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ܡܪܟܟܢܘܬܐ ܝܢ ܡܨܥܝܘܬܐ؟

ܬܪܝܢ ܫܘܐ̈ܠܐ ܦܪ̈ܝܫܐ ܥܠ ܡܫܬܚܠܦܢܐ ܬܠܝܬܝܐ. ܡܪܟܟܢܘܬܐ (moderation) – ܡܫܬܚܠܦܢܐ ܬܠܝܬܝܐ ܟܡܫܢܐ ܠܐܣܘܪܐ ܒܝܢܝ ܬܪܝܢ ܐܚܪ̈ܢܐ: "ܡܫܬܚܠܦܢܐ ܡܪܟܟܢܐ ܝܠܗ ܡܫܬܚܠܦܢܐ ܕܟܡܥܒܕ ܥܠ ܐܣܘܪܐ ܒܝܢܝ ܬܪܝܢ ܡܫܬܚܠܦ̈ܢܐ ܐܚܪ̈ܢܐ" (Field, 2024, Section 11.3.1). ܐܣܘܪܐ ܡܨܐ ܕܡܟܪܗ، ܕܡܚܣܢ ܝܢ ܕܡܬܗܦܟ – "ܠܐ ܣܢܝܩ ܝܠܗ ܕܗܘܝܐ ܡܥܒܕܢܘܬܐ ܓܘ ܓܘܕܐ ܚܕܐ ܘܠܐ ܓܘ ܐܚܪܬܐ" (ܬܡܢ). ܓܘ ܨܘܪܬܐ، ܡܪܟܟܢܐ ܝܠܗ ܓܐܪܐ ܕܟܡܚܐ ܥܠ ܓܐܪܐ (Cohen et al., 2003, p. 458). ܡܨܥܝܘܬܐ (mediation) – ܡܫܬܚܠܦܢܐ ܬܠܝܬܝܐ ܟܡܦܫܩ ܠܐܣܘܪܐ: X ܟܡܥܒܕ ܥܠ M، ܘ-M ܟܡܥܒܕ ܥܠ Y (Field, 2024, Section 11.4.1). ܡܨܥ̈ܝܐ (mediators) ܝܢܐ ܡܫܬܚܠܦ̈ܢܐ ܕ"ܟܛܥܢܝ ܡܥܒܕܢܘܬܐ" (Cohen et al., 2003, p. 477).

ܓܘ ܡܬܠܐ ܕܦܐܬܐ – 240 ܬܠܡܝ̈ܕܐ ܒܕܝ̈ܐ – ܡܨܝܚ ܕܫܐܠܚ ܬܪܘܝܗܝ ܫܘܐ̈ܠܐ ܥܠ ܗܢ ܝܗܝ̈ܒܬܐ: ܐܝܢܐ ܡܥܕܪܢܘܬܐ ܟܢܫܝܬܐ ܟܡܪܟܟܐ ܚܒܠܐ ܕܥܩܬܐ ܕܝܘܠܦܢܐ ܠܫܝܢܐ ܕܢܦܫܐ (ܡܘܕܝܠ 1)؟ ܘܐܝܢܐ ܥܩܬܐ ܟܡܚܒܠܐ ܠܫܝܢܐ ܒܐܘܪܚܐ ܕܚܘܫܒܐ ܡܬܢܝܐ ܘܫܢܬܐ (ܡܘܕܝܠ 4)؟ ܘܡܘܕܝ̈ܠܐ 7 ܘ-14 ܟܡܚܠܛܝ: ܐܝܢܐ ܡܥܕܪܢܘܬܐ ܟܫܢܝܐ ܡܥܒܕܢܘܬܐ ܠܐ ܬܪܝܨܬܐ – ܓܘ ܕܪܓܐ ܩܕܡܝܐ (ܥܩܬܐ ← ܚܘܫܒܐ ܡܬܢܝܐ) ܝܢ ܓܘ ܬܪܝܢܝܐ (ܫܢܬܐ ← ܫܝܢܐ)؟

ܡܘܕܝܠ ܕܡܪܟܟܢܘܬܐ (ܡܘܕܝܠ 1)

ܟܡܢܒܚ Y ܡܢ X، ܡܢ W ܘܡܢ product ܕܝܠܗܘܢ: Ŷ = b₀ + b₁X + b₂W + b₃XW (Field, 2024, Equation 11.3; Cohen et al., 2003, Equation 7.1.2). product ܝܠܗ ܥܒܕܐ ܕܚܕ̈ܕܐ (interaction) – "ܫܪܝܪܐܝܬ ܬܪܝܢ ܡܫܬܚܠܦ̈ܢܐ ܡܣܘܓܐ̈ܐ ܚܕ ܒܚܕ" (Field, 2024, Section 11.3.4) – ܘܐܢ b₃ ܪܫܝܡܐ ܝܠܗ، ܐܝܬ ܡܪܟܟܢܘܬܐ. X ܘ-W ܣܢܝܩ̈ܐ ܝܢܐ ܕܗܘܝܢ ܓܘ ܡܘܕܝܠ ܓܢܒ product: b₃ ܟܡܚܘܐ ܥܒܕܐ ܕܚܕ̈ܕܐ "ܐܢ ܘܒܣ ܐܢ" ܬܪܝܢ ܡܫܬܚܠܦ̈ܢܐ ܥܠܝܠ̈ܐ ܝܢܐ ܓܘ ܫܘܝܘܬܐ (Cohen et al., 2003, p. 284; Field, 2024, Section 11.3.2).

ܟܡܐ ܥܒܕܐ ܕܚܕ̈ܕܐ ܟܡܘܣܦ؟ ΔR² – ܦܘܪܫܢܐ ܓܘ R² ܒܝܢܝ ܡܘܕܝܠ ܥܡ product ܘܡܘܕܝܠ ܕܠܐ ܐܝܗ، ܥܡ ܒܘܚܪܢܐ F ܩܐ ܬܘܣܦܬܐ (Cohen et al., 2003, p. 275). ܥܒ̈ܕܐ ܕܚܕ̈ܕܐ ܒܥܕܢܐ ܣܓܝ ܟܡܘܣܦܝ "ܒܣ ܩܠܝܠ ܡܢ̈ܘܬܐ ܒܡܐܐ" ܕܫܘܚܠܦܐ (variance)، ܘܥܒ̈ܕܐ ܕܚܕ̈ܕܐ ܪܒ̈ܐ "ܩܠܝ̈ܠܐ ܝܢܐ" ܓܘ ܒܘܨ̈ܝܐ ܕܚܙܝܬܐ (ܦܐܬܐ 297) – ܘܡܛܠ ܗܕܐ ܬܘܣܦܬܐ ܕ-2%-5% ܠܐ ܝܠܗ ܙܥܘܪܬܐ ܛܒܐ. ܒܘܚܪܢܐ F ܩܐ ܬܘܣܦܬܐ ܫܘܐ ܝܠܗ ܠ-t² ܕ-b₃ ܓܘ ܛܥܝ̈ܘܬܐ ܪ̈ܓܝܠܬܐ.

ܡܫܢܝܢܘܬܐ ܠܡܨܥܝܬܐ

ܐܡܬܝ ܕܐܝܬ product ܓܘ ܡܘܕܝܠ، b₁ ܝܠܗ ܡܥܒܕܢܘܬܐ ܕ-X ܐܡܬܝ ܕ-W = 0 (Cohen et al., 2003, p. 260; Field, 2024, Section 11.3.3) – ܘܨܦܪܐ ܒܥܕܢܐ ܣܓܝ ܛܝܡܐ ܝܠܗ ܕܠܐ ܡܨܐ ܕܗܘܐ: ܥܘܡܪܐ ܨܦܪܐ، ܢܩܫܐ ܕܠܒܐ ܨܦܪܐ، ܡܥܕܪܢܘܬܐ ܨܦܪܐ ܓܘ ܣܒܠܬܐ 1-7. ܡܫܢܝܢܘܬܐ ܠܡܨܥܝܬܐ (mean-centering) – ܡܒܨܪܬܐ ܕܡܨܥܝܬܐ ܡܢ ܟܠ ܛܝܡܐ – ܟܥܒܕܐ b₁ ܡܥܒܕܢܘܬܐ ܕ-X ܐܡܬܝ ܕ-W ܓܘ ܡܨܥܝܬܐ ܝܠܗ، ܘܐܦ "ܪܝܓܪܫܢ ܡܨܥܝܐ" ܕ-Y ܥܠ X ܒܐܘܪܟܐ ܕ-W (Cohen et al., 2003, pp. 261-262; Field, 2024, Section 11.3.3). ܡܫܢܝܢܘܬܐ ܠܡܨܥܝܬܐ "ܠܐ ܟܡܥܒܕܐ ܥܠ ܡܢܝܢܐ ܡܫܘܬܦܐ ܕܗܕܡܐ ܕܛܟܣܐ ܥܠܝܐ ܝܬܝܪ" (Cohen et al., 2003, p. 266) – b₃، ܒܘܚܪܢܐ ܕܥܒܕܐ ܕܚܕ̈ܕܐ ܘܡܨܠܝܢ̈ܘܬܐ ܦܫܝ̈ܛܬܐ ܕܡ̈ܝܐ ܝܢܐ ܥܡ ܡܫܢܝܢܘܬܐ ܘܕܠܐ ܐܝܗ̇ (ܦܐܬܐ 271). ܡܚܝܪܢܘܬܐ: ܕܫܢܚ ܠܡܨܥܝܬܐ ܡܫܬܚܠܦ̈ܢܐ ܡܬܡܫܚ̈ܢܐ ܕܓܘ product (p. 266; Field, 2024, Section 11.3.3)، ܐܠܐ ܐܢ ܠܨܦܪܐ ܐܝܬ ܣܘܟܠܐ. Y ܠܐ ܣܢܝܩ ܝܠܗ ܠܡܫܢܝܢܘܬܐ (Cohen et al., 2003, p. 266).

Hayes (2022، ܦܣܩܐ 9.1) ܟܡܚܝܠ ܠܓܢܒܐ ܐܚܪܢܐ: ܡܐܡܪܐ ܕܣܢܝܩ ܝܠܗ ܠܡܫܢܝܢܘܬܐ ܩܐ "ܙܟܘܬܐ ܥܠ multicollinearity" ܝܠܗ "ܬܫܥܝܬܐ ܕܒܕܝܐ" (ܦܐ̈ܬܐ 320-321). ܡܫܢܝܢܘܬܐ ܫܪܝܪܐܝܬ ܟܡܙܥܪܐ ܐܣܘܪܐ ܕܚܕ̈ܕܐ (correlation) ܒܝܢܝ X ܘ-product، ܐܠܐ ܛܥܝܘܬܐ ܬܩܝܢܬܐ ܕ-b₃، t ܘ-p ܠܐ ܟܫܢܝ ܒܟܠ (ܦܐ̈ܬܐ 324-325). ܗܢܘ ܕܐܡܪ – ܐܦ ܐܗܐ ܘܐܦ ܐܗܐ: ܡܫܢܝܢܘܬܐ ܠܐ ܟܡܫܢܝܐ ܒܘܚܪܢܐ ܕܡܪܟܟܢܘܬܐ، ܐܠܐ ܟܥܒܕܐ b₁ ܘ-b₂ ܕܒܥܠ ܣܘܟܠܐ؛ Hayes ܟܡܪܚܩ ܕܡܦܫܩܚ ܠܗ̇ ܗܟܢܐ، ܘܒܣ ܐܡܬܝ ܕܕܠܐ ܐܝܗ̇ ܡܢ̈ܝܢܐ ܡܫܘܬ̈ܦܐ ܠܝܬ ܠܗܘܢ ܣܘܟܠܐ (ܦܐܬܐ 328).

ܓܘ ܦܐܬܐ – ܬܠܬܐ ܓܒܝ̈ܬܐ، ܐܝܟ ܓܘ PROCESS: ܒܣ ܡܬܡܫܚ̈ܢܐ ܕܓܘ product (center=2؛ ܓܘܒܝܐ ܡܩܕܡܐ ܓܘ ܦܐܬܐ، ܘܓܘܒܝܐ ܕ-Field – ܦܣܩܐ 11.3.6)، ܟܠܗܘܢ (center=1)، ܝܢ ܕܠܐ – ܓܘܒܝܐ ܡܩܕܡܐ (default) ܕ-PROCESS ܓܢܣܗ (Hayes, 2022, pp. 328-329, 602). ܡܫܬܚܠܦܢܐ ܕܬܪܝܢ ܛܝ̈ܡܐ (binary) ܠܐ ܟܫܢܐ ܠܡܨܥܝܬܐ ܓܘ ܓܒܝܬܐ ܩܕܡܝܬܐ، ܡܛܠ ܕܠܛܝ̈ܡܐ ܕܝܠܗ ܐܝܬ ܣܘܟܠܐ. ܛܝ̈ܡܐ ܕ-W ܓܘ ܡܦܩܢܐ ܡܚܘܝ̈ܐ ܝܢܐ ܟܠ ܐܡܬܝ ܓܘ ܣܒܠܬܐ ܫܪܫܝܬܐ.

ܡܨܠܝܢ̈ܘܬܐ ܦܫܝ̈ܛܬܐ ܘ-Johnson-Neyman

ܥܒܕܐ ܕܚܕ̈ܕܐ (interaction) ܪܫܝܡܐ ܟܐܡܪ ܕܐܣܘܪܐ ܟܫܢܐ، ܐܠܐ ܠܐ ܐܝܟܢܐ. ܡܨܠܝܢ̈ܘܬܐ ܦܫܝ̈ܛܬܐ (simple slopes): ܟܣܝܡܚ ܛܝܡܐ ܕ-W ܘܟܫܩܠܚ ܣܪܛܐ ܕܪܝܓܪܫܢ (regression line) ܕ-Y ܥܠ X ܓܘ ܗܘ ܛܝܡܐ، Ŷ = (b₁ + b₃W)X + (b₂W + b₀) – ܡܨܠܝܢܘܬܐ θ = b₁ + b₃W (Cohen et al., 2003, Equation 7.3.1, p. 270). ܛܥܝܘܬܐ ܬܩܝܢܬܐ (standard error) ܕܝܠܗ̇ – ܡܢ ܡܐܛܪܝܟܣ ܕܫܘܚܠܦܐ ܕܡܢ̈ܝܢܐ ܡܫܘܬ̈ܦܐ: SE = √(s²_b1 + 2W·cov_b1b3 + W²·s²_b3)، ܥܡ t ܥܠ n − k − 1 ܕܪ̈ܓܐ ܕܚܐܪܘܬܐ (degrees of freedom) (ܫܘܝ̈ܘܬܐ 7.4.2 ܘ-7.4.4، ܦܐܬܐ 273). ܦܐܬܐ ܫܪܝܪܐ ܝܠܗ ܩܘܒܠ ܡܬܠܐ ܛܒܝܥܐ ܬܡܢ (ܠܘܚܐ 7.4.1، ܦܐܬܐ 276).

ܓܘ ܐܝܢܝ ܛܝ̈ܡܐ؟ Cohen et al. (2003، ܦܐܬܐ 269) ܟܡܪܚܩܝ ܡܨܥܝܬܐ ܘ-±1 ܣܛܝܘܬܐ ܬܩܝܢܬܐ (standard deviation)، ܝܢ ܛܝ̈ܡܐ ܕܒܥܠ ܣܘܟܠܐ، ܐܝܟ ܢܘܩ̈ܙܐ ܕܦܣܩܐ ܩܠܝܢܝ̈ܐ؛ ܐܦ Field (2024، ܦܣܩܐ 11.3.5) ܟܟܬܒ ܕܐܗܐ ܝܠܗ "ܡܐ ܕܡܬܚܙܐ ܣܓܝ". Hayes ܡܢ ܓܢܒܗ ܟܡܪܚܩ ܕܪ̈ܓܐ ܡܢ ܡܐܐ (percentiles) 16، 50 ܘ-84 – ܓܘܒܝܐ ܡܩܕܡܐ (default) ܕ-PROCESS: "ܐܢ W ܠܐ ܫܘܝܐ ܝܠܗ ܣܓܝ"، ܣܛܝܘܬܐ ܬܩܝܢܬܐ ܠܬܚܬ ܡܢ ܡܨܥܝܬܐ ܝܢ ܠܥܠ ܡܢܗ̇ ܡܨܝܐ ܕܢܦܠܐ ܠܒܪ ܡܢ ܣܒܠܬܐ، ܐܠܐ ܕܪ̈ܓܐ ܡܢ ܡܐܐ "ܟܠ ܐܡܬܝ ܓܘ ܦܬܝܘܬܐ ܕܝܗܝ̈ܒܬܐ ܝܢܐ"، ܘܓܘ ܦܘܠܓܐ ܢܘܪܡܠܝܐ (normal distribution) ܐܢܝ ܚܬܝܬܐܝܬ ܡܨܥܝܬܐ ܘ-±1 ܣܛܝܘܬܐ ܬܩܝܢܬܐ ܝܢܐ (2022، ܦܐ̈ܬܐ 259، 265-266، 268). ܫܡܐ "pick-a-point" – Rogosa (1980, as cited in Bauer & Curran, 2005, p. 374)، ܕܟܡܥܗܕܝ ܕܛܝ̈ܡܐ "ܓܒܝ̈ܐ ܝܢܐ ܒܐܘܪܚܐ ܣܓܝ ܕܨܒܝܢܐ". ܓܘ ܦܐܬܐ ܡܨܝܬܘܢ ܕܓܒܝܬܘܢ؛ ܐܡܬܝ ܕܓܒܝܬܘܢ ܡܨܥܝܬܐ ܘ-±1 ܣܛܝܘܬܐ ܬܩܝܢܬܐ، ܛܝܡܐ ܕܟܢܦܠ ܠܒܪ ܡܢ ܝܗܝ̈ܒܬܐ ܟܡܫܬܚܠܦ ܒܛܝܡܐ ܬܚܬܝܐ (minimum) ܝܢ ܒܛܝܡܐ ܥܠܝܐ (maximum)، ܐܝܟ ܓܘ PROCESS (Hayes, 2022, p. 268). Hayes ܠܐ ܟܡܚܘܐ ܐܝܟܢܐ PROCESS ܟܚܫܒ ܕܪ̈ܓܐ ܡܢ ܡܐܐ؛ ܓܘ ܦܐܬܐ – type 6 ܕ-R (ܥܝܕܐ ܕܣܐܝܛ). PROCESS ܐܦ ܟܡܚܘܐ ܡܨܠܝܢ̈ܘܬܐ ܦܫܝ̈ܛܬܐ ܒܣ ܐܡܬܝ ܕܥܒܕܐ ܕܚܕ̈ܕܐ ܪܫܝܡܐ ܝܠܗ ܓܘ ܪܡܐ .10 (ܦܐܬܐ 599)؛ ܦܐܬܐ ܟܡܚܘܐ ܠܗܘܢ ܟܠ ܐܡܬܝ.

Johnson-Neyman (Johnson & Neyman, 1936، ܐܝܟ ܕܡܬܡܠܠܝ ܓܘ Bauer & Curran, 2005) – ܒܕܘܟܬܐ ܕܬܠܬܐ ܛܝ̈ܡܐ، ܟܠ ܛܝ̈ܡܐ: ܐܝܢܝ ܛܝ̈ܡܐ ܕ-W ܟܥܒܕܝ ܡܥܒܕܢܘܬܐ ܕ-X ܪܫܝܡܬܐ (significant)؟ ܬܚܘ̈ܡܐ ܝܢܐ ܛܝ̈ܡܐ ܕܓܘܗܘܢ t ܕܡܨܠܝܢܘܬܐ ܦܫܝܛܬܐ ܫܘܐ ܝܠܗ ܚܬܝܬܐܝܬ ܠܛܝܡܐ ܚܪܝܦܐ (critical value) – t²_crit·SE²(W) − (b₁ + b₃W)² = 0، ܫܘܝܘܬܐ ܕܡܪܒܥܐ ܓܘ W ܕܟܫܪܚ ܠܗ̇ ܒܢܘܣܚܐ ܕܥܩܪ̈ܐ (Bauer & Curran, 2005, Equations 16-21, p. 380; Hayes, 2022, p. 270). ܡܨܝܐ ܕܗܘܝܢ ܬܪܝܢ ܬܚܘ̈ܡܐ، ܚܕ ܝܢ ܠܐ ܚܕ ܓܘ ܦܬܝܘܬܐ ܕܝܗܝ̈ܒܬܐ (Hayes, 2022, pp. 270-271)؛ Field ܟܡܚܘܐ ܒܣ ܓܕܫܐ ܕܬܪܝܢ ܬܚܘ̈ܡܐ، ܕܒܝܢܝܗܘܢ ܡܥܒܕܢܘܬܐ ܠܐ ܝܠܗ ܪܫܝܡܬܐ (2024، ܦܣܩܐ 11.3.5)، ܘܓܘ ܡܬܠܐ ܕܦܐܬܐ ܐܝܬ ܬܚܘܡܐ ܚܕ. ܥܩܪ̈ܐ ܠܒܪ ܡܢ ܦܬܝܘܬܐ "ܣܢܝܩ ܝܠܗ ܕܠܐ ܚܫܒܚ ܠܗܘܢ" (Hayes, 2022, p. 270)؛ ܐܦ Cohen et al. ܟܡܪܚܩܝ ܕܦܫܩܚ ܪܝܓܪܫܢ "ܒܣ ܓܘ ܦܬܝܘܬܐ ܕܝܗܝ̈ܒܬܐ ܕܚܙܝ̈ܐ ܝܢܐ" (2003، ܦܐܬܐ 282). ܡܛܠ ܗܕܐ ܦܐܬܐ ܟܡܘܕܥ ܒܣ ܬܚܘ̈ܡܐ ܓܘ ܦܬܝܘܬܐ ܕ-W، ܘܡܢܬܐ ܒܡܐܐ ܕܡܫܬܘܬܦ̈ܢܐ (participants) ܡܢ ܟܠ ܓܢܒܐ، ܐܝܟ PROCESS (Hayes, 2022, p. 271). ܐܡܬܝ ܕܓܘ ܚܕ ܓܢܒܐ ܕܬܚܘܡܐ ܐܝܬ ܩܠܝܠ ܡܫܬܘܬܦ̈ܢܐ، Hayes "ܗܘܐ ܡܬܟܠܝܐ" ܡܢ ܫܘܠܡܐ ܣܓܝ ܡܢ ܐܗܐ ܐܬܪܐ (ܦܐܬܐ 275). ܘܙܘܗܪܐ ܐܚܪܢܐ: ܒܘܚܪܢܐ ܥܒܝܕܐ ܝܠܗ ܓܘ ܟܠ ܛܝܡܐ ܕ-W ܒܦܪܝܫܘܬܐ، ܘܠܐ ܩܐ ܟܠ ܛܝ̈ܡܐ ܐܟܚܕܐ؛ Bauer ܘ-Curran ܡܛܠ ܗܕܐ ܟܚܙܝ ܓܘ ܐܬܪ̈ܘܬܐ "ܛܝܡܐ heuristic ܒܝܚܝܕܝܘܬܐ" (2005، ܦܐܬܐ 383)، ܘܬܘܪܨܐ ܕܒܚܕ ܙܒܢܐ (simultaneous) (Potthoff, 1964، ܐܝܟ ܕܡܬܡܠܠܐ ܓܘܝܗܘܢ) ܠܐ ܝܠܗ ܓܘ PROCESS (Hayes, 2022, p. 271, Note 6) ܘܠܐ ܝܠܗ ܓܘ ܦܐܬܐ.

ܡܘܕܝܠ ܕܡܨܥܝܘܬܐ (ܡܘܕܝܠ 4)

ܬܪܬܝܢ ܫܘܝ̈ܘܬܐ (ܘܒܢܘܬ، ܐܢ ܐܝܬ ܟܡܐ ܡܨܥ̈ܝܐ)، ܟܠ ܚܕܐ ܪܝܓܪܫܢ (regression) ܦܪܝܫܐ: M = i₁ + aX، ܘ-Y = i₂ + c'X + bM. a – ܡܥܒܕܢܘܬܐ ܕ-X ܥܠ M؛ b – ܕ-M ܥܠ Y ܐܡܬܝ ܕ-X ܩܝܡܐ ܝܠܗ؛ c' – ܡܥܒܕܢܘܬܐ ܬܪܝܨܬܐ (direct effect) ܕ-X ܥܠ Y؛ ܘ-product ab – ܡܥܒܕܢܘܬܐ ܠܐ ܬܪܝܨܬܐ (indirect effect) (Field, 2024, Sections 11.4.1-11.4.3, Equation 11.6). "ܠܦܘܬ ܢܡܘܣܐ ܕܥܩܒܬܐ (tracing rule)، ܡܥܒ̈ܕܢܘܝܬܐ ܠܐ ܬܪ̈ܝܨܬܐ ܡܫܘܥܪ̈ܐ ܝܢܐ ܐܝܟ products ܕܡܥܒ̈ܕܢܘܝܬܐ ܬܪ̈ܝܨܬܐ"، ܘܡܨܝܚ ܕܓܡܪܚ ܠܗܘܢ (Cohen et al., 2003, p. 462). ܡܥܒܕܢܘܬܐ ܟܠܢܝܬܐ (total effect) c – ܡܢܝܢܐ ܡܫܘܬܦܐ ܕ-X ܐܡܬܝ ܕ-Y ܡܢܒܝܐ ܝܠܗ ܡܢ X ܒܠܚܘܕ – ܫܘܐ ܝܠܗ ܚܬܝܬܐܝܬ ܠܬܪܝܨܬܐ ܘܥܡܗ̇ ܠܐ ܬܪܝܨܬܐ، c = c' + ab (p. 463, Equation 12.2.1; p. 465; Hayes, 2022, Section 3.2). ܓܘ OLS ܐܗܐ ܫܘܝܘܬܐ ܟܩܝܡܐ "ܟܠ ܐܡܬܝ، ܓܘ ܟܠ ܛܘܟܣܐ ܕܝܗܝ̈ܒܬܐ" (Hayes, 2022, p. 95; p. 87)، ܥܕܡܐ ܕܡܫܬܚܠܦ̈ܢܐ ܕܒܘܚܪܢܐ (control variables) ܐܝܬܝܗܘܢ ܐܦ ܓܘ ܫܘܝܘܬܐ ܕ-M ܘܐܦ ܓܘ ܫܘܝܘܬܐ ܕ-Y (ܦܐܬܐ 136) ܘܫܘܝ̈ܘܬܐ ܥܠ ܗܢ ܡܫܬܘܬܦ̈ܢܐ ܝܢܐ – ܘܡܛܠ ܗܕܐ ܦܐܬܐ ܟܫܩܠ ܡܫܬܘܬܦ̈ܢܐ ܕܚܣܝ̈ܪܐ ܝܢܐ ܡܢ ܟܠ ܫܘܝ̈ܘܬܐ ܐܟܚܕܐ.

ܟܡܐ ܡܨܥ̈ܝܐ ܒܓܢܒ ܚܕ̈ܕܐ (Field, 2024, Section 11.4.7): ܩܐ ܟܠ ܡܨܥܝܐ (mediator) a_j ܘ-b_j ܕܝܠܗ، ܘܠܐ ܬܪܝܨܬܐ ܕܝܠܗ a_jb_j؛ ܓܘܡܪܐ ܝܠܗ ܡܥܒܕܢܘܬܐ ܠܐ ܬܪܝܨܬܐ ܟܠܢܝܬܐ. ܡܨܥ̈ܝܐ ܐܣܝܪ̈ܐ ܝܢܐ ܚܕ ܥܡ ܚܕ ("ܓܐܪܐ ܕܬܪܝܢ ܪ̈ܫܐ"، ܬܡܢ)، ܘ-b_j ܝܠܗ ܡܥܒܕܢܘܬܐ ܕܟܠ ܡܨܥܝܐ ܥܡ ܒܘܚܪܢܐ ܕܐܚܪ̈ܢܐ. ܦܐܬܐ ܟܡܘܣܦ ܦܘܪ̈ܫܢܐ ܒܝܢܝ ܡܥܒ̈ܕܢܘܝܬܐ ܠܐ ܬܪ̈ܝܨܬܐ – ܐܝܢܐ ܫܒܝܠܐ ܒܐܘܪܚܐ ܕܚܘܫܒܐ ܡܬܢܝܐ ܚܣܝܢܐ ܝܬܝܪ ܝܠܗ ܡܢ ܫܒܝܠܐ ܒܐܘܪܚܐ ܕܫܢܬܐ – ܥܡ ܬܚܘܡܐ ܕ-bootstrap ܕܝܠܗܘܢ، ܐܝܟ contrast=1 ܓܘ PROCESS (Hayes, 2022, pp. 176-178, 591; Preacher & Hayes, 2008, p. 884). ܡܨܝܚ ܕܦܚܡܚ ܐܦ ܡܨܥ̈ܝܐ ܓܘ ܣܒ̈ܠܬܐ ܦܪ̈ܝܫܬܐ، ܡܛܠ ܕܡܥܒ̈ܕܢܘܝܬܐ ܠܐ ܬܪ̈ܝܨܬܐ ܓܘ ܡܫܘ̈ܚܬܐ ܕ-X ܘ-Y ܝܢܐ (Hayes, 2022, p. 176). ܐܠܐ ܦܘܪܫܢܐ ܝܠܗ ܦܘܪܫܢܐ ܓܘ "ܚܝܠܐ" ܒܣ ܐܡܬܝ ܕܬܪܘܝܗܝ ܠܐ ܬܪ̈ܝܨܬܐ ܓܘ ܗܘ ܪܘܫܡܐ ܝܢܐ (ܦܐܬܐ 178). ܡܘܕܝܠ ܚܕ ܥܡ ܟܠ ܡܨܥ̈ܝܐ ܛܒܐ ܝܬܝܪ ܝܠܗ ܡܢ ܟܡܐ ܡܘܕܝ̈ܠܐ ܦܪ̈ܝܫܐ: ܟܠ ܠܐ ܬܪܝܨܬܐ ܓܘܗ ܥܡ ܒܘܚܪܢܐ ܕܐܚܪ̈ܢܝܬܐ، ܘܗܟܢܐ "ܟܙܥܪܐ ܣܟܘܝܐ ܕܡܣܒ ܒܐܦ̈ܐ (bias)" ܡܛܠ ܡܫܬܚܠܦ̈ܢܐ ܕܫܩܝܠ̈ܐ ܝܢܐ (Preacher & Hayes, 2008, p. 881).

ܐܝܟܢܐ ܟܒܚܪܚ ܡܥܒܕܢܘܬܐ ܠܐ ܬܪܝܨܬܐ؟

ܐܘܪܚܐ ܥܬܝܩܬܐ – ܐܪܒܥܐ ܫܪ̈ܛܐ ܕ-Baron ܘ-Kenny (1986، ܐܝܟ ܕܡܬܡܠܠܝ ܓܘ Field, 2024، ܦܣܩܐ 11.4.2): X ܟܡܢܒܐ Y، X ܟܡܢܒܐ M، M ܟܡܢܒܐ Y، ܘܡܥܒܕܢܘܬܐ ܕ-X "ܟܡܟܪܗܐ" ܐܡܬܝ ܕܟܡܘܣܦܚ M. Field ܟܡܦܫܩ ܕܒܥܬܐ ܓܘ ܫܪܛܐ ܪܒܝܥܝܐ ܝܠܗ – ܟܡܐ ܢܚܬܬܐ ܣܦܩܐ ܝܠܗ؟ – ܘܥܝܕܐ ܕܒܥܝܐ ܥܒܪܐ ܡܢ ܪܫܝܡܐ ܠܠܐ ܪܫܝܡܐ "ܟܡܛܝܐ ܠܟܠ ܙܢ̈ܐ ܕܫܛܝܘܬܐ" (ܬܡܢ). Hayes (2022، ܦܣܩܐ 4.1) ܟܡܘܣܦ ܕܠܝܬ ܣܢܝܩܘܬܐ ܒܟܠ ܠܡܥܒܕܢܘܬܐ ܟܠܢܝܬܐ ܪܫܝܡܬܐ: "ܡܥܒܕܢܘܬܐ ܠܐ ܬܪܝܨܬܐ ܡܨܝܐ ܕܗܘܝܐ ܦܪܝܫܬܐ ܡܢ ܨܦܪܐ ܐܦ ܐܡܬܝ ܕܡܥܒܕܢܘܬܐ ܟܠܢܝܬܐ ܠܐ ܝܠܗ̇" (ܦܐܬܐ 123؛ ܘܗܟܢܐ Preacher & Hayes, 2008، ܦܐܬܐ 880). Cohen et al. (2003، ܦܐܬܐ 467) ܟܒܚܪܝ ܒܣ ܫܒ̈ܝܠܐ ܓܢܣܗܘܢ، ܘܠܐ ܟܝܗܒܝ ܛܥܝܘܬܐ ܬܩܝܢܬܐ ܠܡܥܒܕܢܘܬܐ ܠܐ ܬܪܝܨܬܐ.

ܒܘܚܪܢܐ ܕ-Sobel (Sobel, 1982, as cited in Hayes, 2022, Section 3.4) – z = ab/SE. ܦܐܬܐ ܟܡܦܠܚ ܛܥܝܘܬܐ ܬܩܝܢܬܐ (standard error) "ܕܛܟܣܐ ܬܪܝܢܝܐ"، SE = √(a²s²_b + b²s²_a + s²_as²_b) (Hayes, 2022, Equation 3.7, p. 97) – ܗܝ ܕ-PROCESS ܟܚܫܒ (ܦܐܬܐ 590). Preacher ܘ-Hayes (2008، ܦܐ̈ܬܐ 880، 882) ܟܡܚܘܝ ܢܘܣܚܐ ܕܛܟܣܐ ܩܕܡܝܐ، ܕܠܐ ܗܕܡܐ ܐܚܪܝܐ، ܘܟܡܥܗܕܝ ܕܦܘܪܫܢܐ "ܒܥܕܢܐ ܣܓܝ ܙܥܘܪܐ ܛܒܐ ܝܠܗ". ܒܘܚܪܢܐ ܟܣܐܡ ܕ-product ab ܦܠܝܓܐ ܝܠܗ ܢܘܪܡܠܐܝܬ، ܐܠܐ ܦܘܠܓܐ ܕܝܠܗ "ܠܐ ܛܟܣܢܝܐ ܝܠܗ" ܓܘ ܕܘ̈ܡܝܐ ܪ̈ܓܝܠܐ، ܘܚܝܠܐ ܣܛܐܛܝܣܛܝܩܝܐ (statistical power) ܕܝܠܗ ܡܢ ܢܚ̈ܝܬܐ ܝܠܗ – Hayes: "ܟܡܪܚܩܢ ܕܡܬܪܚܩܚ ܡܢ ܐܗܐ ܐܘܪܚܐ" (2022، ܦܐܬܐ 99). ܦܐܬܐ ܟܡܚܘܐ ܠܗ ܩܐ ܦܘܚܡܐ ܒܠܚܘܕ.

Bootstrap – ܐܘܪܚܐ ܕ-Field ܘܕ-PROCESS (ܦܣ̈ܩܐ 11.4.4-11.4.6): ܟܓܒܚ ܡܢ ܝܗܝ̈ܒܬܐ، ܥܡ ܕܥܪܬܐ، ܕܘܡܝܐ (sample) ܒܗܝ ܪܒܘܬܐ؛ ܟܫܥܪܚ ܡܢ ܪܝܫ ܟܠ ܫܘܝ̈ܘܬܐ ܘ-ab؛ ܟܡܬܢܚ 5,000 ܙܒܢ̈ܐ؛ ܟܛܟܣܚ ܫܘ̈ܥܪܐ؛ ܘܬܚܘܡܐ ܕܬܘܟܠܢܐ (confidence interval) ܕ-95% ܝܠܗ ܛܝ̈ܡܐ ܓܘ ܕܘ̈ܟܝܬܐ 0.005k(100 − ci) ܘ-k[1 − 0.005(100 − ci)] + 1 – ܓܘ 5,000 ܕܘܡ̈ܝܐ، 125 ܘ-4,876 (Hayes, 2022, pp. 100, 102). ܐܗܐ ܝܠܗ ܬܚܘܡܐ ܕܕܪ̈ܓܐ ܡܢ ܡܐܐ (percentile interval)، ܓܘܒܝܐ ܡܩܕܡܐ ܕ-PROCESS؛ 5,000-10,000 ܕܘܡ̈ܝܐ "ܣܦܩܝ ܓܘ ܣܓܝܐܐ ܡܢ ܦܘܠܚ̈ܢܐ" (ܦܐܬܐ 105). "ܐܢ ܬܚܘܡܐ ܕܬܘܟܠܢܐ ܟܐܚܕ ܨܦܪܐ – ܟܡܝܠܚ ܕܣܝܡܚ ܕܠܝܬ ܡܨܥܝܘܬܐ" (Field, 2024, Section 11.4.6). ܫܘܥܪܐ ܘܬܚܘܡܐ ܕܬܘܟܠܢܐ ܛܒ̈ܐ ܝܬܝܪ ܝܢܐ ܡܢ Baron ܘ-Kenny ܘܡܢ Sobel، ܡܛܠ ܕ"ܥܣܩ ܝܬܝܪ ܝܠܗ ܕܢܦܠܚ ܠܚܘܫܒܐ ܕܐܘܟܡܐ-ܚܘܪܐ" (ܦܣܩܐ 11.4.2). ܡܢܝܢܐ ܕܕܘܡ̈ܝܐ ܡܨܐ ܕܫܢܐ (200 ܥܕܡܐ 20,000)؛ ܐܡܬܝ ܕܕܘܟܬܐ ܠܐ ܝܠܗ ܡܢܝܢܐ ܓܡܝܪܐ، ܦܐܬܐ ܟܡܥܓܠ ܠܬܚܬܝܐ ܠܬܚܬ ܘܠܥܠܝܐ ܠܥܠ (ܥܝܕܐ ܕܣܐܝܛ).

ܕܕܪ̈ܓܐ ܡܢ ܡܐܐ ܝܢ ܡܬܘܪܨܐ ܡܢ ܡܣܒ ܒܐܦ̈ܐ؟ ܐܦ ܐܗܐ ܘܐܦ ܐܗܐ ܓܘ ܡܒܘ̈ܥܐ: Preacher ܘ-Hayes (2008، ܦܐܬܐ 886) ܡܘܪܚܩܠܗܘܢ ܬܚܘܡܐ ܡܬܘܪܨܐ ܡܢ ܡܣܒ ܒܐܦ̈ܐ (bias-corrected)؛ Hayes (2022، ܦܐܬܐ 109) ܟܟܬܒ ܒܬܪ ܗܕܐ ܕܬܘܪܨܐ "ܡܨܐ ܕܡܪܒܐ ܩܠܝܠ" ܛܥܝܘܬܐ ܕܙܢܐ I ܐܡܬܝ ܕܚܕ ܡܢ ܫܒ̈ܝܠܐ ܨܦܪܐ ܝܠܗ، ܘܕܬܚܘܡܐ ܕܕܪ̈ܓܐ ܡܢ ܡܐܐ ܗܘܐ ܠܗ "ܐܘܪܚܐ ܡܪܚܩܬܐ ܝܬܝܪ". ܬܚܘ̈ܡܐ ܕ-BCa "ܠܐ ܐܝܬܝܗܘܢ ܓܘ PROCESS ܘܚܕ ܙܒܢܐ ܠܐ ܗܘܘ" (ܦܐܬܐ 104). ܦܐܬܐ ܟܚܫܒ ܬܚܘܡܐ ܕܕܪ̈ܓܐ ܡܢ ܡܐܐ.

ܙܪܥܐ (random seed): ܗܘ ܙܪܥܐ – ܗܢ ܕܘܡ̈ܝܐ. ܕܠܐ ܙܪܥܐ ܩܝܡܐ، "ܒܕ ܫܩܠܝܬܘܢ ܛܝ̈ܡܐ ܦܪ̈ܝܫܐ ܩܠܝܠ" ܓܘ ܟܠ ܪܗܛܐ (Field, 2024, Section 11.4.5, Note 13)، ܘ-Hayes ܟܡܪܚܩ ܟܠ ܐܡܬܝ ܕܩܝܡܚ ܙܪܥܐ ܘܡܘܕܥܚ ܠܗ (2022، ܦܐ̈ܬܐ 106-107). ܙܪܥܐ ܟܡܬܚܙܐ ܓܘ ܡܦܩܢܐ ܘܓܘ ܣܩܪܝܦܬ R، ܕܟܡܦܠܚ ܗܘ ܡܘܠܕܢܐ (generator) ܕ-R – ܘܡܛܠ ܗܕܐ ܣܩܪܝܦܬ ܕܟܡܚܬܝܬܘܢ ܟܝܗܒ ܚܬܝܬܐܝܬ ܗܢ ܬܚܘ̈ܡܐ. ܓܘ PROCESS ܩܐ SPSS ܝܢ ܩܐ SAS ܗܘ ܙܪܥܐ ܟܝܗܒ ܕܘܡ̈ܝܐ ܐܚܪ̈ܢܐ، ܡܛܠ ܕܡܘܠܕܢܐ ܦܪܝܫܐ ܝܠܗ (Hayes, 2022, p. 106). ܓܘܒܝܐ ܡܩܕܡܐ ܓܘ ܦܐܬܐ ܝܠܗ ܙܪܥܐ 42، ܐܝܟ ܓܘ ܡܬ̈ܠܐ ܕܡܕܒܪܢܐ؛ "ܙܪܥܐ ܚܕܬܐ" ܟܝܗܒ ܙܪܥܐ ܐܚܪܢܐ، ܘܬܚܘ̈ܡܐ ܕ-bootstrap ܟܫܢܝ ܒܟܡܐ ܡܢ̈ܘܬܐ ܡܢ ܐܠܦܐ.

ܪܒܘܬܐ ܕܡܥܒܕܢܘܬܐ ܕܡܥܒܕܢܘܬܐ ܠܐ ܬܪܝܨܬܐ

ܡܥܒܕܢܘܬܐ ܠܐ ܬܪܝܨܬܐ (indirect effect) ab ܝܠܗ̇ "ܡܢܝܢܐ ܡܫܘܬܦܐ ܕܪܝܓܪܫܢ ܠܐ ܡܬܩܢܐ ܐܝܟ ܟܠ ܡܢܝܢܐ ܡܫܘܬܦܐ" – ܓܘ ܡܫܘ̈ܚܬܐ ܕ-Y ܩܐ ܟܠ ܡܫܘܚܬܐ ܕ-X (Field, 2024, Section 11.4.3). ܬܪܝܢ ܙܢ̈ܐ ܕܡܬܩܢܘܬܐ (standardization): ܡܬܩܢܐ ܡܢܬܢܐܝܬ – ab/s_Y: ܟܡܐ ܣܛܝ̈ܘܬܐ ܬܩܝܢ̈ܬܐ ܕ-Y ܩܐ ܟܠ ܡܫܘܚܬܐ ܕ-X (Hayes, 2022, Table 4.2, p. 148; MacKinnon, 2008, as cited in Field, 2024, Equation 11.7). ܡܬܩܢܐ ܓܡܝܪܐܝܬ – ab·s_X/s_Y (Hayes, 2022, p. 116; Field, 2024, Equation 11.8)، "ܡܚܘܝܢܐ ܕܡܨܥܝܘܬܐ"، ܕܡܨܝܚ ܕܦܚܡܚ ܠܗ ܒܝܢܝ ܡܘܕܝ̈ܠܐ ܘܕܡܘܣܦܚ ܠܗ ܠܡܝܛܐ-ܐܢܐܠܝܣܝܣ (meta-analysis)؛ Field ܟܡܘܕܥ ܠܗ ܓܘ ܡܬܠܐ، β = 0.04 (ܦܣܩܐ 11.4.6). ܐܡܬܝ ܕ-X ܕܬܪܝܢ ܛܝ̈ܡܐ ܝܠܗ، Hayes ܟܡܪܚܩ "ܕܡܬܪܚܩܚ" ܡܢ ܡܬܩܢܐ ܓܡܝܪܐܝܬ ܘܕܡܘܕܥܚ ܡܬܩܢܐ ܡܢܬܢܐܝܬ (2022، ܦܐܬܐ 148)، ܘ-PROCESS ܠܐ ܟܚܫܒ ܠܗ (ܦܐܬܐ 145) – ܘܗܟܢܐ ܐܦ ܦܐܬܐ. ܡܚܘ̈ܝܢܐ ܐܚܪ̈ܢܐ، ܐܝܟ "ܡܢܬܐ ܕܡܨܥܝܘܬܐ" ab/c، Hayes ܟܡܣܠܐ ܠܗܘܢ: ܠܐ ܐܝܬ ܠܗܘܢ ܬܚܘ̈ܡܐ ܘܠܐ ܝܢܐ ܩܝܡ̈ܐ ܓܘ ܕܘ̈ܡܝܐ ܕܪܒܘܬܐ ܪܓܝܠܬܐ (ܦܐ̈ܬܐ 149-151).

ܡܨܥܝܘܬܐ ܡܪܟܟܬܐ (ܡܘܕܝ̈ܠܐ 7 ܘ-14)

ܒܥܕܢ̈ܐ ܫܘܐܠܐ ܝܠܗ ܐܢ ܡܟܢܘܬܐ ܬܠܝܐ ܝܠܗ̇ ܥܠ ܡܫܬܚܠܦܢܐ ܬܠܝܬܝܐ. ܡܘܕܝܠ 7 – W ܟܡܪܟܟ ܫܒܝܠܐ ܩܕܡܝܐ: M = i₁ + a₁X + a₂W + a₃XW، ܘܡܛܠ ܗܕܐ ܡܥܒܕܢܘܬܐ ܠܐ ܬܪܝܨܬܐ ܓܘ ܛܝܡܐ ܦܣܝܩܐ ܕ-W ܝܠܗ̇ (a₁ + a₃W)·b. ܡܘܕܝܠ 14 – W ܟܡܪܟܟ ܫܒܝܠܐ ܬܪܝܢܝܐ: Y = i₂ + c'X + b₁M + b₂W + b₃MW، ܘܡܥܒܕܢܘܬܐ ܠܐ ܬܪܝܨܬܐ ܝܠܗ̇ a·(b₁ + b₃W). (Hayes, 2022، ܫܘܝ̈ܘܬܐ 12.6-12.8، ܦܐ̈ܬܐ 468-469، ܘܫܘܝܘܬܐ 11.13، ܦܐܬܐ 434). ܓܘ ܬܪܘܝܗܝ ܡܘܕܝ̈ܠܐ ܡܥܒܕܢܘܬܐ ܬܪܝܨܬܐ c' ܠܐ ܝܠܗ̇ ܡܪܟܟܬܐ (ܦܐ̈ܬܐ 419، 480)؛ ܓܘ ܡܘܕܝܠ 7، W ܟܥܐܠ ܓܘ ܫܘܝܘܬܐ ܕ-M ܒܠܚܘܕ، ܘܓܘ ܡܘܕܝܠ 14 – ܓܘ ܫܘܝܘܬܐ ܕ-Y. ܡܥܒܕܢܘܬܐ ܠܐ ܬܪܝܨܬܐ ܣܪܛܐ ܬܪܝܨܐ ܝܠܗ̇ ܓܘ W، ܘܡܨܠܝܢܘܬܐ ܕܝܠܗ – a₃b ܝܢ ab₃ – ܝܠܗ̇ ܡܚܘܝܢܐ ܕܡܨܥܝܘܬܐ ܡܪܟܟܬܐ (index of moderated mediation) (Hayes, 2015, as cited in Hayes, 2022, pp. 440, 476): ܟܡܐ ܡܥܒܕܢܘܬܐ ܠܐ ܬܪܝܨܬܐ ܟܫܢܝܐ ܐܡܬܝ ܕ-W ܟܣܠܩ ܒܡܫܘܚܬܐ ܚܕܐ. ܬܚܘܡܐ ܕ-bootstrap ܕܡܚܘܝܢܐ ܝܠܗ ܒܘܚܪܢܐ ܪܫܡܝܐ: ܐܢ ܠܐ ܟܐܚܕ ܨܦܪܐ – ܡܥܒܕܢܘܬܐ ܠܐ ܬܪܝܨܬܐ ܬܠܝܐ ܝܠܗ̇ ܥܠ W (ܦܐܬܐ 441). ܗܘ ܬܚܘܡܐ ܟܒܚܪ ܐܦ ܦܘܪܫܢܐ ܒܝܢܝ ܟܠ ܬܪܬܝܢ ܠܐ ܬܪ̈ܝܨܬܐ ܬܠܝ̈ܬܐ، ܡܛܠ ܕܦܘܪܫܢܐ ܝܠܗ ܡܚܘܝܢܐ ܡܣܘܓܐܐ ܥܠ ܦܘܪܫܢܐ ܒܝܢܝ ܛܝ̈ܡܐ ܕ-W (ܦܐܬܐ 449). ܡܫܢܝܢܘܬܐ ܠܡܨܥܝܬܐ ܠܐ ܟܡܫܢܝܐ ܠܐ ܬܪ̈ܝܨܬܐ ܬܠܝ̈ܬܐ (ܦܐܬܐ 426، ܡܥܝܪܢܘܬܐ 1).

ܬܪܬܝܢ ܡܥܝܪ̈ܢܘܬܐ. ܩܕܡܝܬ، "ܠܐ ܬܪܝܨܬܐ ܪܫܝܡܬܐ ܝܠܗ̇ ܓܘ ܛܝܡܐ ܢܚܝܬܐ ܕ-W ܘܠܐ ܓܘ ܪܡܐ" ܠܐ ܝܠܗ ܚܘܝܬܐ ܕܡܨܥܝܘܬܐ ܡܪܟܟܬܐ – ܦܘܪܫܢܐ ܒܝܢܝ ܬܪܬܝܢ ܠܐ ܬܪ̈ܝܨܬܐ ܝܠܗ ܡܐ ܕܣܢܝܩ ܝܠܗ ܠܒܘܚܪܢܐ، ܘܐܗܐ ܝܠܗ ܡܚܘܝܢܐ. ܓܘ ܡܬܠܐ ܕܡܘܕܝܠ 14 ܚܬܝܬܐܝܬ ܗܟܢܐ: ܡܥܒܕܢܘܬܐ ܠܐ ܬܪܝܨܬܐ ܒܐܘܪܚܐ ܕܫܢܬܐ ܪܫܝܡܬܐ ܝܠܗ̇ ܓܘ ܡܥܕܪܢܘܬܐ ܢܚܝܬܐ ܘܡܨܥܝܬܐ ܘܠܐ ܓܘ ܪܡܬܐ، ܐܠܐ ܬܚܘܡܐ ܕܬܘܟܠܢܐ ܕܡܚܘܝܢܐ ܟܐܚܕ ܨܦܪܐ. Hayes ܟܐܡܪ ܐܗܐ ܓܠܝܐܝܬ: "ܠܐ ܦܝܫ ܡܢܗ" ܐܢ ܥܒܕܐ ܕܚܕ̈ܕܐ ܓܘ ܚܕ ܡܢ ܫܒ̈ܝܠܐ ܪܫܝܡܐ ܝܠܗ؛ "ܡܐ ܕܚܫܝܚܐ ܝܠܗ ܐܝܢܐ ܡܚܘܝܢܐ ܕܡܨܥܝܘܬܐ ܡܪܟܟܬܐ ܦܪܝܫܐ ܝܠܗ ܡܢ ܨܦܪܐ" (2022، ܦܐܬܐ 441؛ ܘܚܙܝܡܘܢ ܦܐܬܐ 468). ܬܪܝܢܝܬ، ܠܝܬܘܬܐ ܕܡܥܒܕܢܘܬܐ ܠܐ ܬܪܝܨܬܐ ܟܠܢܝܬܐ ܠܐ ܟܐܡܪܐ ܡܕܡ ܥܠ ܐܝܢܐ ܝܠܗ̇ ܡܪܟܟܬܐ (ܦܐܬܐ 441). ܦܐܬܐ ܫܪܝܪܐ ܝܠܗ ܩܘܒܠ ܚܘܫܒܢܐ ܝܚܝܕܝܐ ܓܘ R.

ܛܥܝ̈ܘܬܐ ܬܩܝܢ̈ܬܐ ܚܣܝܢ̈ܬܐ

ܟܠ ܫܘܝ̈ܘܬܐ ܡܫܘܥܪ̈ܐ ܝܢܐ ܒ-OLS، ܘܓܘ ܓܘܒܝܐ ܡܩܕܡܐ (default) – ܥܡ ܛܥܝ̈ܘܬܐ ܬܩܝܢ̈ܬܐ ܚܣܝܢ̈ܬܐ (robust standard errors) ܩܐ heteroscedasticity، HC4. Field ܟܡܪܚܩ ܕܓܒܚ HC4 "ܘܕܡܬܒܣܡܚ ܒܢܝܚܐ ܕܠܐ ܚܫܒܬܐ ܬܘܒ ܥܠ ܣܝܡܐ" (2024، ܦܣܩܐ 11.3.6؛ ܘܗܟܢܐ ܐܦ ܓܘ ܡܨܥܝܘܬܐ، ܦܣ̈ܩܐ 11.4.4 ܘ-11.4.7). Hayes ܠܐ ܟܡܪܚܩ ܚܕ ܡܢܝܗܘܢ؛ PROCESS ܟܡܩܪܒ HC0 ܥܕܡܐ HC4 (hc=0 ܥܕܡܐ hc=4)، ܘܐܝܟ ܓܘܒܝܐ ܡܩܕܡܐ – ܛܥܝ̈ܘܬܐ ܪ̈ܓܝܠܬܐ (Hayes, 2022، ܦܐܬܐ 608؛ Hayes & Cai, 2007، ܐܝܟ ܕܡܬܡܠܠܝ ܬܡܢ). ܓܘ ܦܐܬܐ ܡܨܝܬܘܢ ܕܓܒܝܬܘܢ HC3 ܝܢ ܛܥܝ̈ܘܬܐ ܪ̈ܓܝܠܬܐ. ܛܥܝ̈ܘܬܐ ܬܩܝܢ̈ܬܐ ܚܣܝܢ̈ܬܐ ܟܡܫܢܝܐ t، p، ܬܚܘ̈ܡܐ ܕܬܘܟܠܢܐ ܕܡܢ̈ܝܢܐ ܡܫܘܬ̈ܦܐ ܘܡܨܠܝܢ̈ܘܬܐ ܦܫܝ̈ܛܬܐ ܘ-Johnson-Neyman، ܘܒܘܚܪܢܐ F ܕܡܘܕܝܠ ܟܗܘܐ ܒܘܚܪܢܐ ܕ-Wald – ܐܠܐ ܠܐ ܫܘ̈ܥܪܐ، ܘܠܐ ܬܚܘ̈ܡܐ ܕ-bootstrap ܕܡܥܒ̈ܕܢܘܝܬܐ ܠܐ ܬܪ̈ܝܨܬܐ. ܦܘܪܫܢܐ ܡܨܐ ܕܗܘܐ ܫܪܝܪܐ: ܓܘ ܡܬܠܐ ܕܡܨܥܝܘܬܐ ܕ-Field ܡܥܒܕܢܘܬܐ ܬܪܝܨܬܐ "ܗܠ ܐܕܝܘܡ ܪܫܝܡܬܐ ܝܠܗ̇" ܓܘ ܛܥܝ̈ܘܬܐ ܪ̈ܓܝܠܬܐ (ܦܣܩܐ 11.4.2)، ܘܠܐ ܝܠܗ̇ ܪܫܝܡܬܐ ܓܘ HC4، p = .079 (ܦܣܩܐ 11.4.5).

ܩܪܝܢܐ ܕܡܦܩܢܐ (How to read the output)

ܡܘܕܝܠ 1. ܠܘܚܐ 1 – ܪܒܘܬܐ ܕܡܘܕܝܠ ܘܬܘܣܦܬܐ ܕܥܒܕܐ ܕܚܕ̈ܕܐ (ΔR² ܥܡ F). ܠܘܚܐ 2 – ܡܢ̈ܝܢܐ ܡܫܘܬ̈ܦܐ (coefficients): b₃ ܝܠܗ ܒܘܚܪܢܐ ܕܡܪܟܟܢܘܬܐ؛ b₁ ܘ-b₂ – ܡܥܒ̈ܕܢܘܝܬܐ ܬܠܝ̈ܬܐ (ܓܘ ܡܨܥܝܬܐ ܕܡܫܬܚܠܦܢܐ ܐܚܪܢܐ، ܐܢ ܡܫܢܝܐ ܝܠܗ ܠܡܨܥܝܬܐ). ܠܘܚܐ 3 – ܡܨܠܝܢ̈ܘܬܐ ܦܫܝ̈ܛܬܐ. ܒܬܪܗ – Johnson-Neyman (ܡܐܡܪܐ، ܨܘܪܬܐ ܘܠܘܚܐ ܡܦܪܫܐ) ܘܨܘܪܬܐ ܕܥܒܕܐ ܕܚܕ̈ܕܐ. ܓܘ ܡܬܠܐ (238 ܡܫܬܘܬܦ̈ܢܐ ܥܡ ܝܗܝ̈ܒܬܐ ܓܡܝܪ̈ܬܐ، HC4): ܥܒܕܐ ܕܚܕ̈ܕܐ ܥܩܬܐ × ܡܥܕܪܢܘܬܐ ܪܫܝܡܐ ܝܠܗ، b = 0.28, t(234) = 3.44, p < .001، ܘܟܡܘܣܦ ΔR² = .046. ܥܩܬܐ ܟܡܚܒܠܐ ܠܫܝܢܐ ܒܨܝܪ ܟܡܐ ܕܡܥܕܪܢܘܬܐ ܪܡܬܐ ܝܬܝܪ ܝܠܗ̇: θ = −1.14 ܓܘ ܡܥܕܪܢܘܬܐ 3.21 (ܕܪܓܐ ܡܢ ܡܐܐ 16)، −0.80 ܓܘ 4.42 ܘ-−0.45 ܓܘ 5.68 (ܕܪܓܐ ܡܢ ܡܐܐ 84). ܬܚܘܡܐ ܕ-Johnson-Neyman – ܡܥܕܪܢܘܬܐ 6.18: ܠܥܠ ܡܢܗ، ܓܘ 7.1% ܡܢ ܡܫܬܘܬܦ̈ܢܐ، ܡܥܒܕܢܘܬܐ ܕܥܩܬܐ ܠܐ ܝܠܗ̇ ܬܘܒ ܪܫܝܡܬܐ.

ܡܘܕܝܠ 4. ܠܘܚܐ ܕܫܘܝ̈ܘܬܐ – a ܩܐ ܟܠ ܡܨܥܝܐ، b ܘ-c'، ܘܡܘܕܝܠ ܟܠܢܝܐ. ܒܬܪܗ – ܡܥܒܕܢܘܬܐ ܟܠܢܝܬܐ ܘܬܪܝܨܬܐ، ܡܥܒ̈ܕܢܘܝܬܐ ܠܐ ܬܪ̈ܝܨܬܐ ܥܡ ܬܚܘ̈ܡܐ ܕ-bootstrap، ܪܒܘܬܐ ܕܡܥܒܕܢܘܬܐ، Sobel (ܟܪܝܟܐ) ܘܨܘܪܬܐ ܕܫܒ̈ܝܠܐ. ܓܘ ܡܬܠܐ (ܚܘܫܒܐ ܡܬܢܝܐ ܘܫܢܬܐ ܒܓܢܒ ܚܕ̈ܕܐ، ܙܪܥܐ 42): ܡܥܒܕܢܘܬܐ ܠܐ ܬܪܝܨܬܐ ܒܐܘܪܚܐ ܕܚܘܫܒܐ ܡܬܢܝܐ −0.29, 95% CI [−0.43, −0.17]، ܒܐܘܪܚܐ ܕܫܢܬܐ −0.14 [−0.22, −0.06]، ܘܐܟܚܕܐ −0.42 – ܒܢܘܬ ܡܢ ܦܠܓܐ ܕܡܥܒܕܢܘܬܐ ܟܠܢܝܬܐ، c = −0.75؛ ܡܥܒܕܢܘܬܐ ܬܪܝܨܬܐ c' = −0.32 ܗܠ ܐܕܝܘܡ ܪܫܝܡܬܐ ܝܠܗ̇ – ܡܨܥܝܘܬܐ ܡܢܬܢܝܬܐ (partial mediation).

ܡܘܕܝ̈ܠܐ 7 ܘ-14. ܠܘܚܐ ܕܫܘܝ̈ܘܬܐ، ܡܥܒ̈ܕܢܘܝܬܐ ܠܐ ܬܪ̈ܝܨܬܐ ܬܠܝ̈ܬܐ ܓܘ ܬܠܬܐ ܛܝ̈ܡܐ ܕ-W، ܘܡܚܘܝܢܐ ܕܡܨܥܝܘܬܐ ܡܪܟܟܬܐ. ܓܘ ܡܬܠܐ (ܙܪܥܐ 42): ܓܘ ܡܘܕܝܠ 7 (ܚܘܫܒܐ ܡܬܢܝܐ ܐܝܟ ܡܨܥܝܐ) ܡܥܕܪܢܘܬܐ ܟܡܟܪܗܐ ܐܣܘܪܐ ܒܝܢܝ ܥܩܬܐ ܘܚܘܫܒܐ ܡܬܢܝܐ، ܘܡܚܘܝܢܐ 0.073 [0.028, 0.122] ܠܐ ܟܐܚܕ ܨܦܪܐ – ܡܥܒܕܢܘܬܐ ܠܐ ܬܪܝܨܬܐ ܟܡܟܪܗܐ ܡܢ −0.38 ܠ-−0.20. ܓܘ ܡܘܕܝܠ 14 (ܫܢܬܐ ܐܝܟ ܡܨܥܝܐ) ܡܚܘܝܢܐ 0.051 [−0.005, 0.119] ܟܐܚܕ ܨܦܪܐ – ܠܝܬ ܣܗܕܘܬܐ ܕܡܨܥܝܘܬܐ ܡܪܟܟܬܐ، ܐܦ ܐܢ ܠܐ ܬܪܝܨܬܐ ܬܠܝܬܐ ܓܘ ܡܥܕܪܢܘܬܐ ܪܡܬܐ ܠܐ ܝܠܗ̇ ܪܫܝܡܬܐ ܘܐܚܪ̈ܢܝܬܐ ܝܢܐ.

ܫܪ̈ܛܐ ܘܙܘܗܪ̈ܐ (Assumptions and warnings)

ܥܠܬܢܘܬܐ (causality). ܥܒܕܐ ܕܚܕ̈ܕܐ ܪܫܝܡܐ "ܠܐ ܟܡܙܕܩ" ܣܝܡܐ ܕܥܠܬܢܘܬܐ، ܘ"ܡܪܟܟܢܐ ܝܠܗ ܒܣ ܡܢܒܝܢܐ ܒܫܡܐ ܐܚܪܢܐ" – ܡܨܝܚ ܕܡܚܠܦܚ ܬܘ̈ܦܩܐ ܕ-X ܘ-W ܓܘ ܗܘ ܡܘܕܝܠ (Field, 2024, Box 11.1). ܡܨܥܝܘܬܐ ܝܠܗ̇ ܡܐܡܪܐ ܕܥܠܬܢܘܬܐ ܓܠܝܐܝܬ: X ܩܕܡ ܡܢ M، M ܩܕܡ ܡܢ Y، ܘܠܝܬ ܥܠܬܐ ܡܫܘܬܦܬܐ ܕܠܐ ܡܫܘܚܬܐ ܝܠܗ̇. ܫܪ̈ܛܐ ܩܐ ܫܘܠܡܐ ܕܥܠܬܢܘܬܐ – ܐܣܘܪܐ، ܩܕܡܘܬܐ ܓܘ ܙܒܢܐ ܘܡܣܠܝܢܘܬܐ ܕܦܘܫ̈ܩܐ ܡܬܟܬܫ̈ܢܐ (Cohen et al., 2003, pp. 454-455)؛ ܥܠ̈ܠܬܐ ܕܠܐ ܡܫܘ̈ܚܬܐ ܝܢܐ ܣܢܝܩ̈ܐ ܝܢܐ ܕܗܘܝܢ ܠܐ ܐܣܝܪ̈ܐ ܥܡ ܐܢܝ ܕܡܫܘ̈ܚܬܐ ܝܢܐ (ܦܐܬܐ 460). ܝܗܝ̈ܒܬܐ ܡܨܝܐ ܕܡܚܘܝܢ ܒܣ "ܫܠܡܘܬܐ" ܥܡ ܡܘܕܝܠ، ܠܐ ܕܡܚܘܝܢ ܚܘܝܬܐ ܕܝܠܗ (ܦܐܬܐ 79)، ܘܒܥܕܢܐ ܣܓܝ ܐܝܬ ܡܘܕܝ̈ܠܐ ܐܚܪ̈ܢܐ ܕܦܐܝ̈ܐ ܝܢܐ ܠܝܗܝ̈ܒܬܐ ܒܗܝ ܡܫܘܚܬܐ (ܦܐܬܐ 475). ܓܘ ܝܗܝ̈ܒܬܐ ܕܒܘܨܝܐ ܕܚܕ ܙܒܢܐ (cross-sectional) – ܐܝܟ ܓܘ ܡܬܠܐ – ܣܝܡܐ ܥܠ ܛܟܣܐ ܕܙܒܢ̈ܐ ܣܝܡܐ ܝܠܗ، ܠܐ ܡܫܟܚܢܘܬܐ (ܦܐܬܐ 477).

ܡܫܘܚܬܐ. ܛܥܝܘܬܐ ܕܡܫܘܚܬܐ ܓܘ ܡܨܥܝܐ ܟܡܨܠܝܐ ܡܥܒ̈ܕܢܘܝܬܐ (Cohen et al., 2003, p. 475)؛ ܘܫܪܝܪܘܬܐ (reliability) ܕ-product ܢܚܝܬܐ ܝܠܗ̇ ܡܢ ܫܪܝܪܘܬܐ ܕܟܠ ܡܫܬܚܠܦܢܐ – ܒܩܘܪܒܐ product ܕܫܪܝܪ̈ܘܬܐ، ܠܡܬܠܐ .8 × .8 = .64 (ܦܐܬܐ 297) – ܘܡܛܠ ܗܕܐ ܚܝܠܐ ܣܛܐܛܝܣܛܝܩܝܐ (statistical power) ܕܡܫܟܚܬܐ ܕܥܒܕܐ ܕܚܕ̈ܕܐ ܢܚܝܬܐ ܝܠܗ. ܥܒܕܐ ܕܚܕ̈ܕܐ ܕܪܒܘܬܐ ܡܨܥܝܬܐ ܣܢܝܩ ܝܠܗ ܠ-55 ܡܫܬܘܬܦ̈ܢܐ ܓܘ ܡܫܘܚܬܐ ܓܡܝܪܬܐ، ܘܠ-100-150 ܘܒܢܘܬ ܓܘ ܫܪܝܪܘܬܐ .88 (ܦܐܬܐ 297).

ܡܘܕܝܠ ܣܪܛܢܝܐ (linear). ܟܠ ܫܘܝܘܬܐ ܝܠܗ̇ ܪܝܓܪܫܢ ܣܪܛܢܝܐ (linear regression) ܪܓܝܠܐ، ܥܡ ܟܠ ܫܪ̈ܛܐ (assumptions) ܕܝܠܗ – ܣܪܛܢܝܘܬܐ، ܚܙ̈ܝܬܐ ܠܐ ܬܠܝ̈ܬܐ، ܫܪ̈ܟܐ (residuals) ܕܠܐ ܛܝ̈ܡܐ ܢܘܟܪ̈ܝܐ ܩܫ̈ܝܐ. ܛܥܝ̈ܘܬܐ ܬܩܝܢ̈ܬܐ ܚܣܝܢ̈ܬܐ ܟܫܪܝ ܒܣ ܫܘܝܘܬܐ ܕܫܘܚܠ̈ܦܐ. Y ܝܢ M ܕܬܪܝܢ ܛܝ̈ܡܐ ܣܢܝܩ̈ܐ ܝܢܐ ܠܪܝܓܪܫܢ ܠܘܓܝܣܛܝܩܝܐ (logistic regression) (PROCESS ܟܥܒܕ ܐܗܐ)، ܘܦܐܬܐ ܠܐ ܟܚܫܒ ܠܗ – ܟܡܙܗܪ. ܡܪܟܟܢܐ ܕܓܢ̈ܣܐ (categorical) ܥܡ ܒܢܘܬ ܡܢ ܬܪܬܝܢ ܓܘ̈ܕܐ ܣܢܝܩ ܝܠܗ ܠܪܡܙܢܘܬܐ dummy (dummy coding) (Cohen et al., 2003, Section 9.3)، ܘܦܐܬܐ ܟܚܫܒ ܠܗ ܐܝܟ ܡܬܡܫܚܢܐ.

ܡܘܕܝ ܠܐ ܟܚܫܒܐ ܐܗܐ ܦܐܬܐ. ܡܘܕܝ̈ܠܐ ܐܚܪ̈ܢܐ ܕ-PROCESS (ܡܨܥܝܘܬܐ ܕܣܕܪܐ (serial)، ܡܪܟܟܢܘܬܐ ܬܢܝܢܬܐ، ܡܪܟܟܢܘܬܐ ܕܡܥܒܕܢܘܬܐ ܬܪܝܨܬܐ)، ܥܒ̈ܕܐ ܕܚܕ̈ܕܐ ܕܬܠܬܐ ܐܘܪ̈ܚܬܐ (Cohen et al., 2003, Section 7.8)، ܥܒܕܐ ܕܚܕ̈ܕܐ ܥܡ ܗܕܡܐ ܕܡܪܒܥܐ (ܦܣܩܐ 7.9)، ܡܪܟܟܢܐ ܝܢ ܡܢܒܝܢܐ ܕܓܢ̈ܣܐ ܥܡ ܒܢܘܬ ܡܢ ܬܪܬܝܢ ܓܘ̈ܕܐ، ܘܬܚܘ̈ܡܐ ܕ-bootstrap ܕܙܢܐ BCa. ܩܐ ܡܨܥܝܘܬܐ ܓܘ ܡܘܕܝܠ ܕܫܒ̈ܝܠܐ ܡܪܟܒܐ ܝܬܝܪ (ܒܫܘܥܪܐ ML، ܥܡ ܡܚܘ̈ܝܢܐ ܕܦܐܝܘܬܐ) – ܦܐܬܐ "ܦܘܫܩܐ ܕܫܒ̈ܝܠܐ ܘܡܨܥܝܘܬܐ"؛ ܩܐ ܡܨܥܝܘܬܐ ܒܝܢܝ ܥܠ̈ܠܬܐ ܟܣ̈ܝܬܐ – "ܡܨܥܝܘܬܐ ܒܝܢܝ ܥܠ̈ܠܬܐ ܟܣ̈ܝܬܐ"؛ ܩܐ ܪܝܓܪܫܢ ܪܓܝܠܐ – "ܪܝܓܪܫܢ ܣܪܛܢܝܐ".

ܘܕܟܝ ܟܥܒܕܚ ܐܗܐ ܒ-SPSS؟ (And how do you do it in SPSS?)

ܐܘܪܚܐ ܦܫܝܩܬܐ – PROCESS، ܡܐܩܪܘ (macro) ܡܓܢ ܕ-Andrew Hayes ܕܟܡܘܣܦ ܠ-SPSS ܪܫܝܡܬܐ Analyze › Regression › PROCESS؛ ܐܘܬܒܬܐ ܡܦܫܩܬܐ ܝܠܗ̇ ܓܘ Field (2024، ܦܣܩܐ 4.13.1)، ܘܡܕܒܪܢܐ (guide) ܓܡܝܪܐ ܕܦܘܩ̈ܕܢܐ – ܓܘ ܬܘܣܦܬܐ A ܕ-Hayes (2022، ܦܐ̈ܬܐ 579-650). ܟܓܒܚ Y، X، W ܝܢ M ܘܡܢܝܢܐ ܕܡܘܕܝܠ؛ ܓܘ ܓܒܝ̈ܬܐ – HC4، ܡܫܢܝܢܘܬܐ ܠܡܨܥܝܬܐ ܕ"ܒܣ ܡܫܬܚܠܦ̈ܢܐ ܡܬܡܫܚ̈ܢܐ ܕܟܬܚܡܝ products"، Johnson-Neyman، ܘܛܝ̈ܡܐ ܕ-W (ܦܣ̈ܩܐ 11.3.6، 11.4.4). ܬܪܝܢ ܦܚ̈ܐ (SPSS Tip 11.1): PROCESS ܣܢܝܩ ܝܠܗ ܠܫܡ̈ܗܐ ܕܥܕܡܐ 8 ܐܬܘ̈ܬܐ، ܘܫܡ̈ܗܐ ܐܪ̈ܝܟܐ ܕܡ̈ܝܐ ܟܡܬܦܣܩܝ ܠܗܘ ܫܡܐ؛ ܘܡܫܬܚܠܦ̈ܢܐ ܕܡ̈ܠܐ (string) "ܟܡܫܓܫܝ" ܠܗ. ܣܝܢܬܐܟܣ (syntax) ܕܦܐܬܐ ܟܒܢܐ products ܒ-COMPUTE ܘܟܪܗܛܐ REGRESSION ܩܐ ܟܠ ܫܘܝܘܬܐ – ܐܗܐ ܪܗܛܐ ܐܦ ܓܘ PSPP، ܚܘܫܒܢܐ ܚܐܪܐ (free software)، ܘܟܝܗܒ ܡܢ̈ܝܢܐ ܡܫܘܬ̈ܦܐ ܕܦܐܬܐ (ܓܘ ܛܥܝ̈ܘܬܐ ܪ̈ܓܝܠܬܐ)؛ ܦܘܩܕܢܐ ܕ-PROCESS ܟܡܬܚܙܐ ܓܘ ܡܥܝܪܢܘܬܐ، ܥܡ ܓܒܝ̈ܬܐ ܕܓܘ ܬܘܣܦܬܐ A (model, center, hc, jn, boot, seed; Hayes, 2022, pp. 581-582)؛ ܠܐ ܪܗܛܠܢ ܠܗ – ܠܝܬ ܠܢ SPSS. ܐܘܪ̈ܚܬܐ ܓܘ ܪܫܝܡܬܐ (Menu) ܝܢܐ ܝܕܥܬܐ ܓܘܢܝܬܐ ܥܠ ܚܘܫܒܢܐ.

ܘܕܟܝ ܟܥܒܕܚ ܐܗܐ ܒ-R؟ (And how do you do it in R?)

ܠܝܬ ܣܢܝܩܘܬܐ ܠܚܒܝܫܘܬܐ (package) ܝܚܝܕܝܬܐ: lm ܩܐ ܟܠ ܫܘܝܘܬܐ، vcovHC ܡܢ ܚܒܝܫܘܬܐ sandwich ܩܐ ܛܥܝ̈ܘܬܐ HC3 ܘ-HC4، ܘ-loop ܦܫܝܛܐ ܩܐ bootstrap. ܡܨܠܝܢ̈ܘܬܐ ܦܫܝ̈ܛܬܐ ܘ-Johnson-Neyman – ܡܢ ܢܘ̈ܣܚܐ ܕܠܥܠ، ܥܡ ܡܐܛܪܝܟܣ ܕܫܘܚܠܦܐ ܕܡܢ̈ܝܢܐ ܡܫܘܬ̈ܦܐ. ܣܩܪܝܦܬ (script) ܕܦܐܬܐ ܟܡܚܬܐ ܟܥܒܕ ܟܠ ܐܗܐ ܩܐ ܝܗܝ̈ܒܬܐ ܕܝܘܟܘܢ ܘܩܐ ܡܘܕܝܠ ܕܓܒܝܬܘܢ، ܥܡ ܗܘ ܙܪܥܐ ܘܗܘ ܡܘܠܕܢܐ (generator) – ܗܢܘ ܕܐܡܪ ܚܬܝܬܐܝܬ ܗܢ ܬܚܘ̈ܡܐ ܕܬܘܟܠܢܐ. ܣܩܪܝܦܬ ܕܠܬܚܬ ܪܗܛܐ ܝܠܗ ܐܝܟ ܕܐܝܬܘܗܝ ܥܠ ܦܐܝܠ ܕܡܬܠܐ ܐܢܓܠܝܙܝܐ (R 4.3.3)، ܘܛܝ̈ܡܐ ܓܘ ܡܥܝܪ̈ܢܘܬܐ ܕܡ̈ܝܐ ܝܢܐ ܠܦܐܬܐ. ܢܡܘܣܐ ܕܣܐܝܛ ܩܐ ܣܘܪܝܬ ܓܘ R: ܦܐܝܠ UTF-8، ܟܠ ܣܕܪܐ ܕܡܥܝܪܢܘܬܐ ܟܫܪܐ ܒܡܠܬܐ ܕܣܘܪܝܬ، ܘܫܡ̈ܗܐ ܕܡܫܬܚܠܦ̈ܢܐ ܒܐܢܓܠܝܙܝܐ.

# ܡܪܟܟܢܘܬܐ ܘܡܨܥܝܘܬܐ – ܦܪܘܦܣܘܪ ܣܛܐܛ. ܐܗܐ ܦܐܝܠ ܢܛܝܪܐ ܝܠܗ ܒ-UTF-8؛ ܟܠ ܣܕܪܐ ܕܡܥܝܪܢܘܬܐ ܟܫܪܐ ܒܡܠܬܐ ܕܣܘܪܝܬ
library(readxl)     # ܩܪܝܢܐ ܕܐܩܣܠ
library(sandwich)   # ܛܥܝ̈ܘܬܐ ܬܩܝܢ̈ܬܐ ܚܣܝܢ̈ܬܐ (install.packages("sandwich"))

# ܛܥܢܐ: ܓܠܝܘܢܐ "Data" ܓܘ ܦܐܝܠ ܕܡܬܠܐ ܐܢܓܠܝܙܝܐ
d0 <- as.data.frame(read_excel("C:/Rdata/DATA_mod_example_eng.xlsx", sheet = "Data"))

# ===== ܡܘܕܝܠ 1: ܐܝܢܐ ܡܥܕܪܢܘܬܐ (W) ܟܡܪܟܟܐ ܐܣܘܪܐ ܒܝܢܝ ܥܩܬܐ (X) ܘܫܝܢܐ (Y)؟ =====
# ܫܩܠܬܐ ܕܣܕܪܐ ܟܠܗ ܓܘ ܡܫܬܚܠܦ̈ܢܐ ܕܡܘܕܝܠ ܒܠܚܘܕ، ܐܝܟ ܓܘ ܦܐܬܐ
d <- d0[complete.cases(d0[, c("stress", "support", "wellbeing")]), ]; nrow(d)
# ܦܐܪܐ: 238
# ܡܫܢܝܢܘܬܐ ܠܡܨܥܝܬܐ ܘ-product
d$x <- d$stress - mean(d$stress); d$w <- d$support - mean(d$support); d$xw <- d$x * d$w
f <- lm(wellbeing ~ x + w + xw, data = d)
V <- vcovHC(f, type = "HC4")                       # ܛܥܝ̈ܘܬܐ HC4، ܐܝܟ ܓܘ PROCESS ܥܡ hc=4
round(cbind(b = coef(f), SE = sqrt(diag(V)), t = coef(f) / sqrt(diag(V))), 3)
# ܦܐܪܐ: ܥܩܬܐ b = -0.794 (ܐܡܬܝ ܕܡܥܕܪܢܘܬܐ ܓܘ ܡܨܥܝܬܐ ܝܠܗ̇)، ܥܒܕܐ ܕܚܕ̈ܕܐ b = 0.280, SE = 0.081, t = 3.44
r <- lm(wellbeing ~ x + w, data = d); anova(r, f)   # ܬܘܣܦܬܐ ܕܥܒܕܐ ܕܚܕ̈ܕܐ (ܛܥܝ̈ܘܬܐ ܪ̈ܓܝܠܬܐ)
summary(f)$r.squared - summary(r)$r.squared
# ܦܐܪܐ: F(1, 234) = 15.29 ܘ-ΔR² = .046

# ܡܨܠܝܢ̈ܘܬܐ ܦܫܝ̈ܛܬܐ ܓܘ ܕܪ̈ܓܐ ܡܢ ܡܐܐ 16، 50، 84 ܕ-W
wv <- quantile(d$support, c(.16, .50, .84), type = 6) - mean(d$support)
th <- coef(f)["x"] + coef(f)["xw"] * wv
se <- sqrt(V["x", "x"] + 2 * wv * V["x", "xw"] + wv^2 * V["xw", "xw"])
round(cbind(W = wv + mean(d$support), effect = th, se = se, t = th / se), 3)
# ܦܐܪܐ: ܓܘ W = 3.214, 4.415, 5.675 ܡܥܒܕܢܘܬܐ ܕܥܩܬܐ -1.139, -0.803, -0.450 – ܥܩܬܐ ܟܡܚܒܠܐ ܒܨܝܪ ܐܡܬܝ ܕܐܝܬ ܡܥܕܪܢܘܬܐ ܝܬܝܪ

# ܬܚܘ̈ܡܐ ܕ-Johnson-Neyman: ܛܝ̈ܡܐ ܕ-W ܕܓܘܗܘܢ t ܕܡܥܒܕܢܘܬܐ ܫܘܐ ܝܠܗ ܚܬܝܬܐܝܬ ܠܛܝܡܐ ܚܪܝܦܐ
tc <- qt(.975, df.residual(f)); b <- coef(f)
a2 <- b["xw"]^2 - tc^2 * V["xw", "xw"]; a1 <- 2 * (b["x"] * b["xw"] - tc^2 * V["x", "xw"]); a0 <- b["x"]^2 - tc^2 * V["x", "x"]
sort(Re(polyroot(c(a0, a1, a2)))) + mean(d$support)
# ܦܐܪܐ: 6.181 ܘ-10.981؛ ܬܚܘܡܐ ܥܠܝܐ ܠܒܪ ܡܢ ܦܬܝܘܬܐ ܕܝܗܝ̈ܒܬܐ ܝܠܗ، ܘܡܛܠ ܗܕܐ ܒܣ 6.181 ܚܫܝܒܐ ܝܠܗ – ܠܥܠ ܡܢܗ ܡܥܒܕܢܘܬܐ ܠܐ ܝܠܗ̇ ܪܫܝܡܬܐ

# ===== ܡܘܕܝܠ 4: ܐܝܢܐ ܚܘܫܒܐ ܡܬܢܝܐ ܘܫܢܬܐ ܟܡܨܥܝ ܐܣܘܪܐ ܒܝܢܝ ܥܩܬܐ ܘܫܝܢܐ؟ =====
d <- d0[complete.cases(d0[, c("stress", "rumination", "sleep", "wellbeing")]), ]; nrow(d)
# ܦܐܪܐ: 238
X <- d$stress; Y <- d$wellbeing; M <- as.matrix(d[, c("rumination", "sleep")]); n <- nrow(d)
fitb <- function(Xm, y) as.numeric(solve(crossprod(Xm), crossprod(Xm, y)))
eff <- function(i) {                               # ܡܥܒ̈ܕܢܘܝܬܐ ܠܐ ܬܪ̈ܝܨܬܐ ܓܘ ܕܘܡܝܐ i
  a <- sapply(1:2, function(j) fitb(cbind(1, X[i]), M[i, j])[2])
  bb <- fitb(cbind(1, X[i], M[i, ]), Y[i])[3:4]
  c(rumination = a[1] * bb[1], sleep = a[2] * bb[2], total = sum(a * bb))
}
round(eff(1:n), 3)
# ܦܐܪܐ: -0.287, -0.136, -0.423
set.seed(42)                                       # ܗܘ ܙܪܥܐ ܓܘ ܦܐܬܐ – ܗܢ ܕܘܡ̈ܝܐ
bs <- t(sapply(1:5000, function(r) eff(sample.int(n, n, replace = TRUE))))
# ܬܚܘܡܐ ܕܕܪ̈ܓܐ ܡܢ ܡܐܐ ܐܝܟ ܓܘ PROCESS: ܛܝ̈ܡܐ 125 ܘ-4,876 ܡܢ 5,000 ܛܟܝܣ̈ܐ (Hayes, 2022، ܦܐܬܐ 100)
round(apply(bs, 2, function(v) sort(v)[c(125, 4876)]), 3)
# ܦܐܪܐ: [-0.432, -0.172], [-0.218, -0.062], [-0.570, -0.293] – ܬܪܘܝܗܝ ܡܨܥ̈ܝܐ ܪܫܝܡ̈ܐ ܝܢܐ

ܬܘܢܝܐ ܕܡܫܟܚ̈ܢܘܬܐ (reporting the results)

Hayes (2022، ܦܣܩܐ 14.2) ܟܡܪܚܩ: ܕܡܦܠܚܚ ܣܛܐܛܝܣܛܝܩܐ ܐܝܟ "ܪ̈ܘܫܡܐ ܕܦܣܩܐ" ܩܐ ܡܐܡܪ̈ܐ ܘܠܐ ܐܝܟ ܥܝܩܪܐ (ܦܐܬܐ 539)؛ ܕܡܘܕܥܚ ܐܦ ܡܥܒܕܢܘܬܐ ܬܪܝܨܬܐ ܘܐܦ ܠܐ ܬܪܝܨܬܐ، ܟܠ ܚܕܐ ܥܡ ܒܘܚܪܢܐ (ܦܐܬܐ 543)؛ ܕܐܡܪܚ "ܡܥܒܕܢܘܬܐ ܠܐ ܬܪܝܨܬܐ ܕ-X" ܘܠܐ "ܡܥܒܕܢܘܬܐ ܡܨܥܝܬܐ"؛ ܕܡܚܘܝܚ ܡܢܝܢܐ ܕܕܘܡ̈ܝܐ، ܙܢܐ ܕܬܚܘܡܐ ܘܙܪܥܐ (ܦܐ̈ܬܐ 543، 549)؛ ܘܓܘ ܡܪܟܟܢܘܬܐ ܘܡܨܥܝܘܬܐ ܡܪܟܟܬܐ – ܦܘܢܩܣܝܐ ܕܡܥܒܕܢܘܬܐ ܬܠܝܬܐ، ܛܝ̈ܡܐ ܕ-W، ܡܫܢܝܢܘܬܐ ܠܡܨܥܝܬܐ ܘܪܡܙܢܘܬܐ (coding) (ܦܐ̈ܬܐ 548-549). ܡܢ̈ܝܢܐ ܡܫܘܬ̈ܦܐ "ܡܬܩ̈ܢܐ" ܓܘ ܡܘܕܝܠ ܥܡ product – ܚܕ ܙܒܢܐ ܠܐ (ܦܐܬܐ 549). Field ܟܡܩܪܒ ܕܡܘܕܥܚ ܡܪܟܟܢܘܬܐ ܓܘ ܠܘܚܐ ܕܡܢ̈ܝܢܐ ܡܫܘܬ̈ܦܐ – b ܥܡ ܬܚܘܡܐ ܕܬܘܟܠܢܐ، SE، t ܘ-p – ܘܕܡܚܘܝܚ ܢܘܣܚܐ ܕ-PROCESS ܘ-Hayes (Field, 2024, Section 11.3.8, Table 11.1)؛ ܘܡܨܥܝܘܬܐ – ܠܟܡܝܘܬܐ ܡܥܒܕܢܘܬܐ ܠܐ ܬܪܝܨܬܐ ܥܡ ܬܚܘܡܐ ܕ-bootstrap ܘܪܒܘܬܐ ܕܡܥܒܕܢܘܬܐ (effect size)، ܘܛܒܐ ܝܠܗ ܐܦ ܨܘܪܬܐ ܥܡ ܡܢ̈ܝܢܐ ܡܫܘܬ̈ܦܐ (ܦܣܩܐ 11.4.6، ܨܘܪܬܐ 11.12). APA (2020، ܦܣܩܐ 6.43) ܟܒܥܐ "ܝܕܥܬܐ ܣܦܝܩܬܐ ܕܩܪܘܝܐ ܡܨܐ ܕܡܫܪܪ ܦܘܫ̈ܩܐ": ܓܘ ܡܪܟܟܢܘܬܐ – ܐܝܢܐ ܡܫܬܚܠܦ̈ܢܐ ܡܫܢܝ̈ܐ ܝܢܐ ܠܡܨܥܝܬܐ، ܓܘ ܐܝܢܝ ܛܝ̈ܡܐ ܕ-W ܡܨܠܝܢ̈ܘܬܐ ܒܚܝܪ̈ܐ ܝܢܐ، ܘܙܢܐ ܕܛܥܝ̈ܘܬܐ ܬܩܝܢ̈ܬܐ؛ ܓܘ ܡܨܥܝܘܬܐ – ܡܢܝܢܐ ܕܕܘܡ̈ܝܐ ܕ-bootstrap، ܙܢܐ ܕܬܚܘܡܐ (ܕܕܪ̈ܓܐ ܡܢ ܡܐܐ) ܘܙܪܥܐ. ܢܡܘ̈ܣܐ ܕܨܘܪܬܐ (ܦܣܩܐ 6.36): p ܕܠܐ ܨܦܪܐ ܩܕܡ ܢܘܩܙܐ؛ b، t ܘ-F – ܥܡܗ. ܦܣܩܐ ܕܡܫܟܚ̈ܢܘܬܐ ܓܘ ܡܦܩܢܐ ܒܢܝܬܐ ܝܠܗ̇ ܗܟܢܐ، ܒܣܘܪܝܬ ܘܒܐܢܓܠܝܙܝܐ.

ܛܥܝ̈ܘܬܐ ܕܡܬܚܙܝܢ ܣܓܝ (Common mistakes)

ܦܘܠܓܐ ܕܡܫܬܚܠܦܢܐ ܡܬܡܫܚܢܐ ܠܬܪܬܝܢ ܓܘ̈ܕܐ. ܦܘܠܓܐ ܓܘ ܛܝܡܐ ܡܨܥܝܐ (median) ܕܡܢܒܝܢܐ ܚܕ ܟܡܢܚܬ r² ܠ-.64 ܡܢ ܛܝܡܐ ܕܝܠܗ – "ܐܝܟ ܕܫܕܝܚ ܒܢܘܬ ܡܢ ܬܘܠܬܐ ܡܢ ܡܫܬܘܬܦ̈ܢܐ" – ܘܕܬܪܝܢ ܡܢܒ̈ܝܢܐ ܡܨܐ ܕܒܢܐ ܡܥܒ̈ܕܢܘܝܬܐ ܘܥܒܕܐ ܕܚܕ̈ܕܐ ܕܓܠܐ. "ܟܡܪܚܩܚ ܚܣܝܢܐܝܬ ܠܩܘܒܠ ܐܗܐ" (Cohen et al., 2003, p. 256).

product ܕܠܐ ܡܫܬܚܠܦ̈ܢܐ ܓܢܣܗܘܢ. ܕܠܐ X ܘ-W ܓܘ ܡܘܕܝܠ، ܡܢܝܢܐ ܡܫܘܬܦܐ ܕ-product ܠܐ ܝܠܗ ܥܒܕܐ ܕܚܕ̈ܕܐ (Cohen et al., 2003, p. 284; Field, 2024, Section 11.3.2).

ܕܦܫܩܚ b₁ ܐܝܟ "ܡܥܒܕܢܘܬܐ ܪܫܝܬܐ" ܕܠܐ ܡܫܢܝܢܘܬܐ ܠܡܨܥܝܬܐ. ܐܗܐ ܝܠܗ ܡܥܒܕܢܘܬܐ ܕ-X ܐܡܬܝ ܕ-W = 0 – ܒܠܟܝ ܛܝܡܐ ܕܠܐ ܐܝܬܘܗܝ (Cohen et al., 2003, pp. 260-261).

"ܡܢܝܢܐ ܡܫܘܬܦܐ ܡܬܩܢܐ" ܕ-product ܡܢ ܚܘܫܒܢܐ. ܗܘ ܝܠܗ ܡܢܝܢܐ ܬܩܝܢܐ ܕ-product، ܠܐ product ܕܡܢ̈ܝܢܐ ܬܩܝ̈ܢܐ – "ܣܢܝܩ ܝܠܗ ܕܠܐ ܚܫܒܚ ܠܗ" (Cohen et al., 2003, p. 283). ܦܘܫܪܐ ܡܬܩܢܐ ܬܪܝܨܐ – ܕܡܬܩܢܚ X ܘ-W، ܕܡܣܘܓܐܚ، ܘܕܪܗܛܚ (ܬܡܢ).

ܕܦܫܩܚ ܠܒܪ ܡܢ ܝܗܝ̈ܒܬܐ. ܡܨܠܝܢܘܬܐ ܦܫܝܛܬܐ ܝܢ ܬܚܘܡܐ ܕ-Johnson-Neyman ܓܘ ܛܝܡܐ ܕ-W ܕܠܝܬ ܓܘ ܝܗܝ̈ܒܬܐ – ܝܢ ܕܐܝܬ ܓܘܗ ܩܠܝܠ ܣܓܝ ܡܫܬܘܬܦ̈ܢܐ – ܝܠܗ ܫܘܠܡܐ ܠܒܪ ܡܢ ܝܗܝ̈ܒܬܐ (Cohen et al., 2003, p. 282).

ܕܒܥܝܚ ܡܨܥܝܘܬܐ ܓܘ "ܢܚܬܬܐ ܕܪܫܝܡܘܬܐ". ܦܘܚܡܐ ܒܝܢܝ p ܕ-c ܘ-p ܕ-c' ܒܕܘܟܬܐ ܕܒܘܚܪܢܐ ܕܡܥܒܕܢܘܬܐ ܠܐ ܬܪܝܨܬܐ ܓܢܣܗ̇ (Field, 2024, Section 11.4.2).

ܕܫܠܡܚ ܡܨܥܝܘܬܐ ܡܪܟܟܬܐ ܡܢ "ܪܫܝܡܐ ܗܪܟܐ ܘܠܐ ܪܫܝܡܐ ܬܡܢ". ܟܒܚܪܚ ܡܚܘܝܢܐ ܕܡܨܥܝܘܬܐ ܡܪܟܟܬܐ – ܚܙܝܡܘܢ ܡܬܠܐ ܕܡܘܕܝܠ 14.

ܕܡܚܘܝܚ ܡܨܥܝܘܬܐ ܓܘ ܝܗܝ̈ܒܬܐ ܕܚܕ ܙܒܢܐ ܐܝܟ ܡܫܟܚܢܘܬܐ ܕܥܠܬܢܘܬܐ. ܦܘܫܩܐ ܟܡܚܘܐ ܕܝܗܝ̈ܒܬܐ ܫܠܝܡ̈ܬܐ ܝܢܐ ܥܡ ܡܟܢܘܬܐ، ܠܐ ܕܐܝܬܝܗ̇ (Cohen et al., 2003, p. 79).

ܡܒܘ̈ܥܐ

American Psychological Association. (2020). Publication manual of the American Psychological Association (7th ed.). https://doi.org/10.1037/0000165-000

Bauer, D. J., & Curran, P. J. (2005). Probing interactions in fixed and multilevel regression: Inferential and graphical techniques. Multivariate Behavioral Research, 40(3), 373-400. https://doi.org/10.1207/s15327906mbr4003_5

Cohen, J., Cohen, P., West, S. G., & Aiken, L. S. (2003). Applied multiple regression/correlation analysis for the behavioral sciences (3rd ed.). Lawrence Erlbaum Associates.

Field, A. (2024). Discovering statistics using IBM SPSS statistics (6th ed.). Sage.

Hayes, A. F. (2022). Introduction to mediation, moderation, and conditional process analysis: A regression-based approach (3rd ed.). Guilford Press.

Preacher, K. J., & Hayes, A. F. (2008). Asymptotic and resampling strategies for assessing and comparing indirect effects in multiple mediator models. Behavior Research Methods, 40(3), 879-891. https://doi.org/10.3758/BRM.40.3.879

Baron ܘ-Kenny (1986) ܘ-MacKinnon (2008) – ܐܝܟ ܕܡܬܡܠܠܝ ܓܘ Field (2024)؛ Sobel (1982)، Hayes (2015) ܘ-Hayes ܘ-Cai (2007) – ܓܘ Hayes (2022)؛ Johnson ܘ-Neyman (1936)، Rogosa (1980) ܘ-Potthoff (1964) – ܓܘ Bauer ܘ-Curran (2005). ܠܦܘܬ ܢܡܘܣܐ ܕܣܐܝܛ (site rule)، ܓܘ ܪܫܝܡܬܐ ܕܡܒܘ̈ܥܐ (reference list) ܟܡܬܚܙܝ ܒܣ ܡܒܘ̈ܥܐ ܕܩܪܝ̈ܐ ܝܢܐ ܓܘ ܢܘܣܚܐ ܩܕܡܝܐ. Field ܡܝܬܝܐ ܝܠܗ ܠܦܘܬ ܦܣܩܐ، ܫܘܝܘܬܐ ܘܠܘܚܐ (ܟܬܒܐ ܐܠܩܛܪܘܢܝܐ ܠܐ ܟܢܛܪ ܡܢܝ̈ܢܐ ܕܦܐ̈ܬܐ ܛܒܝ̈ܥܐ)؛ ܐܚܪ̈ܢܐ – ܠܦܘܬ ܦܐܬܐ ܛܒܝܥܬܐ. ܩܪܝ̈ܐ ܝܢܐ ܨܚܚܐ 11 ܕ-Field؛ ܨܚ̈ܚܐ 7، 9.3 ܘ-12 ܕ-Cohen et al.؛ ܨܚ̈ܚܐ 1-5، 7-9، 11-12 ܘ-14 ܘܬܘܣܦܬܐ A ܕ-Hayes؛ ܘܬܪܝܢ ܡܐܡܪ̈ܐ ܓܡܝܪܐܝܬ. ܚܘܫܒܢܐ ܓܘ ܦܐܬܐ ܫܪܝܪܐ ܝܠܗ ܩܘܒܠ R 4.3.3 (lm، sandwich، ܘ-bootstrap ܥܡ ܗܘ ܡܘܠܕܢܐ)، ܩܘܒܠ ܠܘܚܐ 7.4.1 ܕ-Cohen et al. (ܡܨܠܝܢ̈ܘܬܐ ܦܫܝ̈ܛܬܐ، ܛܥܝ̈ܘܬܐ ܬܩܝܢ̈ܬܐ ܘܬܚܘ̈ܡܐ ܕܬܘܟܠܢܐ)، ܘܩܘܒܠ ܡܬܠܐ ܕܐܓܪ̈ܐ ܕܨܚܚܐ 12، ܡܢ ܝܗܝ̈ܒܬܐ ܓܘܠܡ̈ܝܬܐ ܕܓܘ ܠܘܚܐ 3.5.1.

ܛܥܝ̈ܘܬܐ ܕܡܫܟܚܠܢ ܓܘ ܡܒܘ̈ܥܐ. Field (2024): ܬܚܘܡܐ ܕܬܘܟܠܢܐ ܕܡܥܒܕܢܘܬܐ ܠܐ ܬܪܝܨܬܐ ܡܘܕܥܐ ܝܠܗ ܐܝܟ [0.02, 0.27] (ܦܣܩܐ 11.4.6 ܘܨܘܪܬܐ 11.12)، ܐܠܐ ܓܘ ܡܦܩܢܐ 11.9 ܬܚܘܡܐ ܬܚܬܝܐ ܝܠܗ .0023 – ܗܢܘ ܕܐܡܪ [0.00, 0.27]؛ ܘܬܚܘܡܐ ܬܚܬܝܐ ܕܡܚܘܝܢܐ ܕܡܨܥܝܘܬܐ ܛܒܝܥܐ ܝܠܗ 0.007 ܒܕܘܟܬܐ ܕ-0.001 (ܦܣܩܐ 11.4.5). Field ܟܩܪܐ ܠܬܚܘ̈ܡܐ "BCa"، ܐܠܐ ܬܚܘ̈ܡܐ ܕ-BCa "ܠܐ ܐܝܬܝܗܘܢ ܓܘ PROCESS ܘܚܕ ܙܒܢܐ ܠܐ ܗܘܘ" (Hayes, 2022, p. 104) – ܐܢܝ ܬܚܘ̈ܡܐ ܕܕܪ̈ܓܐ ܡܢ ܡܐܐ ܝܢܐ، ܓܘܒܝܐ ܡܩܕܡܐ، ܐܝܟ ܓܘ ܦܐܬܐ. Cohen et al. (2003): ܡܥܒܕܢܘܬܐ ܟܠܢܝܬܐ ܕܓܢܣܐ (gender) ܥܠ ܐܓܪܐ ܛܒܝܥܬܐ ܝܠܗ̇ $3,917 ܘܫܒܝܠܐ f = 1.72 (ܨܚܚܐ 12)، ܐܠܐ ܡܢ ܝܗܝ̈ܒܬܐ ܓܘܠܡ̈ܝܬܐ ܕܠܘܚܐ 3.5.1 ܟܢܦܩܝ $3,902 ܘ-1.79، ܘܡܥܒܕܢܘܬܐ ܠܐ ܬܪܝܨܬܐ ܒܐܘܪܚܐ ܕܥܬܝܩܘܬܐ ܓܘ ܥܒܕܐ ܝܠܗ̇ $2,408 ܘܠܐ $2,423؛ ܘܓܘ ܠܘܚܐ 7.4.1D ܠܡܨܠܝܢܘܬܐ ܠܐ ܪܫܝܡܬܐ t = −.40 ܕܒܝܩ̈ܐ ܝܢܐ ܬܪܬܝܢ ܟܘ̈ܟܒܐ. Bauer ܘ-Curran (2005، ܦܐܬܐ 380، ܡܥܝܪܢܘܬܐ 2): ܐܡܬܝ ܕܥܒܕܐ ܕܚܕ̈ܕܐ ܪܫܝܡܐ ܝܠܗ ܘܠܝܬ ܥܩܪ̈ܐ ܫܪ̈ܝܪܐ، ܡܨܠܝܢܘܬܐ ܪܫܝܡܬܐ ܝܠܗ̇ ܓܘ ܟܠ ܛܝܡܐ ܕ-W، ܘܠܐ "ܓܘ ܠܐ ܚܕ ܛܝܡܐ" ܐܝܟ ܕܟܬܝܒܐ ܝܠܗ ܬܡܢ. Hayes (2022): ܓܘ ܦܐܬܐ 457 ܡܥܒܕܢܘܬܐ ܠܐ ܬܪܝܨܬܐ ܛܒܝܥܬܐ ܝܠܗ̇ −0.218 ܘܓܘ ܡܦܩܢܐ −.1281؛ ܓܘ ܦܐܬܐ 281 F(1, 207) = 4.257 ܥܡ p = .016 – ܬܪܝܨܐ .040؛ ܘܣܝܢܬܐܟܣ ܕܬܘܣܦܬܐ ܟܡܚܘܐ hc=0 ܐܝܟ ܓܘܒܝܐ ܡܩܕܡܐ (ܦܐܬܐ 581)، ܠܩܘܒܠ ܦܐܬܐ 608. ܪܫܝܡܬܐ ܓܡܝܪܬܐ – ܓܘ ܡܘܕܥܢܘܬܐ ܕܫܘܪܪܐ.