error (ME) (c) 03 by Ali Muhso 6 8
3/7/03 Uji Homogeitas Varias F SD SD B K F tabel: Alha () db = b db = k Biasa ditulis F(; b ; k ) (c) 03 by Ali Muhso 7 Cotoh Soal Seorag guru Ekoomi di SMA meyataka bahwa siswa kelas akselerasi memiliki ilai yag lebih tiggi dibadigka dega kelas reguler. Gua membuktika eryataa tersebut dilakuka eelitia dega megambil samel secara acak di kedua kelas tersebut. Dari 0 samel siswa kelas akselerasi dieroleh ilai rerata 8,4 dega stadar deviasi 5,3 semetara 5 samel siswa di kelas reguler dieroleh ilai rerata 76,8 dega stadar deviasi 8,. Dega = 0,05, bearkah eryataa guru tersebut? (c) 03 by Ali Muhso 8 9
3/7/03 Cotoh Hasil Aalisis Kelas N Mea Std. Deviatio Std. Error Mea IPK A 7 3.087.8459.0756 B 0.7760.9463.0937 (c) 03 by Ali Muhso 9 Cotoh Hasil Aalisis IPK Equal variaces assumed Equal variaces ot assumed Levee's Test for Equality of Variaces F Sig. t df Sig. (- tailed) t-test for Equality of Meas Mea Differece Std. Error Differece 95% Cofidece Iterval of the Differece Lower Uer.305.589.7 5.046.3.434.00584.6644.86 3.365.047.3.430.00456.677 (c) 03 by Ali Muhso 0 0
3/7/03 Paired t test Tujua Meguji erbedaa rerata dua kelomok oulasi yag berasaga. Syarat: Samel harus diambil secara radom Data berskala iterval Data ada masig-masig kelomok berdistribusi ormal Dua kelomok tersebut salig berhubuga atau berasaga (c) 03 by Ali Muhso Paired t test t d SD d d X d d d X X X Nilai Kritis t: Alha () db = - (c) 03 by Ali Muhso
3/7/03 Estimasi Parameter Dega tigkat keyakia (-) tertetu daat estimasi ilai arameter. X X t SE X X t SE Margi Error (ME) (c) 03 by Ali Muhso 3 Paired t test Examle: A readig ceter claims that studets will erform better o a stadardized readig test after goig through the readig course offered by their ceter. The table shows the readig scores of 6 studets before ad after the course. At = 0.05, is there eough evidece to coclude that the studets scores after the course are better tha the scores before the course? Studet 3 4 5 6 Score (before) 85 96 70 76 8 78 Score (after) 88 85 89 86 9 89 H 0 : d 0 H a : d > 0 (Claim) Cotiued.
3/7/03 t-test for the Differece Betwee Meas H 0 : d 0 H a : d > 0 (Claim) d = (score before) (score after) d.f. = 6 = 5-3 - - Studet 3 4 5 6 Score (before) 85 96 70 76 8 78 Score (after) 88 85 89 86 9 89 d 3 9 0 d 9 36 00 0 3 d 43 d 833 = 0.05 t 0 =.05 t d 43 d 7.67 6 s d ( d ) ( d ) 6(833) 849 04.967 0.45 ( ) 6(5) Cotiued. t-test for the Differece Betwee Meas H 0 : d 0 H a : d > 0 (Claim) The stadardized test statistic is d μ t d 7.67 0.74. s 0.45 6 d -3 - - 0 3 t 0 =.05 t Fail to reject H 0. There is ot eough evidece at the 5% level to suort the claim that the studets scores after the course are better tha the scores before the course. (c) 03 by Ali Muhso 6 3
3/7/03 Hasil Aalisis: Mea N Std. Deviatio Std. Error Mea Pair Nilai Pre Test 54.4000 0 7.33636.3996 Nilai Post Test 68.7000 0 8.75658.76908 Pair Nilai Pre Test - Nilai Post Test Std. Deviatio Paired Differeces Std. Error Mea 95% Cofidece Iterval of the Differece Lower Uer t df Sig. (- tailed)mea -4.300 8.94489.886-0.699-7.90-5.055 9.00 (c) 03 by Ali Muhso 7 Uji Beda Proorsi Tujua meguji erbedaa roorsi dua kelomok Syarat: Samel harus diambil secara radom Dua kelomok tersebut salig bebas Jumlah samel harus cuku besar utuk daat megguaka distribusi ormal, yaitu: 5, q 5, 5, da q 5. (c) 03 by Ali Muhso 8 4
3/7/03 Uji Beda Proorsi z q X X X X q (c) 03 by Ali Muhso 9 Examle A recet survey stated that male college studets smoke less tha female college studets. I a survey of 45 male studets, 36 said they smoke at least oe ack of cigarettes a day. I a survey of 065 female studets, 34 said they smoke at least oe ack a day. At = 0,0, ca you suort the claim that the roortio of male college studets who smoke at least oe ack of cigarettes a day is lower the the roortio of female college studets who smoke at least oe ack a day? (c) 03 by Ali Muhso 30 5
3/7/03 Two Samle z-test for Proortios H 0 : H a : < (Claim) -3 - - z 0 =.33 x x ˆ ˆ 36 34 45 065 q 0.304 0.696 0 3 70 0.304 30 z Because 45(0.304), 45(0.696), 065(0.304), ad 065(0.696) are all at least 5, we ca use a two-samle z-test. Cotiued. (c) 03 by Ali Muhso 3 Two Samle z-test for Proortios H 0 : z0 =.33 H a : < (Claim) -3 - - 0 3 z z q (0.9 0.3) 0 (0.304)(0.696) 45 065.56 Fail to reject H 0. There is ot eough evidece at the % level to suort the claim that the roortio of male college studets who smoke is lower the the roortio of female college studets who smoke. (c) 03 by Ali Muhso 3 6
3/7/03 Home Work Halama 446 soal omor 6 Halama 458 soal omor 4 (c) 03 by Ali Muhso 33 7