ܪܝܓܪܫܢ ܣܪܛܢܝܐ ܦܫܝܛܐ ܘܣܓܝܐܐ

ܛܥܢܐ ܕܝܗܝ̈ܒܬܐ (loading the data)

ܟܡܕܒܩܚ ܥܡܘ̈ܕܐ ܬܪܝܨܐܝܬ ܡܢ ܓܠܝܘܢܐ (worksheet)، ܥܡ ܣܕܪܐ ܕܪ̈ܫܐ (header row) – ܟܪܫܡܚ ܓܘ ܐܩܣܠ، ܟܢܣܚܚ، ܘܟܡܕܒܩܚ ܠܐܟܐ:

ܓܘܒܝܐ ܕܡܫܬܚܠܦ̈ܢܐ (Variable selection)

ܐܝܡܢ ܡܦܠܚܝܚ (When to use)؟

ܐܝܡܢ ܕܟܒܥܝܚ ܠܡܢܒܝܐ ܚܕ ܡܫܬܚܠܦܢܐ ܟܡܝܝܐ (quantitative variable) – ܡܢܝܢܐ، ܥܘܡܪܐ، ܙܒܢܐ، ܡܦܩܬܐ ܕܟܣܦܐ – ܡܢ ܡܫܬܚܠܦܢܐ ܐܚܪܢܐ (ܪܝܓܪܫܢ ܦܫܝܛܐ) ܝܢ ܡܢ ܟܡܐ ܡܫܬܚܠܦ̈ܢܐ ܐܟܚܕܐ (ܪܝܓܪܫܢ ܣܓܝܐܐ)، ܘܠܡܝܕܥ ܟܡܐ ܡܢ ܫܘܚܠܦܐ (variance) ܕܝܠܗ ܐܢܝ ܟܡܦܫܩܝ ܘܐܝܢܐ ܡܢܝܗܝ ܟܡܘܬܪ. Gravetter ܘ-Wallnau (2017، ܦܐܬܐ 530) ܟܡܚܘܝ ܠܗ ܐܝܟ ܡܬܚܬܐ ܬܪܝܨܬܐ ܕܐܣܘܪܐ ܕܚܕ̈ܕܐ (correlation): ܐܣܘܪܐ ܕܚܕ̈ܕܐ ܟܐܡܪ ܕܐܝܬ ܐܣܘܪܐ ܣܪܛܢܝܐ (linear)، ܘܪܝܓܪܫܢ ܟܡܫܟܚ ܣܪܛܐ ܬܪܝܨܐ ܕܟܡܬܚܘܐ ܠܗ ܘܟܡܦܣܐ ܠܡܢܒܝܐ Y ܩܐ ܟܠ ܛܝܡܐ ܕ-X؛ ܥܡ ܬܪܝܢ ܡܢܒ̈ܝܢܐ ܘܝܬܝܪ (ܦܐܬܐ 544) "ܡܨܝܚ ܠܡܚܝܕܐ ܟܡܐ ܡܢܒ̈ܝܢܐ ܩܐ ܡܫܩܠܐ ܡܢܒܝܢܘܬܐ (prediction) ܚܬܝܬܬܐ ܝܬܝܪ". Pallant (2020، ܨܚܚܐ 13) ܟܡܢܝܐ ܫܘܐ̈ܠܐ ܕܪܝܓܪܫܢ ܣܓܝܐܐ ܟܡܦܢܐ ܥܠܝܗܝ: ܟܡܐ ܫܘܚܠܦܐ ܟܡܦܫܩ ܟܢܘܫܝܐ ܕܡܫܬܚܠܦ̈ܢܐ، ܐܝܢܐ ܡܢܝܗܝ ܝܠܗ ܡܢܒܝܢܐ ܛܒܐ ܝܬܝܪ، ܘܐܢ ܡܢܒܝܢܐ ܦܝܫܐ ܡܢܒܝܢܐ ܐܝܡܢ ܕܟܢܛܪܚ ܥܠ ܐܚܪܢܐ. Field (2024، ܦܣܩܐ 9.2) ܟܡܚܘܐ ܕܐܗܐ ܝܠܗ "ܡܘܕܝܠ ܣܪܛܢܝܐ" ܓܘܢܝܐ – ܗܘ ܡܘܕܝܠ ܕܐܝܬ ܒܬܪ ܒܘܚܪܢܐ t ܘܦܘܫܩܐ ܕܫܘܚܠܦܐ (analysis of variance)، ܒܣ ܥܡ ܡܢܒ̈ܝܢܐ ܟܡܝ̈ܐ.

ܦܐܬܐ ܟܚܫܒܐ ܪܝܓܪܫܢ ܬܩܝܢܐ – ܟܠ ܡܢܒ̈ܝܢܐ (predictors) ܟܥܐܠܝ ܒܚܕ ܙܒܢܐ (ܐܘܪܚܐ Enter؛ Pallant, 2020، ܨܚܚܐ 13 – "ܕܡܬܚܙܝܐ ܝܬܝܪ ܡܢ ܟܠܗܝܢ"). ܪܝܓܪܫܢ ܕܕܪ̈ܓܐ (hierarchical؛ ܓܘ̈ܫܡܐ ܠܦܘܬ ܬܐܘܪܝܐ، ܥܡ R² change)، ܕ-Field (ܦܣܩܐ 9.9.1) ܟܓܒܐ ܐܝܡܢ ܕܐܝܬ ܝܕܥܬܐ ܩܕܡܝܬܐ، ܠܐ ܐܝܬ ܓܘ ܦܐܬܐ؛ ܪܝܓܪܫܢ ܕܦܣ̈ܥܬܐ (stepwise) – Pallant "ܟܡܪܚܩܐ ܒܚܝܠܐ ܕܠܐ"، ܘ-Field: "ܣܛܐܛܝܣܛܝܩܝ̈ܐ ܟܡܩܡܛܝ ܦܬܐ ܕܝܗܝ". ܥܒܕܐ ܕܚܕ̈ܕܐ (interaction) ܒܝܢܝ ܡܢܒ̈ܝܢܐ (ܡܪܟܟܢܘܬܐ – moderation) ܘܡܨܥܝܘܬܐ (mediation) – ܦܐܬܐ ܡܪܟܟܢܘܬܐ ܘܡܨܥܝܘܬܐ؛ ܡܫܬܚܠܦܢܐ ܕܦܐܪܐ ܕܬܪܝܢ ܛܝ̈ܡܐ (ܐܝܢ/ܠܐ) – ܦܐܬܐ ܪܝܓܪܫܢ ܠܘܓܝܣܛܝܩܝܐ؛ ܐܣܘܪܐ ܒܝܢܝ ܬܪܝܢ ܡܫܬܚܠܦ̈ܢܐ ܕܠܐ ܦܢܝܬܐ ܕܡܢܒܝܢܘܬܐ – ܦܐܬܐ ܐܣܘܪ̈ܐ ܕܚܕ̈ܕܐ؛ ܡܢܒ̈ܝܢܐ ܕܓܢ̈ܣܐ (categorical) ܥܡ ܬܠܬܐ ܓܘ̈ܕܐ ܘܝܬܝܪ – ܦܘܫܩܐ ܕܫܘܚܠܦܐ، ܝܢ ܪܡܙܢܘܬܐ ܕܡܫܬܚܠܦ̈ܢܐ ܕܓܠܐ (dummy coding) ܕܠܐ ܐܝܬ ܓܘ ܦܐܬܐ. ܡܢܝܢܐ ܕܣܒܠܬܐ ܕܦܣܘ̈ܩܐ ܣܓܝ̈ܐܐ (multi-item scale؛ ܦܐܬܐ ܐܠܦܐ ܕ-Cronbach ܘܡܢܝܢܐ ܕܣܒܠܬܐ) ܡܬܦܠܚܐ ܝܠܗ ܐܝܟ ܡܫܬܚܠܦܢܐ ܕܪܘ̈ܚܩܐ ܫܘ̈ܝܐ (interval variable) ܠܦܘܬ ܥܝܕܐ ܕܣܐܝܛ (site convention؛ ܦܐܬܐ ܡܫܬܚܠܦ̈ܢܐ ܘܕܪ̈ܓܐ ܕܡܫܘܚܬܐ)؛ ܦܣܘܩܐ ܕ-Likert ܝܚܝܕܝܐ – ܠܐ.

ܚܘܫܒܐ: ܣܪܛܐ ܕܟܡܙܥܪ ܡܪ̈ܒܥܐ ܕܛܥܝ̈ܘܬܐ

ܫܘܝܘܬܐ ܕܪܝܓܪܫܢ Ŷ = bX + a (Gravetter & Wallnau, 2017, Equation 16.5) ܝܠܗ̇ ܣܪܛܐ ܬܪܝܨܐ ܕܟܥܒܪ "ܩܪܝܒ ܝܬܝܪ" ܠܟܠ ܢܘܩ̈ܙܐ: ܩܐ ܟܠ ܡܫܬܘܬܦܢܐ (participant) ܪܘܚܩܐ ܙܩܝܦܐ ܒܝܢܝ ܛܝܡܐ ܕܝܠܗ ܒܫܪܪܐ ܘܣܪܛܐ ܝܠܗ ܛܥܝܘܬܐ، Y − Ŷ، ܘܣܪܛܐ ܓܒܝܐ ܝܠܗ ܗܟܐ ܕܓܘܡܪܐ ܕܡܪ̈ܒܥܐ ܕܛܥܝ̈ܘܬܐ ܗܘܐ ܙܥܘܪܐ ܝܬܝܪ ܕܡܨܐ – "ܐܘܪܚܐ ܕܡܪ̈ܒܥܐ ܒܨܝܪ̈ܐ" (least squares؛ pp. 533-535; Field, 2024, Section 9.2.4). ܡܨܠܝܢܘܬܐ (slope) b – ܟܡܐ Y ܟܡܫܬܚܠܦ ܩܐ ܟܠ ܣܠܩܬܐ ܕܚܕ ܚܕܝܘܬܐ ܓܘ X (b = SP/SS_X, Equation 16.2)؛ ܡܢܝܢܐ ܩܝܡܐ (constant) a – ܛܝܡܐ ܡܢܒܝܐ ܐܝܡܢ ܕ-X = 0. ܓܘ ܡܬܠܐ 16.1 ܕ-Gravetter ܘ-Wallnau (ܦܐܬܐ 535؛ ܬܡܢܝܐ ܙܘ̈ܓܐ) ܟܦܠܛ Ŷ = 2X − 1. ܥܡ ܟܡܐ ܡܢܒ̈ܝܢܐ (ܦܐܬܐ 545-546): Ŷ = b₁X₁ + b₂X₂ + a، ܘܟܠ b ܟܡܬܚܘܐ ܝܗܒܬܐ ܕܡܢܒܝܢܐ ܐܝܡܢ ܕܐܚܪ̈ܢܐ ܩܝ̈ܡܐ ܝܢܐ.

ܟܡܐ ܛܒܐ ܝܠܗ ܣܪܛܐ؟ Field (ܦܣܩܐ 9.2.4) ܟܡܦܚܡ ܥܡ ܡܘܕܝܠ "ܣܦܪ": ܠܡܢܒܝܐ ܩܐ ܟܠܢܫ ܡܨܥܝܬܐ (mean). ܒܕܪܐ ܚܕܪ ܡܨܥܝܬܐ (SS_T) ܟܡܬܦܪܩ ܠܡܐ ܕܣܪܛܐ ܟܡܦܫܩ (SS_M، "ܪܝܓܪܫܢ") ܘܠܡܐ ܕܦܝܫܐ (SS_R، "ܫܪܟܐ") – ܘ-R² = SS_M/SS_T ܝܠܗ ܡܢܬܐ ܕܫܘܚܠܦܐ ܡܦܫܩܐ (explained variance؛ Equation 9.17; Gravetter & Wallnau, pp. 540-541: r²SS_Y). ܟܦܠܓܚ ܟܠ ܓܘܡܪܐ ܕܡܪ̈ܒܥܐ ܥܠ ܕܪ̈ܓܐ ܕܚܐܪܘܬܐ (degrees of freedom) ܕܝܠܗ (k ܩܐ ܡܘܕܝܠ، N − k − 1 ܩܐ ܫܪܟܐ) ܘܟܫܩܠܚ F، ܕܟܒܚܪ ܐܢ ܡܘܕܝܠ ܛܒܐ ܝܠܗ ܡܢ ܡܨܥܝܬܐ (Field، ܫܘܝ̈ܘܬܐ 9.19-9.20؛ Gravetter & Wallnau، "ܦܘܫܩܐ ܕܪܝܓܪܫܢ"، ܦܐܬܐ 541-543). ܓܘ ܡܢܒܝܢܐ ܝܚܝܕܝܐ ܐܗܐ ܚܬܝܬܐܝܬ ܝܠܗ ܒܘܚܪܢܐ ܕܪܫܝܡܘܬܐ ܕܐܣܘܪܐ ܕܚܕ̈ܕܐ ܕ-Pearson: F = t² (ܦܐܬܐ 543). ܡܬܠ̈ܐ ܕ-Gravetter ܘ-Wallnau ܚܫܝ̈ܒܐ ܝܢܐ ܓܘ ܦܐܬܐ ܘܟܝܗܒܝ ܡܢܝ̈ܢܐ ܕܓܘ ܟܬܒܐ: ܡܬܠܐ 16.5 (ܦܐܬܐ 542-543) – SS_ܪܝܓܪܫܢ = 112.01, SS_ܫܪܟܐ = 43.99, F(1, 6) = 15.28؛ ܡܬܠܐ 16.6 (ܦܐܬܐ 546-551، ܡܦܩܢܐ SPSS ܓܘ ܨܘܪܬܐ 16.8) – R² = .557, F(2, 7) = 4.392, p = .058، b ܕ-2.552، .672 ܘ-.293.

ܩܪܝܢܐ ܕܡܦܩܢܐ (How to read the output)

Pallant (2020، ܨܚܚܐ 13) ܟܡܩܪܒܐ ܐܪܒܥܐ ܦܣ̈ܥܬܐ – ܒܘܚܪܢܐ ܕܫܪ̈ܛܐ (assumptions)، ܫܘܥܪܐ ܕܡܘܕܝܠ، ܫܘܥܪܐ ܕܟܠ ܡܢܒܝܢܐ، ܘܡܦܠܚܢܘܬܐ ܒܦܐܪ̈ܐ – ܘܠܘ̈ܚܐ ܕܦܐܬܐ ܛܟܝܣ̈ܐ ܝܢܐ ܠܦܘܬܗܘܢ (ܫܪ̈ܛܐ: ܦܣܩܐ "ܫܪ̈ܛܐ، ܒܘܚܪܢܐ ܘܙܘܗܪ̈ܐ" ܘܠܘܚܐ 4).

ܠܘܚܐ 1 – ܟܢܘܫܝܐ ܕܡܘܕܝܠ (Model Summary). R² – "ܟܡܐ ܡܢ ܫܘܚܠܦܐ ܓܘ ܡܫܬܚܠܦܢܐ ܬܠܝܐ ܡܦܫܩܐ ܝܠܗ ܒܝܕ ܡܘܕܝܠ"؛ ܓܘ ܡܬܠܐ ܕ-Pallant .468، "ܦܐܪܐ ܝܩܝܪܐ ܒܣܓܝ". R² ܡܬܘܪܨܐ (adjusted) – ܓܘ ܕܘܡܝܐ (sample) ܙܥܘܪܐ R² "ܡܣܒܪܐ ܒܣܓܝ"، ܘܡܬܘܪܨܐ ܟܬܪܨ ܠܫܘܥܪܐ ܓܘ ܟܢܫܐ ܟܠܢܝܐ (population؛ Pallant؛ Field, 2024، ܦܣܩܐ 9.2.4 – "shrinkage")؛ Field ܟܡܘܣܦ ܕܟܬܪܨ ܠܡܢܝܢܐ ܕܡܢܒ̈ܝܢܐ، ܡܛܠ ܕܟܠ ܡܢܒܝܢܐ ܝܬܝܪܐ ܟܡܪܝܡ R² ܐܦ ܐܝܡܢ ܕܝܗܒܬܐ ܕܝܠܗ ܣܦܪ ܝܠܗ̇. R – ܐܣܘܪܐ ܕܚܕ̈ܕܐ ܒܝܢܝ ܛܝ̈ܡܐ ܡܢܒ̈ܝܐ ܘܚܙ̈ܝܐ (ܓܘ ܡܢܒܝܢܐ ܝܚܝܕܝܐ: Pearson ܒܝܢܝ ܡܢܒܝܢܐ ܘܡܫܬܚܠܦܢܐ ܕܦܐܪܐ؛ Field، ܦܣܩܐ 9.8.1). ܛܥܝܘܬܐ ܬܩܝܢܬܐ ܕܫܘܥܪܐ (standard error of the estimate) – "ܪܘܚܩܐ ܬܩܝܢܐ" ܒܝܢܝ ܢܘܩ̈ܙܐ ܘܣܪܛܐ، ܒܚܕܝ̈ܘܬܐ ܕܡܫܬܚܠܦܢܐ ܕܦܐܪܐ (Gravetter & Wallnau, 2017, pp. 538-539, 548-549): ܙܥܘܪܬܐ – ܡܢܒܝܢܘܬܐ ܚܬܝܬܬܐ. Durbin-Watson – ܦܣܩܐ ܕܫܪ̈ܛܐ.

ܠܘܚܐ 2 – ANOVA. ܟܒܚܪ "H₀: R ܣܓܝܐܐ ܓܘ ܟܢܫܐ ܟܠܢܝܐ ܫܘܝܐ ܝܠܗ ܠܣܦܪ" (Pallant): p ܙܥܘܪܐ ܡܢ .05 – ܡܘܕܝܠ ܟܡܢܒܐ ܛܒ ܝܬܝܪ ܡܢ ܡܨܥܝܬܐ ܒܠܚܘܕ. Field (ܦܣܩܐ 9.8.1): "ܡܘܕܝܠ ܣܪܛܢܝܐ ܒܟܠܗ ܟܡܢܒܐ ܪܫܝܡܐܝܬ". F ܪܫܝܡܐ ܣܛܐܛܝܣܛܝܩܐܝܬ (statistically significant) ܠܐ ܟܐܡܪ ܥܕܟܝܠ ܐܝܢܐ ܡܢ ܡܢܒ̈ܝܢܐ ܟܡܘܬܪ.

ܠܘܚܐ 3 – ܡܢܝ̈ܢܐ ܡܫܘܬܦ̈ܐ (Coefficients). Pallant: ܟܒܨܚ ܥܡܘܕܐ Sig. – ܡܢܒܝܢܐ ܥܡ p ܙܥܘܪܐ ܡܢ .05 "ܟܝܗܒ ܝܗܒܬܐ ܝܚܝܕܝܬܐ ܪܫܝܡܬܐ"؛ ܡܢܒܝܢܐ ܠܐ ܪܫܝܡܐ ܡܨܐ ܕܗܘܐ ܗܟܐ "ܡܛܠ ܚܠܛܘܬܐ ܥܡ ܡܢܒ̈ܝܢܐ ܐܚܪ̈ܢܐ ܓܘ ܡܘܕܝܠ". B – "ܟܡܐ ܡܫܬܚܠܦܢܐ ܕܦܐܪܐ ܟܡܫܬܚܠܦ ܩܐ ܟܠ ܣܠܩܬܐ ܕܚܕ ܚܕܝܘܬܐ ܓܘ ܡܢܒܝܢܐ، ܐܝܡܢ ܕܐܚܪ̈ܢܐ ܩܝ̈ܡܐ ܝܢܐ" (Field، ܦܣܩܐ 9.11.3 – ܓܘ ܡܬܠܐ ܕܡܙܒܢܢܘܬܐ ܕ-albums: ܟܠ 1,000 ܠܝܪ̈ܐ ܐܢܓܠܝܙ̈ܝܐ ܕܡܘܕܥܢܘܬܐ = 85 albums)؛ ܡܢܝܢܐ ܩܝܡܐ (constant) ܟܡܓܡܪ ܫܘܝܘܬܐ ܕܡܢܒܝܢܘܬܐ. β – ܡܢܝܢܐ ܡܫܘܬܦܐ ܡܬܩܢܐ (standardized)، "ܡܢܝܢܐ ܕܣܛܝ̈ܘܬܐ ܬܩܝ̈ܢܬܐ ܕܡܫܬܚܠܦܢܐ ܕܦܐܪܐ ܟܡܫܬܚܠܦ ܩܐ ܟܠ ܣܛܝܘܬܐ ܬܩܝܢܬܐ ܕܡܢܒܝܢܐ"؛ ܡܛܠ ܕܠܐ ܝܠܗ ܬܠܝܐ ܒܚܕܝ̈ܘܬܐ، ܟܡܦܚܡ ܐܝܩܪܐ ܕܡܢܒ̈ܝܢܐ (Gravetter & Wallnau، ܦܐܬܐ 550 – "b ܪܒܐ ܝܬܝܪ ܠܐ ܟܐܡܪ ܡܢܒܝܢܐ ܛܒܐ ܝܬܝܪ"؛ Pallant؛ Field). t ܘ-p – ܟܒܚܪܝ H₀: b = 0 ("ܣܪܛܐ ܦܫܝܛܐ"؛ Field، ܦܣܩܐ 9.2.5)؛ ܬܚܘܡܐ ܕܬܘܟܠܢܐ (confidence interval) ܩܐ B ܕܐܝܬ ܓܘܗ ܣܦܪ ܟܐܡܪ ܕܛܝܡܐ ܓܘ ܟܢܫܐ ܟܠܢܝܐ "ܡܨܐ ܕܗܘܐ ܥܠ ܡܢ ܣܦܪ ܐܠܐ ܐܦ ܬܚܬ ܣܦܪ" (ܦܣܩܐ 9.11.3). ܬܠܬܐ ܐܣܘܪ̈ܐ ܕܚܕ̈ܕܐ (Zero-order, Partial, Part ܓܘ SPSS): ܕܛܟܣܐ ܣܦܪ (zero-order) – Pearson ܦܫܝܛܐ؛ ܡܢܬܢܝܐ (partial) – ܒܫܩܠܬܐ ܕܡܢܒ̈ܝܢܐ ܐܚܪ̈ܢܐ ܡܢ ܬܪܝܢ ܡܫܬܚܠܦ̈ܢܐ؛ ܦܠܓܐ-ܡܢܬܢܝܐ (semi-partial، sr، "Part") – Pallant ܟܡܚܫܟܐ ܠܗ: ܡܪܒܥܐ ܝܠܗ "ܟܡܐ ܡܢ ܫܘܚܠܦܐ ܟܠܢܝܐ ܡܦܫܩܐ ܝܠܗ ܝܚܝܕܐܝܬ ܒܝܕ ܡܢܒܝܢܐ، ܘܟܡܐ R² ܒܕ ܢܚܬ ܗܘܐ ܕܠܐ ܐܝܠܗ" (ܓܘ ܡܬܠܐ ܕܝܠܗ̇ −.40² = 16% ܘ-−.30² = 9%، ܕܐܟܚܕܐ 25% ܘܠܐ 46.8% – ܦܝܫܬܐ ܫܘܚܠܦܐ ܡܫܘܬܦܐ ܝܠܗ̇). Gravetter ܘ-Wallnau (ܦܐܬܐ 550-551) ܟܡܛܝ ܠܗܝ ܝܗܒܬܐ ܝܚܝܕܝܬܐ ܒܝܕ "R² ܥܡ ܬܪܝܢ ܡܢܒ̈ܝܢܐ ܒܨܝܪ r² ܥܡ ܩܕܡܝܐ ܒܠܚܘܕ"، ܘܟܡܚܘܝ ܕ-t ܕܡܢܒܝܢܐ ܝܠܗ ܫܪܫܐ ܕ-F ܕܬܘܣܦܬܐ. VIF – ܦܣܩܐ ܕܫܪ̈ܛܐ.

ܠܘܚܐ 4 – ܒܘܚܪܢܐ ܕܫܪ̈ܟܐ (residuals) ܘܕܚܙ̈ܝܬܐ ܡܥܒܕܢ̈ܝܬܐ (influential cases) ܘܨܘܪܬܐ ܕܫܪ̈ܟܐ – ܦܣܩܐ "ܫܪ̈ܛܐ، ܒܘܚܪܢܐ ܘܙܘܗܪ̈ܐ". ܩܘܛܝܐ ܕ"ܩܪܝܢܐ ܕܦܐܪܐ" ܟܡܟܢܫ: ܪܒܘܬܐ ܕܡܥܒܕܢܘܬܐ (effect size)، ܪܒܘܬܐ ܕܕܘܡܝܐ ܩܘܒܠ ܢܡܘ̈ܣܐ ܕܨܒܥܐ، ܝܗ̈ܒܬܐ ܝܚܝܕ̈ܝܬܐ، multicollinearity ܘܒܘܚܪܢܐ.

ܪܒܘܬܐ ܕܡܥܒܕܢܘܬܐ (effect size)

R² ܝܠܗ ܪܒܘܬܐ ܕܡܥܒܕܢܘܬܐ (effect size) ܕܡܘܕܝܠ ܟܠܗ – ܡܢܬܐ ܕܫܘܚܠܦܐ ܡܦܫܩܐ، ܕ-Field (2024، ܦܣܩܐ 9.2.4) ܟܩܪܐ ܠܗ "ܡܚܘܝܢܐ ܕܪܒܘܬܐ ܫܪܫܢܝܬܐ ܕܦܐܝܘܬܐ". ܡܫܘܚܬܐ: Cohen (1988، ܦܐܬܐ 413-414) ܟܡܚܕܕ ܩܐ ܪܝܓܪܫܢ ܣܓܝܐܐ f² = .02, .15, .35 ܩܐ ܡܥܒܕܢܘܬܐ ܙܥܘܪܬܐ، ܡܨܥܝܬܐ ܘܪܒܬܐ، ܘܟܡܦܩ ܠܗܘܢ ܠ-R² ܕ-.02، .13 ܘ-.26 (R ܕ-.14، .36 ܘ-.51) – ܬܚܘ̈ܡܐ "ܪ̈ܡܐ ܩܠܝܠ" ܡܢ ܕܐܣܘܪܐ ܕܚܕ̈ܕܐ (correlation) ܝܚܝܕܝܐ، ܡܛܠ ܕܓܘ ܡܘܕܝܠ ܣܓܝ ܓܗ̈ܝ ܐܝܬ ܟܡܐ ܡܢܒ̈ܝܢܐ؛ Field (ܦܣܩܐ 9.5) ܟܡܦܠܚ ܒܗܢܝ ܬܠܬܐ ܛܝ̈ܡܐ ܩܐ ܚܘܫܒ̈ܢܐ ܕܪܒܘܬܐ ܕܕܘܡܝܐ. Cohen ܟܡܥܗܕ ܕܬܚܘ̈ܡܐ ܫܠܡܘܬܐ (compromise) ܝܢܐ: "ܙܥܘܪܐ" ܓܘ ܝܕܥܬܐ ܕܢܦܫܐ ܕܐܣܝܘܬܐ (clinical psychology) ܡܨܐ ܕܗܘܐ "ܪܒܐ" ܓܘ ܝܕܥܬܐ ܕܟܢܫܐ (sociology). ܩܐ ܟܠ ܡܢܒܝܢܐ ܒܦܪܝܫܘܬܐ ܪܒܘܬܐ ܕܡܥܒܕܢܘܬܐ ܝܠܗ̇ β (ܚܕܝ̈ܘܬܐ ܕܣܛܝܘܬܐ ܬܩܝܢܬܐ) ܘ-sr² (ܫܘܚܠܦܐ ܝܚܝܕܝܐ؛ Pallant, 2020، ܨܚܚܐ 13)، ܘ-B ܥܡ ܬܚܘܡܐ ܕܬܘܟܠܢܐ ܕܝܠܗ ܝܠܗ ܪܒܘܬܐ ܕܡܥܒܕܢܘܬܐ ܒܚܕܝ̈ܘܬܐ ܫܪܫܢ̈ܝܬܐ – Field (ܦܣܩܐ 9.14) ܟܒܥܐ ܠܡܘܕܥܐ ܠܗ ܩܕܡ ܟܠ. ܓܘ ܕܘܡܝܐ ܪܒܐ R² ܙܥܘܪܐ ܒܣܓܝ ܟܦܠܛ ܪܫܝܡܐ؛ ܟܡܘܕܥܚ R² ܐܦ ܐܝܡܢ ܕܡܘܕܝܠ ܠܐ ܝܠܗ ܪܫܝܡܐ.

ܫܪ̈ܛܐ، ܒܘܚܪܢܐ ܘܙܘܗܪ̈ܐ

ܙܢ̈ܐ ܕܡܫܬܚܠܦ̈ܢܐ. Field (2024، ܦܣܩܐ 9.4.1): ܡܢܒ̈ܝܢܐ (predictors) ܟܡܝ̈ܐ ܝܢ ܕܓܢ̈ܣܐ ܕܬܪܝܢ ܛܝ̈ܡܐ ܝܢܐ، ܘܡܫܬܚܠܦܢܐ ܕܦܐܪܐ "ܟܡܝܝܐ، ܡܬܡܫܚܢܐ ܘܠܐ ܟܪܝܐ". ܡܫܬܚܠܦܢܐ ܕܬܪܝܢ ܛܝ̈ܡܐ (binary؛ ܡܬܠܐ ܓܢܣܐ 1/2، ܓܘܕܐ 0/1) ܟܥܐܠ ܐܝܟ ܡܢܒܝܢܐ ܘ-B ܕܝܠܗ ܝܠܗ ܦܘܪܫܢܐ ܡܢܒܝܐ ܕܡܨܥܝ̈ܬܐ ܒܝܢܝ ܓܘ̈ܕܐ؛ ܡܫܬܚܠܦܢܐ ܕܓܢ̈ܣܐ (categorical variable) ܥܡ ܬܠܬܐ ܕܪ̈ܓܐ ܘܝܬܝܪ ܠܐ ܝܠܗ ܡܢܝܢܐ – ܣܢܝܩܘܬܐ ܐܝܬ ܠܪܡܙܢܘܬܐ ܕܡܫܬܚܠܦ̈ܢܐ ܕܓܠܐ (dummy coding؛ k − 1 ܡܫܬܚܠܦ̈ܢܐ 0/1)، ܘܦܐܬܐ ܟܡܙܗܪܐ. ܡܫܬܚܠܦܢܐ ܕܛܟܣܐ (ordinal variable؛ ܝܘܠܦܢܐ 1-4) ܒܫܪܪܐ ܟܥܐܠ ܐܝܟ ܡܢܝܢܐ، ܒܣܒܪܐ ܕܟܠ ܦܣܥܬܐ ܫܘܝܬܐ ܝܠܗ̇ – ܥܝܕܐ ܝܠܗ، ܐܠܐ ܣܢܝܩ ܝܠܗ ܠܙܘܗܪܐ ܓܘ ܦܘܫܩܐ.

ܪܒܘܬܐ ܕܕܘܡܝܐ. Pallant (2020، ܨܚܚܐ 13) ܟܡܝܬܝܐ ܬܪܝܢ ܢܡܘ̈ܣܐ: Stevens – "ܩܪܝܒ 15 ܡܫܬܘܬܦ̈ܢܐ (participants) ܩܐ ܟܠ ܡܢܒܝܢܐ"، ܘ-Tabachnick ܘ-Fidell – N > 50 + 8m (m – ܡܢܝܢܐ ܕܡܢܒ̈ܝܢܐ؛ ܚܡܫܐ ܡܢܒ̈ܝܢܐ – ܠܦܚܘܬ 90 ܡܫܬܘܬܦ̈ܢܐ)، ܘܝܬܝܪ ܐܝܡܢ ܕܡܫܬܚܠܦܢܐ ܕܦܐܪܐ ܥܩܝܡܐ ܝܠܗ. Field (ܦܣܩܐ 9.5) ܟܐܡܪ ܕܢܡܘ̈ܣܐ ܕ"10 ܝܢ 15 ܩܐ ܟܠ ܡܢܒܝܢܐ" ܟܦܫܛܝ "ܗܠ ܕܠܐ ܡܘܬܪܢܘܬܐ": ܡܐ ܕܣܢܝܩ ܝܠܗ ܬܠܝܐ ܝܠܗ ܒܪܒܘܬܐ ܕܡܥܒܕܢܘܬܐ (effect size) – ܩܐ ܡܥܒܕܢܘܬܐ ܪܒܬܐ 77 ܡܫܬܘܬܦ̈ܢܐ ܣܦܩܝ ܐܦ ܩܐ 20 ܡܢܒ̈ܝܢܐ، ܩܐ ܡܥܒܕܢܘܬܐ ܡܨܥܝܬܐ 160 (ܘܥܡ ܗܠ ܫܬܐ ܡܢܒ̈ܝܢܐ ܩܪܝܒ 100)، ܘܩܐ ܡܥܒܕܢܘܬܐ ܙܥܘܪܬܐ "ܠܐ ܡܠܐܝܬܘܢ ܕܠܐ ܡܐܐ̈ ܡܫܬܘܬܦ̈ܢܐ"؛ ܘ-R ܡܣܟܝܐ ܩܐ ܝܗܝ̈ܒܬܐ ܓܕܫܢ̈ܝܬܐ ܝܠܗ k/(N − 1) – ܫܬܐ ܡܢܒ̈ܝܢܐ ܥܠ 21 ܡܫܬܘܬܦ̈ܢܐ ܟܝܗܒܝ R = 0.3 ܡܢ ܠܐ ܡܕܡ. ܩܘܛܝܐ ܕܩܪܝܢܐ ܟܒܚܪ ܬܪܝܢ ܢܡܘ̈ܣܐ ܕ-Pallant ܘܟܛܒܥ R ܓܕܫܢܝܐ ܡܣܟܝܐ.

multicollinearity. ܡܢܒ̈ܝܢܐ ܕܐܣܝܪ̈ܐ ܝܢܐ ܚܕ ܥܡ ܐܚܪܢܐ ܒܣܓܝ (Pallant: r ܕ-.7 ܘܠܥܠ؛ Field، ܦܣܩܐ 9.9.3: .8-.9) "ܟܥܣܩܝ ܠܪܝܓܪܫܢ ܠܡܦܪܫܐ ܝܗܒܬܐ ܝܚܝܕܝܬܐ ܕܟܠ ܚܕ"، ܟܡܢܦܚܝ ܛܥܝ̈ܘܬܐ ܬܩܝ̈ܢܬܐ (standard errors)، ܘܡܨܝ ܕܥܒܕܝ ܡܢܒ̈ܝܢܐ ܐܝܩܪ̈ܢܐ ܠܐ ܪ̈ܫܝܡܐ. ܠܘܚܐ ܟܛܒܥ VIF ܩܐ ܟܠ ܡܢܒܝܢܐ (tolerance = 1/VIF): Pallant ܘ-Field – VIF ܒܢܘܬ ܡܢ 10 ܝܢ tolerance ܬܚܬ .10 ܝܢܐ "ܥܩܬܐ ܪܒܬܐ" (Bowerman & O'Connell, 1990; Myers, 1990)؛ Field ܟܡܘܣܦ: tolerance ܬܚܬ .2 – "ܥܩܬܐ ܕܡܨܝܐ ܕܗܘܝܐ" (Menard, 1995)، ܘܡܨܥܝܬܐ ܕ-VIF ܪܒܬܐ ܒܣܓܝ ܡܢ 1 – ܥܩܝܡܘܬܐ (bias) ܕܡܨܝܐ ܕܗܘܝܐ. Pallant ܟܡܙܗܪܐ ܕܬܚܘ̈ܡܐ "ܥܕܟܝܠ ܟܡܦܣܝ ܐܣܘܪ̈ܐ ܕܚܕ̈ܕܐ ܪ̈ܡܐ ܩܠܝܠ" ܘܟܡܩܪܒܐ ܠܡܒܚܪܐ ܐܦ ܡܐܛܪܝܟܣ ܕܐܣܘܪ̈ܐ ܕܚܕ̈ܕܐ (correlation matrix). ܡܢܝܢܐ ܕܣܒܠܬܐ (scale score) ܥܡ ܦܣܘ̈ܩܐ (items) ܕܝܠܗ، ܝܢ ܓܘܡܪܐ ܥܡ ܣܒܠ̈ܬܐ ܙܥܘ̈ܪܐ ܕܝܠܗ، ܝܢܐ "singularity" – ܦܐܬܐ ܟܩܝܡܐ ܥܡ ܛܥܝܘܬܐ.

ܐܪܒܥܐ ܫܪ̈ܛܐ (assumptions) ܥܠ ܫܪ̈ܟܐ (Pallant، ܒܬܪ Tabachnick & Fidell؛ Field، ܦܣܩܐ 9.4.1، ܠܦܘܬ ܛܟܣܐ ܕܐܝܩܪܐ): ܣܪܛܢܝܘܬܐ (linearity) ܘ-additivity – ܐܣܘܪܐ ܬܪܝܨܐ ܝܠܗ، ܘܡܢܒ̈ܝܢܐ ܟܡܬܚܝܕܝ ܒܡܘܣܦܐ؛ ܬܒܪܐ "ܟܥܒܕ ܡܘܕܝܠ ܠܐ ܬܪܝܨܐ" (Field). ܠܐ ܬܠܝܘܬܐ ܕܫܪ̈ܟܐ (independence of residuals) – ܬܒܪܐ ܟܡܚܒܠ ܛܥܝ̈ܘܬܐ ܬܩܝ̈ܢܬܐ، ܬܚܘ̈ܡܐ ܕܬܘܟܠܢܐ ܘܒܘܚܪ̈ܢܐ؛ Durbin-Watson (ܠܘܚܐ 1) ܟܒܚܪ ܐܣܘܪܐ ܕܚܕ̈ܕܐ ܒܝܢܝ ܫܪ̈ܟܐ ܩܪܝܒ̈ܐ: 2 – ܠܝܬ؛ "ܢܡܘܣܐ ܕܨܒܥܐ ܢܛܘܪܐ ܒܣܓܝ" – ܬܚܬ 1 ܝܢ ܒܢܘܬ ܡܢ 3 ܟܡܦܠܚ؛ ܘܐܝܬ ܠܗ ܣܘܟܠܐ ܒܣ ܐܝܡܢ ܕܠܛܟܣܐ ܕܡܫܬܘܬܦ̈ܢܐ ܐܝܬ ܣܘܟܠܐ (ܙܒܢܐ، ܕܘܟܬܐ)، ܠܐ ܓܘ ܦܐܝܠ ܕܛܟܣܐ ܕܝܠܗ ܓܕܫܢܝܐ ܝܠܗ. ܫܘܝܘܬܐ ܕܫܘܚܠ̈ܦܐ (homoscedasticity) – ܒܕܪܐ ܕܫܪ̈ܟܐ ܫܘܝܐ ܝܠܗ ܥܠ ܐܘܪܟܐ ܕܛܝ̈ܡܐ ܡܢܒ̈ܝܐ. ܢܘܪܡܠܝܘܬܐ ܕܫܪ̈ܟܐ (normality) – ܐܝܩܪܬܐ ܝܠܗ̇ ܓܘ ܕܘܡܝܐ ܙܥܘܪܐ؛ ܓܘ ܕܘܡܝܐ ܪܒܐ ܢܡܘܣܐ ܕܬܚܘܡܐ ܡܨܥܝܐ (central limit theorem) ܟܡܟܣܐ (Field)، ܘܡܢܒ̈ܝܢܐ ܒܓܢܣܗܘܢ "ܠܐ ܣܢܝܩ ܝܠܗ ܕܗܘܝܐ ܢܘܪܡܠܝ̈ܐ". ܬܠܬܐ ܐܚܪ̈ܝܐ ܒܚܝܪ̈ܐ ܝܢܐ ܓܘ ܨܘܪܬܐ ܕܫܪ̈ܟܐ (*ZRESID ܩܘܒܠ *ZPRED، ܨܘܪܬܐ 2 ܓܘ ܡܦܩܢܐ): Pallant – ܟܡܣܒܪܚ "ܦܘܠܓܐ ܐܝܟ ܡܪܒܥܐ ܡܓܪܓܐ ܩܪܝܒܐܝܬ، ܣܓܝܐܐ ܡܢ ܡܢܝ̈ܢܐ ܓܘ ܡܨܥܬܐ ܥܠ ܐܘܪܟܐ ܕܣܦܪ"؛ Field (ܦܣܩܐ 9.11.7) – "ܛܟܣܐ ܓܕܫܢܝܐ ܕܢܘܩ̈ܙܐ"؛ ܩܡܥܐ (funnel) – heteroscedasticity، ܩܫܬܐ – ܠܐ ܣܪܛܢܝܘܬܐ. histogram ܘܨܘܪܬܐ ܕ-P-P ܕܫܪ̈ܟܐ، ܕܡܢܝܗܝ ܟܒܚܪܚ ܢܘܪܡܠܝܘܬܐ، ܠܐ ܐܝܬ ܓܘ ܦܐܬܐ (ܓܘ SPSS ܡܢ ܣܝܢܬܐܟܣ؛ ܓܘ ܦܐܬܐ ܛܝ̈ܡܐ ܢܘܟܪ̈ܝܐ ܘܫܪ̈ܛܐ – ܥܠ ܡܫܬܚܠܦ̈ܢܐ ܒܓܢܣܗܘܢ).

ܛܝ̈ܡܐ ܢܘܟܪ̈ܝܐ (outliers) ܘܚܙ̈ܝܬܐ ܡܥܒܕܢ̈ܝܬܐ (ܠܘܚܐ 4). Field (ܦܣܩܐ 9.3.1) ܟܦܪܫ ܒܝܢܝ ܛܝܡܐ ܢܘܟܪܝܐ – ܡܫܬܘܬܦܢܐ ܕܡܘܕܝܠ ܟܡܢܒܐ ܠܗ ܒܝܫܐܝܬ – ܘܚܙܝܬܐ ܡܥܒܕܢܝܬܐ – ܡܫܬܘܬܦܢܐ ܕܕܠܐ ܐܝܠܗ ܡܘܕܝܠ ܒܕ ܗܘܐ ܦܪܝܫܐ (ܩܘܛܝܐ 9.1). ܫܪ̈ܟܐ ܡܬܩ̈ܢܐ (standardized residuals؛ ZRESID، ܡܢܝ̈ܢܐ z ܕܛܥܝ̈ܘܬܐ): ܓܘ ܕܘܡܝܐ ܓܘܢܝܐ ܩܪܝܒ 5% ܠܒܪ ܡܢ ±1.96 ܘ-1% ܠܒܪ ܡܢ ±2.58؛ ܝܬܝܪ ܡܢ ܗܕܐ – "ܪܡܐ ܕܛܥܝܘܬܐ ܓܘ ܡܘܕܝܠ ܠܐ ܡܩܒܠܐ ܡܨܐ ܕܗܘܐ"؛ ܛܝܡܐ ܠܒܪ ܡܢ ±3.29 – "ܥܠܬܐ ܠܦܘܠܚܢܐ ܕܒܪܢܫܐ" (Pallant: 3.3، ܘܓܘ ܕܘܡܝܐ ܪܒܐ "ܠܐ ܝܠܗ ܢܘܟܪܝܐ ܠܡܫܟܚܐ ܟܡܐ"). ܓܘ ܡܬܠܐ ܕ-albums ܕ-Field (ܦܣܩܐ 9.11.6؛ 200 ܡܫܬܘܬܦ̈ܢܐ): 12 ܒܢܘܬ ܡܢ 2 (6%) ܘ-2 ܒܢܘܬ ܡܢ 2.5 (1%) – "ܐܝܟ ܕܡܣܟܝܐ ܗܘܐ". ܪܘܚܩܐ ܕ-Cook (Cook's distance) – ܡܥܒܕܢܘܬܐ ܥܠ ܡܘܕܝܠ ܟܠܗ: ܒܢܘܬ ܡܢ 1 "ܡܨܐ ܕܡܦܠܚ" (Cook & Weisberg, 1982، ܓܘ Field، ܦܣܩܐ 9.3.2؛ Pallant: ܓܘ ܡܬܠܐ ܕܝܠܗ̇ ܪܒܐ ܝܬܝܪ .094). ܡܪܝܡܢܘܬܐ (leverage) – ܡܨܥܝܬܐ (k + 1)/N، ܘܟܒܚܪܚ ܚܙ̈ܝܬܐ ܒܢܘܬ ܡܢ ܬܪܝܢ ܓܗ̈ܝ ܡܢܗ̇ (Hoaglin & Welsch, 1978، ܓܘ Field). ܘܡܘܕܝ ܟܥܒܕܚ؟ Field (ܦܣܩܐ 9.3.3، ܒܬܪ Belsey ܘܐܚܪ̈ܢܐ، 1980): ܒܘܚܪܢܐ ܝܠܗ ܩܐ ܦܗܡܐ ܕܦܐܝܘܬܐ، "ܠܐ ܐܘܪܚܐ ܩܐ ܡܙܕܕܩܐ ܫܩܠܬܐ ܕܢܘܩ̈ܙܐ ܩܐ ܡܫܩܠܐ ܫܘܢܝܐ ܕܒܥܝܐ ܓܘ ܡܢܝ̈ܢܐ ܡܫܘܬܦ̈ܐ"؛ ܛܝܡܐ ܢܘܟܪܝܐ ܕܠܐ ܟܡܥܒܕ "ܠܐ ܝܠܗ ܥܠܬܐ ܠܦܘܠܚܢܐ"، ܐܠܐ ܛܒ ܝܠܗ ܠܡܦܗܡܐ ܩܐ ܡܘܕܝ ܠܐ ܦܐܐ. Pallant: ܚܙܝܬܐ ܥܡ ܪܘܚܩܐ ܕ-Cook ܒܢܘܬ ܡܢ 1 – ܠܡܒܚܪܐ، "ܡܨܐ ܕܣܢܝܩ ܗܘܐ ܕܚܫܒܝܬܘܢ ܥܠ ܫܩܠܬܐ". ܪܘܚܩܐ ܕ-Mahalanobis (Pallant، ܠܘܚܐ 13.1 – ܛܝ̈ܡܐ ܚܪܝ̈ܦܐ (critical values) ܠܦܘܬ ܡܢܝܢܐ ܕܡܢܒ̈ܝܢܐ) ܘ-DFBeta (Field) ܠܐ ܐܝܬ ܓܘ ܦܐܬܐ، ܐܠܐ ܣܝܢܬܐܟܣ ܟܢܛܪ ܐܢܝ ܠܦܐܝܠ.

ܛܝ̈ܡܐ ܚܣܝ̈ܪܐ (missing values). ܡܫܬܘܬܦܢܐ ܕܚܣܝܪܐ ܝܠܗ ܛܝܡܐ ܓܘ ܚܕ ܡܢ ܡܫܬܚܠܦ̈ܢܐ ܓܒܝ̈ܐ ܠܐ ܥܠܝܠܐ ܝܠܗ ܟܠ ܥܩܪܐ – ܫܩܠܬܐ ܕܣܕܪܐ ܟܠܗ (listwise deletion؛ /MISSING LISTWISE)، ܓܘܒܝܐ ܡܩܕܡܐ (default) ܕ-SPSS، ܕ-Field (ܦܣܩܐ 9.10.5) ܟܒܥܐ ܠܡܫܒܩܐ، "ܡܛܠ ܕܫܩܠܬܐ ܙܘܓܢܝܬܐ (pairwise deletion) ܡܨܝܐ ܕܝܗܒܐ ܡܕܡ̈ܐ ܕܠܐ ܣܘܟܠܐ ܐܝܟ R² ܬܚܬ ܣܦܪ ܝܢ ܪܒܐ ܡܢ 1"؛ Pallant (ܨܚܚܐ 13) ܟܓܒܝܐ ܓܘ dialog Exclude cases pairwise، ܘܡܛܠ ܗܕܐ ܡܢܝ̈ܢܐ ܕܡܬܠܐ ܕܝܠܗ̇ ܡܨܝ ܕܗܘܝܐ ܦܪ̈ܝܫܐ ܩܠܝܠ ܡܢ ܡܐ ܕܦܐܬܐ ܒܕ ܝܗܒܐ ܥܠ ܗܢܝ ܝܗܝ̈ܒܬܐ. ܡܛܠ ܗܕܐ N ܓܘ ܡܘܕܝܠ ܡܨܐ ܕܗܘܐ ܙܥܘܪܐ ܡܢ ܡܢܝܢܐ ܕܣܕܪ̈ܐ (ܦܐܬܐ ܟܡܘܕܥܐ). ܡܘܕܝ ܠܡܥܒܕܐ ܒܚܣܝ̈ܪܐ – ܦܐܬܐ ܛܝ̈ܡܐ ܚܣܝ̈ܪܐ.

ܡܢܒܝܢܘܬܐ ܠܒܪ ܡܢ ܬܚܘܡܐ. Gravetter ܘ-Wallnau (2017، ܦܐܬܐ 536): ܫܘܝܘܬܐ ܬܪܝܨܬܐ ܝܠܗ̇ ܒܣ ܓܘ ܦܬܝܘܬܐ (range) ܕܛܝ̈ܡܐ ܕܡܢܒܝܢܐ ܕܚܙ̈ܝܐ ܝܢܐ – "ܠܝܬ ܝܕܥܬܐ ܥܠ ܐܣܘܪܐ ܠܒܪ ܡܢ ܦܬܝܘܬܐ"؛ ܩܘܛܝܐ ܕܩܪܝܢܐ ܟܛܒܥ ܠܗ̇ ܓܘ ܪܝܓܪܫܢ ܦܫܝܛܐ. ܥܠܬܢܘܬܐ (causality). ܪܝܓܪܫܢ ܟܡܬܚܘܐ ܡܢܒܝܢܘܬܐ، ܠܐ ܥܠܬܐ: "ܡܢܒܝܢܐ" ܘ"ܡܫܬܚܠܦܢܐ ܕܦܐܪܐ" ܦܘܠ̈ܚܢܐ ܝܢܐ ܓܘ ܡܘܕܝܠ (Field، ܦܣܩܐ 9.4.1 – "ܡܫܬܚܠܦ̈ܢܐ ܠܒܪܝ̈ܐ" ܕܠܐ ܡܫܝ̈ܚܐ ܝܢܐ ܡܨܝ ܕܡܦܫܩܝ ܐܣܘܪܐ).

ܡܘܕܝ ܠܐ ܟܚܫܒܐ ܐܗܐ ܦܐܬܐ. ܪܝܓܪܫܢ ܕܕܪ̈ܓܐ (hierarchical) ܘ-R² change، ܪܝܓܪܫܢ ܕܦܣ̈ܥܬܐ (stepwise)، ܪܡܙܢܘܬܐ ܕܡܫܬܚܠܦ̈ܢܐ ܕܓܠܐ (dummy coding) ܐܘܛܘܡܛܝܬܐ، ܥܒ̈ܕܐ ܕܚܕ̈ܕܐ (interactions)، ܪܘܚܩܐ ܕ-Mahalanobis، DFBeta ܘ-DFFit، histogram ܘ-P-P ܕܫܪ̈ܟܐ، ܨܘܪ̈ܬܐ ܡܢܬܢ̈ܝܬܐ (partial plots)، ܬܚܘ̈ܡܐ ܕܬܘܟܠܢܐ ܒ-bootstrap ܘܪܝܓܪܫܢ ܚܣܝܢܐ (robust؛ Field, Section 9.12)، ܪܝܓܪܫܢ ܕ-Bayes (ܦܣܩܐ 9.13)، ܫܘܪܪܐ ܡܚܠܦܢܐ (cross-validation؛ ܦܣܩܐ 9.4.2).

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

ܐܘܪܚܐ (Pallant, 2020, Chapter 13; Field, 2024, Sections 9.7 and 9.10): Analyze › Regression › Linear… – ܡܫܬܚܠܦܢܐ ܕܦܐܪܐ ܠ-Dependent، ܡܢܒ̈ܝܢܐ ܠ-Independent(s)، Method: Enter؛ Statistics… – Estimates، Confidence intervals، Model fit، Descriptives، Part and partial correlations، Collinearity diagnostics، Durbin-Watson، Casewise diagnostics (Pallant: ܛܝ̈ܡܐ ܢܘܟܪ̈ܝܐ ܠܒܪ ܡܢ 3 ܣܛܝ̈ܘܬܐ ܬܩܝ̈ܢܬܐ؛ Field ܟܡܢܚܬ ܠ-2)؛ Plots… – *ZRESID ܠ-Y ܘ-*ZPRED ܠ-X، ܘ-Normal probability plot؛ Save… – Mahalanobis ܘ-Cook's؛ Options… – ܚܣܝ̈ܪܐ: listwise (Field) ܝܢ pairwise (Pallant). ܣܝܢܬܐܟܣ (syntax) ܕܦܐܬܐ ܟܒܢܐ (ܥܡ ܓܘܒܝܐ ܡܩܕܡܐ ܕܫܩܠܬܐ ܕܣܕܪܐ ܟܠܗ):

REGRESSION
  /MISSING LISTWISE
  /STATISTICS COEFF OUTS CI(95) R ANOVA COLLIN TOL ZPP
  /CRITERIA=PIN(.05) POUT(.10)
  /NOORIGIN
  /DEPENDENT עמדות_ציון
  /METHOD=ENTER גיל השכלה מין קבוצה
  /SCATTERPLOT=(*ZRESID ,*ZPRED)
  /RESIDUALS DURBIN NORMPROB(ZRESID)
  /CASEWISE PLOT(ZRESID) OUTLIERS(3)
  /SAVE MAHAL COOK.

ܩܪܝܢܐ ܕܡܦܩܢܐ. Model Summary = ܠܘܚܐ 1 (R, R Square, Adjusted R Square, Std. Error of the Estimate, Durbin-Watson)؛ ANOVA = ܠܘܚܐ 2 (Regression, Residual, Total)؛ Coefficients = ܠܘܚܐ 3 – B, Std. Error, Beta, t, Sig.، ܬܚܘ̈ܡܐ ܕܬܚܘܡܐ ܕܬܘܟܠܢܐ، Correlations: Zero-order, Partial, Part، ܘ-Collinearity Statistics: Tolerance, VIF؛ Collinearity Diagnostics (ܛܝ̈ܡܐ ܕܝܠܢ̈ܝܐ (eigenvalues) ܘ-condition indices؛ Field، ܦܣܩܐ 9.11.5) – ܠܐ ܐܝܬ ܓܘ ܦܐܬܐ؛ Casewise Diagnostics – ܡܫܬܘܬܦ̈ܢܐ ܥܡ |Std. Residual| > 3 (ܦܐܬܐ ܟܡܦܪܫܐ ܒܢܘܬ ܡܢ 1.96 ܓܘ ܡܥܝܪܢܘܬܐ ܕܠܘܚܐ 4)؛ Residuals Statistics – ܛܝܡܐ ܬܚܬܝܐ (minimum) ܘܛܝܡܐ ܥܠܝܐ (maximum) ܕ-Std. Residual، Cook's Distance ܘ-Centered Leverage Value (= ܡܪܝܡܢܘܬܐ ܕܓܘ ܠܘܚܐ 4 ܒܨܝܪ 1/N)؛ ܨܘܪܬܐ Scatterplot ܘܨܘܪܬܐ Normal P-P Plot ܓܘ ܫܘܠܡܐ ܕܡܦܩܢܐ. button "ܡܚܬܬܐ ܕܣܝܢܬܐܟܣ SPSS" ܓܘ ܡܦܩܢܐ ܟܒܢܐ ܛܥܢܐ، ܟܬܒܐ ܕܪ̈ܡܙܐ (codebook؛ ܐܢ ܐܝܬ ܗܘܐ ܡܦܫܩܢܐ) ܘܦܘܩܕܢܐ REGRESSION ܥܠ ܡܫܬܚܠܦ̈ܢܐ ܓܒܝ̈ܐ.

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

ܓܘ R ܫܬܐܣܝܐ: lm() ܟܡܦܐܐ ܡܘܕܝܠ، summary() ܟܝܗܒ ܡܢܝ̈ܢܐ ܡܫܘܬܦ̈ܐ (coefficients)، R²، R² ܡܬܘܪܨܐ (adjusted)، ܛܥܝܘܬܐ ܬܩܝܢܬܐ ܕܫܘܥܪܐ (standard error of the estimate) ܘ-F (ܠܘ̈ܚܐ 1-3)، confint() ܬܚܘ̈ܡܐ ܕܬܘܟܠܢܐ (confidence intervals)، anova() ܠܘܚܐ ANOVA؛ rstandard() ܟܝܗܒ ܫܪ̈ܟܐ ܡܬܩ̈ܢܐ ܓܘ̈ܝܐ (internally standardized residuals؛ ܦܪ̈ܝܫܐ ܩܠܝܠ ܡܢ ZRESID ܕ-SPSS – ܚܙܝܡܘܢ ܓܘ ܣܩܪܝܦܬ)، cooks.distance() ܘ-hatvalues() ܪܘܚܩܐ ܕ-Cook ܘܡܪܝܡܢܘܬܐ (leverage)؛ vif() ܘ-durbinWatsonTest() ܡܢ ܚܒܝܫܘܬܐ car. β ܘ-sr ܚܫܝ̈ܒܐ ܝܢܐ ܒܐܝܕܐ. ܣܩܪܝܦܬ ܪܗܛܐ ܝܠܗ ܐܝܟ ܕܐܝܬܘܗܝ ܥܠ ܦܐܝܠ ܕܡܬܠܐ ܘܝܗܒܠܗ ܛܝ̈ܡܐ ܕܠܘ̈ܚܐ (ܓܘ ܡܥܝܪ̈ܢܘܬܐ). ܢܡܘܣܐ ܕܣܐܝܛ ܩܐ ܣܘܪܝܬ ܓܘ R: ܦܐܝܠ UTF-8، ܟܠ ܣܕܪܐ ܕܡܥܝܪܢܘܬܐ ܟܫܪܐ ܒܡܠܬܐ ܕܣܘܪܝܬ، ܘܣܒܝܒܘܬܐ UTF-8 ܩܐ ܫܡ̈ܗܐ ܥܒܪ̈ܝܐ (ܓܘ Windows: R 4.2 ܘܠܥܠ، ܝܢ Sys.setlocale('LC_ALL', 'Hebrew')).

# ܪܝܓܪܫܢ ܣܪܛܢܝܐ – ܦܪܘܦܣܘܪ ܣܛܐܛ. ܐܗܐ ܦܐܝܠ ܢܛܝܪܐ ܝܠܗ ܒ-UTF-8؛ ܟܠ ܣܕܪܐ ܕܡܥܝܪܢܘܬܐ ܟܫܪܐ ܒܡܠܬܐ ܕܣܘܪܝܬ
library(readxl)   # ܩܪܝܢܐ ܕܐܩܣܠ
library(car)      # vif, durbinWatsonTest

# ܛܥܢܐ: ܛܘܦܣܐ ܬܩܝܢܐ – ܣܕܪܐ = ܡܫܬܘܬܦܢܐ، ܥܡܘܕܐ = ܡܫܬܚܠܦܢܐ؛ ܓܠܝܘܢܐ "נתונים"
d <- read_excel("C:/Rdata/DATA_regression_example_heb.xlsx", sheet = "נתונים")
v <- c("עמדות_ציון", "גיל", "השכלה", "מין", "קבוצה")
d <- d[complete.cases(d[, v]), v]                       # ܫܩܠܬܐ ܕܣܕܪܐ ܟܠܗ (113 ܡܢ 120)
names(d) <- c("y", "age", "edu", "sex", "grp")           # ܫܡ̈ܗܐ ܟܪ̈ܝܐ ܩܐ ܡܬܢܝܬܐ

# ܠܘ̈ܚܐ 1-3 – ܡܘܕܝܠ، R ܡܪܒܥܐ، F، ܡܢܝ̈ܢܐ ܡܫܘܬܦ̈ܐ، ܬܚܘ̈ܡܐ ܕܬܘܟܠܢܐ
m <- lm(y ~ age + edu + sex + grp, data = d)
summary(m)                                               # R² = .138، R² ܡܬܘܪܨܐ = .107، ܛܥܝܘܬܐ ܬܩܝܢܬܐ 0.713، F(4, 108) = 4.337، p = .003؛ B: ܡܢܝܢܐ ܩܝܡܐ 3.064، ܥܘܡܪܐ 0.012 (p = .028)، ܝܘܠܦܢܐ 0.022، ܓܢܣܐ 0.197، ܓܘܕܐ −0.406 (p = .003)
confint(m)                                               # ܬܚܘ̈ܡܐ ܕܬܘܟܠܢܐ 95%: ܥܘܡܪܐ [0.001, 0.022]، ܓܘܕܐ [−0.673, −0.138]
anova(m)                                                 # ܫܪܟܐ: SS 54.915، df 108، MS 0.509؛ ܪܝܓܪܫܢ = 3.376 + 0.003 + 0.847 + 4.594 = 8.820 (ܠܘܚܐ 2)
# ܡܥܝܪܢܘܬܐ: anova(m) ܟܡܦܪܩ ܪܝܓܪܫܢ ܠܦܘܬ ܡܢܒܝܢܐ (Type I)؛ ܣܕܪܐ Regression ܕ-SPSS = ܓܘܡܪܐ ܕܐܪܒܥܐ ܣܕܪ̈ܐ ܕܡܢܒ̈ܝܢܐ

# ܒܝܛܐ ܡܬܩܢܐ ܘܐܣܘܪܐ ܕܚܕ̈ܕܐ ܦܠܓܐ-ܡܢܬܢܝܐ (sr) – ܒܐܝܕܐ
b <- coef(m)[-1]; sds <- sapply(d[, c("age", "edu", "sex", "grp")], sd)
b * sds / sd(d$y)                                        # β: ܥܘܡܪܐ .200، ܝܘܠܦܢܐ .030، ܓܢܣܐ .130، ܓܘܕܐ −.270
t <- summary(m)$coefficients[-1, "t value"]; r2 <- summary(m)$r.squared; dfe <- df.residual(m)
t * sqrt((1 - r2) / dfe)                                 # sr: ܥܘܡܪܐ .199، ܝܘܠܦܢܐ .030، ܓܢܣܐ .129، ܓܘܕܐ −.268

# multicollinearity ܘܠܐ ܬܠܝܘܬܐ ܕܫܪ̈ܟܐ
vif(m)                                                   # VIF: 1.013, 1.006, 1.012, 1.012 – ܠܝܬ multicollinearity
durbinWatsonTest(m)                                      # Durbin-Watson 1.956

# ܠܘܚܐ 4 – ܒܘܚܪܢܐ: ZRESID ܕ-SPSS = ܫܪܟܐ/ܛܥܝܘܬܐ ܬܩܝܢܬܐ ܕܫܘܥܪܐ؛ rstandard() = ܫܪܟܐ ܡܬܩܢܐ ܓܘܝܐ (ܦܠܝܓܐ ܐܦ ܥܠ √(1 − h))
z <- resid(m) / sigma(m)
c(over196 = sum(abs(z) > 1.96), over258 = sum(abs(z) > 2.58), over329 = sum(abs(z) > 3.29), maxZ = max(abs(z)))   # 4 ܒܢܘܬ ܡܢ 1.96، 2 ܒܢܘܬ ܡܢ 2.58، 0 ܒܢܘܬ ܡܢ 3.29؛ ܪܒܐ ܝܬܝܪ 3.14
c(maxCook = max(cooks.distance(m)), maxLeverage = max(hatvalues(m)), avgLeverage = mean(hatvalues(m)))             # ܪܘܚܩܐ ܕ-Cook ܪܒܐ ܝܬܝܪ .129؛ ܡܪܝܡܢܘܬܐ ܪܒܬܐ ܝܬܝܪ .114، ܡܨܥܝܬܐ .044 = (k + 1)/N

# ܨܘܪܬܐ ܕܫܪ̈ܟܐ: ZRESID ܩܘܒܠ ZPRED
plot(scale(fitted(m)), z, xlab = "ZPRED", ylab = "ZRESID"); abline(h = c(0, -1.96, 1.96), lty = c(1, 2, 2))

ܬܘܢܝܐ ܕܡܫܟܚ̈ܢܘܬܐ (reporting the results)

ܟܡܘܕܥܚ ܙܢܐ ܕܦܘܫܩܐ (ܬܩܝܢܐ/ܕܕܪ̈ܓܐ)، N، ܘܒܬܪ ܗܕܐ ܡܘܕܝܠ – R² (ܝܢ ܡܬܘܪܨܐ)، F ܥܡ ܬܪܝܢ ܕܪ̈ܓܐ ܕܚܐܪܘܬܐ (degrees of freedom)، p ܚܬܝܬܐ – ܘܒܬܪ ܗܕܐ ܟܠ ܡܢܒܝܢܐ (predictor): B ܥܡ ܛܥܝܘܬܐ ܬܩܝܢܬܐ ܝܢ ܬܚܘܡܐ ܕܬܘܟܠܢܐ (confidence interval)، β، p، ܘܠܦܘܬ Pallant ܐܦ sr (Pallant, 2020, Chapter 13; Field, 2024, Section 9.14; American Psychological Association [APA], 2020, Section 6.43). ܡܬܠܐ ܕ-APA (ܦܣܩܐ 6.43): "High school GPA predicted college mathematics performance, R² = .12, F(1, 148) = 20.18, p < .001, 95% CI [.02, .22]". ܦܣܩܐ ܕ-Pallant: "ܪܝܓܪܫܢ ܣܓܝܐܐ ܕܕܪ̈ܓܐ ܥܒܝܕܐ ܝܠܗ ܩܐ ܫܘܥܪܐ ܕܡܨܝܢܘܬܐ ܕܬܪܝܢ ܡܚܘ̈ܝܢܐ ܕܫܘܠܛܢܐ (control) ܠܡܢܒܝܐ ܥܨܪܐ (stress) ܒܬܪ ܢܛܪܬܐ ܥܠ ܨܒܘܬܐ ܕܟܢܫܐ (social desirability) ܘܥܘܡܪܐ. ܦܘܫܩ̈ܐ ܩܕܡܝ̈ܐ ܥܒܝ̈ܕܐ ܝܢܐ ܩܐ ܡܫܪܪܐ ܕܫܪ̈ܛܐ ܕܢܘܪܡܠܝܘܬܐ، ܣܪܛܢܝܘܬܐ، multicollinearity ܘ-homoscedasticity ܠܐ ܬܒܝܪ̈ܐ ܝܢܐ. … ܫܘܚܠܦܐ ܟܠܢܝܐ ܕܡܦܫܩܐ ܗܘܐ ܒܝܕ ܡܘܕܝܠ ܟܠܗ ܗܘܐ 47%، F(4, 421) = 94.78, p < .001. … ܓܘ ܡܘܕܝܠ ܐܚܪܝܐ ܒܣ ܬܪܝܢ ܡܚܘ̈ܝܢܐ ܕܫܘܠܛܢܐ ܗܘܘ ܪ̈ܫܝܡܐ، ܐܝܡܢ ܕܩܐ Mastery ܐܝܬ ܗܘܐ ܛܝܡܐ ܕܐܣܘܪܐ ܕܚܕ̈ܕܐ ܦܠܓܐ-ܡܢܬܢܝܐ ܪܡܐ ܝܬܝܪ (sr = −.36, p < .001) ܡܢ ܕ-PCOISS (sr = −.26, p < .001)." Field (ܦܣܩܐ 9.14): ܥܡ ܟܡܐ ܡܢܒ̈ܝܢܐ "ܠܐ ܡܨܝܚ ܠܡܙܟܝܐ ܠܘܚܐ ܕܟܢܘܫܝܐ" – B، ܛܥܝܘܬܐ ܬܩܝܢܬܐ، ܬܚܘܡܐ ܕܬܘܟܠܢܐ، p ܘ-β ܩܐ ܟܠ ܡܢܒܝܢܐ ܥܡ ܡܢܝܢܐ ܩܝܡܐ (constant؛ "ܕܩܪ̈ܘܝܐ ܡܨܝ ܕܒܢܝ ܡܘܕܝܠ ܓܡܝܪܐ")، ܘ-R² ܬܚܬ ܠܘܚܐ؛ APA (2020، ܠܘ̈ܚܐ 7.15-7.18) ܟܡܝܬܐ ܠܘ̈ܚܐ ܕܡܬܠܐ ܒܗܘ ܒܢܝܢܐ، ܕܠܐ ܬܚܘ̈ܡܐ ܕܬܘܟܠܢܐ، ܥܡ ܬܚܘ̈ܡܐ ܕܬܘܟܠܢܐ ܓܘ ܩܠ̈ܡܐ ܝܢ ܓܘ ܥܡܘ̈ܕܐ ܦܪ̈ܝܫܐ، ܘܩܐ ܪܝܓܪܫܢ ܕܕܪ̈ܓܐ.

ܢܡܘ̈ܣܐ ܕܨܘܪܬܐ (APA, 2020, Section 6.36): B، F، t ܘܬܚܘܡܐ ܕܬܘܟܠܢܐ ܩܐ B ܥܡ ܣܦܪ ܩܕܡ ܢܘܩܙܐ؛ R²، β، r، sr ܘ-p ܕܠܐ (ܠܐ ܡܨܝ ܕܣܠܩܝ ܒܢܘܬ ܡܢ 1)؛ ܬܚܘܡܐ ܕܬܘܟܠܢܐ (confidence interval) ܒܛܘܦܣܐ 95% CI [LL, UL]. ܡܐܡܪ̈ܐ ܕܬܘܢܝܐ (report sentences) ܕܓܘ ܡܦܩܢܐ ܒܢܝ̈ܐ ܝܢܐ ܗܟܐ، ܒܣܘܪܝܬ ܘܒܐܢܓܠܝܙܝܐ، ܥܡ ܫܘܝܘܬܐ ܕܡܢܒܝܢܘܬܐ ܓܘ ܪܝܓܪܫܢ ܦܫܝܛܐ ܘܥܡ ܡܢܒ̈ܝܢܐ ܪ̈ܫܝܡܐ (ܠܦܘܬ ܪܒܘܬܐ ܕ-β) ܓܘ ܪܝܓܪܫܢ ܣܓܝܐܐ.

ܛܥܝ̈ܘܬܐ ܕܡܬܚܙܝܢ ܣܓܝ (Common mistakes)

ܠܡܦܫܩܐ B ܐܝܟ ܡܚܘܝܢܐ ܕܐܝܩܪܐ. B ܬܠܝܐ ܝܠܗ ܒܚܕܝ̈ܘܬܐ؛ ܟܡܦܚܡܚ ܡܢܒ̈ܝܢܐ (predictors) ܒ-β ܝܢ ܒ-sr² (Gravetter & Wallnau, 2017, p. 550; Pallant, 2020, Chapter 13).

ܠܡܟܢܫܐ sr² ܘܠܡܣܟܝܐ ܠ-R². ܓܘܡܪܐ ܙܥܘܪܐ ܝܠܗ ܡܢ R² – ܦܘܪܫܢܐ ܝܠܗ ܫܘܚܠܦܐ (variance) ܕܡܢܒ̈ܝܢܐ ܟܡܫܘܬܦܝ (Pallant: 25% ܩܘܒܠ 46.8%).

ܡܢܒܝܢܐ ܕܓܢ̈ܣܐ (categorical predictor) ܕܛܝ̈ܡܐ ܣܓܝ̈ܐܐ ܐܝܟ ܡܢܝܢܐ. "ܝܘܠܦܢܐ 1-4" ܐܝܟ ܡܢܝܢܐ ܟܣܒܪ ܦܣ̈ܥܬܐ ܫܘ̈ܝܬܐ؛ "ܐܬܪܐ 1-5" ܐܝܟ ܡܢܝܢܐ ܫܛܝܘܬܐ ܝܠܗ̇ – ܣܢܝܩܘܬܐ ܐܝܬ ܠܪܡܙܢܘܬܐ ܕܡܫܬܚܠܦ̈ܢܐ ܕܓܠܐ (dummy coding؛ Field, 2024, Section 9.4.1).

"ܡܘܕܝܠ ܪܫܝܡܐ ܝܠܗ، ܗܝܕܝܟ ܟܠ ܡܢܒ̈ܝܢܐ ܐܝܩܪ̈ܢܐ ܝܢܐ" – ܝܢ ܗܦܝܟܐܝܬ. F ܟܡܡܠܠ ܥܠ ܡܘܕܝܠ ܟܠܗ؛ ܡܢܒܝܢܐ ܡܨܐ ܕܗܘܐ ܠܐ ܪܫܝܡܐ ܣܛܐܛܝܣܛܝܩܐܝܬ (statistically significant) ܒܣ ܡܛܠ ܚܠܛܘܬܐ ܥܡ ܐܚܪ̈ܢܐ (Pallant; Field, Section 9.9.3).

ܠܫܩܠܐ ܡܫܬܘܬܦ̈ܢܐ (participants) ܩܐ ܡܛܝܒܐ p. ܒܘܚܪܢܐ ܝܠܗ ܩܐ ܒܘܚܪܢܐ ܕܡܘܕܝܠ، ܠܐ "ܐܘܪܚܐ ܩܐ ܡܙܕܕܩܐ ܫܩܠܬܐ" (Belsey ܘܐܚܪ̈ܢܐ، 1980، ܓܘ Field، ܦܣܩܐ 9.3.3).

ܪܝܓܪܫܢ ܕܦܣ̈ܥܬܐ (stepwise). ܡܬܥܒܕܢܐ ܝܠܗ ܡܢ ܓܕܫܢܝܘܬܐ ܘܣܓܝ ܓܗ̈ܝ "ܠܐ ܟܡܬܬܢܐ"؛ Pallant (ܨܚܚܐ 13) ܘ-Field (ܦܣܩܐ 9.9.1) ܟܡܙܗܪܝ – ܟܡܥܠܚ ܡܢܒ̈ܝܢܐ ܠܦܘܬ ܬܐܘܪܝܐ.

ܠܡܢܒܝܐ ܠܒܪ ܡܢ ܦܬܝܘܬܐ ܘܠܡܡܠܠܐ ܥܠ ܥܠܬܢܘܬܐ (causality). ܫܘܝܘܬܐ ܬܪܝܨܬܐ ܝܠܗ̇ ܓܘ ܦܬܝܘܬܐ (range) ܕܚܙܝܬܐ ܝܠܗ̇ (Gravetter & Wallnau, p. 536)، ܘ"ܡܢܒܝܢܐ" ܠܐ ܝܠܗ "ܥܠܬܐ".

ܠܫܒܩܐ ܪܒܘܬܐ ܕܕܘܡܝܐ (sample size). ܫܬܐ ܡܢܒ̈ܝܢܐ ܥܠ 21 ܡܫܬܘܬܦ̈ܢܐ ܟܝܗܒܝ R = 0.3 ܐܦ ܡܢ ܩܠܐ ܕܓܕܫܢܝܘܬܐ (noise؛ Field, Section 9.5)؛ R² ܡܬܘܪܨܐ (adjusted) ܟܡܚܘܐ ܟܡܐ ܦܐܝܘܬܐ ܡܢܦܚܬܐ ܝܠܗ̇.

ܡܒܘ̈ܥܐ

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

Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Lawrence Erlbaum Associates.

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

Gravetter, F. J., & Wallnau, L. B. (2017). Statistics for the behavioral sciences (10th ed.). Cengage Learning.

Pallant, J. (2020). SPSS survival manual: A step by step guide to data analysis using IBM SPSS (7th ed.). Routledge.

Tabachnick ܘ-Fidell (2013)، Stevens (1996، 2002)، Cook ܘ-Weisberg (1982)، Hoaglin ܘ-Welsch (1978)، Belsey، Kuh ܘ-Welsch (1980)، Bowerman ܘ-O'Connell (1990)، Myers (1990)، Menard (1995)، Durbin ܘ-Watson (1951)، Miles ܘ-Shevlin (2001) ܘ-Studenmund ܘ-Cassidy (1987) – ܐܝܟ ܕܡܝܬܝ̈ܐ ܝܢܐ ܓܘ Field (2024) ܘܓܘ Pallant (2020). ܠܦܘܬ ܢܡܘܣܐ ܕܣܐܝܛ (site rule)، ܓܘ ܪܫܝܡܬܐ ܕܡܒܘ̈ܥܐ (reference list) ܟܡܬܚܙܝ ܒܣ ܡܒܘ̈ܥܐ ܕܩܪܝ̈ܐ ܝܢܐ ܓܘ ܫܪܫܐ ܕܝܗܝ. Field (2024) ܘ-Pallant (2020) ܒܢܘܣܚܐ ܕܝܓܝܛܠܝܐ ܕܪܕܝܐ (reflowable) – ܡܬܝܬܐ ܠܦܘܬ ܦܣܩܐ ܘܨܚܚܐ؛ Gravetter ܘ-Wallnau (2017)، Cohen (1988) ܘ-APA (2020) – ܠܦܘܬ ܦܐܬܐ ܘܦܣܩܐ ܕܡܦܩܬܐ ܛܒܝܥܬܐ.