AksiomatikMetodologi dan Statistika

Contingency Table

Bangun tabel kontingensi dan uji asosiasi: Pearson X², Likelihood Ratio, Yates (2×2), Fisher (2×2), serta ukuran asosiasi (Phi, Cramer's V).

Apa yang dihitung?

Tabel O dan E, uji χ² beserta p‑value, ukuran asosiasi, dan langkah perhitungan manual.

Konfigurasi

Input Dataset (Contingency Table)

Baris pertama opsional sebagai header. Dua kolom = daftar pasangan observasi. Tiga kolom = data berfrekuensi.

Ringkasan data

Baris: 2 • Kolom: 2 • N: 3

Ringkasan Hasil

N = 3

Observed Counts

Row \ ColXYRow Total
A112
B101
Col Total213

Expected Counts

Row \ ColXY
A1.330.67
B0.670.33

Chi‑Square Tests

TestValuedfAsymp. Sig.
Pearson Chi‑Square0.75001–
Likelihood Ratio1.04651–
Continuity Correction0.18751–
Fisher's Exact Test––1.0000
p‑value dihitung dengan jStat (χ²) dan Fisher exact (2×2) seperti di SPSS.

Nominal by Nominal

MeasureValue
Phi0.5000
Cramer's V0.5000
Contingency Coefficient0.4472

Keputusan Hipotesis

α = 0.05. p (Pearson X²) = –
menunggu jStat.

Ordinal by Ordinal

MeasureValue
Goodman & Kruskal's Gamma-1
Kendall's tau‑b-0.5000

Langkah Perhitungan (Manual)

Sumber Nilai

N = total observasi = Σ semua sel = 3

Expected count per sel: Eij = (Total baris i × Total kolom j) / N

Derajat bebas: df = (r−1)(c−1) = (2−1)(2−1) = 1

Hitung nilai harapan (Eij)

Sel (i,j)OijEij
(1,1)11.33
(1,2)10.67
(2,1)10.67
(2,2)00.33

Statistik uji Chi‑Square

X2=(1−1.33)21.33+(1−0.67)20.67+(1−0.67)20.67+(0−0.33)20.33\displaystyle X^2 = \frac{(1-1.33)^2}{1.33} + \frac{(1-0.67)^2}{0.67} + \frac{(1-0.67)^2}{0.67} + \frac{(0-0.33)^2}{0.33}

Keputusan: bandingkan p‑value Pearson X² dengan α = 0.05. Jika p ≤ α ⇒ tolak H0 (ada asosiasi).

Ukuran Asosiasi (Nominal)

φ=X2N ,  V=X2N min⁡(r−1, c−1) ,  C=X2X2+N\displaystyle \varphi = \sqrt{\tfrac{X^2}{N}}\,,\; V = \sqrt{\tfrac{X^2}{N\,\min(r-1,\,c-1)}}\,,\; C = \sqrt{\tfrac{X^2}{X^2+N}}

Nilai X² dan N berasal dari perhitungan di atas; r dan c adalah jumlah baris dan kolom pada tabel.

Estimasi Risiko (2×2)

OR=a db c ,  ln⁡(OR)±1.961a+1b+1c+1d\displaystyle \text{OR} = \frac{a\,d}{b\,c}\,,\; \ln(OR) \pm 1.96\sqrt{\tfrac{1}{a}+\tfrac{1}{b}+\tfrac{1}{c}+\tfrac{1}{d}}
RR=a/(a+b)c/(c+d) ,  ln⁡(RR)±1.961a−1a+b+1c−1c+d\displaystyle \text{RR} = \frac{a/(a+b)}{c/(c+d)}\,,\; \ln(RR) \pm 1.96\sqrt{\tfrac{1}{a}-\tfrac{1}{a+b}+\tfrac{1}{c}-\tfrac{1}{c+d}}

a,b,c,d adalah isi sel tabel 2×2 (baris1×kolom1, baris1×kolom2, baris2×kolom1, baris2×kolom2).