Presentasi sedang didownload. Silahkan tunggu

Presentasi sedang didownload. Silahkan tunggu

UJI NORMALITAS Kolmogorov-Smirnov & Chi-Square Oleh: Roni Saputra, M.Si.

Presentasi serupa


Presentasi berjudul: "UJI NORMALITAS Kolmogorov-Smirnov & Chi-Square Oleh: Roni Saputra, M.Si."— Transcript presentasi:

1 UJI NORMALITAS Kolmogorov-Smirnov & Chi-Square Oleh: Roni Saputra, M.Si

2 POPULASI SAMPLING SAMPEL KESIMPULAN PARAMETER :   statistik :  x sd

3 LANGKAH-LANGKAH MENARIK SIMPULAN UJI HIPOTESIS 1.Hipotesis 2.Tentukan  3.Tentukan rumus statistik penguji 4.Hitung rumus statistik penguji 5.Tentukan nilai df/db/dk 6.Lihat nilai tabel 7.Tentukan daerah penolakan 8.Simpulan

4 NOXiFTFT FSFS  F T - F S  dst Metode Kolmogorov- Smirnov

5 Keterangan : X i =Angka pada data Z=Transformasi dari angka ke notasi pada distribusi normal F T =Probabilitas komulatif normal ; komulatif proporsi luasan kurva normal berdasarkan notasi Zi, dihitung dari luasan kurva mulai ujung kiri kurva sampai dengan titik Z. F S =Probabilitas komulatif empiris (1/data ke n)

6 –Data berskala interval atau ratio (kuantitatif) –Data tunggal / belum dikelompokkan pada tabel distribusi frekuensi –Dapat untuk n besar maupun n kecil. Persyaratan

7 Signifikansi uji, nilai  FT - FS  terbesar dibandingkan dengan nilai tabel Kolmogorov Smirnov. –Jika nilai  FT - FS  terbesar < nilai tabel Kolmogorov Smirnov, maka Ho diterima ; Ha ditolak. –Jika nilai  FT - FS  terbesar ≥ nilai tabel Kolmogorov Smirnov, maka Ho ditolak ; Ha diterima. Siginifikansi

8 Contoh Suatu penelitian tentang berat badan peserta pelatihan kebugaran fisik/jasmani dengan sampel sebanyak 27 orang diambil secara random, didapatkan data sebagai berikut ; 78, 78, 95, 90, 78, 80, 82, 77, 72, 84, 68, 67, 87, 78, 77, 88, 97, 89, 97, 98, 70, 72, 70, 69, 67, 90, 97 kg. Selidikilah dengan  = 5%, apakah data tersebut di atas diambil dari populasi yang berdistribusi normal ?

9 Penyelesaian Hipotesis –Ho : tidak beda dengan populasi normal –Ha : Ada beda populasi normal Level signifikansi (  ) –Nilai  = 5% = 0,05 Rumus Statistik penguji

10 NOXi Mean 81,2963 SD10,28372

11 NOXiFTFT FSFS  F T - F S  ,39020,08230,07410, ,29290,09850,11110, ,19570,11510,14810, ,09850,13570,22220, ,90400,18410,29630, ,41780,33720,37040, ,32050,37450,51850, ,12610,44830,55560, ,06840,52790,59260, ,26290,60260,62960, ,55460,70880,66670, ,65190,74220,70370, ,74910,77340,74070, ,84640,80230,81480, ,33260,90820,85190, ,52700,93700,9630-0, ,62430,94741,0000-0,0526 Mean 81,2963 SD10,28372

12 Z0,000,010,020,030,040,050,060,070,080,09 0,00,50000,49600,49200,48800,48400,48010,47610,47210,46810,4641 0,10,46020,45620,45220,44830,44430,44040,43640,43250,42860,4247 0,20,42070,41680,41290,40900,40520,40130,39740,39360,38970,3859 0,30,38210,37830,37450,37070,36690,36320,35940,35570,35200,3483 0,40,34460,34090,33720,33360,33000,32640,32280,31920,31560,3121 0,50,30850,30500,30150,29810,29460,29120,28770,28430,28100,2776 0,60,27430,27090,26760,26430,26110,25780,25460,25140,24830,2451 0,70,24200,23890,23580,23270,22960,22660,22360,22060,21770,2148 0,80,21190,20900,20610,20330,20050,19770,19490,19220,18940,1867 0,90,18410,18140,17880,17620,17360,17110,16850,16600,16350,1611 1,00,15870,15620,15390,15150,14920,14690,14460,14230,14010,1379 1,10,13570,13350,13140,12920,12710,12510,12300,12100,11900,1170 1,20,11510,11310,11120,10930,10750,10560,10380,10200,10030,0985 1,30,09680,09510,09340,09180,09010,08850,08690,08530,08380,0823 1,40,08080,07930,07780,07640,07490,07350,07210,07080,06940,0681 1,50,06680,06550,06430,06300,06180,06060,05940,05820,05710,0559 1,60,05480,05370,05260,05160,05050,04950,04850,04750,04650,0455 1,70,04460,04360,04270,04180,04090,04010,03920,03840,03750,0367 1,80,03590,03510,03440,03360,03290,03220,03140,03070,03010,0294 1,90,02870,02810,02740,02680,02620,02560,02500,02440,02390,0233 2,00,02280,02220,02170,02120,02070,02020,01970,01920,01880,0183 2,10,01790,01740,01700,01660,01620,01580,01540,01500,01460,0143 2,20,01390,01360,01320,01290,01250,01220,01190,01160,01130,0110 2,30,01070,01040,01020,00990,00960,00940,00910,00890,00870,0084 2,40,00820,00800,00780,00750,00730,00710,00690,00680,00660,0064 2,50,00620,00600,00590,00570,00550,00540,00520,00510,00490,0048 2,60,00470,00450,00440,00430,00410,00400,00390,00380,00370,0036 2,70,00350,00340,00330,00320,00310,00300,00290,00280,00270,0026 2,80,00260,00250,00240,0023 0,00220,0021 0,00200,0019 2,90,00190,0018 0,00170,0016 0,0015 0,0014 3,00,0013 0,0012 0,0011 0,0010 3,10,00100,0009 0,0008 0,0007 3,20,0007 0,0006 0,0005 3,30,0005 0,0004 0,0003 3,40,0003 0,0002 3,50,0002 3,60,0002 0,0001 3,70,0001 3,80,0001

13 Df/db/dk –Df =  = tidak diperlukan Nilai tabel –Nilai Kuantil Penguji Kolmogorov,  = 0,05 ; N = 27 ;  0,254. Tabel Kolmogorov Smirnov Daerah penolakan –Menggunakan rumus –  0,1440  <  0,2540  ; berarti Ho diterima, Ha ditolak Kesimpulan –Sampel diambil dari populasi normal, pada  = 0,05.

14 Tingkat Signifikansi untuk tes satu sisi N0,1000,0750,0500,0250,010,005 Tingkat Signifikansi untuk tes dua sisi 0,2000,1500,1000,0500,0200,010 10,9000,9250,9500,9750,9900,995 20,6840,7260,7760,8420,9000,929 30,5650,5970,6420,7080,7850,828 40,4940,5250,5640,6240,6890,733 50,4460,4740,5100,5650,6270,669 60,4100,4360, ,5770,618 70,3810,4050,4380,4860,5380,577 80,3580,3810,4110,4570,5070,543 90,3390,3600,3880,4320,4800, ,3220,3420,3680,4100,4570, ,3070,3260,3520,391 0,437 0, ,2950,3130,3380,3750,4190, , ,3250,3610,4040, ,2740,2920,3140,3490,3900, ,2660,2830,3040,3380,3770, ,2580,2740,2950,3280,3660, ,2500,2660,2860,3180,3550, ,2440,2590,2780,3090,3460, ,2370,2520,2720,3010,3370, ,2310,2460,2640,2940,3290, ,2260,2590,2870,3210, ,2210,2530,2810,3140, ,2160,2470,2750,3070, ,2120,2420,2690,3010, ,2080,220,2380,2640,2950, ,2040,2330,2590,2900, ,2000,2290,2540,2840, ,1970,2250,2500,2790, ,1930,2210,2460,2750, ,1900,200,2180,2420,2700, ,1870,2140,2380,2660, ,1840,2110,2340,2620, ,1820,2080,2310,2580, ,1790,2050,2270,2540, ,1710,190,2020,2240,2510, ,1740,1990,2210,2470, ,1720,1960,2180,2440, ,1700,1940,2150,2410, ,1680,1910,2130,2380, ,1650,1890,2100,2350, ,2080,2380,264 0,295 0, ,1900,2180,242 0,270 0, ,1770,2020,224 0,251 0, ,1650,1890,2100,2350,252 >40

15 Metode Chi-Square atau X 2 Uji Goodness of fit Distribusi Normal, menggunakan pendekatan penjumlahan penyimpangan data observasi tiap kelas dengan nilai yang diharapkan.

16 Rumus X 2 Keterangan : X 2 =Nilai X 2 O i =Nilai observasi E i =Nilai expected / harapan, luasan interval kelas berdasarkan tabel normal dikalikan N (total frekuensi)  p i x N N=Banyaknya angka pada data (total frekuensi)

17 N BATAS INTERVAL KELAS (batas tidak nyata)pi Oi Ei (pi x N) ds t Keterangan : Xi=Batas tidak nyata interval kelas Z=Transformasi dari angka batas interval kelas ke notasi pada distribusi normal Pi=Luas proporsi kurva normal tiap interval kelas berdasar tabel normal Oi=Nilai observasi Ei=Nilai expected / harapan, luasan interval kelas berdasarkan tabel normal dikalikan N (total frekuensi)  pi x N

18 –Data tersusun berkelompok atau dikelompokkan dalam tabel distribusi frekuensi. –Cocok untuk data dengan banyaknya angka besar ( n > 30 ) –Setiap sel harus terisi, yang kurang dari 5 digabungkan. Persyaratan

19 –Signifikansi uji, nilai X 2 hitung dibandingkan dengan X 2 tabel (Chi-Square). –Jika nilai X 2 hitung < nilai X 2 tabel, maka Ho diterima ; Ha ditolak. –Jika nilai X 2 hitung ≥ nilai X 2 tabel, maka Ho ditolak ; Ha diterima. Signifikansi

20 TINGGI BADAN MASYARAKAT KALIMAS TAHUN 2006 NO.TINGGI BADANJUMLAH – – – – – – 1991 JUMLAH100 Contoh Selidikilah dengan  = 5%, apakah data tersebut di atas berdistribusi normal ?

21 Penyelesaian : Hipotesis –Ho : tidak beda dengan populasi normal –Ha : Ada beda populasi normal Level signifikansi (  ) –Nilai  = = 5% = 0,05 Rumus Statistik penguji

22 N BATAS INTERVAL KELAS (batas tidak nyata)pi Oi Ei (pi x N) 1.139,5 – 149,5-2,49 – -1,530,0064 – 0,0630=0,056665, ,5 – 159,5-1,53 – -0,560,0630 – 0,2877=0, , ,5 – 169,5-0,56 – 0,410,2877 – 0,6591=0, , ,5 – 179,50,41 – 1,370,6591 – =0, , ,5 – 189,51,37 – 2,340,9147 – 0,9904=0,075777, ,5 – 199,52,34 – 3,300,9904 – 0,9995=0,009110,91 JUMLAH100 Telah dihitung Mean = 165,3 ; Standar deviasi = 10,36

23 Z0,000,010,020,030,040,050,060,070,080,09 0,00,50000,49600,49200,48800,48400,48010,47610,47210,46810,4641 0,10,46020,45620,45220,44830,44430,44040,43640,43250,42860,4247 0,20,42070,41680,41290,40900,40520,40130,39740,39360,38970,3859 0,30,38210,37830,37450,37070,36690,36320,35940,35570,35200,3483 0,40,34460,34090,33720,33360,33000,32640,32280,31920,31560,3121 0,50,30850,30500,30150,29810,29460,29120,28770,28430,28100,2776 0,60,27430,27090,26760,26430,26110,25780,25460,25140,24830,2451 0,70,24200,23890,23580,23270,22960,22660,22360,22060,21770,2148 0,80,21190,20900,20610,20330,20050,19770,19490,19220,18940,1867 0,90,18410,18140,17880,17620,17360,17110,16850,16600,16350,1611 1,00,15870,15620,15390,15150,14920,14690,14460,14230,14010,1379 1,10,13570,13350,13140,12920,12710,12510,12300,12100,11900,1170 1,20,11510,11310,11120,10930,10750,10560,10380,10200,10030,0985 1,30,09680,09510,09340,09180,09010,08850,08690,08530,08380,0823 1,40,08080,07930,07780,07640,07490,07350,07210,07080,06940,0681 1,50,06680,06550,06430,06300,06180,06060,05940,05820,05710,0559 1,60,05480,05370,05260,05160,05050,04950,04850,04750,04650,0455 1,70,04460,04360,04270,04180,04090,04010,03920,03840,03750,0367 1,80,03590,03510,03440,03360,03290,03220,03140,03070,03010,0294 1,90,02870,02810,02740,02680,02620,02560,02500,02440,02390,0233 2,00,02280,02220,02170,02120,02070,02020,01970,01920,01880,0183 2,10,01790,01740,01700,01660,01620,01580,01540,01500,01460,0143 2,20,01390,01360,01320,01290,01250,01220,01190,01160,01130,0110 2,30,01070,01040,01020,00990,00960,00940,00910,00890,00870,0084 2,40,00820,00800,00780,00750,00730,00710,00690,00680,00660,0064 2,50,00620,00600,00590,00570,00550,00540,00520,00510,00490,0048 2,60,00470,00450,00440,00430,00410,00400,00390,00380,00370,0036 2,70,00350,00340,00330,00320,00310,00300,00290,00280,00270,0026 2,80,00260,00250,00240,0023 0,00220,0021 0,00200,0019 2,90,00190,0018 0,00170,0016 0,0015 0,0014 3,00,0013 0,0012 0,0011 0,0010 3,10,00100,0009 0,0008 0,0007 3,20,0007 0,0006 0,0005 3,30,0005 0,0004 0,0003 3,40,0003 0,0002 3,50,0002 3,60,0002 0,0001 3,70,0001 3,80,0001

24

25

26 Df/db/dk Df = ( k – 3 ) = ( 5 – 3 ) = 2 Nilai tabel Nilai tabel X 2 ;  = 0,05 ; df = 2 ; = 5,991. Daerah penolakan Menggunakan gambar Menggunakan rumus  0,1628  <  5,991  ; berarti Ho diterima, Ha ditolak Kesimpulan Sampel diambil dari populasi normal, pada  = 0,05.

27 dfKemungkinan di bawah Ho bahwa X 2 Chi - Square 0,0050,0100,0250,0500,1000,200 17,8796,6355,0243,8412,7061, ,5979,2107,3785,9914,6053, ,83811,3419,3487,8156,2514, ,86013,27711,1439,4887,7795, ,75015,08612,83211,0709,2367, ,54816,81214,44912,59210,6458, ,27818,47516,01314,06712,0179, ,95520,09017,53515,50713,36211, ,58921,66019,02316,91914,68412, ,18823,20920,48318,30715,98713, ,75724,72521,92019,67517,27514, ,30026,21723,33721,02618,54915, ,81927,68824,73622,36219,81216, ,31929,14126,11923,68521,06418, ,80130,57827,48824,99622,30719, ,26732,00028,84526,29623,54220, ,71833,40930,19127,58724,76921, ,15634,80531,52628,86925,98922, ,58236,19132,85230,14427,20423, ,99737,56634,17031,41028,41225, ,40138,93235,47932,67129,61526, ,79640,28936,78133,92430,81327, ,18141,63838,07635,17232,00728, ,55842,98039,36436,41533,19629, ,92844,31440,64637,65234,38230, ,29045,64241,92338,88535,56331, ,64546,96343,19440,11336,74132, ,99348,27844,46141,33737,91634, ,33649,58845,72242,55739,08735, ,67250,89246,97943,77340,25636,250

28 df 0,001 0,0050,0100,0200,0250,0500,1000,200 0,2500, ,83 7,8796,6355,415,0243,8412,7061,642 1,321, ,82 10,5979,2107,827,3785,9914,6053,219 2,772, ,27 12,83811,3419,849,3487,8156,2514,642 4,113, ,46 14,86013,27711,6711,1439,4887,7795,989 5,394, ,52 16,75015,08613,3912,83211,0709,2367,289 6,636, ,46 18,54816,81215,0314,44912,59210,6458,558 7,847, ,32 20,27818,47516,6216,01314,06712,0179,803 9,048, ,12 21,95520,09018,1717,53515,50713,36211,030 10,229, ,88 23,58921,66019,6819,02316,91914,68412,242 11,3910, ,59 25,18823,20921,1620,48318,30715,98713,442 12,5511, ,26 26,75724,72522,6221,92019,67517,27514,631 13,7012, ,91 28,30026,21724,0523,33721,02618,54915,812 14,8514, ,53 29,81927,68825,4724,73622,36219,81216,985 15,9815, ,12 31,31929,14126,8726,11923,68521,06418,151 17,1216, ,70 32,80130,57828,2627,48824,99622,30719,311 18,2517, ,29 34,26732,00029,6328,84526,29623,54220,465 19,3718, ,75 35,71833,40931,0030,19127,58724,76921,615 20,4919, ,31 37,15634,80532,2531,52628,86925,98922,760 21,6020, ,82 38,58236,19133,6932,85230,14427,20423,900 22,7221, ,32 39,99737,56635,0234,17031,41028,41225,038 23,8322, ,80 41,40138,93236,3435,47932,67129,61526,171 24,9323, ,27 42,79640,28937,6636,78133,92430,81327,301 26,0424, ,73 44,18141,63838,9738,07635,17232,00728,429 27,1426, ,18 45,55842,98040,2739,36436,41533,19629,553 28,2427, ,62 46,92844,31441,5740,64637,65234,38230,675 29,3428, ,05 48,29045,64242,8641,92338,88535,56331,795 30,4329, ,48 49,64546,96344,1443,19440,11336,74132,912 31,5330, ,89 50,99348,27845,4244,46141,33737,91634,027 32,6232, ,30 52,33649,58846,6945,72242,55739,08735,139 33,7132, ,70 53,67250,89247,9646,97943,77340,25636,250 34,8033, ,7763,6959,3455,7651,80 45, ,4976,1571,4267,5063,17 56, ,9588,3883,3079,0874,40 66, ,22100,4295,0290,5385,53 77, ,32112,33106,63101,8896,58 88, ,30124,12118,14113,14107,56 98, ,17135,81129,56124,34118,50 10,9,14


Download ppt "UJI NORMALITAS Kolmogorov-Smirnov & Chi-Square Oleh: Roni Saputra, M.Si."

Presentasi serupa


Iklan oleh Google