Analisis Chi-Square (x - bankselgamet.com · contoh soal peternakan. CHI-SQUARE DISTRIBUTION TABLE...

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Analisis Chi-Square (x 2 ) Chi square ("χ 2 " dari huruf Yunani "Chi"Kai") to determine if data “good” or not. Expl. .. to determine possible outcomes for genetic crosses. How will we know if our fruit fly data is “good”? x Black F1: all wild wild 5610: 9 1881:3 1896:3 622: 1 Jika F1 X F1 menghasilkan F2 dengan Rasio : 9:3:3:1 ?
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Transcript of Analisis Chi-Square (x - bankselgamet.com · contoh soal peternakan. CHI-SQUARE DISTRIBUTION TABLE...

  • Analisis Chi-Square (x2 )

    Chi square ("2" dari huruf Yunani "Chi "Kai") to

    determine if data good or not. Expl. .. to determine possible outcomes for genetic crosses.

    How will we know if our fruit fly data is good?

    xBlack

    F1: all wild

    wild

    5610: 9

    1881:3

    1896:3

    622: 1Jika F1 X F1 menghasilkan F2 dengan Rasio : 9:3:3:1 ?

  • The chi-square distribution

    can be used to see whether or not an observed counts agree with an expected counts.

    (Ringkas: data sesuai harapan/teori atau tidak)

    O = observed count (Observasi)

    E = Expected count (harapan)

    EEO 2)(2

    For testing significance of patterns in

    qualitative data

    based on counts that represent the number of items that fall in

    each category

    measures the agreement between actual counts and expected counts

    assuming the null hypothesis

  • Rumus dasar dari uji Kai Kuadrat adalah :

    Keterangan :

    O = frekuensi hasil observasi

    E = frekuensi yang diharapkan.

    Nilai E = (Jumlah sebaris x Jumlah Sekolom) / Jumlah data

    Derajat bebas: df = (b-1) (k-1)

    Uji Kai Kuadrat dapat digunakan untuk menguji :

    1. Uji 2 : ada tidaknya hubungan antara dua variabel (Independency test).

    2. Uji 2 : homogenitas antar- sub kelompok (Homogenity test).

    3. Uji 2 : untuk Bentuk Distribusi (Goodness of Fit)

    EEO 2)(2

    http://1.bp.blogspot.com/-23ppxaGoOlw/UqHj2pZ5ClI/AAAAAAAAADs/3w6iEChSbP8/s1600/chi+square+2.jpghttp://1.bp.blogspot.com/-23ppxaGoOlw/UqHj2pZ5ClI/AAAAAAAAADs/3w6iEChSbP8/s1600/chi+square+2.jpg

  • Tahapan Uji Hipotesis

    1. Nyatakan Hipotesis null (Ho = Specifies a distribution of proportions)

    there is no substantial statistical deviation between observed and expected data.

    Research (H1= Specifies that the distribution will be different than that indicated in the null hypothesis

    2. Select an alpha level and determine the critical value ( pada tabel distribusi chi-square)

    3. Hitung test statistik:

    4. Make a decision (Kesimpulan) .

    EEO 2)(2

  • Calculating the test statistic Observed frequencies (Observasi)

    the number of individuals from the sample who are classified in a particular category

    fo

    Expected frequencies (Harapan)

    the number of individuals from the sample who are expected to be classified in a particular category

    fe

  • Hitungan Contoh Sederhana:

    Heads Tails

    Percentages 50%50%

    Proportions .5 .5

    Pelemparan mata uang :

    What percentage of people will predict heads? tails?

    Expected Heads Tails

    Proportions .5 .5

    Frequencies 25 25

    Expected frequency = fe = pn

    n = 50 (sample size)

    fe = .5 x 50 = 25

  • Calculating the test statistic

    x2 = (fo - fe)2

    fe

    Heads Tails

    Observed 35 15

    Expected 25 25

    Steps

    1. find the difference between fo and fe for

    each category

    2. square the difference

    3. divide the squared difference by fe

    4. sum the values from all categories

  • Hitungan:

    x2 = (fo - fe)2 = 4 + 4 = 8

    fe

    Heads Tails

    Observed

    (fo)35 15

    Expected

    (fe)25 25

    fo - fe 10 -10

    (fo - fe)2 100 100

    (fo - fe)2/fe 4 4

    Membuat Kesimpulan:

    Critical value = 3.84 (with df = 1 and = .05)

    Observed chi square = 8.0

    8.0 > 3.84

    We reject the null hypothesis

    Conclude that category frequencies are different

    People were more likely to predict heads than tails

    Goodness of fit

  • Observed Expected

    Frequency Frequency

    H 40 50

    T 60 50

    --------------------------------------------------------

    Jumlah 100 100

    2

    22

    2 2

    2 2

    40 50

    50

    60 50

    50

    10

    50

    10

    50

    100

    50

    100

    50

    2 2

    4

    statistic formula

    O E

    E

    ( )

    ( ) ( )

    ( ) ( )

    Contoh Soal :

    Hasil observasi suatu data percobaan

    HITUNGAN TEST STATISTIK

  • Data Observed Expected

    Die Frequency Frequency--------------------------------------------------------

    1 4 10

    2 6 10

    3 17 10

    4 16 10

    5 8 10

    6 9 10

    ===============================

    Jumlah 60 60

    2

    22

    2 2

    2 2

    2 2

    4 10

    10

    6 10

    10

    17 10

    10

    16 10

    10

    8 10

    10

    9 10

    50

    14 2

    statistic formula

    O E

    E

    ( )

    ( ) ( )

    ( ) ( )

    ( ) ( )

    .

    HITUNGAN TEST STATISTIK

  • Tabel: Critical values for chi square

    distributionCritical value (df = 1, = .05) = 3.84

    Catatan: Setiap mahasiswa harus punya tabel lengkap. Chi-square

  • (3.1) .Chi-Square (tes independensi) : menguji apakah ada hubungan antara baris dengan

    kolom pada sebuah tabel kontingensi. Data yang digunakan adalah data kualitatif.

    X2 =(O E)2

    E Di mana O = skor yang diobservasi

    E = skor yang diharapkan (expected)

    Contoh :Terdapat 20 siswa perempuan dan 10 siswa laki-laki yang fasih berbahasa Inggris, serta

    10 siswa perempuan dan 30 siswa laki-laki yang tidak fasih berbahasa Inggris.

    Apakah ada hubungan antara jenis kelamin dengan kefasihan berbahasa Inggris ?

    Ho = tidak ada hubungan antara baris dengan kolom

    H1 = ada hubungan antara baris dengan kolom

    LP

    Fasih

    Tidak fasih

    a b

    c d

    O E (O-E) (O-E)2 (O-E)2/E

    a 20 (a+b)(a+c)/N

    b 10 (a+b)(b+d)/N

    c 10 (c+d)(a+c)/N

    d 30 (c+d)(b+d)/N

    df = (kolom 1)(baris 1)

    Jika X2 hitung < X2 tabel, maka Ho diterima

    Jika X2 hitung > X2 tabel, maka Ho ditolak

  • contoh soal peternakan

  • CHI-SQUARE DISTRIBUTION TABLE

    Accept Hypothesis Reject Hypothesis

    Probability (p)

    Degrees of Freedom

    0.95 0.90 0.80 0.70 0.50 0.30 0.20 0.10 0.05 0.01 0.001

    1 0.004 0.02 0.06 0.15 0.46 1.07 1.64 2.71 3.84 6.64 10.83

    2 0.10 0.21 0.45 0.71 1.39 2.41 3.22 4.60 5.99 9.21 13.82

    3 0.35 0.58 1.01 1.42 2.37 3.66 4.64 6.25 7.82 11.34 16.27

    4 0.71 1.06 1.65 2.20 3.36 4.88 5.99 7.78 9.49 13.38 18.47

    5 1.14 1.61 2.34 3.00 4.35 6.06 7.29 9.24 11.07 15.09 20.52

    6 1.63 2.20 3.07 3.83 5.35 7.23 8.56 10.64 12.59 16.81 22.46

    7 2.17 2.83 3.82 4.67 6.35 8.38 9.80 12.02 14.07 18.48 24.32

    8 2.73 3.49 4.59 5.53 7.34 9.52 11.03 13.36 15.51 20.09 26.12

    9 3.32 4.17 5.38 6.39 8.34 10.66 12.24 14.68 16.92 21.67 27.88

    10 3.94 4.86 6.18 7.27 9.34 11.78 13.44 15.99 18.31 23.21 29.59