Uji Sobel

Uji Sobel digunakan untuk menguji signifikansi efek mediasi dalam analisis jalur. Masukkan koefisien regresi dan standard error untuk menghitung statistik uji.

Konfigurasi Sobel

Input Parameter

Koefisien a (IV → Mediator)

Nilai koefisien regresi dari variabel independen ke mediator

Standard Error sa

Nilai standar error untuk koefisien a (tingkat ketidakpastian)

Koefisien b (Mediator → DV)

Nilai koefisien regresi dari mediator ke variabel dependen

Standard Error sb

Nilai standar error untuk koefisien b (tingkat ketidakpastian)

Hasil Perhitungan

Uji Sobel (Formula Asli)

z = \frac{a \times b}{\sqrt{b^2 \times sa^2 + a^2 \times sb^2}}

z-value:6.2428

p-value:< 0.0001

📊 Ringkasan Hasil Uji Sobel

a	b	a × b	SE	z-value	p-value	Signifikan
0.4500	0.5200	0.2340	0.0375	6.2428	< 0.0001	Ya

📊 Langkah Perhitungan Detail

Langkah 1: Parameter Input

a = 0.4500sa = 0.0500b = 0.5200sb = 0.0600

Langkah 2: Hitung Efek Tidak Langsung

\begin{align} a \times b &= 0.4500 \times 0.5200 \\[12pt] &= 0.2340 \end{align}

Langkah 3: Hitung Komponen Varians

\begin{align} b^2 \times sa^2 &= 0.5200^2 \times 0.0500^2 \\[12pt] &= 0.2704 \times 0.0025 \\[12pt] &= 0.0007 \end{align}

\begin{align} a^2 \times sb^2 &= 0.4500^2 \times 0.0600^2 \\[12pt] &= 0.2025 \times 0.0036 \\[12pt] &= 0.0007 \end{align}

Langkah 4: Hitung Standard Error

\begin{align} SE &= \sqrt{b^2 \times sa^2 + a^2 \times sb^2} \\[12pt] &= \sqrt{0.0007 + 0.0007} \\[12pt] &= \sqrt{0.0014} \\[12pt] &= 0.0375 \end{align}

Langkah 5: Hitung Z-value

\begin{align} z &= \frac{a \times b}{SE} \\[12pt] &= \frac{0.2340}{0.0375} \\[12pt] &= 6.2428 \end{align}

Langkah 6: Hitung P-value

\begin{align} p\text{-value} &= 2 \times P(Z > |z|) \\[12pt] &= 2 \times P(Z > |6.2428|) \\[12pt] &= 2 \times P(Z > 6.2428) \\[12pt] &= 2 \times 0.0000 \\[12pt] &= 0.0000 \end{align}

KeteranganMenggunakan distribusi normal standar (two-tailed test)P(Z > 6.2428) ≈ 0.0000

📚 Daftar Pustaka

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Goodman, L. A. (1960). On the exact variance of products. Journal of the American Statistical Association, 55(292), 708–713. https://doi.org/10.1080/01621459.1960.10482134

Hoyle, R. H., & Kenny, D. A. (1999). Sample size, reliability, and tests of statistical mediation. In R. H. Hoyle (Ed.), Statistical strategies for small sample research (pp. 195–227). Guilford Press.

Krull, J. L., & MacKinnon, D. P. (1999). Multilevel mediation modeling in group-based intervention studies. Evaluation Review, 23(4), 418–444. https://doi.org/10.1177/0193841X9902300404

MacKinnon, D. P., Lockwood, C. M., Hoffman, J. M., West, S. G., & Sheets, V. (2002). A comparison of methods to test mediation and other intervening variable effects. Psychological Methods, 7(1), 83–104. https://doi.org/10.1037/1082-989X.7.1.83

MacKinnon, D. P., Warsi, G., & Dwyer, J. H. (1995). A simulation study of mediated effect measures. Multivariate Behavioral Research, 30(1), 41–62. https://doi.org/10.1207/s15327906mbr3001_3

Preacher, K. J., & Hayes, A. F. (2004). SPSS and SAS procedures for estimating indirect effects in simple mediation models. Behavior Research Methods, Instruments, & Computers, 36(4), 717–731. https://doi.org/10.3758/BF03206553

Shrout, P. E., & Bolger, N. (2002). Mediation in experimental and nonexperimental studies: New procedures and recommendations. Psychological Methods, 7(4), 422–445. https://doi.org/10.1037/1082-989X.7.4.422

Sobel, M. E. (1982). Asymptotic confidence intervals for indirect effects in structural equation models. Sociological Methodology, 13, 290–312. https://doi.org/10.2307/270723