ܨܘܪܬܐ ܕܒܕܪܐ ܘܣܪܛܐ ܕܪܝܓܪܫܢ

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ܛܥܢܐ ܕܝܗܝ̈ܒܬܐ (loading the data)

ܟܡܕܒܩܚ ܥܡܘ̈ܕܐ ܡܢ ܓܠܝܘܢܐ ܬܪܝܨܐܝܬ (ܥܡ ܣܕܪܐ ܕܪ̈ܫܐ) – ܟܪܫܡܚ ܓܘ ܐܩܣܠ، ܟܢܣܚܚ، ܘܟܡܕܒܩܚ ܐܟܐ (ܐܦ ܛܝ̈ܡܐ ܦܪܝܫ̈ܐ ܒܦܣܝ̈ܩܐ، ܐܝܟ ܐܪܒܥܐ ܣܕܪ̈ܐ ܕ-Anscombe ܕܓܘ ܡܕܒܪܢܐ):

ܓܘܒܝܐ ܕܡܫܬܚܠܦ̈ܢܐ (Variable selection)

ܡܕܒܪܢܐ (guide)

ܐܝܡܢ ܡܦܠܚܝܚ ܒܨܘܪܬܐ ܕܒܕܪܐ؟

ܨܘܪܬܐ ܕܒܕܪܐ (ܟܡܬܩܪܝܐ ܐܦ ܕܝܐܓܪܡܐ ܕܒܕܪܐ، scatter plot) ܟܡܚܘܝܐ ܐܣܘܪܐ ܒܝܢܝ ܬܪܝܢ ܡܫܬܚܠܦ̈ܢܐ ܟܡܝ̈ܝܐ. ܟܠ ܢܘܩܙܐ ܚܕ ܡܫܬܘܬܦܢܐ ܝܠܗ: ܕܘܟܬܐ ܕܝܠܗ ܦܣܝܩܬܐ ܝܠܗ ܠܦܘܬ ܛܝܡܐ ܕܝܠܗ ܓܘ ܬܪܝܢ ܡܫܬܚܠܦ̈ܢܐ – ܚܕ ܡܫܬܚܠܦܢܐ ܥܠ ܣܪܛܐ X، ܬܪܝܢܐ ܥܠ ܣܪܛܐ Y، ܘܟܠ ܡܫܬܘܬܦܢܐ ܝܠܗ ܙܘܓܐ (x, y) ܕܝܠܗ. ܨܘܪܬܐ ܝܠܗ ܦܣܥܬܐ ܩܕܡܝܬܐ ܩܕܡ ܚܘܫܒܢܐ ܕܐܣܘܪܐ ܕܚܕ̈ܕܐ، ܡܛܠ ܕܟܓܠܝܐ ܡܕ̈ܡܐ ܕܡܢܝܢܐ ܒܠܚܘܕ ܟܛܫܝܐ – ܐܣܘܪܐ ܠܐ ܣܪܛܢܝܐ، ܚܙ̈ܝܬܐ ܢܘܟܪ̈ܝܬܐ، ܝܢ ܓܘ̈ܕܐ ܦܪ̈ܝܫܐ ܓܘ ܕܘܡܝܐ. ܘܗܠܐ ܩܕܡ ܟܠ ܚܘܫܒܢܐ، ܚܙܝܬܐ ܓܘ ܥܢܢܐ ܕܢܘܩ̈ܙܐ ܟܡܚܘܝܐ ܬܠܬܐ ܕܝܠܝ̈ܬܐ ܕܡܢܝܢܐ ܡܫܘܬܦܐ ܕܐܣܘܪܐ ܕܚܕ̈ܕܐ ܒܕ ܟܢܫܐ ܒܬܪ ܗܕܐ ܒܚܕ ܡܢܝܢܐ: ܐܘܪܚܐ – ܟܣܠܩ ܝܢ ܟܢܚܬ؛ ܐܣܟܝܡܐ – ܣܪܛܐ ܬܪܝܨܐ، ܣܪܛܐ ܟܦܝܦܐ، ܝܢ ܠܐ ܡܕܡ؛ ܘܚܝܠܐ – ܟܡܐ ܢܘܩ̈ܙܐ ܩܪܝ̈ܒܐ ܝܢܐ ܠܐܗܘ ܐܣܟܝܡܐ (Gravetter & Wallnau, 2017, pp. 487-488; Pallant, 2020, pp. 153-154). ܡܢ ܐܢܝ ܬܠܬܐ، ܡܢܝܢܐ ܟܟܢܫ ܛܒܐܝܬ ܒܣ ܩܕܡܝܐ ܘܬܠܝܬܝܐ – ܘܬܪܝܢܐ ܟܣܝܡ ܠܗ ܡܢ ܩܕܡ.

ܡܐܡܪܐ ܕܥܒܕܠܗ ܨܘܪܬܐ ܕܒܕܪܐ ܣܢܝܩܘܬܐ ܟܦܬܚ ܒܬܠܬܐ ܗܝܡܢ̈ܘܬܐ ܕܩܪܝܒܐ ܟܠܢ ܝܠܦܠܢ ܥܠܝܗܝܢ، ܘܟܠܗܝܢ ܛܥ̈ܝܬܐ ܝܢܐ: ܕܚܘܫ̈ܒܢܐ ܚܬܝܬ̈ܐ ܝܢܐ ܘܨܘܪ̈ܬܐ "ܩܪܝܒܐܝܬ" ܝܢܐ؛ ܕܩܐ ܟܠ ܙܢܐ ܕܝܗܝ̈ܒܬܐ ܐܝܬ ܚܕ ܚܘܫܒܢܐ ܬܪܝܨܐ؛ ܘܕܚܘܫ̈ܒܢܐ ܥܣܩ̈ܐ ܡܥܠܝܘܬܐ ܝܢܐ، ܘܚܙܝܬܐ ܓܘ ܝܗܝ̈ܒܬܐ ܓܢܒܘܬܐ ܝܠܗ (Anscombe, 1973, p. 17). ܚܫܘܒܬܐ، ܟܟܬܒ Anscombe، ܣܢܝܩܬܐ ܝܠܗ ܕܡܦܩܐ ܐܦ ܚܘܫ̈ܒܢܐ ܘܐܦ ܨܘܪ̈ܬܐ – ܘܬܪܘܝܗܝ ܣܢܝܩܝ ܕܝܠܦܚ. ܘܐܝܡܢ ܕܟܨܝܪܚ Y ܩܘܒܠ X ܩܕܡ ܟܠ ܚܘܫܒܢܐ، ܚܕ ܡܢ ܚܡܫܐ ܡܕ̈ܡܐ ܒܕ ܗܘܐ: ܢܘܩ̈ܙܐ ܩܪܝܒܐ ܝܬܝ̈ܒܐ ܝܢܐ ܥܠ ܣܪܛܐ ܬܪܝܨܐ؛ ܝܬܝ̈ܒܐ ܝܢܐ ܥܠ ܣܪܛܐ ܟܦܝܦܐ ܫܥܝܥܐ ܕܠܐ ܝܠܗ ܣܪܛܐ ܬܪܝܨܐ؛ ܒܕܝܪ̈ܐ ܝܢܐ ܕܠܐ ܐܣܘܪܐ ܥܡ X؛ ܡܕܡ ܒܦܠܓܐ؛ ܝܢ – ܗܘܝܐ ܕܚܫܝܚܐ ܝܠܗ ܡܢ ܟܠܗ – ܒܝܫܐ ܕܝܠܗܘܢ ܩܪܝ̈ܒܐ ܝܢܐ ܠܣܪܛܐ ܝܢ ܠܣܪܛܐ ܟܦܝܦܐ، ܘܩܠܝܠ ܒܣܓܝ ܪܚܝܩ̈ܐ ܝܢܐ. ܓܘ ܗܘܝܐ ܐܚܪܝܐ ܐܝܬ ܡܥܒܕܢܘܬܐ ܕܚܙܝܚ، ܐܠܐ ܚܘܫ̈ܒܢܐ ܥܝܕ̈ܝܐ ܕܪܝܓܪܫܢ ܡܨܝ ܕܦܝܫܝ ܠܐ ܚܙܝܐ ܠܗ (ܬܡܐ). ܬܪܝܢܐ ܒܙܒ̈ܢܐ ܡܨܝܚ ܕܕܥܪܚ ܠܗ ܠܩܕܡܝܐ ܒܫܘܢܝܐ ܕܣܒܠܬܐ ܕ-X ܝܢ Y؛ ܘܓܘ ܚܡܝܫܝܐ ܒܟܠ ܙܒܢ ܟܫܪܚ ܒܒܘܚܪܢܐ ܕܛܝ̈ܡܐ ܢܘܟܪ̈ܝܐ ܬܪܝܨܐܝܬ ܟܬܝܒ̈ܐ ܝܢܐ – ܘܐܢ ܫܪܝܪ̈ܐ ܝܢܐ، ܟܡܢܚܚ ܠܗܘܢ ܒܓܢܒܐ ܩܐ ܚܙܝܬܐ ܝܚܝܕܝܬܐ، ܕ"ܡܨܐ ܕܗܘܝܐ ܒܣܓܝ ܡܦܪܥܢܝܬܐ".

ܘܡܢ ܐܟܐ ܢܡܘܣܐ ܦܫܝܛܐ ܕ-Gelman & Hill (2007، ܦܐܬܐ 554): ܓܢܒ ܟܠ ܪܝܓܪܫܢ ܕܟܪܗܛܚ – ܟܨܝܪܚ ܨܘܪܬܐ ܕܒܕܪܐ؛ ܘܠܐ ܒܣ ܝܗܝ̈ܒܬܐ، ܐܠܐ ܐܦ ܡܘܕܝܠ ܕܦܐܝܐ ܝܠܗ ܠܗܘܢ، ܡܛܠ ܕ"ܠܘܚܐ ܕܡܢܝ̈ܢܐ ܡܫܘܬ̈ܦܐ ܠܐ ܟܝܗܒ ܪܓܫܐ ܕܨܘܪܬܐ ܟܝܗܒܐ" (ܬܡܐ، ܦܐܬܐ 548). ܘܬܪܬܝܢ ܡܥܝܪ̈ܢܘܬܐ ܕܝܠܗܘܢ ܥܠ ܐܝܢܐ ܨܘܪܬܐ: ܡܐܛܪܝܟܣ ܕܒܕܪܐ ܕܟܠ ܙܘ̈ܓܐ (ܚܙܝܡܘܢ ܬܘܣܦ̈ܬܐ) ܐܝܟ ܪܗܛܐ ܝܠܗ ܕܪܝܓܪܫܢ ܕܟܠ ܡܫܬܚܠܦܢܐ ܥܠ ܟܠ ܡܫܬܚܠܦܢܐ – ܦܝܫܐ ܝܠܗ، ܐܠܐ ܟܝܠܦܚ ܒܙܘܕܐ ܡܢ ܨܘܪ̈ܬܐ ܕܓܒܝ̈ܐ ܝܢܐ ܒܚܘܫܒܐ؛ ܘܐܝܡܢ ܕܩܐ ܬܪܝܢ ܡܫܬܚܠܦ̈ܢܐ ܐܝܬ ܛܟܣܐ ܒܙܒܢܐ ܝܢ ܛܟܣܐ ܕܥܠܬܢܘܬܐ، "ܩܕܡ" ܥܠ ܣܪܛܐ X ܘ"ܒܬܪ" ܥܠ ܣܪܛܐ Y (ܬܡܐ، ܦܐܬܐ 553).

ܐܝܟܢܐ ܟܩܪܚ ܨܘܪܬܐ: ܣܪܛܐ ܕܪܝܓܪܫܢ ܘ-R²

ܣܪܛܐ ܕܪܝܓܪܫܢ ܝܠܗ ܣܪܛܐ ܬܪܝܨܐ ܕܟܡܙܥܪ ܓܘܡܪܐ ܕܪܘ̈ܚܩܐ ܙܩܝ̈ܦܐ ܡܪ̈ܒܥܐ ܡܢ ܢܘܩ̈ܙܐ ܠܣܪܛܐ – "ܣܪܛܐ ܛܒܐ ܡܢ ܟܠܗ" ܒܐܗܐ ܣܘܟܠܐ ܒܠܚܘܕ، ܘܠܐ ܒܣܘܟܠܐ ܕܟܥܒܪ ܩܪܝܒܐ ܡܢ ܟܠܗ ܠܟܠ ܢܘܩܙܐ ܒܦܪܝܫܘܬܐ. ܡܨܠܝܢܘܬܐ (slope) ܕܝܠܗ ܟܡܚܘܝܐ ܒܟܡܐ ܚܕܝܘ̈ܬܐ ܡܫܬܚܠܦܢܐ Y ܡܣܟܝܐ ܝܠܗ ܕܫܚܠܦ ܩܐ ܣܘܠܩܐ ܕܚܕ ܚܕܝܘܬܐ ܓܘ X: ܡܨܠܝܢܘܬܐ ܕܙܘܕܐ ܟܡܚܘܝܐ ܐܣܘܪܐ ܕܣܠܩ، ܡܨܠܝܢܘܬܐ ܕܒܨܪܐ – ܐܣܘܪܐ ܕܢܚܬ، ܘܡܨܠܝܢܘܬܐ ܩܪܝܒܬܐ ܠܨܦܪܐ – ܠܐ ܐܝܬܘܬܐ ܕܐܣܘܪܐ ܣܪܛܢܝܐ.

R² (coefficient of determination) ܟܡܚܘܐ ܡܢܬܐ ܕܫܘܚܠܦܐ ܓܘ ܡܫܬܚܠܦܢܐ Y ܕܣܪܛܐ ܕܪܝܓܪܫܢ "ܟܡܦܫܩ" ܒܝܕ X. ܛܝܡܐ ܕܝܠܗ ܒܟܠ ܙܒܢ ܒܝܢܝ 0 ܘ-1 ܝܠܗ (ܝܢ 0% ܘ-100%)، ܘܠܐ ܬܠܐ ܝܠܗ ܒܐܘܪܚܐ ܕܐܣܘܪܐ: R² = .25 ܟܐܡܪ ܕ-25% ܡܢ ܫܘܚܠܦܐ ܓܘ Y ܡܦܫܩ̈ܐ ܝܢܐ ܒܝܕ X، ܐܢ ܐܣܘܪܐ ܟܣܠܩ ܘܐܢ ܟܢܚܬ. ܐܣܘܪܐ ܒܝܢܝ ܕܝܠܗ ܘܡܢܝܢܐ ܡܫܘܬܦܐ ܕ-Pearson ܦܫܝܛܐ ܝܠܗ – R² ܡܪܒܥܐ ܝܠܗ ܕ-r – ܘܡܛܠ ܗܕܐ ܩܐ ܕܕܥܪܚ ܡܢ R² ܠ-r ܟܫܩܠܚ ܫܪܫܐ ܘܟܡܙܝܕܚ ܪܘܫܡܐ ܠܦܘܬ ܐܘܪܚܐ ܕܣܪܛܐ ܕܪܝܓܪܫܢ (ܟܣܠܩ = ܕܙܘܕܐ، ܟܢܚܬ = ܕܒܨܪܐ). ܡܢ ܐܟܐ ܐܦ ܣܒܠܬܐ ܕܪܒܘܬܐ ܕܡܥܒܕܢܘܬܐ: R² ܕ-.01 ܐܣܘܪܐ ܙܥܘܪܐ ܝܠܗ، .09 – ܡܨܥܝܐ، ܘ-.25 ܘܒܐܬܪܗ – ܪܒܐ (Gravetter & Wallnau, 2017, p. 501) – ܒܚܬܝܬܘܬܐ ܬܚܘ̈ܡܐ r = .1 / .3 / .5 ܕܠܦܘܬܝܗܘܢ ܡܚܫܒܢܐ ܟܡܚܘܝܐ ܚܝܠܐ ܕܐܣܘܪܐ ܒܡ̈ܠܐ. ܘܡܛܠ ܕܡܪܒܥܐ ܟܫܐܦ ܪܘܫܡܐ، ܐܣܘܪܐ ܕܚܕ̈ܕܐ ܕ-+.80 ܘܐܣܘܪܐ ܕܚܕ̈ܕܐ ܕ-−.80 ܐܣܘܪ̈ܐ ܫܠܝܡ̈ܐ ܝܢܐ ܒܐܗܝ ܡܫܘܚܬܐ – ܪܘܫܡܐ ܘܚܝܠܐ ܠܐ ܬܠܝ̈ܐ ܝܢܐ ܚܕ ܒܚܕ (ܬܡܐ، ܦܐܬܐ 489).

ܡܨܠܝܢܘܬܐ ܠܐ ܝܠܗ ܚܝܠܐ. ܛܥܝܘܬܐ ܕܡܬܚܙܝܐ ܣܓܝ ܝܠܗ ܕܩܪܚ ܣܪܛܐ ܙܩܝܦܐ ܐܝܟ "ܐܣܘܪܐ ܚܝܠܬܢܐ" ܘܣܪܛܐ ܡܡܫܚܐ ܐܝܟ "ܐܣܘܪܐ ܟܪܝܗܐ". ܚܝܠܐ ܕܐܣܘܪܐ ܝܠܗ ܟܡܐ ܢܘܩ̈ܙܐ ܩܪܝ̈ܒܐ ܝܢܐ ܠܣܪܛܐ – ܘܠܐ ܟܡܐ ܣܪܛܐ ܙܩܝܦܐ ܝܠܗ. ܡܨܠܝܢܘܬܐ ܟܡܚܘܝܐ ܒܟܡܐ ܚܕܝܘ̈ܬܐ Y ܟܡܫܬܚܠܦ ܩܐ ܟܠ ܚܕܝܘܬܐ ܕ-X، ܘܡܛܠ ܗܕܐ ܬܠܝܐ ܝܠܗ ܒܚܕܝܘ̈ܬܐ ܕܡܫܘܚܬܐ: ܐܢܝ ܝܗܝ̈ܒܬܐ ܒܚܬܝܬܘܬܐ ܒܕ ܝܗܒܝ ܣܪܛܐ ܙܩܝܦܐ ܐܢ Y ܡܫܝܚܐ ܝܠܗ ܒܢܘܩ̈ܙܐ ܘܡܡܫܚܐ ܐܢ ܡܫܝܚܐ ܝܠܗ ܒܡܐ̈ܐ ܕܢܘܩ̈ܙܐ – ܘܐܣܘܪܐ ܕܚܕ̈ܕܐ ܫܘܝܐ ܓܘ ܬܪܘܝܗܝ ܗܘ̈ܝܐ. ܘܒܡ̈ܠܐ ܕ-Cohen (1988، ܦܐܬܐ 75، 77): r ܒܓܢܗ ܡܨܠܝܢܘܬܐ ܝܠܗ – ܡܨܠܝܢܘܬܐ ܕܣܪܛܐ ܐܝܡܢ ܕܬܪܝܢ ܡܫܬܚܠܦ̈ܢܐ ܡܬܩ̈ܢܐ ܝܢܐ ܠܐܗܘ ܫܘܚܠܦܐ – ܘ-b ܐܗܝ ܡܨܠܝܢܘܬܐ ܝܠܗ ܒܚܕܝܘ̈ܬܐ ܓܘܠܡ̈ܝܬܐ، b = r·s_Y/s_X؛ ܘܐܝܡܢ ܕܚܕܝܘ̈ܬܐ ܐܝܬܠܗܝܢ ܣܘܟܠܐ ܕܝܠܗܝܢ (ܙܘ̈ܙܐ، ܫܢ̈ܐ، ܢܘܩ̈ܙܐ ܓܘ ܒܘܚܪܢܐ) ܒܪܘܒܐ ܛܒܐ ܝܠܗ ܕܡܬܢܚ b، ܕܐܦ ܟܦܐܫ ܩܝܡܐ ܐܝܡܢ ܕܒܕܪܐ ܕ-X ܟܡܫܬܚܠܦ ܒܝܢܝ ܕܘ̈ܡܝܐ. ܓܘ ܠܘܚܐ ܕܡܚܫܒܢܐ ܟܡܦܩ ܬܪܝܢ ܡܕ̈ܡܐ ܦܪ̈ܝܫܐ ܝܢܐ ܓܠܝܐܝܬ: r ܘ-R² ܟܡܫܚܝ ܚܝܠܐ، b ܟܡܫܚ ܡܨܠܝܢܘܬܐ. ܡܨܝܚ ܕܚܙܝܚ ܐܗܐ ܐܦ ܓܘ ܝܗܝ̈ܒܬܐ ܕܡܬܠܐ: self-efficacy×ܬܘܟܠܢܐ ܘܡܕܒܪܢܘܬܐ×ܡܛܝܒܘܬܐ ܬܪܝܢ ܙܘ̈ܓܐ ܝܢܐ ܥܡ ܡܨܠܝܢܘܬܐ ܩܪܝܒܐ ܫܘܝܬܐ (0.687 ܘ-0.716) ܐܠܐ R² ܦܪܝܫܐ (.545 ܩܘܒܠ .522) – ܘܡܨܠܝܢܘܬܐ ܪܒܬܐ ܒܙܘܕܐ ܓܘ ܙܘܓܐ ܟܪܝܗܐ ܒܙܘܕܐ ܝܠܗ.

ܘܡܘܕܝ ܟܗܘܐ ܐܝܡܢ ܕܟܡܫܚܠܦܚ ܣܪ̈ܛܐ. ܐܣܘܪܐ ܕܚܕ̈ܕܐ ܠܐ ܟܝܕܥ ܡܢܘ X ܘܡܢܘ Y – r ܫܘܝܐ ܠܬܪܝܢ ܓܢ̈ܒܐ ܝܠܗ، ܘܐܗܘ ܛܝܡܐ ܒܕ ܡܬܛܝܐ ܓܘ ܬܪܝܢ ܛܟ̈ܣܐ. ܣܪܛܐ ܕܪܝܓܪܫܢ ܟܝܕܥ ܛܒܐ: ܣܪܛܐ ܕ-Y ܥܠ X ܟܡܙܥܪ ܪܘ̈ܚܩܐ ܙܩܝ̈ܦܐ، ܘܣܪܛܐ ܕ-X ܥܠ Y ܟܡܙܥܪ ܪܘ̈ܚܩܐ ܦܫܝ̈ܛܐ، ܘܐܢܝ ܬܪܝܢ ܣܪ̈ܛܐ ܦܪ̈ܝܫܐ ܝܢܐ ܕܒܣ ܟܡܬܚܕܝ ܐܝܡܢ ܕܐܣܘܪܐ ܕܚܕ̈ܕܐ ܓܡܝܪܐ ܝܠܗ. ܐܦ ܬܪܝܢ ܡܢܝ̈ܢܐ ܡܫܘܬ̈ܦܐ ܕܡܨܠܝܢܘܬܐ ܦܪ̈ܝܫܐ ܝܢܐ – ܫܘ̈ܝܐ ܝܢܐ ܚܕ ܠܚܕ ܒܣ ܐܝܡܢ ܕܣܛܝ̈ܘܬܐ ܬܩܝܢ̈ܬܐ ܕܬܪܝܢ ܡܫܬܚܠܦ̈ܢܐ ܫܘ̈ܝܐ ܝܢܐ – ܘܡܛܠ ܗܕܐ ܐܦ ܨܘܪܬܐ ܕܒܕܪܐ ܒܓܢܗ ܠܐ ܝܠܗ ܫܘܝܐ ܠܬܪܝܢ ܓܢ̈ܒܐ: ܐܢܝ ܝܗܝ̈ܒܬܐ ܟܡܬܚܙܝ ܒܨܘܪܬܐ ܐܚܪܬܐ ܐܝܡܢ ܕܟܡܫܚܠܦܚ ܣܪ̈ܛܐ (Cohen, Cohen, West & Aiken, 2003, p. 110). ܓܘ ܝܗܝ̈ܒܬܐ ܕܡܬܠܐ: ܬܘܟܠܢܐ ܥܠ self-efficacy ܟܝܗܒ b = 0.687؛ self-efficacy ܥܠ ܬܘܟܠܢܐ ܟܝܗܒ b = 0.793 – ܘܐܗܘ r = .738 ܓܘ ܬܪܘܝܗܝ ܗܘ̈ܝܐ. ܡܨܝܚ ܕܒܚܪܚ ܐܗܐ ܓܘ ܡܚܫܒܢܐ ܒܚܕ ܡܚܝܬܐ، ܒܫܘܚܠܦܐ ܕܬܪܝܢ ܡܫܬܚܠܦ̈ܢܐ. ܐܗܐ ܝܠܗ ܥܠܬܐ ܕܣܝܡܬܐ – ܡܢܒܝܢܐ ܓܘ X، ܦܐܪܐ ܓܘ Y – ܦܣܩܐ ܝܠܗ ܕܣܢܝܩܐ ܝܠܗ ܕܫܩܠܚ ܩܕܡ ܚܘܫܒܢܐ ܘܡܬܢܚ ܥܠܝܗ، ܘܠܐ ܡܕܡ ܕܦܫܝܩܘܬܐ.

ܡ̈ܠܐ ܥܝܕܐ ܝܢܐ، ܡܢܝܢܐ ܡܫܟܚܢܘܬܐ ܝܠܗ. ܡܚܫܒܢܐ ܟܡܚܘܝܐ ܚܝܠܐ ܒܡ̈ܠܐ ܠܦܘܬ ܬܚܘ̈ܡܐ .1 / .3 / .5 ܕ-Cohen (1988) – ܡܩܒ̈ܠܐ ܓܘ ܝܕ̈ܥܬܐ ܕܟܢܫܐ، ܐܠܐ ܠܐ ܒܠܚܘܕ. ܐܝܬ ܟܬܒ̈ܐ ܕܝܘܠܦܢܐ ܕܟܡܦܠܚܝ ܒܣܒܠܬܐ ܕܚܡܫܐ ܕܪ̈ܓܐ: ܗܕܟܐ .1 ܠܝܬ ܐܣܘܪܐ، .1-.3 ܟܪܝܗܐ، .3-.5 ܡܨܥܝܐ، .5-.7 ܪܡܐ، ܘܒܐܬܪܐ ܕ-.7 ܒܣܓܝ ܪܡܐ. ܐܣܘܪܐ ܕܚܕ̈ܕܐ .738 ܕܓܘ ܝܗܝ̈ܒܬܐ ܕܡܬܠܐ "ܚܝܠܬܢܐ" ܝܠܗ ܠܦܘܬ ܚܕ ܣܒܠܬܐ ܘ"ܒܣܓܝ ܪܡܐ" ܠܦܘܬ ܐܚܪܬܐ – ܘܡܛܠ ܗܕܐ ܒܟܠ ܙܒܢ ܟܡܬܢܚ ܡܢܝܢܐ، ܘܟܡܥܗܕܚ ܬܚܘܝܬܐ ܒܡ̈ܠܐ ܐܝܟ ܬܘܣܦܬܐ. ܛܒܐ ܝܠܗ ܕܝܕܥܚ ܕ-Cohen ܒܓܢܗ ܡܘܩܪܒܠܗ ܬܚܘ̈ܡܐ ܓܠܝܐܝܬ ܐܝܟ ܥܝܕܐ "ܩܐ ܦܘܠܚܢܐ ܐܝܡܢ ܕܠܝܬ ܬܚܘ̈ܡܐ ܦܐܝ̈ܐ ܒܙܘܕܐ"، ܘܩܪܐܠܗ ܠܟܠ ܐܬܪܐ ܕܝܕܥܬܐ ܕܣܐܡ ܩܐ ܓܢܗ ܬܚܘ̈ܡܐ ܐܚܪ̈ܢܐ (1988، ܦܐܬܐ 79). ܒܬܪ ܟܠ ܬܚܘܡܐ ܐܝܬ ܥܠܬܐ: .10 ܐܣܘܪܐ ܝܠܗ ܕܠܐ ܟܡܬܚܙܐ ܒܚܙܝܬܐ ܥܝܕܝܬܐ، ܐܠܐ ܣܓܝ ܐܣܘܪ̈ܐ ܕܝܕ̈ܥܬܐ "ܪܟܝ̈ܟܬܐ" ܟܪܕܦܝ ܒܬܪܝܗܘܢ ܡܢ ܐܗܐ ܪܒܘܬܐ ܝܢܐ (ܦܐܬܐ 79)؛ .30 – "ܦܠܓܐ ܕܦܬܝܘܬܐ" ܕܐܣܘܪ̈ܐ ܕܚܕ̈ܕܐ ܒܝܢܝ ܡܫܬܚܠܦ̈ܢܐ ܕܢܦܫܐ ܦܪ̈ܝܫܐ، ܘܐܣܘܪܐ ܕ"ܚܙܝܢܐ ܪܓܝܫܐ ܡܩܒܠܐ" ܟܦܪܫ ܠܗ ܒܥܝܢܐ (ܦܐܬܐ 80)؛ ܘ-.50 – "ܪܡܐ ܐܝܟ ܕܟܡܛܝ": ܬܚܘܡܐ ܥܒܕܢܝܐ ܕܐܣܘܪ̈ܐ ܕܚܕ̈ܕܐ ܒܝܢܝ ܡܫܬܚܠܦ̈ܢܐ ܦܪ̈ܝܫܐ ܓܘ ܝܕܥܬܐ ܕܢܦܫܐ ܕܦܪܨܘܦܘܬܐ، ܕܝܘܠܦܢܐ ܘܕܡܠܟܐ، ܐܝܟ ܐܣܘܪܐ ܕܚܕ̈ܕܐ ܒܝܢܝ ܗܘܢܐ ܘܡܢܝ̈ܢܐ ܓܘ ܡܕܪܫܬܐ (ܦܐܬܐ 80-81). ܒܐܬܪܗ، ܟܡܥܝܪ Cohen، ܒܪܘܒܐ ܒܣ ܡܢܝ̈ܢܐ ܡܫܘܬ̈ܦܐ ܕܫܪܝܪܘܬܐ (reliability) ܐܝܬ (ܦܐܬܐ 78) – ܘܡܛܠ ܗܕܐ ܐܣܘܪܐ ܕܚܕ̈ܕܐ ܐܝܟ .74 ܒܝܢܝ ܬܪܬܝܢ ܣܒ̈ܠܬܐ ܕܦܢܩܝܬܐ ܕܫܘܐ̈ܠܐ، ܐܝܟ ܓܘ ܝܗܝ̈ܒܬܐ ܕܡܬܠܐ، ܪܡܐ ܝܠܗ ܒܝܚܝܕܝܘܬܐ ܠܦܘܬ ܐܢܝ ܡܫܘ̈ܚܬܐ، ܘܛܒܐ ܝܠܗ ܕܫܐܠܚ ܐܢ ܬܪܬܝܢ ܣܒ̈ܠܬܐ ܠܐ ܟܡܫܚܝ ܡܢܬܐ ܡܢ ܐܗܘ ܡܕܡ. ܘܐܢ ܟܒܥܝܚ ܡܢܝܢܐ ܕܟܡܫܚ ܬܪܝܨܐܝܬ ܒܕܪܐ ܚܕܪ ܣܪܛܐ – "ܟܡܐ ܢܘܩ̈ܙܐ ܩܪܝ̈ܒܐ ܝܢܐ ܠܗ" – ܐܗܐ ܝܠܗ ܛܥܝܘܬܐ ܬܩܝܢܬܐ ܕܫܘܥܪܐ (standard error of the estimate): ܣܛܝܘܬܐ ܬܩܝܢܬܐ ܕܫܪ̈ܟܐ، ܒܚܕܝܘ̈ܬܐ ܕ-Y؛ ܟܡܐ ܕܙܥܘܪܬܐ ܝܠܗ ܒܙܘܕܐ، ܡܢܒܝܢܘܬܐ ܚܬܝܬܬܐ ܝܠܗ ܒܙܘܕܐ (Cohen, Cohen, West & Aiken, 2003, pp. 40-41). ܠܐ ܝܠܗ ܓܘ ܠܘܚܐ ܕܐܗܐ ܦܐܬܐ، ܐܠܐ ܟܡܬܚܙܝܐ ܓܘ ܠܘܚܐ Model Summary ܕܐܘܪܚܐ ܕܪܝܓܪܫܢ (ܚܙܝܡܘܢ ܡܢ ܨܘܪܬܐ ܠܪܝܓܪܫܢ).

ܘܐܝܡܢ ܐܣܘܪܐ ܕܚܕ̈ܕܐ ܕ-Spearman. ܠܘܚܐ ܕܡܚܫܒܢܐ ܟܡܦܩ ܟܡܚܘܝܐ ܓܢܒ Pearson ܐܦ ܐܣܘܪܐ ܕܚܕ̈ܕܐ ܕ-Spearman، ܕܚܫܝܒܐ ܝܠܗ ܥܠ ܕܪ̈ܓܐ ܕܛܟܣܐ ܕܛܝ̈ܡܐ ܘܠܐ ܥܠ ܛܝ̈ܡܐ ܒܓܢܗܘܢ. Gravetter & Wallnau (2017، ܦܐܬܐ 510-511) ܟܡܢܝܝ ܬܪܝܢ ܗܘ̈ܝܐ ܕܓܘܗܘܢ ܟܡܦܠܚܝ ܒܗ: ܐܝܡܢ ܕܡܫܬܚܠܦ̈ܢܐ ܡܫܝܚ̈ܐ ܝܢܐ ܒܣܒܠܬܐ ܕܛܟܣܐ (ܕܪ̈ܓܐ ܕܛܟܣܐ)، ܘܐܝܡܢ ܕܟܣܟܝܚ ܐܣܘܪܐ ܫܠܝܡܐ ܒܚܕ ܐܘܪܚܐ ܕܠܐ ܝܠܗ ܒܐܢܢܩܝ ܣܪܛܐ ܬܪܝܨܐ – ܡܬܠܐ ܡܪܓܠܢܘܬܐ ܘܥܒܕܐ، ܕܟܡܛܝܒ ܥܡ ܟܠ ܡܪܓܠܢܘܬܐ ܐܠܐ ܒܪܗܛܐ ܕܟܒܨܪ؛ Spearman ܟܡܫܚ ܫܠܝܡܘܬܐ ܕܐܣܘܪܐ ܕܠܐ ܬܠܝܘܬܐ ܒܐܣܟܝܡܐ ܕܝܠܗ، ܡܛܠ ܕܐܝܡܢ ܕܐܣܘܪܐ ܫܠܝܡܐ ܝܠܗ ܕܪ̈ܓܐ ܕܛܟܣܐ ܟܡܬܬܩܢܝ ܥܠ ܣܪܛܐ ܬܪܝܨܐ ܐܦܢ ܕܛܝ̈ܡܐ ܠܐ. ܒܠܫܢܐ ܕܨܘܪܬܐ ܕܒܕܪܐ: Spearman ܟܫܐܠ ܐܢ ܥܢܢܐ ܟܣܠܩ (ܝܢ ܟܢܚܬ) ܫܠܝܡܐܝܬ، ܠܐ ܒܐܢܢܩܝ ܒܣܪܛܐ ܬܪܝܨܐ، ܘܡܛܠ ܗܕܐ ܒܨܝܪ ܪܓܝܫܐ ܝܠܗ ܠܚܕ ܚܙܝܬܐ ܢܘܟܪܝܬܐ ܘܠܟܦܝܦܘܬܐ ܕܠܐ ܟܡܫܚܠܦܐ ܐܘܪܚܐ. ܦܘܚܡܐ ܕܬܪܝܢ ܣܕܪ̈ܐ ܓܘ ܠܘܚܐ ܒܘܚܪܢܐ ܩܠܝܠܐ ܝܠܗ: ܐܝܡܢ ܕܬܪܘܝܗܝ ܩܪܝ̈ܒܐ ܝܢܐ، ܐܣܘܪܐ ܩܪܝܒܐܝܬ ܣܪܛܢܝܐ ܝܠܗ ܘܕܠܐ ܛܝ̈ܡܐ ܢܘܟܪ̈ܝܐ ܚܫܝ̈ܚܐ؛ ܐܝܡܢ ܕ-Spearman ܒܣܓܝ ܪܒܐ ܝܠܗ ܡܢ Pearson، ܐܝܬ ܓܘ ܥܢܢܐ ܡܕܡ – ܟܦܝܦܘܬܐ ܝܢ ܢܘܩܙܐ ܪܚܝܩܐ – ܕܛܒܐ ܝܠܗ ܕܕܥܪܚ ܘܚܙܝܚ ܠܗ.

ܘܐܝܡܢ ܕܐܣܘܪܐ ܠܐ ܝܠܗ ܣܪܛܐ ܬܪܝܨܐ. ܐܣܘܪܐ ܕܚܕ̈ܕܐ ܬܚܬܝܐ ܠܐ ܟܡܚܘܐ ܕܠܝܬ ܐܣܘܪܐ: ܡܨܐ ܕܗܘܐ ܐܣܘܪܐ ܚܝܠܬܢܐ ܘܫܠܝܡܐ ܕܠܐ ܝܠܗ ܣܪܛܢܝܐ، ܕܣܪܛܐ ܬܪܝܨܐ ܘܡܢܝܢܐ ܡܫܘܬܦܐ ܕ-Pearson ܒܣ ܠܐ ܟܚܙܝ ܠܗ. ܡܬܠܐ ܥܬܝܩܐ ܡܢ ܝܕܥܬܐ ܕܢܦܫܐ ܝܠܗ ܐܣܘܪܐ ܒܝܢܝ ܙܘܥܐ ܘܥܒܕܐ – ܗܕܟܐ ܚܕ ܪܡܐ ܕܙܘܥܐ ܥܒܕܐ ܟܡܛܝܒ، ܘܒܐܬܪܗ ܟܢܚܬ؛ ܓܘ ܨܘܪܬܐ ܕܒܕܪܐ ܐܗܐ ܐܣܟܝܡܐ ܕ-U ܗܘܦܟܐ ܝܠܗ، ܘܐܣܘܪܐ ܕܚܕ̈ܕܐ ܕ-Pearson ܡܨܐ ܕܩܪܒ ܠܨܦܪܐ ܐܦܢ ܕܐܣܘܪܐ ܓܠܝܐ ܝܠܗ ܠܥܝܢܐ – Pearson ܟܡܫܚ ܒܣ ܐܣܘܪ̈ܐ ܒܣܪܛܐ ܬܪܝܨܐ، ܘܩܐ ܐܣܟܝܡ̈ܐ ܐܚܪ̈ܢܐ ܐܝܬ ܡܚܘ̈ܝܢܐ ܐܚܪ̈ܢܐ (Gravetter & Wallnau, 2017, p. 488; Pallant, 2020, p. 153). ܐܗܐ ܥܠܬܐ ܐܚܪܬܐ ܝܠܗ ܕܒܟܠ ܙܒܢ ܫܪܚ ܡܢ ܨܘܪܬܐ – ܚܙܝܡܘܢ ܐܦ ܐܪܒܥܐ ܣܕܪ̈ܐ ܕ-Anscombe (Anscombe's quartet) ܓܘ ܦܐܬܐ ܕܐܣܘܪ̈ܐ ܕܚܕ̈ܕܐ.

ܐܪܒܥܐ ܣܕܪ̈ܐ – ܢܣܝܘܢܐ ܓܘ ܡܚܫܒܢܐ. ܐܪܒܥܐ ܟܢܘܫܝ̈ܐ ܕܝܗܝ̈ܒܬܐ ܒܕܝ̈ܐ ܕ-Anscombe (1973، ܦܐܬܐ 19)، ܚܕܥܣܪ ܙܘ̈ܓܐ ܟܠ ܚܕ، ܟܝܗܒܝ ܐܗܘ ܡܦܩܢܐ ܬܩܝܢܐ ܒܚܬܝܬܘܬܐ: n = 11، ܡܨܥܝܬܐ ܕ-X 9.0، ܡܨܥܝܬܐ ܕ-Y 7.5، ܣܪܛܐ ܕܪܝܓܪܫܢ Ŷ = 3 + 0.5·X، R² = .667 – ܘܥܡ ܗܕܐ ܒܣ ܩܕܡܝܐ ܝܠܗ ܡܐ ܕܒܝܫܐ ܕܐܢܫ̈ܐ ܟܡܨܘܪܝ ܐܝܡܢ ܕܟܚܙܝ ܐܢܝ ܡܢܝ̈ܢܐ: ܬܪܝܢܐ ܣܪܛܐ ܟܦܝܦܐ ܫܥܝܥܐ ܝܠܗ، ܬܠܝܬܝܐ ܣܪܛܐ ܬܪܝܨܐ ܓܡܝܪܐ ܥܡ ܚܕ ܢܘܩܙܐ ܕܣܛܐ، ܘܪܒܝܥܝܐ ܥܣܪܐ ܢܘܩ̈ܙܐ ܓܘ ܐܗܘ X ܘܚܕ ܢܘܩܙܐ ܕܒܠܚܘܕܗ ܟܦܣܩ ܡܨܠܝܢܘܬܐ. ܡܨܝܚ ܕܚܙܝܚ ܐܗܐ ܓܘ ܡܚܫܒܢܐ ܕܐܗܐ ܦܐܬܐ: ܢܣܘܚܘܢ ܓܘܫܡܐ ܕܬܚܬ ܠܦܐܬܐ ܕܡܕܒܩܬܐ، ܘܓܒܘܢ ܚܕ ܒܬܪ ܚܕ x ܥܡ y1، y2، y3، ܘܒܬܪܗ x4 ܥܡ y4:

x,y1,y2,y3,x4,y4
10,8.04,9.14,7.46,8,6.58
8,6.95,8.14,6.77,8,5.76
13,7.58,8.74,12.74,8,7.71
9,8.81,8.77,7.11,8,8.84
11,8.33,9.26,7.81,8,8.47
14,9.96,8.10,8.84,8,7.04
6,7.24,6.13,6.08,8,5.25
4,4.26,3.10,5.39,19,12.50
12,10.84,9.13,8.15,8,5.56
7,4.82,7.26,6.42,8,7.91
5,5.68,4.74,5.73,8,6.89

ܚܙܝܡܘܢ ܬܪܝܢ ܣܕܪ̈ܐ ܓܘ ܠܘܚܐ. r ܘ-R² ܫܘ̈ܝܐ ܝܢܐ ܓܘ ܐܪܒܥܬܝܗܘܢ (.816، .667؛ ܦܘܪ̈ܫܢܐ ܕܥܘܓܠܐ ܓܘ ܡܢܝܢܐ ܬܠܝܬܝܐ) – ܐܗܐ ܒܚܬܝܬܘܬܐ ܢܘܩܙܐ ܝܠܗ ܕ-Anscombe. ܐܠܐ ܐܣܘܪܐ ܕܚܕ̈ܕܐ ܕ-Spearman ܒܣܓܝ ܦܪܝܫܐ ܝܠܗ: .82، .69، .99 ܘ-.50 – ܓܘ ܟܢܘܫܝܐ ܬܠܝܬܝܐ Spearman ܒܣܓܝ ܪܡܐ ܝܠܗ ܡܢ Pearson (ܣܪܛܐ ܓܡܝܪܐ ܥܡ ܚܕ ܛܝܡܐ ܢܘܟܪܝܐ)، ܘܓܘ ܪܒܝܥܝܐ ܒܣܓܝ ܬܚܬܝܐ ܝܠܗ (ܥܣܪܐ ܕܪ̈ܓܐ ܕܛܟܣܐ ܫܘ̈ܝܐ ܘܚܕ ܢܘܩܙܐ) – ܒܚܬܝܬܘܬܐ ܪܘܫܡܐ ܕܡܚܘܝܐ ܝܠܗ ܠܥܠ ܓܘ "ܘܐܝܡܢ ܐܣܘܪܐ ܕܚܕ̈ܕܐ ܕ-Spearman". ܡܢܝ̈ܢܐ، ܐܢ ܟܝܕܥܚ ܐܝܟܐ ܕܚܙܝܚ، ܟܪܡܙܝ ܛܒܐ؛ ܐܠܐ ܨܘܪܬܐ ܒܣ ܟܡܚܘܝܐ.

ܘܐܝܡܢ ܕܥܢܢܐ ܟܦܠܓ ܠܓܘ̈ܫܡܐ. ܥܢܢܐ ܕܟܡܬܚܙܐ ܐܝܟ ܬܪܝܢ-ܬܠܬܐ ܓܘ̈ܫܡܐ ܦܪ̈ܝܫܐ، ܡܬܬܩ̈ܢܐ ܒܣܪܛܐ ܡܨܠܝܢܐ، ܪܘܫܡܐ ܕܙܘܗܪܐ ܝܠܗ ܩܐ ܡܫܬܚܠܦܢܐ ܬܠܝܬܝܐ. ܡܬܠܐ ܕ-Gravetter & Wallnau (2017، ܦܐܬܐ 497، 502-503): ܒܝܢܝ ܡܢܝܢܐ ܕܥܕ̈ܬܐ ܘܡܢܝܢܐ ܕܥܘ̈ܠܐ ܓܘ ܡܕܝ̈ܢܬܐ ܡܫܟܚܐ ܝܠܗ ܐܣܘܪܐ ܕܚܕ̈ܕܐ ܕܙܘܕܐ ܚܝܠܬܢܐ – ܠܐ ܡܛܠ ܕܨܠܘܬܐ ܟܝܠܕܐ ܥܘܠܐ، ܐܠܐ ܡܛܠ ܕܬܪܘܝܗܝ ܟܪܒܝ ܥܡ ܪܒܘܬܐ ܕܡܕܝܢܬܐ؛ ܓܘ ܟܠ ܓܘܕܐ ܕܪܒܘܬܐ، ܐܣܘܪܐ ܟܦܐܫ ܓܢܝܙܐ. ܓܘ ܨܘܪܬܐ ܕܒܕܪܐ ܐܗܐ ܟܡܬܚܙܐ ܐܝܟ ܓܘ̈ܫܡܐ ܠܦܘܬ ܪܒܘܬܐ ܕܡܕܝܢܬܐ، ܕܟܠ ܚܕ ܡܢܗܘܢ ܒܠܚܘܕܗ ܠܝܬܠܗ ܐܘܪܚܐ. ܐܝܡܢ ܕܟܚܫܕܚ ܒܐܗܐ، ܟܨܒܥܚ ܝܢ ܟܦܠܓܚ ܨܘܪܬܐ ܠܦܘܬ ܡܫܬܚܠܦܢܐ ܬܠܝܬܝܐ (ܚܙܝܡܘܢ Overlay Scatter ܘ-Panel by ܓܘ ܬܘܣܦ̈ܬܐ)، ܝܢ ܟܚܫܒܚ ܐܣܘܪܐ ܕܚܕ̈ܕܐ ܡܢܬܢܝܐ (partial correlation) – ܓܘ ܦܐܬܐ ܕܐܣܘܪ̈ܐ ܕܚܕ̈ܕܐ.

ܘܡܐ ܕܣܪܛܐ ܟܡܫܬܥܐ ܥܠ ܡܫܬܘܬܦ̈ܢܐ ܕܒܣܘܦ̈ܐ. ܐܝܡܢ ܕܐܣܘܪܐ ܕܚܕ̈ܕܐ ܠܐ ܝܠܗ ܓܡܝܪܐ، ܢܘܩ̈ܙܐ ܕܒܣܘܦ̈ܐ ܓܘ X ܠܐ ܝܢܐ ܐܢܝ ܕܒܣܘܦ̈ܐ ܓܘ Y: ܡܫܬܘܬܦ̈ܢܐ ܪ̈ܡܐ ܡܢ ܟܠܗ ܓܘ ܚܕ ܡܫܬܚܠܦܢܐ ܟܡܨܠܝ ܕܗܘܝ ܪ̈ܡܐ – ܐܠܐ ܒܨܝܪ – ܓܘ ܡܫܬܚܠܦܢܐ ܬܪܝܢܐ، ܘܐܗܟܐ ܐܦ ܬܚܬ̈ܝܐ ܡܢ ܟܠܗ. ܐܗܐ ܝܠܗ ܕܥܪܬܐ ܠܡܨܥܝܬܐ (regression toward the mean; Gravetter & Wallnau, 2017, pp. 501-502)، ܘܐܝܠܗ ܥܠܬܐ ܕܣܪܛܐ ܕܪܝܓܪܫܢ ܒܟܠ ܙܒܢ ܡܡܫܚܐ ܝܠܗ ܒܙܘܕܐ ܡܢ ܣܪܛܐ ܡܨܠܝܢܐ ܕܥܢܢܐ. ܠܝܬ ܐܟܐ ܚܕ ܚܝܠܐ ܕܟܓܪܫ – ܐܗܐ ܫܪܪܐ ܣܛܐܛܝܣܛܝܩܝܐ ܝܠܗ ܕܟܐܬܐ ܡܢ ܕܐܣܘܪܐ ܠܐ ܝܠܗ ܓܡܝܪܐ؛ ܐܠܐ ܟܡܦܫܩ، ܡܬܠܐ، ܠܡܢܐ "ܡܛܥܡܢܐ ܕܫܢܬܐ" ܓܘ ܙܒܢܐ ܩܕܡܝܐ ܕܝܠܗ ܟܡܓܡܪ ܓܘ ܬܪܝܢܐ، ܘܠܡܢܐ ܐܝܢܐ ܕܫܩܠܠܗ ܡܢܝܢܐ ܪܡܐ ܡܢ ܟܠܗ ܓܘ ܒܘܚܪܢܐ ܐ ܒܪܘܒܐ ܒܣ ܒܐܬܪܐ ܕܡܨܥܝܬܐ ܒܕ ܗܘܐ ܓܘ ܒܘܚܪܢܐ ܒ. Gelman, Hill & Vehtari (2020، ܦܐܬܐ 87-90) ܟܫܪܝ ܐܦ ܦܪܕܘܟܣܐ ܕܟܡܥܩܐ ܠܣܓܝܐܐ: ܐܢ ܒܢ̈ܬܐ ܕܝܡ̈ܗܬܐ ܐܪ̈ܝܟܬܐ ܒܡܨܥܝܬܐ ܟܪ̈ܝܬܐ ܝܢܐ ܡܢܝܗܝܢ، ܐܢ ܟܠܢ ܠܐ ܒܕ ܗܘܚ ܒܐܗܘ ܐܘܪܟܐ ܒܬܪ ܟܡܐ ܫܪ̈ܒܬܐ؟ ܠܐ – ܡܛܠ ܕܡܢܒܝܢܘܬܐ ܟܕܥܪܐ ܠܡܨܥܝܬܐ، ܐܠܐ ܚܙܝܬܐ ܠܐ ܝܠܗ ܡܢܒܝܢܘܬܐ: ܛܥܝܘܬܐ ܕܡܢܒܝܢܘܬܐ ܟܡܙܝܕܐ ܒܚܬܝܬܘܬܐ ܐܗܘ ܒܕܪܐ ܕܕܥܪܬܐ ܟܡܒܨܪܐ، ܘܫܘܚܠܦܐ ܒܝܢܝ ܫܪ̈ܒܬܐ ܟܦܐܫ ܩܝܡܐ. ܡܐ ܕܒܙܘܕܐ ܕܣܘܟܢܐ ܝܠܗ ܝܠܗ ܛܥܝܘܬܐ ܕܕܥܪܬܐ (regression fallacy) – ܕܝܗܒܚ ܥܠܬܐ ܠܕܥܪܬܐ. ܡܬܠܐ ܕ-Tversky ܘ-Kahneman، ܕܐܢܝ ܟܡܝܬܝ: ܡܠܦܢ̈ܐ ܕܛܝܣܐ ܕܚܙܠܗܘܢ ܕܒܬܪ ܫܘܒܚܐ ܥܠ ܥܒܕܐ ܡܨܠܚܐ ܥܒܕܐ ܕܒܬܪܗ ܒܝܫ ܝܠܗ، ܘܒܬܪ ܟܐܪܘܬܐ – ܛܒ ܝܠܗ، ܘܦܩܚܠܗܘܢ ܫܘܠܡܐ ܕܫܘܒܚܐ ܟܡܙܝܩ؛ ܒܫܪܪܐ ܥܒܕܐ ܛܒܐ ܐܦ ܦܐܪܐ ܝܠܗ ܕܓܕܫܐ، ܘܒܬܪܗ ܡܣܟܝܐ ܝܠܗ ܢܚܬܐ ܕܠܐ ܐܣܘܪܐ ܥܡ ܦܘܢܝܐ ܕܡܠܦܢܐ. ܐܗܘ ܡܕܡ ܥܡ ܬܠܡܝܕ̈ܐ ܕ"ܦܝܫܠܗܘܢ ܡܡܝܢ̈ܐ" ܒܬܪ ܡܢܝܢܐ ܪܡܐ ܓܘ ܒܘܚܪܢܐ ܕܦܠܓܐ: ܓܘ ܢܣܝܘܢܐ ܕܚܘܫܒܢܐ (simulation) ܕܓܘܗ ܡܢܝ̈ܢܐ ܡܨܝܐܘܬܐ ܫܪܝܪܬܐ ܝܢܐ ܘܙܘܕܐ ܩܠܐ ܫܦܝܐ، ܕܠܐ ܚܕ ܡܘܬܒܐ ܕܢܦܫܐ، ܟܡܬܛܝܐ ܒܚܬܝܬܘܬܐ ܐܗܘ ܐܣܟܝܡܐ. ܨܘܪܬܐ ܕܒܕܪܐ ܕ"ܩܕܡ" ܩܘܒܠ "ܒܬܪ" – ܥܡ ܣܪܛܐ ܕܪܝܓܪܫܢ ܡܡܫܚܐ ܒܙܘܕܐ ܡܢ ܣܪܛܐ ܡܨܠܝܢܐ – ܒܚܬܝܬܘܬܐ ܗܘܝܐ ܝܠܗ ܕܓܘܗ ܛܒܐ ܝܠܗ ܕܡܥܗܕܚ ܐܗܐ.

ܘܩܐ ܨܘܪܬܐ ܕܐܗܐ ܙܢܐ ܐܝܬ ܥܘܕܪܢܐ ܚܙܝܢܝܐ ܦܫܝܛܐ، ܕܠܝܬ ܓܘ ܡܚܫܒܢܐ ܕܐܗܐ ܦܐܬܐ ܘܡܨܝܚ ܕܡܙܝܕܚ ܠܗ ܒ-SPSS ܝܢ ܒ-R: Gelman & Hill (2007، ܦܐܬܐ 556) ܟܡܦܝܣܝ ܕܨܝܪܚ "ܣܪܛܐ ܕܓܘܒܝܐ ܡܩܕܡܐ" – ܣܪܛܐ ܦܫܝܛܐ ܒܪܘܡܐ ܕܨܦܪܐ، ܝܢ، ܓܘ ܨܘܪܬܐ ܕܩܕܡ ܩܘܒܠ ܒܬܪ ܒܐܢܝ ܚܕܝܘ̈ܬܐ، ܣܪܛܐ ܡܨܠܝܢܐ y = x ܕܟܪܫܡ ܫܘܝܘܬܐ. ܡܢ ܕܣܪܛܐ ܡܨܠܝܢܐ ܥܠ ܨܘܪܬܐ ܝܠܗ، ܕܥܪܬܐ ܠܡܨܥܝܬܐ ܟܡܬܚܙܝܐ ܒܥܝܢܐ: ܐܝܢܐ ܕܪܡܐ ܗܘܐ ܓܘ "ܩܕܡ" ܒܪܘܒܐ ܝܬܝܒܐ ܝܠܗ ܬܚܘܬ ܣܪܛܐ ܡܨܠܝܢܐ، ܐܝܢܐ ܕܬܚܬܝܐ ܗܘܐ – ܒܐܬܪܗ، ܘܣܪܛܐ ܕܪܝܓܪܫܢ ܟܦܣܩ ܣܪܛܐ ܡܨܠܝܢܐ ܓܘ ܡܨܥܝܬܐ. ܘܓܘ ܐܗܘ ܣܝܩܐ – ܐܝܡܢ ܕܬܪܝܢ ܣܪ̈ܛܐ ܟܡܫܚܝ ܐܗܘ ܡܕܡ ܒܐܢܝ ܚܕܝܘ̈ܬܐ، ܟܨܝܪܚ ܨܘܪܬܐ ܡܪܒܥܬܐ ܘܒܐܗܝ ܣܒܠܬܐ ܓܘ ܬܪܝܢ ܣܪ̈ܛܐ، ܐܦܢ ܕܡܢܘ̈ܬܐ ܪ̈ܒܐ ܡܢܗ ܦܝܫܝ ܣܦܝܩ̈ܐ؛ ܘܐܝܡܢ ܕܡܫܬܚܠܦ̈ܢܐ ܦܪ̈ܝܫܐ ܝܢܐ، ܛܒܐ ܠܐ ܡܪܒܥܬܐ، ܩܐ ܕܠܐ ܡܚܘܝܚ ܒܪܡܙܐ ܫܘܝܘܬܐ ܕܠܝܬ (ܬܡܐ).

ܬܠܬܐ ܚܙ̈ܝܬܐ، ܒܐܗܐ ܛܟܣܐ. Pallant (2020، ܦܐܬܐ 156-157) ܟܡܩܪܒܐ ܕܩܪܚ ܟܠ ܨܘܪܬܐ ܕܒܕܪܐ ܒܬܠܬܐ ܕܪ̈ܓܐ ܩܝ̈ܡܐ، ܩܕܡ ܕܚܫܒܚ ܡܕܡ:

ܢܡܘܣܐ ܕܨܒܥܐ ܩܐ ܓܕܪܐ. Gravetter & Wallnau (2017، ܦܐܬܐ 489) ܟܡܩܪܒܝ ܐܘܪܚܐ ܕܫܥܪܚ r ܒܥܝܢܐ: ܟܨܝܪܚ ܚܕܪ ܢܘܩ̈ܙܐ ܓܕܪܐ (envelope) – ܣܪܛܐ ܚܒܝܫܐ ܥܝܩܐ ܡܢ ܟܠܗ ܕܐܝܬܠܗ ܟܠܗܘܢ. ܓܕܪܐ ܒܐܣܟܝܡܐ ܕܟܘܪܐ ܕ-football ܐܣܘܪܐ ܕܚܕ̈ܕܐ ܝܠܗ ܩܪܝܒܐܝܬ ܕ-.7؛ ܓܕܪܐ ܦܬܝܐ ܒܙܘܕܐ – ܐܣܘܪܐ ܩܪܝܒܐ ܒܙܘܕܐ ܠ-0؛ ܓܕܪܐ ܥܝܩܐ ܒܙܘܕܐ – ܩܪܝܒܐ ܒܙܘܕܐ ܠ-1. ܥܡ ܝܗܝ̈ܒܬܐ ܦܪ̈ܝܫܬܐ (discrete) ܐܝܟ ܣܒ̈ܠܬܐ ܕ-Likert، ܕܓܘܗܝܢ ܚܕ ܢܘܩܙܐ ܟܛܫܐ ܥܣܪ̈ܐ ܕܡܫܬܘܬܦ̈ܢܐ (ܚܙܝܡܘܢ ܠܥܠ)، ܐܗܐ ܫܘܥܪܐ ܡܛܥܝܢܐ ܝܠܗ – ܬܡܐ ܟܬܟܠܚ ܥܠ ܡܢܝܢܐ.

ܣܪܛܐ ܕܥܝܢܐ ܟܨܝܪܐ ܠܐ ܝܠܗ ܣܪܛܐ ܕܪܝܓܪܫܢ. ܐܝܡܢ ܕܟܒܥܝܚ ܡܢ ܬܠܡܝܕ̈ܐ ܕܨܝܪܝ ܒܐܝܕܐ ܣܪܛܐ ܕܪܝܓܪܫܢ ܥܠ ܥܢܢܐ ܕܢܘܩ̈ܙܐ، ܩܪܝܒܐ ܒܟܠ ܙܒܢ ܟܨܝܪܝ ܣܪܛܐ ܕܐܘܪܟܐ ܕܥܢܢܐ – ܣܪܛܐ ܕ"ܟܥܒܪ ܩܪܝܒܐ ܡܢ ܟܠܗ" ܠܟܠ ܢܘܩ̈ܙܐ (ܒܠܫܢܐ ܣܛܐܛܝܣܛܝܩܝܐ: ܣܪܛܐ ܕܡܢܬܐ ܪܫܝܬܐ، principal component). ܐܠܐ ܣܪܛܐ ܕܪܝܓܪܫܢ ܟܡܙܥܪ ܒܣ ܪܘ̈ܚܩܐ ܙܩܝ̈ܦܐ، ܘܒܟܠ ܙܒܢ ܡܡܫܚܐ ܝܠܗ ܒܙܘܕܐ: ܓܘ ܡܫܬܚܠܦ̈ܢܐ ܡܬܩ̈ܢܐ ܥܡ ܐܣܘܪܐ ܕܚܕ̈ܕܐ ܕ-.5 ܡܨܠܝܢܘܬܐ ܕܝܠܗ ܒܚܬܝܬܘܬܐ ܦܠܓܐ ܝܠܗ ܕܡܨܠܝܢܘܬܐ ܕܣܪܛܐ ܕܥܢܢܐ (Gelman, Hill & Vehtari, 2020, pp. 187-188). ܘܥܡ ܕܡܬܚܙܝܢܘܬܐ، ܐܝܠܗ ܣܪܛܐ ܬܪܝܨܐ ܩܐ ܡܢܒܝܢܘܬܐ: ܓܘ ܣܘܦܐ ܣܡܠܝܐ ܕܥܢܢܐ ܟܠ ܢܘܩ̈ܙܐ ܝܬܝ̈ܒܐ ܝܢܐ ܒܐܬܪܐ ܕܣܪܛܐ ܕܐܘܪܟܐ – ܐܗܘ ܟܡܢܒܐ ܬܚܬܝܐ ܒܝܬܝܪܘܬܐ ܩܐ ܛܝ̈ܡܐ ܬܚܬ̈ܝܐ ܕ-X ܘܪܡܐ ܒܝܬܝܪܘܬܐ ܩܐ ܪ̈ܡܐ – ܘܣܪܛܐ ܕܪܝܓܪܫܢ ܟܥܒܪ ܓܘ ܡܨܥܝܬܐ ܕ-Y ܓܘ ܟܠ ܛܝܡܐ ܕ-X. ܐܗܐ ܐܦ ܡܦܫܩܢܘܬܐ ܓܐܘܡܛܪܝܬܐ ܝܠܗ ܕܕܥܪܬܐ ܠܡܨܥܝܬܐ ܕܡܚܘܝܐ ܝܠܗ ܠܥܠ.

ܣܪܛܐ ܡܘܕܝܠ ܝܠܗ، ܘܡܘܕܝܠ ܟܡܢܒܐ. ܣܪܛܐ ܕܪܝܓܪܫܢ ܐܣܟܝܡܐ ܦܫܝܛܐ ܡܢ ܟܠܗ ܝܠܗ ܕܡܐ ܕ-Field (2024، ܦܣܩܐ 9.2) ܟܩܪܐ "ܡܘܕܝܠ ܣܪܛܢܝܐ": Ŷ = b₀ + b₁X. ܬܪܝܢ ܦܪܡܝ̈ܛܪܐ ܒܚܬܝܬܘܬܐ ܬܪܝܢ ܣܕܪ̈ܐ ܐܚܪ̈ܝܐ ܝܢܐ ܓܘ ܠܘܚܐ ܕܡܚܫܒܢܐ ܟܡܦܩ – ܡܢܝܢܐ ܩܝܡܐ (intercept) b₀ (a ܓܘ ܠܘܚܐ): ܛܝܡܐ ܡܣܟܝܐ ܕ-Y ܐܝܡܢ ܕ-X = 0؛ ܘܡܨܠܝܢܘܬܐ b₁ (b ܓܘ ܠܘܚܐ): ܫܘܚܠܦܐ ܡܣܟܝܐ ܓܘ Y ܩܐ ܟܠ ܣܘܠܩܐ ܕܚܕ ܚܕܝܘܬܐ ܓܘ X. ܟܘܒܥܐ ܥܠ Y ܟܡܥܗܕ ܕܐܗܐ ܛܝܡܐ ܡܢܒܝܐ ܝܠܗ (predicted value)، ܠܐ ܛܝܡܐ ܕܚܙܝܐ ܝܠܗ: ܟܣܝܡܚ ܛܝܡܐ ܕ-X ܘܟܫܩܠܚ Y ܕܡܘܕܝܠ ܟܡܣܟܐ. ܓܘ ܝܗܝ̈ܒܬܐ ܕܡܬܠܐ، ܡܬܠܐ، ܩܐ ܡܦܢܝܢܐ ܕܪܡܐ ܕ-self-efficacy ܕܝܠܗ 4.0 ܝܠܗ ܡܘܕܝܠ ܟܡܣܟܐ ܬܘܟܠܢܐ ܕ-1.159 + 0.687 × 4.0 ≈ 3.91. ܐܗܐ ܡܢܒܝܢܘܬܐ ܠܐ ܝܠܗ ܚܬܝܬܬܐ ܩܐ ܟܠ ܡܫܬܘܬܦܢܐ – ܦܘܪܫܢܐ ܒܝܢܝ ܛܝܡܐ ܕܚܙܝܐ ܝܠܗ ܘܛܝܡܐ ܡܢܒܝܐ ܝܠܗ ܫܪܟܐ (residual)، ܘܣܪܛܐ ܓܒܝܐ ܝܠܗ ܕܓܘܡܪܐ ܕܫܪ̈ܟܐ ܡܪ̈ܒܥܐ ܗܘܐ ܙܥܘܪܐ ܡܢ ܟܠܗ ܕܡܨܐ ܕܗܘܐ (ܐܘܪܚܐ ܕܡܪ̈ܒܥܐ ܒܨܝܪ̈ܐ ܡܢ ܟܠܗ، least squares، Field، 2024، ܦܣܩܐ 9.2.4). ܬܠܬܐ ܫܪ̈ܪܐ ܦܫܝ̈ܛܐ ܥܠ ܐܗܐ ܣܪܛܐ ܟܡܥܕܪܝ ܕܩܪܚ ܟܠ ܨܘܪܬܐ (Gravetter & Wallnau, 2017, Section 16.1): ܒܟܠ ܙܒܢ ܟܥܒܪ ܓܘ ܢܘܩܙܐ (ܡܨܥܝܬܐ ܕ-X، ܡܨܥܝܬܐ ܕ-Y)؛ ܪܘܫܡܐ ܕܡܨܠܝܢܘܬܐ ܕܝܠܗ ܪܘܫܡܐ ܝܠܗ ܕܐܣܘܪܐ ܕܚܕ̈ܕܐ؛ ܘܐܝܡܢ ܕܐܣܘܪܐ ܕܚܕ̈ܕܐ ܨܦܪܐ ܝܠܗ، ܣܪܛܐ ܦܫܝܛܐ ܝܠܗ ܒܪܘܡܐ ܕܡܨܥܝܬܐ ܕ-Y – ܒܚܬܝܬܘܬܐ ܡܘܕܝܠ ܕ"ܠܝܬ ܐܣܘܪܐ" ܕܓܘ ܦܣܩܐ ܕܒܬܪܗ.

ܡܢ ܐܝܟܐ ܟܐܬܐ R²، ܘܡܘܕܝ ܝܠܗ ܒܘܚܪܢܐ ܕܒܬܪ p. ܩܐ ܕܝܕܥܚ ܐܢ ܡܘܕܝܠ ܛܒܐ ܝܠܗ، ܟܦܚܡܚ ܠܗ ܥܡ ܡܘܕܝܠ ܦܫܝܛܐ ܡܢ ܟܠܗ ܕܐܝܬ – "ܠܝܬ ܐܣܘܪܐ": ܕܡܢܒܚ ܩܐ ܟܠ ܡܫܬܘܬܦܢܐ ܡܨܥܝܬܐ ܕ-Y، ܡܐ ܕܗܘܐ X. ܓܘܡܪܐ ܕܪܘ̈ܚܩܐ ܡܪ̈ܒܥܐ ܕܚܙ̈ܝܬܐ ܡܢ ܡܨܥܝܬܐ (SS_T) ܟܡܝܘܬܐ ܝܠܗ ܕܫܘܚܠܦܐ ܕܣܢܝܩ ܝܠܗ ܠܡܦܫܩܬܐ؛ ܓܘܡܪܐ ܕܪܘ̈ܚܩܐ ܡܪ̈ܒܥܐ ܡܢ ܣܪܛܐ ܕܪܝܓܪܫܢ (SS_R) ܡܐ ܝܠܗ ܕܦܝܫܐ ܠܐ ܡܦܫܩܐ ܒܬܪ ܕܦܐܝܠܢ ܣܪܛܐ؛ ܘܦܘܪܫܢܐ ܒܝܢܝ ܕܝܠܗܘܢ (SS_M) ܡܛܝܒܘܬܐ ܝܠܗ ܕܣܪܛܐ ܡܝܬܐ. R² ܒܣ ܦܘܚܡܐ ܝܠܗ SS_M / SS_T – ܡܢܬܐ ܕܫܘܚܠܦܐ ܕܡܘܕܝܠ ܟܡܦܫܩ ܡܢ ܓܘ ܡܐ ܕܐܝܬ ܗܘܐ ܠܡܦܫܩܬܐ (Field, 2024, Section 9.2.4). ܥܠ ܐܢܝ ܓܘܡܪ̈ܐ ܕܡܪ̈ܒܥܐ ܒܢܝܐ ܝܠܗ ܒܘܚܪܢܐ F، ܕܟܫܐܠ ܐܢ ܡܘܕܝܠ ܛܒܐ ܝܠܗ ܡܢ ܡܨܥܝܬܐ ܒܐܘܪܚܐ ܪܫܝܡܬܐ؛ ܘܥܠ ܡܨܠܝܢܘܬܐ ܒܢܝܐ ܝܠܗ ܒܘܚܪܢܐ t ܥܡ n − 2 ܕܪ̈ܓܐ ܕܚܐܪܘܬܐ، ܕܟܫܐܠ ܐܢ b₁ ܦܪܝܫܐ ܝܠܗ ܡܢ ܨܦܪܐ (ܦܣܩܐ 9.2.5). ܐܝܡܢ ܕܐܝܬ ܒܣ ܚܕ ܡܢܒܝܢܐ، ܐܢܝ ܬܪܝܢ ܒܘܚܪ̈ܢܐ ܘܒܘܚܪܢܐ ܕܪܫܝܡܘܬܐ ܕܐܣܘܪܐ ܕܚܕ̈ܕܐ ܕ-Pearson ܚܕ ܒܘܚܪܢܐ ܝܢܐ ܒܬܠܬܐ ܨܘܪ̈ܬܐ: F = t²، ܘܛܝܡܐ p ܫܘܝܐ ܝܠܗ ܓܘ ܬܠܬܝܗܘܢ. ܡܛܠ ܗܕܐ p ܕܓܘ ܠܘܚܐ ܕܡܚܫܒܢܐ ܒܚܕ ܙܒܢܐ ܪܫܝܡܘܬܐ ܝܠܗ ܕܐܣܘܪܐ ܕܚܕ̈ܕܐ، ܕܡܨܠܝܢܘܬܐ ܘܕܡܘܕܝܠ ܟܠܗ.

ܫܪ̈ܛܐ، ܛܝ̈ܡܐ ܢܘܟܪ̈ܝܐ ܘܚܙ̈ܝܬܐ ܡܥܒܕ̈ܢܝܬܐ

ܫܪ̈ܛܐ – ܠܦܘܬ ܛܟܣܐ ܕܚܫܝܚܘܬܐ ܕܝܠܗܘܢ

ܬܪܝܢ ܡܫܬܚܠܦ̈ܢܐ ܟܡܝ̈ܝܐ ܝܢܐ (ܡܬܡܫܚܢܐ ܝܢ ܕܛܟܣܐ)؛ ܡܫܬܚܠܦܢܐ ܕܓܢ̈ܣܐ (ܡܬܠܐ ܐܬܪܐ ܝܢ ܬܘܕܝܬܐ) ܠܐ ܦܐܝܐ ܝܠܗ ܩܐ ܨܘܪܬܐ ܕܒܕܪܐ – ܬܡܐ ܦܐܝܐ ܝܠܗ boxplot ܝܢ ܦܘܫܩܐ ܕܫܘܚܠܦܐ. ܒܐܬܪ ܗܕܐ، Field (2024، ܦܣܩܐ 9.4.1) ܟܬܩܢ ܫܪ̈ܛܐ ܕܡܘܕܝܠ ܣܪܛܢܝܐ ܠܦܘܬ ܚܫܝܚܘܬܐ ܕܝܠܗܘܢ، ܒܬܪ Field & Wilcox (2017) ܘ-Gelman, Hill & Vehtari (2020، ܦܣܩܐ 11.1). ܓܘ ܐܚܪ̈ܝܐ ܪܫܝܡܬܐ ܟܦܬܚܐ ܒܬܪܝܢ ܫܪ̈ܛܐ ܕܠܐ ܝܢܐ ܣܛܐܛܝܣܛܝܩ̈ܝܐ ܡܕܡ، ܘܐܢܝ ܚܫܝ̈ܚܐ ܝܢܐ ܡܢ ܟܠܗ: ܬܪܝܨܘܬܐ – ܕܝܗܝ̈ܒܬܐ ܟܦܢܝ ܠܫܘܐܠܐ ܕܒܘܨܝܐ: ܡܫܬܚܠܦܢܐ ܕܦܐܪܐ ܒܫܪܪܐ ܟܡܫܚ ܬܚܘܝܬܐ (ܡܢܝ̈ܢܐ ܕܒܘܚܪܢܐ ܠܐ ܝܢܐ "ܗܘܢܐ")، ܡܘܕܝܠ ܐܝܬܠܗ ܡܢܒ̈ܝܢܐ ܚܫܝ̈ܚܐ، ܘܡܨܐ ܕܡܬܦܫܛ ܠܗܘ̈ܝܐ ܕܥܠܝܗܘܢ ܟܒܥܝܚ ܕܡܡܠܠܚ؛ ܘܕܡܝܘܬܐ (representativeness) – ܕܕܘܡܝܐ ܟܡܚܘܐ ܦܘܠܓܐ ܕ-Y ܐܝܡܢ ܕܝܗܝܒܐ ܝܠܗ X. ܦܘܪܫܐ ܥܒܕܢܝܐ ܕܟܐܬܐ ܡܢ ܐܗܐ ܛܝܡܐ ܕܕܗܒܐ ܐܝܬܠܗ: ܓܘܒܝܐ ܕܕܘܡܝܐ ܠܦܘܬ X (ܡܬܠܐ ܒܝܬܝܪܘܬܐ ܢܫ̈ܐ ܝܢ ܒܝܬܝܪܘܬܐ ܐܪ̈ܝܟܐ ܓܘ ܕܘܡܝܐ ܥܠ ܐܘܪܟܐ ܘܡܦܩܬܐ) ܠܐ ܟܡܙܝܩ ܠܪܝܓܪܫܢ؛ ܓܘܒܝܐ ܠܦܘܬ Y (ܒܝܬܝܪܘܬܐ ܥܬܝܪ̈ܐ) ܟܡܙܝܩ (ܦܐܬܐ 153-154). ܒܣ ܒܬܪܝܗܝܢ ܟܐܬܝ ܐܪܒܥܐ ܫܪ̈ܛܐ ܣܛܐܛܝܣܛܝܩ̈ܝܐ، ܒܐܗܐ ܛܟܣܐ:

ܢܘܩܙܐ ܚܫܝܚܐ ܕܒܬܪ ܐܗܐ ܛܟܣܐ: ܬܒܪܐ ܕܫܪ̈ܛܐ ܟܡܙܝܩ ܒܪܘܒܐ ܠܦܘܫܛܐ ܕܡܫܟܚ̈ܢܘܬܐ (generalization) – ܠܒܘܚܪ̈ܢܐ ܕܪܫܝܡܘܬܐ ܘܠܬܚܘ̈ܡܐ ܕܬܘܟܠܢܐ – ܘܠܐ ܠܫܘܥܪ̈ܐ ܕܣܪܛܐ. ܡܨܠܝܢܘܬܐ ܘܡܢܝܢܐ ܩܝܡܐ ܕܡܚܫܒܢܐ ܟܡܚܘܝܐ ܬܪܝ̈ܨܐ ܝܢܐ ܩܐ ܝܗܝ̈ܒܬܐ ܕܩܕܡܘܟܘܢ ܐܦ ܐܝܡܢ ܕܫܪ̈ܛܐ ܠܐ ܝܢܐ ܡܫܡܠܝ̈ܐ؛ ܡܐ ܕܟܗܘܐ ܡܦܘܠܓܐ ܝܠܗ ܫܘܠܡܐ ܡܢ ܕܘܡܝܐ ܥܠ ܟܢܫܐ ܟܠܢܝܐ (Field, 2024, Section 9.4). ܒܚܬܝܬܘܬܐ ܒܙܘܕܐ (Field & Wilcox, 2017, Section Critical assumptions): ܐܝܡܢ ܕܫܘܚܠܦܐ ܕܫܪ̈ܟܐ ܠܐ ܝܠܗ ܫܘܝܐ ܝܢ ܚܙ̈ܝܬܐ ܬܠܝ̈ܐ ܝܢܐ ܚܕ ܒܚܕ، ܫܘܥܪ̈ܐ ܕ-a ܘ-b ܟܦܝܫܝ ܕܠܐ ܡܣܒ ܒܐܦ̈ܐ (unbiased) – ܐܠܐ ܡܬܘܪܓܡܐ ܕܛܥܝܘܬܐ ܬܩܝܢܬܐ ܕܝܠܗܘܢ ܟܣܝܡ ܫܘܚܠܦܐ ܩܝܡܐ، ܘܡܛܠ ܗܕܐ ܛܥܝ̈ܘܬܐ ܬܩܝܢ̈ܬܐ ܥܡ ܡܣܒ ܒܐܦ̈ܐ ܝܢܐ، ܘܥܡܗܝܢ ܛܝ̈ܡܐ p ܘܬܚܘ̈ܡܐ ܕܬܘܟܠܢܐ. ܣܪܛܐ ܬܪܝܨܐ ܝܠܗ؛ ܡܫܘܚܬܐ ܕܓܘܗ ܡܨܝܚ ܕܬܟܠܚ ܥܠܝܗ – ܠܐ. ܐܗܟܐ ܐܦ Cohen (1988، ܦܐܬܐ 75): ܐܝܟ ܡܚܘܝܢܐ ܕܬܚܘܝܬܐ ܕܐܣܘܪܐ ܣܪܛܢܝܐ، r ܠܐ ܣܢܝܩ ܝܠܗ ܠܚܕ ܫܪܛܐ – ܠܐ ܥܠ ܦܘܠܓܐ ܕܡܫܬܚܠܦ̈ܢܐ ܘܠܐ ܥܠ ܫܘܝܘܬܐ ܕܫܘܚܠܦܐ؛ ܫܪ̈ܛܐ ܟܥܐܠܝ ܒܣ ܥܡ ܒܘܚܪܢܐ ܕܪܫܝܡܘܬܐ، ܘܐܦ ܗܝܓ ܬܒܪܐ ܡܡܫܚܐ ܕܝܠܗܘܢ، ܒܝܚܝܕܝܘܬܐ ܓܘ ܕܘܡܝܐ ܪܒܐ، ܠܐ ܟܡܙܝܩ ܒܚܦܝܛܘܬܐ ܠܬܪܝܨܘܬܐ ܕܒܘܚܪܢܐ. ܬܪܬܝܢ ܣܢܝ̈ܩܘܝܬܐ ܥܒܕ̈ܢܝܬܐ ܐܚܪ̈ܢܝܬܐ: ܠܡܫܬܚܠܦ̈ܢܐ ܣܢܝܩ ܝܠܗ ܕܐܝܬ ܫܘܚܠܦܐ – ܡܫܬܚܠܦܢܐ ܕܟܠ ܛܝ̈ܡܐ ܕܝܠܗ ܫܘ̈ܝܐ ܝܢܐ ܠܐ ܡܨܐ ܕܡܢܒܐ ܡܕܡ (ܡܚܫܒܢܐ ܟܡܚܘܝܐ ܓܘ ܗܘܝܐ ܕܐܗܐ ܙܢܐ ܡܘܕܥܢܘܬܐ ܕܛܥܝܘܬܐ)؛ ܘܡܫܬܚܠܦܢܐ ܕܦܐܪܐ ܣܢܝܩ ܝܠܗ ܕܗܘܐ ܡܬܡܫܚܢܐ ܘܠܐ "ܟܪܝܐ" – ܣܒܠܬܐ ܕ-1-5 ܕܓܘܗ ܟܠ ܦܘܢ̈ܝܐ ܟܢܝ̈ܫܐ ܝܢܐ ܓܘ 4 ܘ-5 ܟܟܪܝܐ ܡܐ ܕܡܨܝܚ ܕܡܫܟܚܚ.

ܘܐܝܟܢܐ ܟܒܚܪܚ. ܣܪܛܢܝܘܬܐ ܟܒܚܪܚ ܠܗ ܓܘ ܨܘܪܬܐ ܕܒܕܪܐ ܒܓܢܗ – ܐܗܐ ܝܠܗ ܟܠܗ ܢܝܫܐ ܕܐܗܐ ܦܐܬܐ. ܬܪܝܢ ܫܪ̈ܛܐ ܥܠ ܫܪ̈ܟܐ ܟܒܚܪܚ ܠܗܘܢ ܓܘ ܨܘܪܬܐ ܕܫܪ̈ܟܐ (residual plot)، ܕܟܡܬܛܝܐ ܡܢ ܐܘܪܚܐ ܕܪܝܓܪܫܢ ܘܠܐ ܡܢ ܨܘܪܬܐ ܕܒܕܪܐ: ܥܠ ܣܪܛܐ X ܛܝ̈ܡܐ ܡܢܒ̈ܝܐ، ܥܠ ܣܪܛܐ Y ܫܪ̈ܟܐ، ܘܟܒܥܝܚ ܕܚܙܝܚ ܥܢܢܐ ܫܘܝܐ ܥܠ ܟܠܗ ܐܘܪܟܐ ܕܦܬܝܘܬܐ – ܕܠܐ funnel (ܬܒܪܐ ܕܫܘܝܘܬܐ ܕܫܘܚܠܦܐ) ܘܕܠܐ ܩܫܬܐ (ܫܪܟܐ ܕܐܣܘܪܐ ܠܐ ܣܪܛܢܝܐ). ܒ-SPSS: ܓܘ ܟܘܬܐ ܕܪܝܓܪܫܢ، ܦܬܝܪܐ Plots، *ZPRED ܠ-X ܘ-*ZRESID ܠ-Y. ܘܢܘܪܡܠܝܘܬܐ ܕܫܪ̈ܟܐ ܛܒܐ ܝܠܗ ܕܒܚܪܚ ܠܗ ܒܥܝܢܐ – ܓܘ histogram ܝܢ، ܛܒ ܒܙܘܕܐ، ܓܘ ܨܘܪܬܐ Q-Q (ܬܡܐ، ܒܪܘܫܡܐ Normal probability plot): ܟܡܐ ܕܢܘܩ̈ܙܐ ܩܪܝ̈ܒܐ ܝܢܐ ܠܣܪܛܐ ܡܨܠܝܢܐ، ܦܘܠܓܐ ܩܪܝܒܐ ܝܠܗ ܒܙܘܕܐ ܠܢܘܪܡܠܝܐ. ܒܘܚܪ̈ܢܐ ܕܢܘܪܡܠܝܘܬܐ ܪ̈ܫܡܝܐ (Kolmogorov-Smirnov، Shapiro-Wilk) ܬܠܝ̈ܐ ܝܢܐ ܒܪܒܘܬܐ ܕܕܘܡܝܐ ܒܙܘܕܐ ܡܢ ܐܣܟܝܡܐ ܕܦܘܠܓܐ: ܓܘ ܕܘܡܝܐ ܙܥܘܪܐ ܟܪ̈ܝܗܐ ܝܢܐ، ܘܓܘ ܕܘܡܝܐ ܪܒܐ ܩܪܝܒܐ ܒܟܠ ܙܒܢ ܪܫܝ̈ܡܐ ܝܢܐ، ܐܦ ܥܠ ܣܛܝܘܬܐ ܙܥܘܪܬܐ – Pallant (2020، ܦܐܬܐ 138-139) ܟܡܥܝܪܐ ܕܐܗܐ ܟܡܬܚܙܐ ܣܓܝ ܓܘ ܕܘ̈ܡܝܐ ܪ̈ܒܐ ܘܟܡܫܕܪܐ، ܒܬܪ Tabachnick & Fidell، ܠ-histogram ܘܠܨܘܪܬܐ Q-Q ܒܕܘܟܬܝܗܘܢ. ܘGelman, Hill & Vehtari (2020، ܦܐܬܐ 155) ܟܐܙܠܝ ܦܣܥܬܐ ܒܙܘܕܐ: ܩܐ ܫܘܥܪܐ ܕܣܪܛܐ – ܠܐ ܐܝܟ ܡܢܒܝܢܘܬܐ ܕܚܙܝܬܐ ܝܚܝܕܝܬܐ – ܢܘܪܡܠܝܘܬܐ ܕܫܪ̈ܟܐ "ܩܪܝܒܐ ܠܐ ܝܠܗ ܚܫܝܚܬܐ ܡܕܡ"، ܘܡܛܠ ܗܕܐ ܐܢܝ ܡܕܡ ܠܐ ܟܡܦܝܣܝ ܕܒܚܪܚ ܠܗ؛ ܠܝܬ ܒܝܫܘܬܐ ܓܘ ܨܘܪܬܐ Q-Q، ܐܠܐ ܛܒܐ ܝܠܗ ܕܡܦܢܚ ܚܘܫܒܐ ܠܬܪܝܨܘܬܐ، ܠܕܡܝܘܬܐ ܘܠܣܪܛܢܝܘܬܐ.

ܨܘܪܬܐ ܕܫܪ̈ܟܐ ܒܓܢܗ ܪܥܝܢܐ ܝܠܗ ܕ-Anscombe (1973، ܦܐܬܐ 18)، ܘܟܡܦܫܩ ܠܡܢܐ ܨܘܪܬܐ ܕܒܕܪܐ ܠܐ ܝܠܗ ܣܦܩܐ: ܒܚܙܝܬܐ ܨܘܪܬܐ ܕܫܪ̈ܟܐ ܠܐ ܡܨܝܐ ܕܡܚܘܝܐ ܡܕܡ ܕܠܝܬ ܓܘ ܨܘܪܬܐ ܩܕܡܝܬܐ، ܐܠܐ ܐܝܡܢ ܕܫܩܠܠܢ ܣܪܛܐ، ܣܪܛܐ Y ܟܡܬܡܬܚ ܘܡܐ ܕܦܝܫܐ ܓܠܝܐܝܬ ܟܡܬܚܙܝܐ. ܐܪܒܥܐ ܡܕ̈ܡܐ ܕܒܨܚ ܥܠܝܗܘܢ ܓܘܗ: ܟܡܐ ܫܪ̈ܟܐ ܪ̈ܒܐ ܒܣܓܝ ܡܢ ܟܠ ܐܚܪ̈ܢܐ (ܛܝ̈ܡܐ ܢܘܟܪ̈ܝܐ)؛ ܫܪ̈ܟܐ ܕܟܡܬܬܩܢܝ ܒܣܪܛܐ ܟܦܝܦܐ (ܐܣܘܪܐ ܠܐ ܣܪܛܢܝܐ)؛ ܒܕܪܐ ܕܟܪܒܐ ܩܠܝܠ ܩܠܝܠ ܥܡ ܛܝ̈ܡܐ ܡܢܒ̈ܝܐ (ܫܘܚܠܦܐ ܠܐ ܫܘܝܐ)؛ ܘܦܘܠܓܐ ܡܨܠܝܐ ܕܫܪ̈ܟܐ. ܬܠܬܐ ܐܚܪ̈ܝܐ، ܐܢ ܐܝܬ ܓܕܐ، ܟܓܢܙܝ ܚܕܐ ܒܫܘܢܝܐ (transformation) ܕ-Y – ܡܬܠܐ ܠܘܓܪܝܬܡ – ܘ"ܣܪܛܐ ܟܦܝܦܐ" ܟܡܬܫܪܐ ܐܦ ܒܫܘܢܝܐ ܕ-X ܝܢ ܒܡܙܝܕܬܐ ܕ-term ܡܪܒܥܐ. ܘܡܨܝܚ، ܒܫܪܪܐ، ܕܒܚܪܚ ܟܠ ܚܕ ܡܢܝܗܘܢ ܒܒܘܚܪܢܐ ܪܫܡܝܐ، ܐܠܐ ܨܘܪܬܐ "ܟܡܚܘܝܐ ܣܓܝ ܕܝܠܝ̈ܬܐ ܒܥܓܠܘܬܐ ܘܒܚܝܘܬܐ، ܘܒܘܚܪ̈ܢܐ ܪ̈ܫܡܝܐ ܒܙܒ̈ܢܐ ܣܓܝ̈ܐܐ ܟܡܬܚܙܝ ܝܬܝܪ̈ܐ" (ܬܡܐ).

ܘܡܘܕܝ ܠܐ ܨܝܪܚ. ܒܬܪ ܪܫܝܡܬܐ ܕܐܗܐ ܙܢܐ ܕܒܘܚܪ̈ܢܐ، ܛܒܐ ܝܠܗ ܕܡܥܗܕܚ "ܡܠܟܐ ܩܠܝܠܐ" ܕ-Gelman & Hill (2007، ܦܐܬܐ 548): "ܐܢ ܒܫܪܪܐ ܒܥܝܬܘܢ ܕܡܦܩܝܬܘܢ ܟܠ ܨܘܪ̈ܬܐ Q-Q، ܨܘܪ̈ܬܐ ܕܡܥܒܕܢܘܬܐ ܘܟܠ ܡܕ̈ܡܐ ܐܚܪ̈ܢܐ ܕܓܪܒܐ ܣܛܐܛܝܣܛܝܩܝܐ ܟܡܦܩ؟ ܡܘܕܝ ܒܕ ܥܒܕܝܬܘܢ ܥܡ ܟܠ ܐܗܐ؟" – ܘܢܡܘܣܐ ܕܟܡܩܪܒܝ ܒܕܘܟܬܗ: ܟܠ ܨܘܪܬܐ ܕܟܡܚܘܝܚ – ܗܘܘܢ ܡܛܝܒ̈ܐ ܕܡܦܫܩܝܬܘܢ. ܨܘܪܬܐ ܕܒܕܪܐ ܥܡ ܣܪܛܐ ܕܪܝܓܪܫܢ ܘܨܘܪܬܐ ܕܫܪ̈ܟܐ ܬܪܝܢ ܝܢܐ ܕܩܪܝܒܐ ܒܟܠ ܙܒܢ ܟܩܝܡܝ ܓܘ ܐܗܐ ܒܘܚܪܢܐ؛ ܐܚܪ̈ܢܐ ܟܡܙܝܕܚ ܐܝܡܢ ܕܐܝܬܠܗܘܢ ܡܐ ܕܐܡܪܝ.

ܛܝܡܐ ܢܘܟܪܝܐ ܘܚܙܝܬܐ ܡܥܒܕܢܝܬܐ – ܠܐ ܐܗܘ ܡܕܡ

ܡܚܫܒܢܐ ܕܐܗܐ ܦܐܬܐ ܟܪܫܡ ܓܘ ܨܘܪܬܐ ܘܟܟܢܫ ܓܘ ܠܘܚܐ "ܚܙ̈ܝܬܐ ܩܐ ܒܘܚܪܢܐ" ܢܘܩ̈ܙܐ ܕܥܒܪܝ ܡܢ ܬܚܘ̈ܡܐ ܕܬܠܬܐ ܡܚܘ̈ܝܢܐ ܕܡܦܫܩ̈ܐ ܝܢܐ ܐܟܐ – ܫܪܟܐ ܡܬܩܢܐ، ܡܪܝܡܢܘܬܐ ܘܪܘܚܩܐ ܕ-Cook – ܥܡ ܙܘܗܪܐ ܩܝܡܐ: ܥܒܪܬܐ ܥܠܬܐ ܝܠܗ ܩܐ ܒܘܚܪܢܐ، ܠܐ ܩܐ ܫܩܠܬܐ.

ܡܕܡ ܬܪܝܢܐ ܕܨܘܪܬܐ ܕܒܕܪܐ ܟܓܠܝܐ، ܒܬܪ ܐܣܟܝܡܐ ܕܐܣܘܪܐ، ܢܘܩ̈ܙܐ ܝܢܐ ܕܝܬܝ̈ܒܐ ܝܢܐ ܒܠܚܘܕܝܗܘܢ – ܪܚܝܩ̈ܐ ܡܢ ܥܢܢܐ، ܒܣܘܦܐ ܕܚܕ ܡܢ ܣܪ̈ܛܐ ܝܢ ܓܘ ܬܪܘܝܗܝ. ܢܘܩܙܐ ܕܐܗܐ ܙܢܐ ܡܨܐ ܕܗܘܐ ܡܫܬܘܬܦܢܐ ܝܚܝܕܝܐ ܒܫܪܪܐ، ܐܠܐ ܒܙܒ̈ܢܐ ܣܓܝ̈ܐܐ ܒܣ ܡܢܝܢܐ ܝܠܗ ܕܟܬܝܒܐ ܝܠܗ ܠܐ ܬܪܝܨܐܝܬ، ܘܡܛܠ ܗܕܐ ܦܣܥܬܐ ܩܕܡܝܬܐ ܒܟܠ ܙܒܢ ܕܥܪܬܐ ܝܠܗ ܠܦܐܝܠ ܘܒܘܚܪܢܐ ܕܛܝܡܐ. ܐܢ ܫܪܝܪܐ ܝܠܗ، Anscombe (1973، ܦܐܬܐ 17-18) ܟܡܦܝܣ ܕܡܢܚܚ ܚܙܝܬܐ ܒܓܢܒܐ ܩܐ ܚܙܝܬܐ ܦܪܝܫܬܐ ܘܡܦܐܚ ܣܪܛܐ ܠܝܗܝ̈ܒܬܐ ܐܚܪ̈ܢܝܬܐ – ܘܟܡܙܝܕ ܕܐܗܝ ܚܙܝܬܐ "ܡܨܐ ܕܗܘܝܐ ܒܣܓܝ ܡܦܪܥܢܝܬܐ". ܠܡܢܐ ܐܗܐ ܚܫܝܚܐ ܝܠܗ ܒܝܚܝܕܝܘܬܐ ܐܟܐ: ܐܣܘܪܐ ܕܚܕ̈ܕܐ ܕ-Pearson ܒܣܓܝ ܪܓܝܫܐ ܝܠܗ ܠܚܕ ܢܘܩܙܐ. Gravetter & Wallnau (2017، ܦܐܬܐ 499) ܟܡܚܘܝܝ ܐܗܐ ܒܚܡܫܐ ܢܘܩ̈ܙܐ ܕܐܣܘܪܐ ܕܚܕ̈ܕܐ ܒܝܢܝ ܕܝܠܗܘܢ ܩܪܝܒܐ ܨܦܪܐ ܝܠܗ (r = −.08)؛ ܡܙܝܕܬܐ ܕܚܕ ܢܘܩܙܐ ܕܣܘܦܐ ܟܡܫܘܪ ܠܗ ܠ-r = .85 – "ܐܣܘܪܐ ܚܝܠܬܢܐ" ܕܟܠܗ ܟܣܡܟ ܥܠ ܚܕ ܡܫܬܘܬܦܢܐ. ܐܝܢܐ ܕܟܩܪܐ ܒܣ ܡܢܝܢܐ ܠܥܠܡ ܠܐ ܒܕ ܝܕܥ ܐܗܐ. Field (2024، ܦܣܩܐ 9.3) ܟܡܙܝܕ ܦܘܪܫܐ ܕܛܒܐ ܝܠܗ ܕܩܒܠܚ: ܛܝܡܐ ܢܘܟܪܝܐ ܚܙܝܬܐ ܝܠܗ ܕܡܘܕܝܠ ܟܡܢܒܐ ܠܗ ܒܝܫ – ܫܪܟܐ ܕܝܠܗ ܪܒܐ ܝܠܗ؛ ܚܙܝܬܐ ܡܥܒܕܢܝܬܐ ܚܙܝܬܐ ܝܠܗ ܕܕܠܐ ܕܝܠܗ ܣܪܛܐ ܒܕ ܗܘܐ ܡܬܚܙܐ ܐܚܪܢܐ. ܐܢܝ ܬܪܝܢ ܡܕ̈ܡܐ ܦܪ̈ܝܫܐ ܝܢܐ، ܘܚܙܝܬܐ ܡܨܝܐ ܕܗܘܝܐ ܚܕ ܕܠܐ ܐܚܪܢܐ.

ܡܬܠܐ ܕ-Field (2024، Jane Superbrain 9.1) ܛܒ ܟܡܚܘܝܐ ܐܗܐ: ܓܘ ܬܡܢܝܐ ܡܢܘ̈ܬܐ ܕܡܕܝܢܬܐ ܕܠܘܢܕܘܢ ܡܫܝܚ̈ܐ ܝܢܐ ܡܢܝܢܐ ܕܒܝ̈ܬܐ ܕܫܬܝܐ (pubs) ܘܡܢܝܢܐ ܕܡܘ̈ܬܐ. ܓܘ ܫܒܥܐ ܡܢܝܗܝܢ ܐܣܘܪܐ ܣܪܛܢܝܐ ܓܡܝܪܐ ܝܠܗ؛ ܬܡܝܢܝܬܐ – "City" ܕܠܘܢܕܘܢ، ܚܕ ܡܝܠ ܡܪܒܥܐ ܥܡ ܩܠܝܠ ܥܡܘܪ̈ܐ ܘܣܓܝ ܒܝ̈ܬܐ ܕܫܬܝܐ ܩܐ ܐܢܝ ܕܟܐܬܝ ܠܦܘܠܚܢܐ – ܝܬܝܒܬܐ ܝܠܗ ܪܚܝܩܐ ܡܢ ܟܠܗܝܢ. ܘܥܡ ܗܕܐ ܫܪܟܐ ܕܝܠܗ̇ ܩܪܝܒܐ ܙܥܘܪܐ ܡܢ ܟܠܗ ܝܠܗ، ܡܛܠ ܕܐܝܠܗ̇ "ܟܓܪܫܐ" ܣܪܛܐ ܠܦܐܬܗ̇ ܗܕܟܐ ܕܣܪܛܐ ܟܥܒܪ ܩܪܝܒܐ ܡܢܗ̇. ܠܦܘܬ ܫܪܟܐ ܠܐ ܝܠܗ̇ ܢܘܟܪܝܬܐ؛ ܠܦܘܬ ܡܚܘ̈ܝܢܐ ܕܡܥܒܕܢܘܬܐ ܟܫܚܠܦܐ ܣܪܛܐ ܓܡܝܪܐܝܬ. ܫܘܠܡܐ: ܓܘ ܨܘܪܬܐ ܕܒܕܪܐ، ܚܕ ܢܘܩܙܐ ܪܚܝܩܐ ܒܣܘܦܐ ܕܣܪܛܐ X ܕܣܘܟܢܐ ܝܠܗ ܒܙܘܕܐ ܡܢ ܢܘܩܙܐ ܕܪܚܝܩܐ ܝܠܗ ܡܢ ܣܪܛܐ ܓܘ ܡܨܥܬܐ ܕܦܬܝܘܬܐ.

ܫܬܐ ܐܣܟܝ̈ܡܐ ܕܛܒܐ ܝܠܗ ܕܝܕܥܚ ܠܗܘܢ. ܟܬܒܐ ܕܡܢܗ ܦܠܛܠܗܘܢ ܒܝܫܐ ܕܡܚܘ̈ܝܢܐ ܕܡܥܒܕܢܘܬܐ ܚܕ̈ܬܐ ܟܦܬܚ ܛܒܐ ܒܨܘܪܬܐ ܕܒܕܪܐ: Belsley, Kuh & Welsch (1980، ܦܐܬܐ 8-9) ܟܡܚܘܝܝ ܫܬܐ ܐܣܟܝ̈ܡܐ ܦܫܝ̈ܛܐ ܕ"ܢܘܩܙܐ ܢܘܟܪܝܐ"، ܘܐܢܝ ܨܘܪܬܐ ܕܐܬܪܐ ܛܒܬܐ ܝܢܐ ܩܐ ܡܐ ܕܡܨܐ ܕܛܫܐ ܓܘ ܥܢܢܐ. ܓܘ ܨܘܪܬܐ ܕܬܚܬ ܣܪܛܐ ܡܠܝܐ ܣܪܛܐ ܕܪܝܓܪܫܢ ܝܠܗ ܥܠ ܟܠ ܢܘܩ̈ܙܐ، ܘܣܪܛܐ ܦܣܝܩܐ – ܣܪܛܐ ܕܒܕ ܡܬܛܝܐ ܗܘܐ ܕܠܐ ܢܘܩ̈ܙܐ ܪܫܝ̈ܡܐ:

(ܐ) ܒܕܪܐ ܫܘܝܐ – ܗܘܝܐ ܕܟܒܥܝܚ؛ ܐܢ ܒܕܪܐ ܕ-X ܙܥܘܪܐ ܝܠܗ، ܡܨܠܝܢܘܬܐ ܠܐ ܒܕ ܗܘܝܐ ܚܬܝܬܬܐ، ܐܠܐ ܛܥܝܘܬܐ ܬܩܝܢܬܐ ܕܝܠܗ̇ ܟܐܡܪܐ ܐܗܐ. (ܒ) ܛܝܡܐ ܢܘܟܪܝܐ ܓܘ ܡܨܥܬܐ ܕܦܬܝܘܬܐ ܕ-X – ܢܘܩܙܐ ܪܚܝܩܐ ܡܢ ܣܪܛܐ، ܐܠܐ ܩܪܝܒܐ ܠܡܨܥܝܬܐ ܕ-X: ܡܨܠܝܢܘܬܐ ܩܪܝܒܐ ܠܐ ܟܙܝܥܐ، ܒܣ ܡܢܝܢܐ ܩܝܡܐ؛ ܐܗܐ ܝܠܗ ܛܝܡܐ ܢܘܟܪܝܐ "ܬܡܝܡܐ" ܒܦܘܚܡܐ، ܕܪܘܫܡܐ ܕܝܠܗ ܫܪܟܐ ܪܒܐ ܝܠܗ. (ܓ) ܦܘܪܫܐ، ܐܠܐ ܫܠܝܡܐ – ܢܘܩܙܐ ܪܚܝܩܐ ܕܝܬܝܒܐ ܝܠܗ ܒܚܬܝܬܘܬܐ ܥܠ ܡܬܚܬܐ ܕܣܪܛܐ: ܠܐ ܡܙܝܩܢܐ، ܘܐܦ ܦܝܫܐ – ܟܡܙܥܪ ܫܘܚܠܦܐ ܕܫܘܥܪܐ ܕܡܨܠܝܢܘܬܐ. ܐܗܐ ܝܠܗ ܥܘܗܕܢܐ ܕܢܘܩܙܐ ܕܣܘܦܐ ܠܐ ܝܠܗ ܒܐܢܢܩܝ ܢܘܩܙܐ ܒܝܫܐ. (ܕ) ܢܘܩܙܐ ܕܟܦܣܩ ܡܨܠܝܢܘܬܐ – ܐܣܟܝܡܐ ܕܡܥܩܐ ܡܢ ܟܠܗ: ܕܠܐ ܢܘܩܙܐ ܪܚܝܩܐ ܩܪܝܒܐ ܠܝܬ ܐܣܘܪܐ، ܘܥܡܗ ܐܝܬ ܐܣܘܪܐ ܓܠܝܐ؛ ܒܫܪܪܐ، ܐܝܟ ܕܟܬܘ̈ܒܐ ܟܐܡܪܝ، ܐܟܐ ܐܝܬ "ܒܫܪܪܐ ܒܣ ܬܪܝܢ ܢܘܩ̈ܙܐ". ܫܪܟܐ ܕܝܠܗ ܙܥܘܪܐ ܝܠܗ – ܣܪܛܐ ܟܥܒܪ ܓܘܗ – ܘܡܛܠ ܗܕܐ ܡܚܘ̈ܝܢܐ ܕܫܪ̈ܟܐ ܠܐ ܒܕ ܩܢܝ ܠܗ؛ ܡܪܝܡܢܘܬܐ ܐܝܢ. Cook & Weisberg (1982، ܦܐܬܐ 102-103) ܟܦܬܚܝ ܡܡܠܠܐ ܥܠ ܡܥܒܕܢܘܬܐ ܒܚܬܝܬܘܬܐ ܒܨܘܪܬܐ ܕܐܗܐ ܙܢܐ، ܘܟܡܚܫܚܝ ܕܐܦ ܐܝܢܐ ܕܡܢ ܩܕܡ ܟܡܣܟܐ ܫܘܢܝܐ ܕܣܪܛܐ ܒܕ ܬܡܗ ܡܢ ܡܐ ܕܟܗܘܐ ܠܡܚܘ̈ܝܢܐ: ܥܡ ܢܘܩܙܐ ܪܚܝܩܐ R² = .90؛ ܕܠܐ ܕܝܠܗ – ܒܨܝܪ ܡܢ .01. (ܗ) ܬܪܬܝܢ ܕܟܓܪܫܝ – ܬܪܝܢ ܢܘܩ̈ܙܐ ܥܡ ܡܪܝܡܢܘܬܐ ܪܡܬܐ، ܕܟܠ ܚܕ ܡܢܝܗܘܢ ܒܠܚܘܕܗ ܟܡܨܠܐ ܣܪܛܐ؛ ܐܟܐ، ܟܟܬܒܝ ܟܬܘ̈ܒܐ، ܣܢܝܩܘܬܐ ܐܝܬ ܠܥܒܕܐ: ܫܩܠܬܐ، ܝܢ – ܪܟܝܟܐܝܬ ܒܙܘܕܐ – ܡܙܥܪܢܘܬܐ ܕܡܬܩܠܐ ܕܝܠܗܘܢ، ܝܢ ܫܘܢܝܐ ܕܡܘܕܝܠ. (ܘ) ܛܫܝܐ ܕܚܕ̈ܕܐ – ܬܪܝܢ ܢܘܩ̈ܙܐ ܩܪܝ̈ܒܐ: ܫܩܠܬܐ ܕܚܕ ܡܢܝܗܘܢ ܩܪܝܒܐ ܠܐ ܟܡܫܚܠܦܐ ܣܪܛܐ، ܡܛܠ ܕܬܪܝܢܐ ܟܡܬܚܡܐ ܓܪܫܐ، ܘܡܛܠ ܗܕܐ ܡܚܘ̈ܝܢܐ ܕܟܒܚܪܝ ܚܙܝܬܐ ܒܬܪ ܚܙܝܬܐ (ܐܝܟ ܪܘܚܩܐ ܕ-Cook) ܡܨܝ ܕܦܝܫܝ ܠܐ ܚܙܝ̈ܐ ܬܪܘܝܗܝ (ܬܡܐ، ܦܐܬܐ 9، 31). ܐܗܐ ܝܠܗ ܥܠܬܐ ܕܠܝܬ ܚܠܦܐ ܠܥܝܢܐ: ܙܘܓܐ ܕܐܗܐ ܙܢܐ ܡܢ ܫܥܬܗ ܟܡܬܚܙܐ ܓܘ ܨܘܪܬܐ ܕܒܕܪܐ.

ܩܐ ܡܫܘܚܬܐ ܒܡܢܝ̈ܢܐ: ܫܪ̈ܟܐ ܡܬܩ̈ܢܐ (standardized residuals) – ܫܪ̈ܟܐ ܒܡܢܝ̈ܢܐ z: ܛܝܡܐ ܫܪܝܪܐ ܒܐܬܪܐ ܕ-3.29 ܥܠܬܐ ܝܠܗ ܩܐ ܥܩܬܐ؛ ܐܢ ܒܙܘܕܐ ܡܢ 1% ܡܢ ܚܙ̈ܝܬܐ ܒܐܬܪܐ ܕ-2.58 ܝܢܐ، ܝܢ ܒܙܘܕܐ ܡܢ 5% ܒܐܬܪܐ ܕ-1.96 – ܡܘܕܝܠ ܒܝܫ ܟܡܚܘܐ ܝܗܝ̈ܒܬܐ؛ ܪܘܚܩܐ ܕ-Cook – ܡܥܒܕܢܘܬܐ ܕܚܙܝܬܐ ܥܠ ܡܘܕܝܠ ܟܠܗ: ܟܡܐ ܟܙܝܥܝ ܟܠ ܡܢܝ̈ܢܐ ܡܫܘܬ̈ܦܐ ܚܕܐ ܐܝܡܢ ܕܟܫܩܠܚ ܠܗ̇. ܡܚܘܝܢܐ، ܒܦܘܪܩܐ ܕ-Cook & Weisberg (1982، ܦܐܬܐ 117)، product ܝܠܗ ܕܬܪܝܢ ܡܚܘ̈ܝܢܐ ܐܚܪ̈ܢܐ ܓܘ ܐܗܝ ܪܫܝܡܬܐ – ܫܪܟܐ ܡܬܩܢܐ ܡܪܒܥܐ ܙܒܢ "ܡܨܝܐܘܬܐ" ܕܡܪܝܡܢܘܬܐ (h/(1 − h)) – ܘܡܛܠ ܗܕܐ ܚܙܝܬܐ ܡܨܝܐ ܕܗܘܝܐ ܡܥܒܕܢܝܬܐ ܡܛܠ ܬܪܬܝܢ ܥܠ̈ܠܬܐ ܦܪ̈ܝܫܬܐ: ܡܛܠ ܕܪܚܝܩܬܐ ܝܠܗ̇ ܡܢ ܣܪܛܐ، ܝܢ ܡܛܠ ܕܪܚܝܩܬܐ ܝܠܗ̇ ܓܘ ܣܪܛܐ X؛ ܓܘ ܡܬܠܐ ܕܟܡܝܬܝ (3.5.1) ܐܪܒܥܐ ܚܙ̈ܝܬܐ ܟܫܩܠܝ ܒܚܬܝܬܘܬܐ ܐܗܘ D = 3، ܬܪܬܝܢ ܡܢ ܟܠ ܥܠܬܐ. ܬܚܘܡܐ ܡܩܒܠܐ، D > 1، ܟܐܡܪ ܕܫܩܠܬܐ ܕܚܙܝܬܐ ܟܡܙܝܥܐ ܫܘܥܪ̈ܐ ܕܡܘܕܝܠ ܠܒܪ ܡܢ ܐܬܪܐ ܕܬܘܟܠܢܐ ܕ-50% – ܘ-Cook & Weisberg ܟܡܩܪܒܝ ܠܗ ܐܝܟ "ܫܬܐܣܐ ܩܐ ܦܘܚܡܐ" ܒܠܚܘܕ، ܘܟܙܗܪܝ ܕܬܚܘܡܐ ܕ"ܪܒܐ" ܬܠܐ ܝܠܗ ܒܥܩܬܐ (ܦܐܬܐ 118)؛ ܘܡܪܝܡܢܘܬܐ (leverage) – ܟܡܐ ܛܝܡܐ ܕ-X ܕܚܙܝܬܐ ܕܣܘܦܐ ܝܠܗ، ܛܒܐ ܝܠܗ ܕܒܚܪܚ ܛܝ̈ܡܐ ܒܐܬܪܐ ܕܬܪܝܢ ܓܗ̈ܐ ܡܨܥܝܬܐ 2(k + 1)/n (Hoaglin & Welsch، 1978، ܦܣܩܐ 2؛ Belsley, Kuh & Welsch، 1980، ܦܐܬܐ 17؛ ܥܡ ܚܕ ܡܢܒܝܢܐ: 4/n). ܡܪܝܡܢܘܬܐ، h، ܒܬܚܘܡܐ ܡܬܩܠܐ ܝܠܗ ܕܚܙܝܬܐ ܓܘ ܛܝܡܐ ܡܢܒܝܐ ܕܓܢܗ̇ – ܒ-h = 1 ܡܘܕܝܠ "ܟܡܩܕܫ" ܩܐܠܗ̇ ܦܪܡܝܛܪ ܘܣܪܛܐ ܕܪܝܓܪܫܢ ܒܐܢܢܩܝ ܟܥܒܪ ܓܘܗ̇ – ܘܓܘ ܪܝܓܪܫܢ ܦܫܝܛܐ ܐܝܬܠܗ ܡܬܘܪܓܡܐ ܓܠܝܐ: h = 1/n + (x − x̄)² / Σ(x − x̄)² – ܡܢܬܐ ܕܚܙܝܬܐ ܓܘ ܒܕܪܐ ܟܠܢܝܐ ܕ-X (Hoaglin & Welsch, 1978, Section 3). ܡܢ ܐܟܐ ܬܪܝܢ ܡܕ̈ܡܐ ܕܛܒܐ ܝܠܗ ܕܡܥܗܕܚ. ܓܘ ܨܘܪܬܐ ܕܒܕܪܐ ܕܬܪܝܢ ܡܫܬܚܠܦ̈ܢܐ ܡܪܝܡܢܘܬܐ ܒܣ ܟܡܬܚܙܝܐ: ܚܙܝܬܐ ܕܣܘܦܐ ܓܘ ܣܪܛܐ X ܚܙܝܬܐ ܝܠܗ̇ ܥܡ ܡܪܝܡܢܘܬܐ ܪܡܬܐ، ܘܠܝܬ ܣܢܝܩܘܬܐ ܠܡܚܘܝܢܐ؛ ܡܚܘܝܢܐ ܟܗܘܐ ܣܢܝܩܐ ܒܣ ܐܝܡܢ ܕܐܝܬ ܟܡܐ ܡܢܒ̈ܝܢܐ، ܘܗܝܓ ܚܙܝܬܐ ܡܨܝܐ ܕܗܘܝܐ ܪܚܝܩܬܐ ܓܘ ܚܘܠܛܐ ܕܝܠܗܘܢ ܕܠܐ ܗܘܝܐ ܕܣܘܦܐ ܓܘ ܚܕ ܡܢܝܗܘܢ، ܘܚܕ ܨܘܪܬܐ ܠܐ ܒܕ ܓܠܝܐ ܠܗ̇ (ܬܡܐ، ܦܣܩܐ 2). ܘܬܪܝܢܐ، ܐܘܪܚܐ ܕ-Hoaglin & Welsch ܟܡܩܪܒܝ (ܦܣܩܐ 5): ܟܒܚܪܚ ܡܪܝܡܢܘܬܐ ܩܐ ܡܫܟܚܬܐ ܕܢܘܩ̈ܙܐ ܪܓܝ̈ܫܐ ܓܘ ܣܪܛܐ X ܘܫܪ̈ܟܐ studentized ܩܐ ܡܫܟܚܬܐ ܕܛܝ̈ܡܐ ܢܘܟܪ̈ܝܐ ܕ-Y – ܬܪܘܝܗܝ، ܡܛܠ ܕܚܙܝܬܐ ܥܡ ܡܪܝܡܢܘܬܐ ܪܡܬܐ ܡܨܝܐ ܕܡܚܘܝܐ ܫܪܟܐ ܙܥܘܪܐ ܛܒܐ ܡܛܠ ܕܡܢ ܩܕܡ ܓܪܫܠܗ̇ ܣܪܛܐ ܠܦܐܬܗ̇، ܘܡܚܘܝܢܐ ܕܫܪ̈ܟܐ ܒܠܚܘܕܗ ܒܕ ܦܝܫ ܠܐ ܚܙܝܐ ܠܗ̇. ܘܙܘܗܪܐ ܕܝܠܗܘܢ ܕܟܫܩܠ ܟܠ ܡܐ ܕܐܡܝܪܐ ܝܠܗ: ܢܘܩ̈ܙܐ ܕܣܘܦܐ ܓܘ X ܐܢܝ ܝܢܐ ܐܦ ܕܟܛܥܢܝ ܒܝܫܐ ܕܡܘܕܥܢܘܬܐ ܥܠ ܡܨܠܝܢܘܬܐ، ܘܡܛܠ ܗܕܐ ܫܩܠܬܐ ܕܢܘܩܙܐ ܕܡܪܝܡܢܘܬܐ ܡܨܐ ܕܡܙܥܪ ܒܣܓܝ ܚܬܝܬܘܬܐ ܕܓܘܗ̇ ܡܨܝܚ ܕܫܥܪܚ ܠܗ̇ – "ܦܣܩ̈ܐ ܕܐܗܐ ܙܢܐ ܠܐ ܡܨܝܝ ܕܡܬܦܣܩܝ ܒܓܢܗܘܢ". Belsley, Kuh & Welsch ܟܡܙܝܕܝ ܬܪܝܢ ܡܚܘ̈ܝܢܐ ܕܟܡܬܚܙܝ ܐܦ ܐܢܝ ܓܘ ܟܘܬܐ Save ܕ-SPSS: Standardized DfBeta – ܒܟܡܐ ܛܥܝ̈ܘܬܐ ܬܩܝܢ̈ܬܐ ܟܙܝܥܐ ܡܨܠܝܢܘܬܐ ܐܝܡܢ ܕܟܫܩܠܚ ܚܙܝܬܐ، ܬܚܘܡܐ 2/√n؛ ܘ-Standardized DfFit – ܒܟܡܐ ܟܙܝܥ ܛܝܡܐ ܡܢܒܝܐ ܕܝܠܗ̇، ܬܚܘܡܐ 2√(p/n)، ܐܝܡܢ ܕ-p ܡܢܝܢܐ ܝܠܗ ܕܦܪܡܝ̈ܛܪܐ ܥܡ ܡܢܝܢܐ ܩܝܡܐ (1980، ܦܐܬܐ 28). ܡܪܝܡܢܘܬܐ ܟܡܫܚܐ ܣܘܟܢܐ ܕܡܨܐ ܕܗܘܐ – ܟܡܐ ܪܚܝܩܬܐ ܝܠܗ̇ ܚܙܝܬܐ ܓܘ X؛ ܐܢܝ ܬܪܝܢ ܟܡܫܚܝ ܙܝܩܐ ܒܫܪܪܐ. ܟܠ ܐܢܝ ܟܡܦܩܚ ܒ-SPSS ܡܢ ܐܘܪܚܐ ܕܪܝܓܪܫܢ (ܦܬܝܪܐ Save)، ܠܐ ܡܢ ܨܘܪܬܐ ܕܒܕܪܐ – ܚܙܝܡܘܢ ܡܢ ܨܘܪܬܐ ܠܪܝܓܪܫܢ.

ܦܬܝܘܬܐ ܟܪܝܬܐ ܕܛܝ̈ܡܐ. ܦܚܐ ܫܠܝܐ ܕܠܐ ܟܡܬܚܙܐ ܓܘ ܨܘܪܬܐ ܒܓܢܗ̇: ܐܝܡܢ ܕܕܘܡܝܐ ܟܟܣܐ ܒܣ ܡܢܬܐ ܥܝܩܬܐ ܡܢ ܦܬܝܘܬܐ ܕܛܝ̈ܡܐ ܕܡܨܝܐ ܕܗܘܝ – ܡܬܠܐ ܡܫܘܚܬܐ ܕܐܣܘܪܐ ܒܝܢܝ ܗܘܢܐ ܘܡܛܝܢܘܬܐ ܒܣ ܒܝܢܝ ܬܠܡܝܕ̈ܐ ܕܕܪܓܐ ܪܡܐ – ܐܣܘܪܐ ܕܚܕ̈ܕܐ ܕܒܕ ܡܬܛܝܐ ܦܪܝܫܐ ܝܠܗ، ܘܒܪܘܒܐ ܬܚܬܝܐ، ܡܢ ܐܗܘ ܕܒܕ ܡܬܛܝܐ ܗܘܐ ܡܢ ܦܬܝܘܬܐ ܓܡܝܪܬܐ. ܟܡܐ ܕܦܬܝܘܬܐ ܕܬܪܝܢ ܡܫܬܚܠܦ̈ܢܐ ܓܘ ܕܘܡܝܐ ܦܬܝܐ ܝܠܗ ܒܙܘܕܐ، ܗܕܟܐ ܫܘܥܪܐ ܕܐܣܘܪܐ ܡܗܝܡܢܐ ܝܠܗ ܒܙܘܕܐ؛ ܘܐܝܡܢ ܕܟܒܨܚ ܓܘܕܐ ܕܣܘܦܐ ܒܨܒܝܢܐ (ܡܬܠܐ ܟܘܪܗܢ̈ܐ ܒܪܡܐ ܪܡܐ ܕܙܘܥܐ)، ܠܐ ܛܒܐ ܝܠܗ ܕܦܫܛܚ ܐܣܘܪܐ ܕܚܕ̈ܕܐ ܠܒܪ ܡܢ ܦܬܝܘܬܐ ܕܓܒܝܐ ܝܠܗ (Pallant, 2020, p. 136). ܓܘ ܨܘܪܬܐ ܕܒܕܪܐ ܐܗܐ ܟܡܬܚܙܐ ܐܝܟ ܥܢܢܐ ܕܟܟܣܐ ܒܣ ܚܕ ܙܘܝܬܐ ܕܣܪ̈ܛܐ. Cohen, Cohen, West & Aiken (2003، ܦܐܬܐ 57-58) ܟܡܚܘܝܝ ܐܗܐ ܒܡܢܝ̈ܢܐ: ܐܝܡܢ ܕܟܡܙܥܪܚ ܕܘܡܝܐ ܕܚܕ̈ܝܡܐ ܕܣܓܠܐ ܠܐܢܝ ܕܫܠܡܠܗܘܢ ܕܘܩܛܘܪܐ ܩܕܡ 5-11 ܫܢ̈ܐ ܒܠܚܘܕ (ܒܕܘܟܬ 3-18)، ܐܣܘܪܐ ܕܚܕ̈ܕܐ ܒܝܢܝ ܥܬܝܩܘܬܐ ܘܡܢܝܢܐ ܕܡܦܪ̈ܣܢܘܬܐ ܟܢܚܬ ܡܢ .657 ܠ-.388، ܘ-R² ܡܢ .43 ܠ-.15 – ܘܡܨܠܝܢܘܬܐ ܕܪܝܓܪܫܢ ܩܪܝܒܐ ܠܐ ܟܙܝܥܐ (1.98 ܩܘܒܠ 2.46). ܐܗܐ ܕܝܠܝܬܐ ܟܠܢܝܬܐ ܝܠܗ: ܐܝܡܢ ܕܐܣܘܪܐ ܣܪܛܢܝܐ ܝܠܗ، b ܩܝܡܐ ܝܠܗ ܠܫܘܢ̈ܝܐ ܓܘ ܒܕܪܐ ܕ-X، ܘ-r ܠܐ. ܡܢ ܐܟܐ ܬܪܬܝܢ ܡܦܝ̈ܣܢܘܬܐ ܥܒܕ̈ܢܝܬܐ – ܕܡܬܢܚ ܒܟܠ ܙܒܢ ܣܛܝ̈ܘܬܐ ܬܩܝܢ̈ܬܐ ܕܡܫܬܚܠܦ̈ܢܐ، ܩܐ ܕܩܪܘܝܐ ܡܨܐ ܕܦܣܩ ܐܢ ܦܬܝܘܬܐ ܟܪܝܬܐ ܝܠܗ̇؛ ܘܐܝܡܢ ܕܟܦܚܡܚ ܐܣܘܪܐ ܒܝܢܝ ܕܘ̈ܡܝܐ ܕܣܛܝ̈ܘܬܐ ܬܩܝܢ̈ܬܐ ܕܝܠܗܘܢ ܦܪ̈ܝܫܐ ܝܢܐ، ܕܦܚܡܚ ܡܨܠܝܢ̈ܘܬܐ ܘܠܐ ܐܣܘܪ̈ܐ ܕܚܕ̈ܕܐ.

ܡܐ ܕܨܘܪܬܐ ܠܐ ܡܨܝܐ ܕܡܚܘܝܐ: ܫܪܝܪܘܬܐ ܕܡܫܘܚܬܐ. ܦܢܩ̈ܝܬܐ ܕܫܘܐ̈ܠܐ ܟܡܫܚܝ ܥܡ ܛܥܝܘܬܐ، ܘܛܥܝܘܬܐ ܕܡܫܘܚܬܐ ܟܡܙܥܪܐ ܟܠ ܐܣܘܪܐ ܕܚܕ̈ܕܐ: ܐܣܘܪܐ ܕܚܕ̈ܕܐ ܒܝܢܝ ܬܪܝܢ ܡܢܝ̈ܢܐ ܚܙ̈ܝܐ ܠܐ ܡܨܐ ܕܣܠܩ ܒܐܬܪܐ ܕܫܪܫܐ ܕ-product ܕܫܪܝܪ̈ܘܬܐ ܕܝܠܗܘܢ، r_XY ≤ √(r_XX·r_YY). ܬܪܬܝܢ ܣܒ̈ܠܬܐ ܒܫܪܝܪܘܬܐ .80 ܟܠ ܚܕܐ ܠܐ ܡܨܝܐ ܕܐܣܝܪ̈ܐ ܗܘܝܢ ܒܐܬܪܐ ܕ-.80، ܘܐܣܘܪܐ ܕܚܕ̈ܕܐ ܚܙܝܐ ܕ-.44 ܒܝܢܝ ܕܝܠܗܝܢ ܦܐܝܐ ܝܠܗ ܠܐܣܘܪܐ ܕܚܕ̈ܕܐ ܕ-.55 ܒܝܢܝ ܒܢܝ̈ܢܐ "ܫܪܝܪ̈ܐ" (constructs) – ܐܗܐ ܝܠܗ ܬܘܪܨܐ ܩܐ ܡܙܥܪܢܘܬܐ (correction for attenuation): ܟܦܠܓܚ r ܥܠ ܐܗܘ ܫܪܫܐ (Cohen, Cohen, West & Aiken, 2003, pp. 55-57). ܬܪܝܢ ܡܕ̈ܡܐ ܟܐܬܝ ܡܢ ܐܗܐ. ܩܕܡܝܐ، ܠܐ ܫܪܝܪܘܬܐ ܡܦܫܩܢܘܬܐ ܡܣܦܩܬܐ ܝܠܗ ܩܐ ܐܣܘܪܐ ܕܚܕ̈ܕܐ ܬܚܬܝܐ، ܐܠܐ ܠܐ ܡܨܝܐ ܕܒܪܝܐ ܐܣܘܪܐ ܕܚܕ̈ܕܐ ܪܡܐ ܕܓܠܐ – ܐܣܘܪܐ ܕܚܕ̈ܕܐ ܚܝܠܬܢܐ ܒܝܢܝ ܡܚܘ̈ܝܢܐ ܠܐ ܫܪܝܪ̈ܐ ܡܫܟܚܢܘܬܐ ܚܝܠܬܢܬܐ ܝܠܗ ܒܝܚܝܕܝܘܬܐ. Cohen (1988، ܦܐܬܐ 79) ܟܦܠܚ ܒܚܬܝܬܘܬܐ ܒܐܗܐ ܚܘܫܒܢܐ ܩܐ ܕܡܦܫܩ ܠܡܢܐ r = .10 ܠܐ ܝܠܗ "ܒܣܓܝ ܙܥܘܪܐ" ܕܒܨܚ ܥܠܝܗ: ܬܪܝܢ ܒܢܝ̈ܢܐ ܬܐܘܪܝ̈ܝܐ ܕܐܣܘܪܐ ܕܚܕ̈ܕܐ ܫܪܝܪܐ ܕܝܠܗܘܢ .25، ܐܝܡܢ ܕܟܠ ܚܕ ܡܢܝܗܘܢ ܡܫܝܚܐ ܝܠܗ ܒܡܐܢܐ ܕܐܣܝܪܐ ܝܠܗ .63 ܥܡ ܒܢܝܢܐ ܕܝܠܗ، ܒܕ ܗܘܝ ܐܣܝܪ̈ܐ ܓܘ ܡܫܘܚܬܐ .25 × .63 × .63 = .10 ܒܠܚܘܕ – "ܓܘ ܝܕܥܬܐ ܕܢܦܫܐ"، ܒܡܬܦܪܣܢܘܬܐ ܕܟܡܝܬܐ ܡܢ Thurstone، "ܟܡܫܚܚ ܐܢܫ̈ܐ ܠܦܘܬ ܛܠܠ̈ܐ ܕܝܠܗܘܢ". ܬܪܝܢܐ، ܐܣܘܪܐ ܕܚܕ̈ܕܐ ܡܬܘܪܨܐ ܛܝܡܐ ܕܗܘܦܘܬܣܝܣ ܝܠܗ ܘܠܐ ܝܗܝܒܬܐ: ܕܡܬܢܚ ܠܗ ܒܣ ܓܢܒ ܐܣܘܪܐ ܕܚܕ̈ܕܐ ܚܙܝܐ، ܘܒܙܗܝܪܘܬܐ – ܐܝܡܢ ܕܫܪܝܪ̈ܘܬܐ ܫܥܝܪ̈ܐ ܝܢܐ ܓܘ ܕܘܡܝܐ ܐܚܪܢܐ ܝܢ ܫܥܝܪ̈ܐ ܝܢܐ ܬܚܬܝܐܝܬ ܒܝܬܝܪܘܬܐ، ܬܘܪܨܐ ܡܨܐ ܕܝܗܒ ܛܝܡܐ ܡܦܪܣܐ، ܘܐܦ ܪܒܐ ܡܢ 1. ܘܢܘܩܙܐ ܪܟܝܟܐ ܥܠ ܣܪܛܐ ܕܪܝܓܪܫܢ: ܡܨܠܝܢܘܬܐ b ܠܐ ܝܠܗ̇ ܡܥܒܕܬܐ ܡܢ ܠܐ ܫܪܝܪܘܬܐ ܓܘ Y (ܩܠܐ ܬܡܐ ܟܡܬܒܠܥ ܓܘ ܫܪ̈ܟܐ)، ܐܠܐ ܡܥܒܕܬܐ ܝܠܗ̇ ܡܢ ܠܐ ܫܪܝܪܘܬܐ ܓܘ X. ܫܪܝܪܘܬܐ ܒܓܢܗ̇ ܟܚܫܒܚ ܠܗ̇ ܓܘ ܦܐܬܐ ܕܐܠܦܐ ܕ-Cronbach ܘܡܢܝܢܐ ܕܣܒܠܬܐ.

ܦܣܘܩܐ ܩܘܒܠ ܣܒܠܬܐ ܕܐܝܠܗ ܡܢܬܐ ܡܢܗ̇. ܦܚܐ ܩܪܝܒܐ: ܨܘܪܬܐ ܕܒܕܪܐ ܕܚܕ ܦܣܘܩܐ ܩܘܒܠ ܡܢܝܢܐ ܕܣܒܠܬܐ ܕܐܝܬܠܗ̇ ܠܗ ܒܟܠ ܙܒܢ ܒܕ ܡܚܘܝܐ ܐܣܘܪܐ ܕܙܘܕܐ – ܒܣ ܡܛܠ ܕܦܣܘܩܐ ܡܢܬܐ ܝܠܗ ܡܢ ܓܘܡܪܐ. ܥܡ k ܦܣܘ̈ܩܐ ܕܠܐ ܝܢܐ ܐܣܝܪ̈ܐ ܡܕܡ ܚܕ ܥܡ ܚܕ، ܟܠ ܦܣܘܩܐ ܐܣܝܪܐ ܝܠܗ ܥܡ ܓܘܡܪܐ ܒ-1/√k: ܥܡ ܬܪܝܢ ܦܣܘ̈ܩܐ – .71، ܥܡ ܐܪܒܥܐ – .50، ܕܠܐ ܚܕ ܐܣܘܪܐ ܫܪܝܪܐ (Cohen, Cohen, West & Aiken, 2003, p. 59). ܡܛܠ ܗܕܐ ܐܣܘܪܐ ܕܚܕ̈ܕܐ ܕܦܣܘܩܐ ܥܡ ܣܒܠܬܐ ܒܟܠ ܙܒܢ ܚܫܝܒܐ ܝܠܗ ܩܘܒܠ ܣܒܠܬܐ ܕܠܐ ܕܝܠܗ (corrected item-total correlation) – ܘܐܗܐ ܒܚܬܝܬܘܬܐ ܥܡܘܕܐ ܝܠܗ ܕܦܐܬܐ ܕܫܪܝܪܘܬܐ ܟܡܦܩܐ. ܒܐܗܘ ܪܘܚܐ (ܬܡܐ، ܦܐܬܐ 53): r = 1 ܡܨܐ ܕܗܘܐ ܒܣ ܐܝܡܢ ܕܬܪܝܢ ܡܫܬܚܠܦ̈ܢܐ ܐܝܬܠܗܘܢ ܐܗܘ ܐܣܟܝܡܐ ܕܦܘܠܓܐ، ܘܟܡܐ ܕܦܘܠܓ̈ܐ ܦܪ̈ܝܫܐ ܝܢܐ – ܒܝܚܝܕܝܘܬܐ ܐܝܡܢ ܕܡܨܠܝ̈ܐ ܝܢܐ ܠܐܘܪ̈ܚܬܐ ܗܘܦܟ̈ܝܬܐ، ܝܢ ܐܝܡܢ ܕܬܪܝܢ ܡܫܬܚܠܦ̈ܢܐ ܕܬܪܝܢ ܛܝ̈ܡܐ ܝܢܐ ܒܡܢܘ̈ܬܐ ܒܣܓܝ ܦܪ̈ܝܫܬܐ – ܗܕܟܐ ܬܚܘܡܐ ܥܠܝܐ ܕܐܣܘܪܐ ܕܚܕ̈ܕܐ ܬܚܬܝܐ ܝܠܗ ܡܢ 1.

ܘܙܘܗܪܐ ܚܫܝܚܐ ܡܢ ܟܠܗ. ܡܚܘ̈ܝܢܐ ܕܒܘܚܪܢܐ ܥܒܝܕ̈ܐ ܝܢܐ ܩܐ ܕܚܙܝܚ ܟܡܐ ܡܘܕܝܠ ܦܐܝܐ ܝܠܗ ܠܝܗܝ̈ܒܬܐ – ܠܐ ܩܐ ܕܡܙܕܩܚ ܫܩܠܬܐ ܕܢܘܩ̈ܙܐ ܩܐ ܕܫܩܠܚ ܦܐܪܐ ܕܟܒܥܝܚ، ܡܬܠܐ ܕܗܦܟܚ ܡܨܠܝܢܘܬܐ ܠܐ ܪܫܝܡܬܐ ܠܪܫܝܡܬܐ (Field, 2024, Section 9.3.3). Belsley, Kuh & Welsch (1980، ܦܐܬܐ 3-4)، ܕܦܬܚܠܗܘܢ ܣܓܝ ܡܢ ܐܢܝ ܡܚܘ̈ܝܢܐ، ܟܬܒܠܗܘܢ ܠܗܘܢ ܓܠܝܐܝܬ ܩܐ ܕܡܟܠܝ ܐܣܝܘܬܐ ܕܡܬܚܙܝܐ ܣܓܝ ܘܠܐ ܦܐܝܬܐ ܒܐܗܝ ܡܫܘܚܬܐ – "ܕܡܫܕܚ ܛܝ̈ܡܐ ܢܘܟܪ̈ܝܐ"، ܕܣܓܝ ܡܢܝܗܘܢ، ܐܝܟ ܕܐܢܝ ܟܡܥܝܪܝ، ܡܕܡ ܠܐ ܝܢܐ ܡܥܒܕ̈ܢܝܐ: ܚܙܝܬܐ ܢܘܟܪܝܬܐ ܠܐ ܝܠܗ̇ ܒܐܢܢܩܝ ܚܙܝܬܐ ܒܝܫܬܐ، ܘܒܙܒ̈ܢܐ ܐܝܠܗ̇ ܕܟܛܥܢܐ ܡܘܕܥܢܘܬܐ ܕܚܫܝܚܬܐ ܝܠܗ̇ ܡܢ ܟܠܗ ܓܘ ܕܘܡܝܐ؛ ܒܣ ܒܬܪ ܕܡܫܬܘܕܥܐ ܝܠܗ̇ ܡܨܝܚ ܕܕܐܢܚ ܛܒܘܬܐ ܕܝܠܗ̇ ܘܦܣܩܚ ܡܘܕܝ ܥܒܕܚ. ܚܙܝܬܐ ܢܘܟܪܝܬܐ ܕܠܐ ܟܥܒܕܐ ܥܠ ܣܪܛܐ ܠܐ ܟܡܣܟܢܐ ܡܘܕܝܠ، ܘܒܟܠ ܗܘܝܐ ܫܘܐܠܐ ܕܚܫܝܚܐ ܝܠܗ ܠܡܢܐ ܠܐ ܝܠܗ̇ ܦܐܝܬܐ ܠܗ. ܬܪܬܝܢ ܐܘܪ̈ܚܬܐ ܕܡܬܚܙܝܢ ܣܓܝ ܩܐ ܛܝ̈ܡܐ ܢܘܟܪ̈ܝܐ ܚܒܝܠ̈ܐ ܝܢܐ ܡܛܠ ܥܠܬܐ ܫܬܐܣܢܝܬܐ (Field & Wilcox, 2017, Section Alternative estimators): ܦܣܩܬܐ ܠܦܘܬ ܣܛܝ̈ܘܬܐ ܬܩܝܢ̈ܬܐ – ܡܬܠܐ ܫܩܠܬܐ ܕܟܠ ܚܙܝܬܐ ܕܪܚܝܩܬܐ ܝܠܗ̇ ܡܢ ܡܨܥܝܬܐ ܒܙܘܕܐ ܡܢ 2.5 ܣܛܝ̈ܘܬܐ ܬܩܝܢ̈ܬܐ، ܥܝܕܐ ܕܡܬܚܙܐ ܣܓܝ ܓܘ ܝܗܝ̈ܒܬܐ ܕܙܒ̈ܢܐ ܕܦܘܢܝܐ – ܟܣܡܟ ܥܠ ܡܨܥܝܬܐ ܘܣܛܝܘܬܐ ܬܩܝܢܬܐ، ܕܐܢܝ ܒܓܢܗܘܢ ܡܚܘ̈ܝܢܐ ܪܓܝ̈ܫܐ ܝܢܐ ܡܢ ܟܠܗ ܠܛܝ̈ܡܐ ܢܘܟܪ̈ܝܐ، ܘܡܛܠ ܗܕܐ ܚܕ ܛܝܡܐ ܢܘܟܪܝܐ ܪܒܐ "ܟܛܫܐ" ܐܚܪ̈ܢܐ؛ ܘܫܩܠܬܐ ܒܐܝܕܐ ܕܛܝ̈ܡܐ ܢܘܟܪ̈ܝܐ، ܕܒܬܪܗ̇ ܟܪܗܛܚ ܪܝܓܪܫܢ ܥܝܕܝܐ ܥܠ ܡܐ ܕܦܝܫܐ – ܠܐ ܟܚܫܒܐ ܕܝܗܝ̈ܒܬܐ ܡܢ ܩܕܡ "ܡܕܘܟܝ̈ܬܐ" ܝܢܐ، ܘܡܛܠ ܗܕܐ ܛܥܝ̈ܘܬܐ ܬܩܝܢ̈ܬܐ ܕܟܡܬܛܝܢ ܛܥ̈ܝܬܐ ܝܢܐ، ܡܐ ܕܗܘܐ ܪܒܘܬܐ ܕܕܘܡܝܐ. ܚܠ̈ܦܐ ܚܣܝܢ̈ܐ (robust) – ܡܨܥܝ̈ܬܐ ܓܙܝ̈ܙܬܐ ܒ-20%، ܫܘܥܪ̈ܐ-M ܕܟܡܫܬܘܕܥܝ ܛܝܡܐ ܢܘܟܪܝܐ ܒܐܘܪܚܐ ܕܢܣܝܘܢܐ ܘܟܡܙܥܪܝ ܡܬܩܠܐ ܕܝܠܗ، ܘܪܝܓܪܫܢ ܚܣܝܢܐ – ܐܝܬ ܒܪܘܒܐ ܒ-R (ܬܡܐ، ܦܐܬܐ 17-18، 32-34)؛ ܡܐ ܕܐܝܬ ܒ-SPSS، ܘܡܦܝܣܐ ܝܠܗ ܒܟܠ ܗܘܝܐ، ܝܠܗ ܒܘܛܣܛܪܐܦ ܕܓܘ ܦܣܩܐ ܡܢ ܨܘܪܬܐ ܠܪܝܓܪܫܢ. ܘܡܘܕܝ ܟܥܒܕܚ ܒܫܪܪܐ ܐܝܡܢ ܕܚܕ ܚܙܝܬܐ ܝܗܒܠܗ̇ ܣܓܝ ܠܣܪܛܐ؟ Anscombe (1973، ܦܐܬܐ 18-20) ܟܟܬܒ ܒܘܚܪܢܐ ܘܫܪܝܐ. ܒܘܚܪܢܐ: ܚܢܢ ܫܠܝ̈ܐ ܝܘܚ ܒܙܘܕܐ ܥܠ ܐܣܘܪܐ ܕܟܦܐܫ ܓܠܝܐ ܐܦ ܒܬܪ ܕܫܩܠܠܢ ܟܡܐ ܚܙ̈ܝܬܐ – ܐܝܢܝ ܕܗܘܝ – ܗܢܘ ܐܣܘܪܐ ܕ"ܟܡܬܦܪܣ ܓܘ ܟܠ ܚܙ̈ܝܬܐ ܘܠܐ ܟܐܬܐ ܒܪܘܒܐ ܡܢ ܚܕ ܝܢ ܬܪܬܝܢ". ܘܫܪܝܐ، ܡܢ ܡܬܠܐ ܕܡܦܩ̈ܬܐ ܥܠ ܝܘܠܦܢܐ ܓܘ ܚܡܫܝܢ ܡܕܝ̈ܢܬܐ ܕܐܡܪܝܟܐ ܕܓܘܗ̇ ܐܠܐܣܟܐ، ܥܡ ܛܝ̈ܡܐ ܕܡܢܒ̈ܝܢܐ ܪܚܝܩ̈ܐ ܡܢ ܟܠܗܝܢ، ܝܗܒܠܗ̇ ܒܝܚܝܕܝܘܬܐ ܠܣܪܛܐ: ܠܐ ܕܡܦܩܚ ܐܠܐܣܟܐ – ܡܛܠ ܕܒܬܪܗ̇ ܒܕ ܐܬܝܐ ܗܐܘܐܝ، ܩܠܝܦܘܪܢܝܐ، ܢܝܘ ܝܘܪܩ، "ܘܐܝܟܐ ܟܩܐܡܚ؟" – ܐܠܐ ܕܡܬܢܚ ܪܝܓܪܫܢ ܥܠ ܟܠ ܡܕܝ̈ܢܬܐ، ܡܙܝܕܚ ܕܐܠܐܣܟܐ ܝܗܒܠܗ̇ ܣܓܝ ܠܗ، ܘܐܡܪܚ ܡܘܕܝ ܟܗܘܐ ܕܠܐ ܕܝܠܗ̇ (ܬܡܐ: ܣܪܛܐ ܩܪܝܒܐ ܠܐ ܫܚܠܦܠܗ، ܛܥܝ̈ܘܬܐ ܬܩܝܢ̈ܬܐ ܪܒܝ ܩܠܝܠ ܘ-R² ܢܚܬܠܗ). ܬܪܝܢ ܡܕ̈ܡܐ – ܐܣܘܪܐ ܓܘ ܟܠ ܝܗܝ̈ܒܬܐ ܘܝܗܒܬܐ ܝܚܝܕܝܬܐ ܕܚܙܝܬܐ – ܐܢܝ ܝܢܐ ܡܫܟܚܢܘܬܐ. Cook & Weisberg (1982، ܦܐܬܐ 104) ܟܟܢܫܝ ܚܠܐ ܕܡܨܝܐܘܬܐ، ܒܬܪ ܕܟܡܓܠܝܝ ܕܡܚܘ̈ܝܢܐ ܕܦܬܚܠܗܘܢ "ܠܐ ܝܢܐ ܥܒܝܕ̈ܐ ܩܐ ܕܝܗܒܝ ܢܡܘ̈ܣܐ ܩܐ ܡܣܠܝܬܐ ܕܝܗܝ̈ܒܬܐ": ܚܙܝܬܐ ܕܡܒܘܥܐ ܕܝܠܗ̇ ܛܥܝܘܬܐ ܕܡܫܘܚܬܐ، ܕܟܬܝܒܬܐ ܝܢ ܗܘ̈ܝܐ ܕܢܣܝܘܢܐ ܠܐ ܦܐܝ̈ܐ – ܟܬܪܨܚ ܝܢ ܟܫܩܠܚ؛ ܚܙܝܬܐ ܕܠܝܬܠܗ̇ ܡܦܫܩܢܘܬܐ ܕܐܗܐ ܙܢܐ – ܒܘܚܪܢܐ ܪܫܡܝܐ ܕܛܝ̈ܡܐ ܢܘܟܪ̈ܝܐ (ܥܡ ܙܘܗܪܐ ܕܠܐ ܛܒܐ ܝܠܗ ܕܣܟܝܚ ܡܢܗ ܚܝܠܐ ܣܛܐܛܝܣܛܝܩܝܐ ܪܒܐ)، ܟܢܫܐ ܕܝܗܝ̈ܒܬܐ ܐܚܪ̈ܢܝܬܐ، ܝܢ – ܡܐ ܕܒܪܘܒܐ ܦܐܝܐ ܝܠܗ – ܬܘܢܝܐ ܕܬܪܝܢ ܦܘܫܩ̈ܐ، ܥܡ ܚܙܝܬܐ ܘܕܠܐ ܕܝܠܗ̇. ܦܣܩܐ ܐܚܪܝܐ، ܟܟܬܒܝ ܐܢܝ، ܒܟܠ ܙܒܢ ܬܠܐ ܝܠܗ ܒܣܝܩܐ، ܘܡܛܠ ܗܕܐ ܠܝܬ ܡܦܝܣܢܘܬܐ ܕܟܠ ܗܘܝܐ.

ܟܡܐ ܡܫܬܘܬܦ̈ܢܐ ܣܢܝܩ ܝܠܗ؟

ܢܡܘ̈ܣܐ ܕܨܒܥܐ ܕܡܬܚܙܝܢ ܣܓܝ – 10 ܝܢ 15 ܡܫܬܘܬܦ̈ܢܐ ܩܐ ܟܠ ܡܢܒܝܢܐ – ܦܫܝ̈ܛܐ ܝܢܐ ܗܕܟܐ ܕܠܐ ܦܐܕܐ (Field, 2024, Section 9.5): ܪܒܘܬܐ ܕܕܘܡܝܐ ܕܣܢܝܩܐ ܝܠܗ̇ ܬܠܝܐ ܝܠܗ̇ ܒܚܝܠܐ ܕܐܣܘܪܐ ܕܟܣܟܝܚ ܕܡܫܟܚܚ ܘܒܚܝܠܐ ܣܛܐܛܝܣܛܝܩܝܐ ܕܟܒܥܝܚ. ܥܡ ܚܕ ܡܢܒܝܢܐ، ܘܩܐ ܚܝܠܐ ܕ-0.8 ܠܦܘܬ ܡܐ ܕܡܩܒܠܐ ܝܠܗ (Cohen، 1988)، Field ܟܚܫܒ: ܩܪܝܒ ܠ-25 ܡܫܬܘܬܦ̈ܢܐ ܡܣܦܩܝ ܩܐ ܡܫܟܚܬܐ ܕܐܣܘܪܐ ܚܝܠܬܢܐ (R² ≈ .26)، ܩܪܝܒ ܠ-55 ܩܐ ܐܣܘܪܐ ܡܨܥܝܐ (R² ≈ .13)، ܐܠܐ ܩܐ ܐܣܘܪܐ ܟܪܝܗܐ (R² ≈ .02) ܡܐ̈ܐ ܣܢܝܩ̈ܐ ܝܢܐ. ܘܕܘܡܝܐ ܙܥܘܪܐ ܟܡܛܥܐ ܐܦ ܒܐܘܪܚܐ ܗܘܦܟܐ: R ܕܡܣܟܝܐ ܝܠܗ ܡܢ ܝܗܝ̈ܒܬܐ ܓܕܫܢ̈ܝܬܐ ܓܡܝܪܐܝܬ ܝܠܗ k/(N − 1) – ܥܡ 21 ܡܫܬܘܬܦ̈ܢܐ ܘܚܕ ܡܢܒܝܢܐ، ܐܦ ܩܠܐ ܫܦܝܐ ܒܕ ܝܗܒ R ܕ-0.05، ܘܦܫܝܩܐ ܝܠܗ ܕܡܬܥܒܕܚ ܡܢ "ܐܣܘܪܐ" ܕܠܝܬ.

ܡܢܝ̈ܢܐ ܕ-Field ܟܣܡܟܝ ܥܠ ܠܘ̈ܚܐ ܕ-Cohen، ܘܛܒܐ ܝܠܗ ܕܝܕܥܚ ܠܗܘܢ ܓܘ ܡܒܘܥܐ: ܓܘ ܠܘܚܐ 3.4.1 (1988، ܦܐܬܐ 102)، ܩܐ ܒܘܚܪܢܐ ܕܬܪܝܢ ܕܘܢ̈ܒܐ ܒܪܡܐ .05 ܘܚܝܠܐ .80، ܣܢܝܩ̈ܐ ܝܢܐ 28 ܙܘ̈ܓܐ ܩܐ ܡܫܟܚܬܐ ܕ-r = .50، 85 ܩܐ r = .30، ܘ-783 ܩܐ r = .10 (ܘܩܐ ܚܝܠܐ .90: 37، 113 ܘ-1,047). ܦܘܪ̈ܫܢܐ ܙܥܘ̈ܪܐ ܡܢ ܡܢܝ̈ܢܐ ܕ-Field ܟܐܬܝ ܡܢ ܕܐܗܘ ܟܬܚܡ ܡܥܒܕܢܘܬܐ ܒ-R² ܕ-.02 / .13 / .26. ܠܘܚܐ ܟܩܪܚ ܠܗ ܐܦ ܒܗܘܦܟܐ: ܥܡ n = 50، ܡܬܠܐ، ܣܟܘܝܐ ܕܡܫܟܚܬܐ ܕܐܣܘܪܐ ܡܨܥܝܐ ܒܣ .57 ܝܠܗ (ܬܡܐ، ܡܬܠܐ 3.4) – ܘܐܗܐ ܕܘܡܝܐ ܝܠܗ ܕܠܣܓܝܐܐ ܟܡܬܚܙܐ ܡܩܒܠܐ ܓܡܝܪܐܝܬ. ܘܡܥܝܪܢܘܬܐ ܕ-Cohen ܕܛܒܐ ܝܠܗ ܕܡܥܗܕܚ: ܠܘ̈ܚܐ ܠܐ ܝܢܐ ܬܪܝ̈ܨܐ ܐܝܡܢ ܕܦܬܝܘܬܐ ܕܛܝ̈ܡܐ ܓܘ ܕܘܡܝܐ ܟܪܝܬܐ ܝܠܗ̇ (ܦܐܬܐ 100) – ܚܙܝܡܘܢ ܦܬܝܘܬܐ ܟܪܝܬܐ ܕܛܝ̈ܡܐ ܠܥܠ.

ܡܢ ܐܝܟܐ ܟܐܬܝ ܐܢܝ ܡܢܝ̈ܢܐ. Gelman & Hill (2007، ܦܐܬܐ 441) ܟܡܦܫܩܝ ܗܘܢܐ ܕܒܬܪ ܟܠ ܠܘܚܐ ܕܚܝܠܐ ܣܛܐܛܝܣܛܝܩܝܐ ܒܚܕ ܣܕܪܐ: ܩܐ ܕܐܝܬ ܣܟܘܝܐ ܕ-80% ܕܫܩܠܚ ܦܐܪܐ ܪܫܝܡܐ، ܡܥܒܕܢܘܬܐ ܫܪܝܪܬܐ ܣܢܝܩܬܐ ܝܠܗ̇ ܕܗܘܝܐ 2.8 ܛܥܝ̈ܘܬܐ ܬܩܝܢ̈ܬܐ ܡܢ ܨܦܪܐ – 1.96 ܩܐ ܕܬܚܘܡܐ ܕܬܘܟܠܢܐ ܕ-95% ܠܐ ܐܝܬܠܗ ܨܦܪܐ، ܘܙܘܕܐ 0.84 ܩܐ ܕܡܛܚ ܠܕܪܓܐ 80 ܡܢ ܡܐܐ ܕܦܘܠܓܐ ܢܘܪܡܠܝܐ. ܥܡ ܛܥܝܘܬܐ ܬܩܝܢܬܐ ܕܡܢܝܢܐ ܡܫܘܬܦܐ ܕܐܣܘܪܐ ܕܚܕ̈ܕܐ (ܒܫܘܢܝܐ z ܕ-Fisher، 1/√(n − 3)) ܐܗܐ ܢܡܘܣܐ ܟܡܕܥܪ ܡܢܝ̈ܢܐ ܕܠܥܠ: ܩܐ r = .30 ܟܡܬܛܝ 85 ܡܫܬܘܬܦ̈ܢܐ، ܩܐ r = .10 ܩܪܝܒ ܠ-780. ܬܪܝܢ ܫܘ̈ܠܡܐ ܥܒܕ̈ܢܝܐ ܟܐܬܝ ܡܢ ܐܟܐ. ܩܕܡܝܐ: ܛܥܝ̈ܘܬܐ ܬܩܝܢ̈ܬܐ ܟܢܚܬܝ ܐܝܟ 1/√n، ܘܡܛܠ ܗܕܐ ܩܐ ܕܦܠܓܚ ܛܥܝܘܬܐ ܬܩܝܢܬܐ ܣܢܝܩ̈ܐ ܝܢܐ ܐܪܒܥܐ ܓܗ̈ܐ ܡܫܬܘܬܦ̈ܢܐ – ܒ-r = .10 ܐܗܐ ܦܘܪܫܢܐ ܝܠܗ ܒܝܢܝ 783 ܘܩܪܝܒ ܠ-3,100 (ܬܡܐ، ܦܐܬܐ 446). ܬܪܝܢܐ، ܚܫܝܚܐ ܒܙܘܕܐ: ܟܠ ܚܘܫܒܢܐ ܕܚܝܠܐ ܣܛܐܛܝܣܛܝܩܝܐ ܟܣܝܡ ܪܒܘܬܐ ܫܪܝܪܬܐ ܕܡܥܒܕܢܘܬܐ، "ܣܝܡܬܐ ܕܡܢ ܟܝܢܗ̇ ܠܐ ܡܨܝܐ ܕܡܬܒܚܪܐ ܡܢ ܝܗܝ̈ܒܬܐ ܕܐܝܬ" – ܕܘܡܝܐ ܩܕܡܝܐ ܕܝܗܒܠܗ r = .30 ܫܠܝܡܐ ܝܠܗ ܐܦ ܥܡ ܐܣܘܪܐ ܒܣܓܝ ܟܪܝܗܐ ܒܙܘܕܐ – ܘܡܛܠ ܗܕܐ "ܠܐ ܛܒܐ ܝܠܗ ܕܣܟܝܚ ܒܐܢܢܩܝ ܪܫܝܡܘܬܐ ܡܢ ܒܘܨܝܐ ܡܘܩܪܒܐ، ܐܦ ܐܢ ܪܒܘܬܐ ܕܕܘܡܝܐ ܬܪܝܨܐܝܬ ܚܫܝܒܬܐ ܝܠܗ̇" (ܬܡܐ، ܦܐܬܐ 447). ܠܘܚܐ ܕܚܝܠܐ ܣܛܐܛܝܣܛܝܩܝܐ ܡܐܢܐ ܕܬܘܩܢܐ ܝܠܗ، ܠܐ ܫܘܘܕܝܐ.

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

ܡܚܫܒܢܐ ܕܐܗܐ ܦܐܬܐ ܫܘܝܐ ܝܠܗ ܠܐܘܪܚܐ Simple Scatter ܕܓܘ ܪܫܝܡܬܐ Graphs ܒ-SPSS. ܩܐ ܡܕܒܪܢܐ ܡܦܪܫܐ ܚܙܝܡܘܢ Field (2024، ܦܣܩܐ 5.8) ܘ-Pallant (2020، ܦܐܬܐ 153-157). ܠ-SPSS ܐܝܬ ܬܪܬܝܢ ܐܘܪ̈ܚܬܐ ܩܐ ܨܘܪܬܐ ܕܒܕܪܐ: ܟܘ̈ܬܐ ܥܬܝܩ̈ܬܐ ܕܡܡܠܠܐ (Legacy Dialogs)، ܕܓܘܗܝܢ ܒܕ ܐܙܠܚ ܐܟܐ ܦܣܥܬܐ ܒܬܪ ܦܣܥܬܐ، ܘ-Chart Builder ܚܕܬܐ ܒܙܘܕܐ، ܕܡܚܘܝܐ ܝܠܗ ܓܘ ܣܘܦܐ ܕܦܣܩܐ. ܬܪܘܝܗܝ ܟܡܦܩܝ ܐܗܝ ܨܘܪܬܐ.

ܡܥܝܪܢܘܬܐ ܥܠ ܢܘ̈ܣܚܐ. ܨܘܪ̈ܬܐ ܕܡܚܙܝܬܐ ܓܘ ܐܗܐ ܦܣܩܐ ܡܦܩ̈ܐ ܝܢܐ ܒ-SPSS ܢܘܣܚܐ 21. ܐܘܪ̈ܚܬܐ ܒܓܢܗܝܢ ܩܝ̈ܡܐ ܝܢܐ ܥܠ ܟܠ ܢܘ̈ܣܚܐ، ܐܠܐ ܕܘܟܬܐ ܕܡܕ̈ܡܐ ܓܘ ܪܫܝܡܬܐ، ܫܡܗ̈ܐ ܕܦܐܬ̈ܐ ܘܡܢܝܢܐ ܕܓܘܒ̈ܝܐ ܓܘ ܓܠܝܘܢܐ ܕܨܘܪ̈ܬܐ ܡܨܝ ܕܫܚܠܦܝ ܩܠܝܠ – ܘܐܢ ܡܚܙܝܬܐ ܓܘ ܕܝܘܟܘܢ ܩܠܝܠ ܐܚܪܢܐ ܟܡܬܚܙܝܐ، ܐܗܐ ܡܨܐ ܕܗܘܐ ܥܠܬܐ. ܐܦ Field (2024)، ܕܐܗܐ ܦܣܩܐ ܟܣܡܟ ܥܠܝܗ، ܟܬܝܒܐ ܝܠܗ ܠܦܘܬ ܢܘܣܚܐ 29. Field ܒܓܢܗ ܟܡܢܝܚ ܒܐܗܐ ܡܕܡ – ܒܝܢܝ ܡܦܩܬܐ ܠܡܦܩܬܐ ܟܦܠܛܝ ܢܘ̈ܣܚܐ ܚܕ̈ܬܐ، ܘܐܘܪ̈ܚܬܐ ܕܟܬܒܐ ܟܡܚܘܝܐ ܩܪܝܒܐ ܠܐ ܝܢܐ ܡܥܒܕ̈ܐ ܡܢ ܐܗܐ.

ܓܘ ܪܫܝܡܬܐ ܟܓܒܚ Graphs › Legacy Dialogs › Scatter/Dot…:

ܓܘ ܟܘܬܐ ܕܡܡܠܠܐ Scatter/Dot ܕܟܦܬܚܐ ܟܓܒܚ ܙܢܐ ܕܨܘܪܬܐ ܡܢ ܓܘ ܚܡܫܐ ܓܘܒ̈ܝܐ، ܘܒܬܪܗ ܟܡܚܚ Define:

Simple Scatter – ܨܘܪܬܐ ܕܒܕܪܐ ܕܚܕ ܡܫܬܚܠܦܢܐ ܬܠܝܐ ܘܚܕ ܠܐ ܬܠܝܐ؛ ܐܗܐ ܝܠܗ ܙܢܐ ܪܫܝܐ، ܡܐ ܕܐܗܐ ܦܐܬܐ ܟܚܫܒܐ، ܘܐܝܠܗ ܐܦ ܪܫܝܡܐ ܐܝܟ ܓܘܒܝܐ ܡܩܕܡܐ ܓܘ ܦܬܚܐ ܕܟܘܬܐ. Overlay Scatter – ܟܡܐ ܙܘ̈ܓܐ ܕܡܫܬܚܠܦ̈ܢܐ ܥܠ ܐܗܝ ܨܘܪܬܐ. Matrix Scatter – ܡܐܛܪܝܟܣ ܕܟܡܚܘܝܐ ܒܚܕ ܙܒܢܐ ܟܠ ܙܘ̈ܓܐ ܕܡܨܝܐ ܕܗܘܝ ܡܢ ܓܘ ܪܫܝܡܬܐ ܕܡܫܬܚܠܦ̈ܢܐ (ܐܢܝ ܬܪܝܢ ܡܦܪ̈ܫܐ ܝܢܐ ܠܬܚܬ، ܓܘ ܦܣܩܐ ܬܘܣܦ̈ܬܐ). 3-D Scatter – ܨܘܪܬܐ ܕܒܕܪܐ ܕܬܠܬܐ ܡܫܬܚܠܦ̈ܢܐ ܒܚܕ ܙܒܢܐ. ܘ-Simple Dot، ܓܘܒܝܐ ܝܚܝܕܝܐ ܐܟܐ ܕܠܐ ܝܠܗ ܨܘܪܬܐ ܕܒܕܪܐ – ܨܘܪܬܐ ܕܢܘܩ̈ܙܐ ܕܟܡܚܘܝܐ ܦܘܠܓܐ ܕܡܫܬܚܠܦܢܐ ܚܕ، ܐܝܟ histogram ܕܓܘܗ̇ ܟܠ ܚܙܝܬܐ ܢܘܩܙܐ ܝܠܗ̇.

ܒܓܘܒܝܐ ܕ-Simple Scatter ܟܦܬܚܐ ܟܘܬܐ ܕܬܚܘܡܐ Simple Scatterplot: ܡܫܬܚܠܦܢܐ ܬܠܝܐ ܟܡܥܒܪܚ ܠܩܘܛܝܐ Y Axis ܘܡܫܬܚܠܦܢܐ ܠܐ ܬܠܝܐ ܠܩܘܛܝܐ X Axis – ܓܘ ܡܬܠܐ ܕܩܕܡܢ ܬܘܟܠܢܐ (trust) ܓܘ ܣܪܛܐ Y ܘ-self-efficacy (efficacy) ܓܘ ܣܪܛܐ X:

ܬܠܬܐ ܩܘ̈ܛܝܐ ܐܚܪ̈ܢܐ ܓܘ ܟܘܬܐ ܦܝܫ̈ܐ ܝܢܐ، ܐܠܐ ܠܐ ܣܢܝܩ̈ܐ: Set Markers by ܟܨܒܥܐ ܢܘܩ̈ܙܐ ܠܦܘܬ ܓܢ̈ܣܐ ܕܡܫܬܚܠܦܢܐ ܬܠܝܬܝܐ (ܪܥܝܢܐ ܥܬܝܩܐ ܝܠܗ: Anscombe، 1973، ܦܐܬܐ 20، ܩܪܐܠܗ triple scatterplot – ܨܘܪܬܐ ܕܬܪܝܢ ܡܫܬܚܠܦ̈ܢܐ ܕܓܘܗ̇ ܪܘܫܡܐ ܕܢܘܩܙܐ ܟܡܪܡܙ ܡܫܬܚܠܦܢܐ ܬܠܝܬܝܐ، ܘܩܐܠܗ ܐܗܐ ܗܘܐ ܚܠܦܐ ܡܣܟܢܐ-ܐܠܐ-ܡܣܦܩܐ ܩܐ ܨܘܪܬܐ ܕܬܠܬܐ ܡܫܘ̈ܚܬܐ)؛ Label Cases by ܟܡܙܝܕܐ ܪܘܫܡܐ ܩܐ ܟܠ ܢܘܩܙܐ، ܦܝܫܐ ܩܐ ܡܫܟܚܬܐ ܕܚܕ ܚܙܝܬܐ ܢܘܟܪܝܬܐ ܡܚܕܕܬܐ؛ ܘ-Panel by Rows/Columns ܟܦܠܓܐ ܨܘܪܬܐ ܠܨܘܪ̈ܬܐ ܙܥܘ̈ܪܬܐ ܦܪ̈ܝܫܬܐ ܠܦܘܬ ܓܘ̈ܕܐ (ܚܙܝܡܘܢ Overlay Scatter ܓܘ ܦܣܩܐ ܕܒܬܪܗ). ܡܚܝܬܐ ܥܠ OK ܟܡܦܩܐ ܨܘܪܬܐ:

ܬܠܬܐ ܡܕ̈ܡܐ ܓܘ ܐܗܐ ܨܘܪܬܐ ܫܘ̈ܝܐ ܝܢܐ ܠܚܘܫܒܐ ܩܕܡ ܕܐܙܠܚ ܠܩܕܡ. ܩܕܡܝܐ، ܢܘܩ̈ܙܐ ܡܬܬܩ̈ܢܐ ܝܢܐ ܐܝܟ ܡܨܝܕܬܐ. ܬܪܝܢ ܡܫܬܚܠܦ̈ܢܐ ܡܨܥܝ̈ܬܐ ܝܢܐ ܕܦܣܘ̈ܩܐ ܕܣܒܠܬܐ، ܘܡܛܠ ܗܕܐ ܟܫܩܠܝ ܒܣ ܛܝ̈ܡܐ ܒܫܘܪ̈ܐ ܕܦܠܓܐ ܢܘܩܙܐ. ܐܗܐ ܓܡܝܪܐܝܬ ܬܪܝܨܐ ܝܠܗ، ܘܠܐ ܟܡܣܗܕ ܥܠ ܚܒܠܐ ܓܘ ܝܗܝ̈ܒܬܐ.

ܬܪܝܢܐ، ܘܐܗܐ ܚܫܝܚܐ ܝܠܗ ܒܙܘܕܐ – ܥܠ ܡܚܙܝܬܐ ܟܚܙܝܚ ܒܣܓܝ ܒܨܝܪ ܢܘܩ̈ܙܐ ܡܢ 479. ܡܫܬܘܬܦ̈ܢܐ ܕܛܝ̈ܡܐ ܕܝܠܗܘܢ ܫܘ̈ܝܐ ܝܢܐ ܓܘ ܬܪܝܢ ܡܫܬܚܠܦ̈ܢܐ ܨܝܪ̈ܐ ܝܢܐ ܚܕ ܥܠ ܚܕ (overplotting)، ܘܚܕ ܢܘܩܙܐ ܥܠ ܡܚܙܝܬܐ ܡܨܐ ܕܡܚܘܐ ܥܣܪ̈ܐ ܕܚܙ̈ܝܬܐ. ܣܘܟܠܐ ܥܒܕܢܝܐ: ܓܘ ܨܘܪܬܐ ܕܐܗܐ ܙܢܐ ܠܐ ܡܨܝܚ ܕܫܥܪܚ ܚܝܠܐ ܕܐܣܘܪܐ ܒܥܝܢܐ، ܡܛܠ ܕܥܒܝܘܬܐ – ܡܘܕܥܢܘܬܐ ܚܫܝܚܬܐ – ܒܣ ܠܐ ܟܡܬܚܙܝܐ؛ ܡܛܠ ܗܕܐ ܟܡܫܚܚ ܠܗ̇ ܒܡܢܝܢܐ (r ܝܢ R²) ܘܠܐ ܒܪܓܫܐ. ܡܐ ܕܛܒܐ ܟܡܬܚܙܐ ܝܠܗ ܐܣܟܝܡܐ ܕܥܢܢܐ: ܙܘܝܬܐ ܝܡܝܢܝܬܐ-ܬܚܬܝܬܐ – self-efficacy ܪܡܬܐ ܥܡ ܬܘܟܠܢܐ ܬܚܬܝܐ – ܩܪܝܒܐ ܓܡܝܪܐܝܬ ܣܦܝܩܬܐ ܝܠܗ̇، ܘܐܗܐ ܒܚܬܝܬܘܬܐ ܪܘܫܡܐ ܝܠܗ ܕܐܣܘܪܐ ܕܙܘܕܐ. (ܓܘ ܨܘܪܬܐ ܕܐܗܐ ܦܐܬܐ ܢܘܩ̈ܙܐ ܨܝܪ̈ܐ ܝܢܐ ܒܓܠܝܘܬܐ ܡܢܬܢܝܬܐ، ܘܡܛܠ ܗܕܐ ܟܢܫܐ ܕܚܙ̈ܝܬܐ ܓܘ ܐܗܘ ܕܘܟܐ ܟܡܬܚܙܐ ܐܝܟ ܟܬܡܐ ܟܘܡܐ ܒܙܘܕܐ – ܪܡܙܐ ܚܙܝܢܝܐ ܩܐ ܥܒܝܘܬܐ ܕܠܝܬ ܓܘ ܡܦܩܢܐ ܥܝܕܝܐ ܕ-SPSS.) ܐܣܝܘܬܐ ܐܚܪܬܐ ܩܐ overplotting ܝܠܗ̇ jitter (jittering): ܟܡܙܝܕܚ ܥܠ ܛܝܡܐ ܕܟܠ ܡܫܬܘܬܦܢܐ، ܓܘ ܚܕ ܡܢ ܣܪ̈ܛܐ ܝܢ ܓܘ ܬܪܘܝܗܝ، "ܩܠܐ" ܓܕܫܢܝܐ ܙܥܘܪܐ، ܩܐ ܕܢܘܩ̈ܙܐ ܕܝܬܝ̈ܒܐ ܗܘܘ ܚܕ ܥܠ ܚܕ ܡܬܒܕܪܝ ܩܠܝܠ ܘܐܬܝܐ ܪܓܫܐ ܕܥܒܝܘܬܐ. ܛܝ̈ܡܐ ܒܓܢܗܘܢ ܠܐ ܟܡܫܬܚܠܦܝ – ܒܣ ܨܘܪܬܐ – ܘܚܘܫܒܢܐ ܒܫܪܪܐ ܥܠ ܝܗܝ̈ܒܬܐ ܩܕܡ̈ܝܬܐ ܟܡܬܥܒܕ (Cohen, Cohen, West & Aiken, 2003, p. 111). ܗܘܝܐ ܕܓܘܗ ܐܗܐ ܐܘܡܢܘܬܐ ܒܫܪܪܐ ܣܢܝܩܬܐ ܝܠܗ̇ ܨܘܪܬܐ ܕܒܕܪܐ ܝܠܗ̇ ܕܚܕ ܡܢ ܡܫܬܚܠܦ̈ܢܐ ܕܝܠܗ̇ ܕܓܢ̈ܣܐ ܝܠܗ، ܡܬܠܐ ܕܟܪܐ/ܢܩܒܬܐ ܒܪܡܙܢܘܬܐ 0/1: ܕܠܐ jitter ܟܠ ܓܘܕܐ ܚܕ ܥܡܘܕܐ ܙܩܝܦܐ ܝܠܗ̇، ܕܓܘܗ ܠܐ ܡܨܝܚ ܕܦܪܫܚ ܒܝܢܝ ܚܕ ܡܫܬܘܬܦܢܐ ܘܡܐܐ.

ܟܡܐ ܩܠܐ ܕܡܙܝܕܚ؟ Gelman & Hill (2007، ܦܐܬܐ 554) ܟܝܗܒܝ ܢܡܘܣܐ: ܩܐ ܝܗܝ̈ܒܬܐ ܒܛܝ̈ܡܐ ܫܠܡ̈ܐ – ܡܢܝܢܐ ܓܕܫܢܝܐ ܫܘܝܐ ܒܝܢܝ −0.3 ܘ-+0.3 ܩܐ ܟܠ ܛܝܡܐ ܕ-X ܘܕ-Y؛ ܘܒܟܠܢܝܘܬܐ، "ܒܚܬܝܬܘܬܐ ܡܣܦܩܐ ܩܐ ܕܟܝܢܐ ܦܪܝܫܐ (discrete) ܕܝܗܝ̈ܒܬܐ ܗܠܐ ܓܠܝܐ ܗܘܐ". ܩܐ ܝܗܝ̈ܒܬܐ ܕ-Likert ܒܫܘܪ̈ܐ ܕܦܠܓܐ ܢܘܩܙܐ، ܐܝܟ ܓܘ ܡܬܠܐ، ܦܬܝܘܬܐ ܫܘܝܬܐ ܩܪܝܒ ܠ-±0.15 ܝܠܗ̇. ܐܢܝ ܐܦ ܟܡܣܠܝ ܚܠܦܐ ܕܓܘܗ ܟܪܫܡܚ ܢܘܩܙܐ ܕܥܠ ܢܘܩܙܐ ܒܡܢܝܢܐ (2، 3…) ܝܢ ܒܪܘܫܡܐ ܝܚܝܕܝܐ: ܐܗܐ ܡܛܥܝܢܐ ܝܠܗ ܒܚܙܝܬܐ، ܘܒܫܬܐܣܐ ܠܐ ܝܠܗ ܡܣܦܩܐ، ܡܛܠ ܕܗܝܓ ܡܚܘܝܐ ܕܟܠ ܡܫܬܘܬܦܢܐ ܬܠܐ ܝܠܗ ܒܝܬܝܪܘܬܐ ܒܡܫܬܘܬܦ̈ܢܐ ܐܚܪ̈ܢܐ. ܒ-R ܐܗܐ ܝܠܗ geom_jitter(width = 0.15, height = 0.15) ܒܕܘܟܬ geom_point ܓܘ ܣܩܪܝܦܬ ܕܓܘ ܦܣܩܐ ܕ-R.

ܘܬܠܝܬܝܐ، ܐܝܬ ܐܟܐ ܚܙܝܬܐ ܢܘܟܪܝܬܐ. ܓܘ ܙܘܝܬܐ ܣܡܠܝܬܐ-ܥܠܝܬܐ ܝܬܝܒܐ ܝܠܗ ܚܕ ܢܘܩܙܐ ܒܠܚܘܕܗ – self-efficacy 1.00 ܥܡ ܬܘܟܠܢܐ 5.00 – ܪܚܝܩܐ ܡܢ ܐܣܟܝܡܐ ܕܚܙ̈ܝܬܐ ܐܚܪ̈ܢܝܬܐ. ܐܗܐ ܒܚܬܝܬܘܬܐ ܚܙܝܬܐ ܝܠܗ̇ ܕܦܣܩܐ ܕܫܪ̈ܛܐ ܕܠܥܠ ܟܡܦܝܣ ܕܩܐܡܚ ܘܒܚܪܚ: ܐܢ ܛܥܝܘܬܐ ܕܟܬܝܒܬܐ ܝܠܗ̇، ܕܘܟܬܐ ܕܝܠܗ̇ ܠܐ ܝܠܗ̇ ܓܘ ܦܘܫܩܐ؛ ܘܐܢ ܝܗܒܬܐ ܫܪܝܪܬܐ ܝܠܗ̇، ܟܦܝܫܐ – ܐܠܐ ܛܒܐ ܝܠܗ ܕܝܕܥܚ ܕܐܝܠܗ̇ ܬܡܐ، ܘܒܚܪܚ ܟܡܐ ܟܓܪܫܐ ܠܦܐܬܗ̇ ܣܪܛܐ ܕܪܝܓܪܫܢ. ܘܒܣܘܦܐ، ܡܚܘܝܢܘܬܐ ܙܥܘܪܬܐ ܩܐ ܟܠ ܡܐ ܕܐܡܝܪܐ ܝܠܗ ܓܘ ܦܣܩܐ ܕܩܕܡ: ܓܘ ܦܐܝܠ ܕܝܗܝ̈ܒܬܐ ܒܓܢܗ ܠܝܬ ܬܡܐ ܚܕ ܚܙܝܬܐ ܐܠܐ ܬܪܬܝܢ – ܬܪܝܢ ܡܫܬܘܬܦ̈ܢܐ ܥܡ ܐܢܝ ܛܝ̈ܡܐ ܒܚܬܝܬܘܬܐ، ܕܨܝܪ̈ܐ ܝܢܐ ܚܕ ܥܠ ܚܕ ܘܟܡܬܚܙܝ ܐܝܟ ܚܕ ܢܘܩܙܐ.

ܕܪܓܐ ܕܬܘܩܢܐ: ܟܘܬܐ Chart Editor. ܠܐ ܐܝܟ ܓܘ ܡܚܫܒܢܐ ܕܐܗܐ ܦܐܬܐ، ܒ-SPSS ܣܪܛܐ ܕܪܝܓܪܫܢ ܠܐ ܟܡܬܚܙܐ ܒܓܢܗ ܥܡ ܨܘܪܬܐ – ܟܡܙܝܕܚ ܠܗ ܓܘ ܬܘܩܢܐ. ܡܚܝܬܐ ܬܢܝܢܬܐ (double-click) ܥܠ ܨܘܪܬܐ ܓܘ ܟܘܬܐ ܕܡܦܩܢܐ ܟܦܬܚܐ ܠܗ̇ ܓܘ ܟܘܬܐ ܦܪܝܫܬܐ، Chart Editor، ܘܓܢܒܗ̇ ܟܦܬܚܐ ܟܘܬܐ Properties – ܡܨܥܬܐ ܕܬܘܩܢܐ ܕܨܘܪܬܐ:

ܚܕ ܢܡܘܣܐ ܚܫܝܚܐ ܓܘ ܟܘܬܐ Properties: ܦܐܬ̈ܐ ܕܓܘܗ̇ ܟܡܫܬܚܠܦ̈ܢ ܠܦܘܬ ܡܐ ܕܪܫܝܡܐ ܝܠܗ ܓܘ ܨܘܪܬܐ. ܓܘ ܨܘܪܬܐ ܕܠܥܠ ܡܕܡ ܠܐ ܝܠܗ ܪܫܝܡܐ، ܘܡܛܠ ܗܕܐ ܟܡܬܚܙ̈ܝܢ ܒܣ ܬܪܬܝܢ ܦܐܬ̈ܐ – Chart Size، ܕܓܘܗ̇ ܟܡܬܦܣܩܝ ܪܘܡܐ ܘܦܬܝܘܬܐ ܕܨܘܪܬܐ ܒܢܘܩ̈ܙܐ (ܐܟܐ 375 ܥܠ 468.75، ܥܡ ܢܛܘܪܘܬܐ ܕܦܘܚܡܐ ܕܪܘܡܐ-ܦܬܝܘܬܐ)، ܘ-Variables. ܡܚܝܬܐ ܥܠ ܚܕ ܡܢ ܢܘܩ̈ܙܐ ܕܒܕܪܐ ܟܪܫܡܐ ܟܠܗ ܣܕܪܐ ܕܢܘܩ̈ܙܐ، ܘܟܡܙܝܕܐ ܠܟܘܬܐ ܬܪܬܝܢ ܦܐܬ̈ܐ ܐܚܪ̈ܢܝܬܐ:

ܓܘ Marker ܟܡܬܦܣܩ ܚܙܘܐ ܕܢܘܩ̈ܙܐ: Type – ܐܣܟܝܡܐ ܕܪܘܫܡܐ (ܚܘܕܪܐ، ܡܪܒܥܐ، ܡܬܠܬܐ)؛ Size – ܪܒܘܬܐ ܕܝܠܗ؛ ܘ-Fill ܘ-Border – ܓܘܢܐ ܕܡܠܝܐ ܘܓܘܢܐ ܕܬܚܘܡܐ. ܐܝܟ ܓܘܒܝܐ ܡܩܕܡܐ ܡܠܝܐ ܣܦܝܩܐ ܝܠܗ (Transparent) ܘܬܚܘܡܐ ܐܘܟܡܐ، ܘܡܢ ܐܟܐ ܚܘ̈ܕܪܐ ܣܦܝ̈ܩܐ ܕܓܘ ܡܦܩܢܐ. ܐܗܐ ܦܐܬܐ ܦܝܫܬܐ ܝܠܗ̇ ܒܙܘܕܐ ܡܢ ܡܐ ܕܟܡܬܚܙܐ: ܡܙܥܪܢܘܬܐ ܕܪܘܫܡܐ، ܝܢ ܡܠܝܐ ܕܝܠܗ ܒܓܘܢܐ ܢܗܝܪܐ ܒܓܠܝܘܬܐ، ܟܡܥܕܪܐ ܛܒܐ ܓܘ ܨܘܪܬܐ ܥܒܝܬܐ ܐܝܟ ܕܝܠܢ، ܕܓܘܗ̇ ܣܓܝ ܢܘܩ̈ܙܐ ܝܬܝ̈ܒܐ ܝܢܐ ܚܕ ܥܠ ܚܕ.

ܦܐܬܐ Spikes ܟܡܙܝܕܐ ܡܢ ܟܠ ܢܘܩܙܐ ܣܪܛܐ ܩܛܝܢܐ ܠܥܓܢܐ ܩܝܡܐ: Floor – ܠܣܪܛܐ X، Origin – ܠܫܘܪܝܐ ܕܣܪ̈ܛܐ، ܘ-Centroid – ܠܡܨܥܬܐ ܕܝܘܩܪܐ ܕܥܢܢܐ. ܓܘܒܝܐ ܡܩܕܡܐ، None، ܐܝܠܗ ܐܦ ܡܦܝܣܐ ܩܐ ܨܘܪܬܐ ܕܒܕܪܐ ܥܝܕܝܬܐ؛ Centroid ܡܨܐ ܕܡܚܘܐ ܝܘܠܦܢܐ ܥܠ ܒܕܪܐ ܚܕܪ ܡܨܥܬܐ، ܐܠܐ ܓܘ ܨܘܪܬܐ ܥܡ ܡܐ̈ܐ ܕܚܙ̈ܝܬܐ ܟܒܪܐ ܥܒܝܘܬܐ ܕܣܪ̈ܛܐ.

ܦܐܬܐ Variables ܥܡܝܩܬܐ ܝܠܗ̇ ܡܢ ܟܠܗܝܢ: ܟܡܚܘܝܐ ܡܢܘ̈ܬܐ ܕܡܢܝܗܝܢ ܨܘܪܬܐ ܒܢܝܬܐ ܝܠܗ̇ ܘܡܫܬܚܠܦ̈ܢܐ ܕܟܡܣܝܒܪܝ ܠܗܝܢ. ܪܫܝܡܬܐ ܕܟܦܬܚܐ Element Type ܟܓܠܝܐ ܡܘܕܝ ܐܚܪܢܐ ܡܨܝܚ ܕܨܝܪܚ ܥܠ ܐܢܝ ܝܗܝ̈ܒܬܐ – Marker (ܢܘܩ̈ܙܐ، ܘܐܗܐ ܡܢܬܐ ܕܐܝܬ)، Fit Line (ܣܪܛܐ ܕܦܐܝܘܬܐ)، Interpolation Line، Distribution Line، Path ܘܐܚܪ̈ܢܐ. ܐܟܐ ܡܨܝܚ ܐܦ ܕܡܙܝܕܚ ܡܢܬܐ ܚܕܬܐ ܠܨܘܪܬܐ ܒܦܬܝܪܐ New. ܒܪܡ، ܒܪܘܒܐ ܠܝܬ ܣܢܝܩܘܬܐ ܠܐܗܐ ܐܘܪܚܐ: ܣܪܛܐ ܕܪܝܓܪܫܢ ܟܡܬܬܘܣܦ ܒܚܕ ܦܘܩܕܢܐ ܝܚܝܕܝܐ، ܘܐܗܐ ܝܠܗ ܕܪܓܐ ܕܒܬܪܗ.

ܘܡܙܝܕܬܐ ܕܣܪܛܐ ܕܪܝܓܪܫܢ ܒܓܢܗ. ܓܘ ܪܫܝܡܬܐ ܕ-Chart Editor ܟܓܒܚ Elements › Fit Line at Total…. ܦܘܩܕܢܐ ܟܡܙܝܕ ܠܟܘܬܐ Properties ܦܐܬܐ ܚܕܬܐ، Fit Line، ܕܓܘܗ̇ ܟܡܬܓܒܝܐ ܐܘܪܚܐ ܕܦܐܝܘܬܐ (Fit Method): ܓܘܒܝܐ ܡܩܕܡܐ Linear ܝܠܗ ܪܝܓܪܫܢ ܣܪܛܢܝܐ ܦܫܝܛܐ – ܒܚܬܝܬܘܬܐ ܐܗܐ ܕܐܗܐ ܦܐܬܐ ܟܚܫܒܐ – ܘܓܢܒܗ Quadratic، Cubic، Loess ܘ-Mean of Y. ܡܚܝܬܐ ܥܠ Apply ܘܒܬܪܗ Close ܟܡܙܝܕܐ ܣܪܛܐ ܠܨܘܪܬܐ، ܘܟܡܚܘܝܐ ܥܠܗ̇ ܛܝܡܐ R Sq Linear (ܓܘ ܢܘ̈ܣܚܐ ܥܬܝܩ̈ܐ ܒܙܘܕܐ ܕ-SPSS ܟܬܒܐ ܟܡܬܚܙܐ ܕܠܐ ܪܘܫܡܐ ܕܡܪܒܥܐ، ܐܝܟ ܟܬܒܐ "RSq Linear"). ܡܣܟܪܬܐ ܕܟܘܬܐ Chart Editor ܟܡܕܥܪܐ ܨܘܪܬܐ ܡܚܘܕܬܬܐ ܠܟܘܬܐ ܕܡܦܩܢܐ.

ܘܡܘܕܝ ܟܥܒܕ Loess؟ ܐܗܐ ܝܠܗ ܓܘܒܝܐ ܕܚܫܝܚܐ ܝܠܗ ܡܢ ܟܠܗ ܡܢ ܓܘ ܚܠ̈ܦܐ ܕܣܪܛܐ ܬܪܝܨܐ: ܣܪܛܐ ܫܥܝܥܐ ܕܠܐ ܟܣܝܡ ܡܕܡ ܥܠ ܐܣܟܝܡܐ ܕܐܣܘܪܐ، ܐܠܐ ܒܣ ܟܐܙܠ ܒܬܪ ܐܘܪܚܐ ܕܝܗܝ̈ܒܬܐ، ܦܣܩܐ ܒܬܪ ܦܣܩܐ (locally weighted scatterplot smoother). ܦܘܠܚܢܐ ܬܪܝܨܐ ܕܝܠܗ ܐܝܟ ܒܘܚܪܢܐ ܝܠܗ: ܐܢ ܐܣܘܪܐ ܓܘ ܟܢܫܐ ܟܠܢܝܐ ܣܪܛܢܝܐ ܝܠܗ، ܣܪܛܐ ܕ-Loess ܣܢܝܩ ܝܠܗ ܕܡܬܚܙܐ ܐܝܟ ܩܘܪܒܐ ܥܒܝܐ ܕܣܪܛܐ ܬܪܝܨܐ – ܒܡܬܠܐ ܕ-Cohen, Cohen, West & Aiken (2003، ܦܐܬܐ 112)، ܐܝܟ "ܨܘܪܬܐ ܚܐܪܬܐ ܕܝܠܕܐ ܙܥܘܪܐ ܕܣܪܛܐ ܬܪܝܨܐ". ܐܢ ܓܠܝܐܝܬ ܟܦܐܫ ܟܦܝܦܐ، ܣܪܛܐ ܬܪܝܨܐ ܠܐ ܝܠܗ ܡܘܕܝܠ ܬܪܝܨܐ. ܬܪܝܢ ܡܕ̈ܡܐ ܕܛܒܐ ܝܠܗ ܕܝܕܥܚ: ܦܬܝܘܬܐ ܕܟܘܬܐ (ܒ-SPSS: % of points to fit) ܟܦܣܩܐ ܡܫܘܚܬܐ ܕܫܥܝܥܘܬܐ – ܛܝܡܐ ܒܣܓܝ ܙܥܘܪܐ ܟܨܝܪ ܟܠ ܥܘܩܠܐ ܓܘ ܩܠܐ، ܛܝܡܐ ܒܣܓܝ ܪܒܐ ܟܡܬܪܨ ܐܦ ܟܦܝܦܘܬܐ ܫܪܝܪܬܐ، ܘܡܛܠ ܗܕܐ ܛܒܐ ܝܠܗ ܕܡܢܣܚ ܬܪܝܢ-ܬܠܬܐ ܛܝ̈ܡܐ؛ ܘܓܘ ܣܘܦ̈ܐ ܕܦܬܝܘܬܐ ܕ-X، ܕܓܘܗܘܢ ܝܗܝ̈ܒܬܐ ܩܠܝܠ̈ܬܐ ܝܢܐ، ܣܪܛܐ ܒܣܓܝ ܒܨܝܪ ܡܗܝܡܢܐ ܝܠܗ ܡܢ ܓܘ ܡܨܥܬܐ (ܬܡܐ، ܦܐܬܐ 113-114).

ܘܬܚܘ̈ܡܐ ܕܬܘܟܠܢܐ ܚܕܪ ܣܪܛܐ. ܓܘ ܐܗܝ ܦܐܬܐ Fit Line، ܬܚܘܬ Fit Method، ܝܬܝܒܐ ܝܠܗ̇ ܓܘܕܐ ܕܓܘܒ̈ܝܐ Confidence Intervals. ܓܘܒܝܐ ܡܩܕܡܐ ܝܠܗ None – ܣܪܛܐ ܥܪܛܠܝܐ، ܕܠܐ ܬܚܘܡܐ – ܘܓܢܒܗ ܬܪܝܢ ܓܘܒ̈ܝܐ ܕܟܡܬܚܙܝ ܕܡ̈ܝܐ ܘܠܐ ܝܢܐ ܕܡ̈ܝܐ ܡܕܡ: Mean ܘ-Individual (ܥܡ ܚܩܠܐ ܕܪܡܐ ܕܬܘܟܠܢܐ، 95 ܐܝܟ ܓܘܒܝܐ ܡܩܕܡܐ). Mean ܟܨܝܪ ܦܘܠܓ ܪܥܝܢܐ ܓܘ ܣܪܛܐ ܒܓܢܗ – ܐܝܟܐ ܟܥܒܪܐ، ܓܘ ܟܢܫܐ ܟܠܢܝܐ، ܡܨܥܝܬܐ ܕ-Y ܓܘ ܟܠ ܛܝܡܐ ܕ-X. Individual ܟܦܢܐ ܠܫܘܐܠܐ ܐܚܪܢܐ ܓܡܝܪܐܝܬ – ܐܝܟܐ ܡܣܟܝܐ ܝܠܗ ܕܢܦܠ ܡܫܬܘܬܦܢܐ ܝܚܝܕܝܐ ܚܕܬܐ – ܘܬܚܘܡܐ ܕܝܠܗ ܒܣܓܝ ܦܬܝܐ ܝܠܗ، ܡܛܠ ܕܟܛܥܢ ܬܪܝܢ ܡܒܘ̈ܥܐ ܕܦܘܠܓ ܪܥܝܢܐ ܒܕܘܟܬ ܚܕ: ܐܦ ܦܘܠܓ ܪܥܝܢܐ ܓܘ ܣܪܛܐ، ܘܐܦ ܒܕܪܐ ܕܡܫܬܘܬܦ̈ܢܐ ܚܕܪܗ. Gelman & Hill (2007، ܦܐܬܐ 47-48) ܟܟܬܒܝ ܐܗܐ ܐܗܟܐ: ܛܥܝܘܬܐ ܬܩܝܢܬܐ ܕܡܢܒܝܢܘܬܐ ܩܐ ܚܙܝܬܐ ܚܕܬܐ ܩܠܝܠ ܪܒܬܐ ܝܠܗ̇ ܡܢ σ – ܣܛܝܘܬܐ ܬܩܝܢܬܐ ܕܫܪ̈ܟܐ، ܕܐܝܠܗ̇ Std. Error of the Estimate ܕܓܘ ܠܘܚܐ Model Summary – ܘܐܗܐ ܡܛܠ ܦܘܠܓ ܪܥܝܢܐ ܓܘ ܫܘܥܪܐ ܕܡܢܝ̈ܢܐ ܡܫܘܬ̈ܦܐ ܕܪܝܓܪܫܢ؛ ܘܒܩܘܪܒܐ ܢܘܪܡܠܝܐ، ܩܪܝܒ ܠ-50% ܡܢ ܛܝ̈ܡܐ ܒܫܪܪܐ ܟܢܦܠܝ ܓܘ ܦܬܝܘܬܐ ±0.67σ ܚܕܪ ܡܢܒܝܢܘܬܐ، ܩܪܝܒ ܠ-68% ܓܘ ܦܬܝܘܬܐ ±σ ܘܩܪܝܒ ܠ-95% ܓܘ ܦܬܝܘܬܐ ±2σ.

ܘܠܡܢܐ ܬܪܝܢ ܬܚܘ̈ܡܐ ܥܝܩ̈ܐ ܝܢܐ ܓܘ ܡܨܥܬܐ ܘܟܦܬܝ ܓܘ ܣܘܦ̈ܐ. ܐܗܐ ܠܐ ܝܠܗ ܡܕܡ ܕ-SPSS ܐܠܐ ܕܝܠܝܬܐ ܝܠܗ̇ ܕܡܢܒܝܢܘܬܐ ܒܓܢܗ̇: ܦܘܠܓ ܪܥܝܢܐ ܟܪܒܐ ܟܡܐ ܕܟܪܚܩܚ ܡܢ ܡܨܥܝܬܐ ܕܡܢܒܝܢܐ (Gelman & Hill, 2007, p. 44). ܓܘ ܡܬܘܪܓܡܐ ܕܛܥܝܘܬܐ ܬܩܝܢܬܐ ܕܡܢܒܝܢܘܬܐ (ܬܡܐ، ܦܐܬܐ 47، ܡܥܝܪܢܘܬܐ ܕܬܚܬ 3) ܟܚܙܝܚ ܐܗܐ ܬܪܝܨܐܝܬ – σ_forecast = σ √(1 + 1/n + (x − x̄)² / Σ(x_i − x̄)²): term ܡܨܥܝܐ ܟܙܥܪ ܟܡܐ ܕܕܘܡܝܐ ܟܪܒܐ؛ term ܬܠܝܬܝܐ ܟܪܒܐ ܟܡܐ ܕܛܝܡܐ ܕ-X ܕܥܠܝܗ ܟܡܢܒܚ ܪܚܝܩܐ ܝܠܗ ܡܢ ܡܨܥܝܬܐ ܕ-X ܓܘ ܕܘܡܝܐ – ܘܡܢ ܐܟܐ ܐܣܟܝܡܐ ܕܫܥܬܐ ܕܚܠܐ ܕܬܚܘܡܐ؛ ܘ-1 ܕܒܪܝܫܐ ܒܚܬܝܬܘܬܐ ܦܘܪܫܢܐ ܝܠܗ ܒܝܢܝ Individual ܘ-Mean: ܒܕܪܐ ܕܡܫܬܘܬܦܢܐ ܝܚܝܕܝܐ ܚܕܪ ܣܪܛܐ، ܕܠܐ ܟܓܢܙ ܐܦ ܐܝܡܢ ܕܕܘܡܝܐ ܟܪܒܐ ܕܠܐ ܬܚܘܡܐ. ܐܗܐ ܐܗܘ ܙܘܗܪܐ ܝܠܗ ܕܐܡܝܪܐ ܝܠܗ ܐܟܐ ܥܠ ܣܘܦ̈ܐ ܕܣܪܛܐ ܕ-Loess، ܘܓܘ ܢܘܣܚܐ ܣܪܛܢܝܐ ܟܫܩܠ ܚܘܝܐ ܕܨܘܪܬܐ – ܬܚܘܡܐ ܒܓܢܗ ܟܡܘܕܥ ܐܝܟܐ ܣܪܛܐ ܟܝܕܥ ܒܨܝܪ.

ܘܡܘܕܝ ܕܡܬܢܚ. ܬܪܝܢ ܬܚܘ̈ܡܐ ܟܦܢܝ ܠܬܪܝܢ ܫܘ̈ܐܠܐ ܦܪ̈ܝܫܐ، ܘܡܛܠ ܗܕܐ ܓܘܒܝܐ ܒܝܢܝ ܕܝܠܗܘܢ ܠܐ ܝܠܗ ܡܕܡ ܕܛܥܡܐ: Mean ܟܐܡܪ ܟܡܐ ܟܝܕܥܚ ܐܝܟܐ ܟܥܒܪ ܣܪܛܐ، ܘ-Individual ܟܐܡܪ ܟܡܐ ܡܨܝܚ ܕܡܢܒܚ ܚܕ ܒܪܢܫܐ. ܛܥܝܘܬܐ ܕܡܬܚܙܝܐ ܣܓܝ ܝܠܗ̇ ܕܩܪܚ ܬܚܘܡܐ ܥܝܩܐ ܐܝܟ ܕܟܐܡܪ ܐܝܟܐ ܟܢܦܠܝ ܡܫܬܘܬܦ̈ܢܐ، ܐܝܡܢ ܕܒܣ ܟܐܡܪ ܐܝܟܐ ܟܥܒܪܐ ܡܨܥܝܬܐ ܕܝܠܗܘܢ – ܘܓܘ ܕܘܡܝܐ ܪܒܐ ܒܣܓܝ ܥܝܩܐ ܝܠܗ ܐܦ ܐܝܡܢ ܕܒܕܪܐ ܚܕܪ ܣܪܛܐ ܒܣܓܝ ܪܒܐ ܝܠܗ. ܓܘ ܨܚܚܐ ܕܡܫܟܚ̈ܢܘܬܐ، ܐܝܡܢ ܕܨܘܪܬܐ ܕܒܕܪܐ ܟܐܬܝܐ ܩܐ ܕܡܚܘܝܐ ܐܣܘܪܐ ܘܠܐ ܩܐ ܡܢܒܝܢܘܬܐ، ܓܘܒܝܐ ܡܩܒܠܐ ܝܠܗ Mean؛ ܘܓܘ ܡܥܝܪܢܘܬܐ ܕܨܘܪܬܐ ܣܢܝܩ ܝܠܗ ܕܡܥܗܕܚ ܐܝܢܐ ܬܚܘܡܐ ܡܚܘܝܐ ܝܠܗ ܘܒܐܝܢܐ ܪܡܐ ܕܬܘܟܠܢܐ. ܐܗܐ ܠܐ ܝܠܗ ܩܫܝܘܬܐ ܝܬܝܪܬܐ ܐܠܐ ܣܢܝܩܘܬܐ ܓܠܝܬܐ: APA (2020، ܦܣܩܐ 7.28) ܟܡܣܢܩܐ ܕܡܦܫܩܚ ܓܘ ܡܥܝܪܢܘܬܐ ܟܠ ܛܠܠܐ ܝܢ ܡܢܬܐ ܐܚܪܬܐ ܕܨܘܪܬܐ ܕܟܛܥܢܐ ܣܘܟܠܐ، ܘܟܐܡܪܐ ܓܠܝܐܝܬ ܕܐܝܡܢ ܕܨܘܪܬܐ ܐܝܬܠܗ̇ ܪܘܫ̈ܡܐ ܕܛܥܝܘܬܐ ܣܢܝܩ ܝܠܗ ܕܐܡܪܚ ܐܢ ܟܡܚܘܝܝ ܣܛܝ̈ܘܬܐ ܬܩܝܢ̈ܬܐ، ܛܥܝ̈ܘܬܐ ܬܩܝܢ̈ܬܐ، ܬܚܘ̈ܡܐ ܕܬܘܟܠܢܐ ܝܢ ܦܬܝ̈ܘܬܐ – ܘܟܡܙܝܕܐ ܕܛܒܐ ܝܠܗ ܕܡܥܗܕܚ ܓܢܒܝܗܘܢ ܐܦ ܪܒܘܬܐ ܕܕܘܡܝܐ. ܡܚܫܒܢܐ ܕܐܗܐ ܦܐܬܐ ܟܨܝܪ ܣܪܛܐ ܕܠܐ ܬܚܘܡܐ، ܘܡܛܠ ܗܕܐ ܐܗܐ ܬܘܣܦܬܐ ܝܠܗ̇ ܕܟܐܬܝܐ ܒܣ ܡܢ SPSS.

ܡܚܝܬܐ ܥܠ Paste ܓܘ ܟܠ ܚܕܐ ܡܢ ܟܘ̈ܬܐ ܕܡܡܠܠܐ ܟܢܛܪܐ ܥܒܕܐ ܐܝܟ ܣܝܢܬܐܟܣ:

GRAPH
  /SCATTERPLOT(BIVAR)=efficacy WITH trust
  /MISSING=LISTWISE.

ܚܙܝܡܘܢ: ܦܘܩܕܢܐ GRAPH ܐܝܟ ܓܘܒܝܐ ܡܩܕܡܐ ܟܦܠܚ ܒܫܩܠܬܐ ܕܣܕܪܐ ܟܠܗ (/MISSING=LISTWISE)، ܘܠܐ ܒܫܩܠܬܐ ܙܘܓܢܝܬܐ ܕܦܠܚܐ ܝܠܗ̇ ܩܐ ܐܘܪܚܐ ܕܐܣܘܪ̈ܐ ܕܚܕ̈ܕܐ ܘܩܐ ܡܚܫܒܢܐ ܕܐܗܐ ܦܐܬܐ. ܓܘ ܚܕ ܨܘܪܬܐ ܕܒܕܪܐ، ܕܚܕ ܙܘܓܐ ܕܡܫܬܚܠܦ̈ܢܐ ܒܠܚܘܕ، ܠܝܬ ܠܐܗܐ ܣܘܟܠܐ ܥܒܕܢܝܐ: ܬܪܬܝܢ ܐܘܪ̈ܚܬܐ ܟܡܛܝܢ ܠܐܗܝ ܓܘܕܐ ܕܚܙ̈ܝܬܐ ܒܚܬܝܬܘܬܐ، ܡܛܠ ܕܠܝܬ ܐܟܐ ܡܫܬܚܠܦ̈ܢܐ ܐܚܪ̈ܢܐ ܕ"ܡܛܠܬܗܘܢ" ܚܙ̈ܝܬܐ ܐܚܪ̈ܢܝܬܐ ܟܡܬܫܩܠ̈ܢ.

ܐܘܪܚܐ ܬܪܝܢܐ: Chart Builder

ܐܘܪܚܐ ܕܡܚܘܝܐ ܝܠܗ ܗܕܟܐ ܐܝܠܗ ܐܘܪܚܐ ܕܟܘ̈ܬܐ ܥܬܝܩ̈ܬܐ ܕܡܡܠܠܐ. ܓܘ ܢܘ̈ܣܚܐ ܚܕ̈ܬܐ ܕ-SPSS ܡܐܢܐ ܪܫܝܐ ܩܐ ܒܢܝܢܐ ܕܨܘܪ̈ܬܐ ܝܠܗ Chart Builder، ܘܠܗ ܟܡܛܚ ܡܢ Graphs › Chart Builder… (Field, 2024, Sections 5.3 and 5.8). ܦܐܪܐ ܫܘܝܐ ܝܠܗ – ܦܘܪܫܢܐ ܓܘ ܐܘܪܚܐ ܕܒܢܝܢܐ ܝܠܗ.

ܡܘܕܥܢܘܬܐ ܕܟܡܬܚܙܝܐ ܓܘ ܦܬܚܐ، ܘܛܒܐ ܝܠܗ ܕܡܦܠܚܚ ܠܗ̇. ܥܡ ܦܬܚܐ ܕ-Chart Builder ܟܫܘܪܐ ܟܘܬܐ ܕܟܡܥܗܕܐ ܕܪܡܐ ܕܡܫܘܚܬܐ ܕܟܠ ܡܫܬܚܠܦܢܐ ܣܢܝܩ ܝܠܗ ܕܗܘܐ ܬܪܝܨܐܝܬ ܬܚܝܡܐ – Scale، Ordinal ܝܢ Nominal – ܡܛܠ ܕܡܐܢܐ ܟܣܡܟ ܥܠܝܗ ܩܐ ܕܝܕܥ ܐܝܢܝ ܡܫܬܚܠܦ̈ܢܐ ܡܬܡܫܚ̈ܢܐ ܝܢܐ ܘܐܝܢܝ ܕܓܢ̈ܣܐ (Field، 2024، SPSS Tip 5.1). ܐܗܐ ܠܐ ܝܠܗ ܛܥܝܘܬܐ ܐܠܐ ܥܘܗܕܢܐ: ܐܝܢܐ ܕܬܚܡܠܗ ܡܫܬܚܠܦ̈ܢܐ ܬܪܝܨܐܝܬ ܓܘ ܥܡܘܕܐ Measure ܕܓܘ Variable View ܒܣ ܟܡܩܒܠ ܘܟܐܙܠ ܠܩܕܡ. ܓܘ ܨܘܪܬܐ ܩܕܡܝܬܐ ܕܐܗܐ ܦܣܩܐ ܡܨܝܚ ܕܚܙܝܚ ܒܚܬܝܬܘܬܐ ܐܗܐ – ܚܡܫܐ ܡܫܬܚܠܦ̈ܢܐ ܕܚܣܝܢܘܬܐ ܬܚܝܡ̈ܐ ܝܢܐ Scale، ܘܡܫܬܚܠܦ̈ܢܐ ܕܬܚܘܝܬܐ (background variables) Ordinal ܝܢ Nominal.

ܟܘܬܐ ܟܡܥܗܕܐ ܐܦ ܡܕܡ ܬܪܝܢܐ: ܐܢ ܨܘܪܬܐ ܐܝܬ ܓܘܗ ܡܫܬܚܠܦܢܐ ܕܓܢ̈ܣܐ (categorical variable)، ܛܒ ܝܠܗ ܕܬܚܘܡܝ ܩܐܠܗ ܪܘ̈ܫܡܐ ܕܛܝ̈ܡܐ (value labels) – ܩܐ ܕܓܘ ܨܘܪܬܐ ܡܬܚܙܐ "ܥܠܡܝܐ" ܘܠܐ "1". ܐܗܐ button Define Variable Properties ܟܡܒܪܐ ܬܪܝܨܐܝܬ ܠܕܘܟܬܐ ܕܓܘܗ ܟܬܪܨܚ ܬܪܘܝܗܝ ܡܕܡ̈ܝܐ، ܘ-OK ܟܐܙܠ ܠܩܕܡ ܠܟܘܬܐ ܓܘܦܗ.

ܒܢܝܢܐ ܕܟܘܬܐ. ܐܪܒܥܐ ܕܘܟ̈ܝܬܐ: Gallery – ܓܠܪܝܐ ܕܙܢ̈ܐ ܕܨܘܪ̈ܬܐ؛ ܪܫܝܡܬܐ ܕܡܫܬܚܠܦ̈ܢܐ (variables)؛ ܐܗܐ canvas، ܕܓܘܗ ܟܡܬܒܢܝܐ ܚܙܝܬܐ ܩܕܡܝܬܐ ܕܨܘܪܬܐ ܒܥܕܢܐ ܕܥܒܕܐ؛ ܘܠܓܒܐ ܝܡܝܢܐ ܐܢܝ̈ buttons Element Properties ܘ-Options، ܕܟܦܣܩܝ ܡܘܕܝ ܒܚܬܝܬܘܬܐ ܨܘܪܬܐ ܟܡܚܘܝܐ ܘܕܟܝ ܟܥܒܕܐ ܥܡ ܛܝ̈ܡܐ ܚܣܝ̈ܪܐ (missing values). ܓܘ canvas ܐܝܬ ܕܘܟ̈ܝܬܐ ܕܫܒܩܐ (drop zones) ܪܫܝܡ̈ܐ ܒܣܪܛܐ ܦܣܝܩܐ ܙܪܩܐ، ܘܠܓܘܝܗܝ ܟܓܪܫܚ ܡܫܬܚܠܦ̈ܢܐ – ܒܕܘܟܬܐ ܕܡܫܢܝܬܗܘܢ ܒܓܐܪ̈ܐ ܐܝܟ ܓܘ ܩܘܦ̈ܬܐ ܥܬܝܩ̈ܬܐ.

ܬܪܝܢ ܡܕܡ̈ܝܐ ܓܘ ܨܘܪܬܐ ܫܘܝ̈ܐ ܝܢܐ ܠܚܙܝܬܐ. ܩܕܡܝܐ، ܓܒ ܟܠ ܡܫܬܚܠܦܢܐ (variable) ܓܘ ܪܫܝܡܬܐ ܟܡܬܚܙܐ ܐܬܐ ܕܕܪܓܐ ܕܡܫܘܚܬܐ ܕܝܠܗ – ܣܪܓܠܐ ܩܐ Scale، ܥܡܘ̈ܕܐ ܩܐ Ordinal ܘܚܘܕ̈ܪܐ ܓܘܢܢ̈ܝܐ ܩܐ Nominal؛ ܐܗܐ ܝܠܗ ܗܘ ܬܚܘܡܐ ܕܟܘܬܐ ܩܕܡܝܬܐ ܡܥܗܕܠܗ، ܘܐܟܐ ܟܡܬܚܙܐ ܠܥܝܢܐ. ܘܬܪܝܢܐ، ܠܬܚܬ ܡܢ ܪܫܝܡܬܐ ܟܡܬܚܙܝܐ ܡܘܕܥܢܘܬܐ "No categories (scale variable)" – ܝܠܗ ܥܠ ܡܫܬܚܠܦܢܐ ܕܪܫܝܡܐ ܝܠܗ ܓܘ ܪܫܝܡܬܐ ܘܟܡܘܕܥܐ ܕܗܘ ܡܬܡܫܚܢܐ (continuous) ܝܠܗ ܘܡܛܠ ܗܕܐ ܠܝܬ ܠܗ ܓܢ̈ܣܐ. ܒܬܚܬܝܬܐ ܕܟܘܬܐ ܐܝܬ ܐܪܒܥܐ tabs: Gallery – ܐܘܪܚܐ ܡܩܒܠܬܐ، ܓܘܒܝܐ ܡܢ ܓܠܪܝܐ ܡܛܝܒܬܐ؛ Basic Elements – ܒܢܝܢܐ ܡܢ ܪܝܫܐ، ܡܢܬܐ ܒܬܪ ܡܢܬܐ؛ ܘܓܒܝܗܝ Groups/Point ID ܘ-Titles/Footnotes.

ܘܒܢܝܢܐ ܕܨܘܪܬܐ ܕܒܕܪܐ. ܓܘ ܪܫܝܡܬܐ ܕ-Choose from ܟܓܒܚ Scatter/Dot، ܘܟܦܬܚܐ ܓܠܪܝܐ ܕܨܘܪ̈ܬܐ ܕܒܕܪܐ: Simple scatter، Grouped scatter، Scatterplot matrix، Simple dot plot، Summary point plot، Drop-line ܘܢܘܣ̈ܚܐ ܕܬܠܬܐ ܡܫܘܚ̈ܬܐ. ܕܚܩܐ ܬܢܝܢܐ ܥܠ Simple scatter (ܝܢ ܓܪܫܬܗ ܠ-canvas) ܟܣܐܡ ܨܘܪܬܐ ܕܐܝܬ ܓܘܗ ܬܪܬܝܢ ܕܘܟ̈ܝܬܐ ܕܫܒܩܐ – ܚܕܐ ܩܐ ܣܪܛܐ Y ܘܚܕܐ ܩܐ ܣܪܛܐ X. ܟܓܪܫܚ ܠܓܘܝܗܝ ܡܫܬܚܠܦ̈ܢܐ ܘܟܕܚܩܚ OK:

ܘܙܘܗܪܐ ܙܥܘܪܐ ܕܟܡܦܨܐ ܡܢ ܫܓܘܫܝܐ: ܠܥܠ ܡܢ ܚܙܝܬܐ ܩܕܡܝܬܐ ܟܬܝܒܐ ܝܠܗ "Chart preview uses example data" – ܢܘܩ̈ܙܐ ܕܟܚܙܝܬܘܢ ܓܘ ܟܘܬܐ ܠܐ ܝܢܐ ܝܗܝ̈ܒܬܐ ܕܝܘܟܘܢ، ܐܠܐ ܝܗܝ̈ܒܬܐ ܕܡܬܠܐ. ܚܙܝܬܐ ܟܡܚܘܝܐ ܒܢܝܢܐ ܕܨܘܪܬܐ، ܠܐ ܦܐܪܐ ܕܝܠܗ، ܘܨܘܪܬܐ ܫܪܝܪܬܐ ܟܦܝܫܐ ܒܬܪ OK ܒܠܚܘܕ – ܘܐܡܢ ܕܦܝܫܐ، ܓܡܝܪܐܝܬ ܐܝܟ ܨܘܪܬܐ ܕܕܪܓܐ 4 ܠܥܠ ܝܠܗ، ܗܝ ܕܦܝܫܐ ܝܠܗ ܒܐܘܪܚܐ ܥܬܝܩܬܐ. ܬܪܬܝܢ ܐܘܪ̈ܚܬܐ، ܚܕܐ ܨܘܪܬܐ ܒܚܬܝܬܘܬܐ.

ܢܡܘܣܐ ܕܨܒܥܐ (rule of thumb) ܩܐ ܣܝܡܬܐ ܝܠܗ ܗܘ ܕܥܒܕܠܢ ܡܢ ܩܕܡ: ܡܫܬܚܠܦܢܐ ܕܦܐܪܐ (outcome variable) ܓܘ ܣܪܛܐ Y، ܡܢܒܝܢܐ (predictor) ܓܘ ܣܪܛܐ X. Field ܟܡܘܣܦ ܥܠ ܗܕܐ ܚܕ ܥܘܗܕܢܐ ܕܛܒ ܝܠܗ ܠܡܥܗܕܐ – ܓܘ ܒܘܨܝܐ ܕܐܣܘܪܐ ܕܚܕ̈ܕܐ (correlation)، ܕܓܘܗ ܬܪܘܝܗܝ ܡܫܬܚܠܦ̈ܢܐ ܟܡܬܡܫܚܝ ܒܚܕ ܙܒܢܐ، ܡ̈ܠܐ "ܡܢܒܝܢܐ" ܘ"ܦܐܪܐ" ܟܡܚܘ̈ܝܢ ܕܘܟܬܗܘܢ ܓܘ ܨܘܪܬܐ ܒܠܚܘܕ ܘܠܐ ܟܣܗܕܝ ܥܠ ܥܠܬܢܘܬܐ (causality) (2024، ܦܣܩܐ 5.8.1).

ܬܪܬܝܢ ܡܪܘ̈ܚܢܘܝܬܐ ܕܦܣܩܐ ܩܕܡܝܐ ܐܝܬ ܐܦ ܐܟܐ، ܒܫܡܗ̈ܐ ܐܚܪ̈ܢܐ: Grouped scatter ܟܡܘܣܦ ܕܘܟܬܐ ܕܫܒܩܐ ܬܠܝܬܝܬܐ، ܕܠܓܘܗ ܟܓܪܫܚ ܡܫܬܚܠܦܢܐ ܕܓܢ̈ܣܐ (categorical variable) ܘܢܘܩ̈ܙܐ ܟܡܨܛܒܥܝ ܠܦܘܬܗ – ܐܝܟ Set Markers by (ܦܣܩܐ 5.8.2)؛ ܘ-Scatterplot matrix ܟܡܚܘܝܐ ܚܕܐ ܕܘܟܬܐ ܕܫܒܩܐ ܒܠܚܘܕ، ܕܠܓܘܗ ܟܓܪܫܚ ܒܚܕ ܙܒܢܐ ܟܠ ܡܫܬܚܠܦ̈ܢܐ ܕܒܥܝܚ – ܟܓܒܚ ܠܗܘܢ ܓܘ ܪܫܝܡܬܐ ܥܡ Ctrl (ܝܢ Cmd ܓܘ Mac) ܘܟܓܪܫܚ ܠܗܘܢ ܐܟܚܕܐ (ܦܣܩܐ 5.8.4).

ܘܡܢܘ ܝܠܗ ܢܘܩܙܐ ܢܘܟܪܝܐ؟ ܡܠܟܐ ܕ-Pallant (2020، ܦܐܬܐ 76، 157) ܕܟܡܦܨܐ ܡܢ ܒܨܝܐ ܓܘ ܦܐܝܠ: ܓܘ tab Groups/Point ID ܕ-Chart Builder ܟܪܫܡܚ Point ID label ܘܟܓܪܫܚ ܡܫܬܚܠܦܢܐ ܕܡܢܝܢܐ ܡܦܪܫܢܐ (ID variable) ܠܕܘܟܬܐ ܕܫܒܩܐ Point ID. ܓܘ ܨܘܪܬܐ ܕܦܝܫܐ ܟܦܬܚܚ Chart Editor، ܟܓܒܚ Elements › Data Label Mode (ܡܕܡ ܩܕܡܝܐ ܓܘ ܪܫܝܡܬܐ، ܓܘ ܨܘܪܬܐ ܕܡܚܙܝܢܐ ܕܕܪܓܐ 6 ܠܥܠ) ܘܟܕܚܩܚ ܥܠ ܢܘܩܙܐ – ܘܡܢܝܢܐ ܡܦܪܫܢܐ ܕܝܠܗ ܟܡܬܚܙܐ ܓܒܗ. ܕܠܐ ܡܫܬܚܠܦܢܐ ܕܡܢܝܢܐ ܡܦܪܫܢܐ، ܟܡܬܚܙܐ ܡܢܝܢܐ ܕܣܕܪܐ ܕܝܗܒܠܗ SPSS. ܗܕܟܐ ܡܨܝܚ ܕܕܥܪܚ ܠܦܢܩܝܬܐ ܕܫܘܐ̈ܠܐ (questionnaire) ܕܗܘ ܡܫܬܘܬܦܢܐ ܘܕܒܚܪܚ ܐܢ ܐܝܬ ܛܥܝܘܬܐ ܕܟܬܝܒܬܐ. (ܓܘ ܡܚܫܒܢܐ (calculator) ܕܐܗܐ ܦܐܬܐ، ܡܫܢܝܬܐ ܕܡܐܘܣ ܥܠ ܢܘܩܙܐ ܟܡܚܘܝܐ ܛܝ̈ܡܐ ܕܝܠܗ، ܒܣ ܠܐ ܡܢܝܢܐ ܡܦܪܫܢܐ – ܥܡܘܕܐ ܕܡܢܝܢܐ ܡܦܪܫܢܐ ܠܐ ܥܠܝܠܐ ܝܠܗ ܓܘ ܦܘܫܩܐ.)

ܘܣܝܢܬܐܟܣ (syntax) ܐܟܐ ܟܡܬܚܙܐ ܓܡܝܪܐܝܬ ܫܢܝܐ. ܐܦ ܓܘ Chart Builder ܐܝܬ button Paste، ܒܣ ܠܐ ܟܡܦܩ ܦܘܩܕܢܐ ܩܨܝܪܐ GRAPH ܕܚܙܠܢ ܠܥܠ، ܐܠܐ ܦܘܩܕܢܐ GGRAPH، ܘܓܘܗ ܓܘܫܡܐ ܒܠܫܢܐ ܡܝܚܕܐ ܩܐ ܬܚܘܝܬܐ ܕܨܘܪ̈ܬܐ – GPL (Graphics Production Language)، ܕܐܣܝܪܐ ܝܠܗ ܒܝܢܝ BEGIN GPL ܘ-END GPL:

* Chart Builder.
GGRAPH
  /GRAPHDATASET NAME="graphdataset" VARIABLES=efficacy trust MISSING=LISTWISE REPORTMISSING=NO
  /GRAPHSPEC SOURCE=INLINE.
BEGIN GPL
  SOURCE: s=userSource(id("graphdataset"))
  DATA: efficacy=col(source(s), name("efficacy"))
  DATA: trust=col(source(s), name("trust"))
  GUIDE: axis(dim(1), label("efficacy"))
  GUIDE: axis(dim(2), label("trust"))
  ELEMENT: point(position(efficacy*trust))
END GPL.

ܐܪܝܟܐ ܝܠܗ ܒܝܫ – ܒܣ ܓܠܝܐ ܝܠܗ ܒܝܫ، ܘܡܛܠ ܗܕܐ ܫܘܝܐ ܝܠܗ ܠܝܠܦܐ ܕܩܪܝܚ ܠܗ. ܟܠ ܣܕܪܐ ܟܡܦܢܐ ܥܠ ܫܘܐܠܐ ܐܚܪܢܐ: DATA – ܐܝܢܝ ܡܫܬܚܠܦ̈ܢܐ ܟܥܐܠܝ ܠܨܘܪܬܐ؛ GUIDE: axis – ܡܘܕܝ ܟܬܝܒܐ ܝܠܗ ܥܠ ܟܠ ܣܪܛܐ؛ SCALE – ܐܝܢܐ ܙܢܐ ܕܣܒܠܬܐ (scale) ܟܡܬܦܠܚ ܩܐ ܟܠ ܣܪܛܐ؛ ܘ-ELEMENT – ܡܘܕܝ ܟܡܬܨܝܪ ܒܥܒܕܐ (point، ܝܥܢܝ ܢܘܩ̈ܙܐ). ܣܕܪܐ ܩܕܡܝܐ، * Chart Builder.، ܡܥܝܪܢܘܬܐ ܝܠܗ ܒܠܚܘܕ – SPSS ܟܡܘܣܦ ܠܗ ܩܐ ܕܟܬܒ ܡܢ ܐܝܢܐ ܟܘܬܐ ܐܬܐ ܦܘܩܕܢܐ، ܘܢܘܩܙܐ ܕܒܚܪܬܗ ܝܠܗ ܕܟܡܫܠܡ ܠܗ. ܡܕܡ̈ܝܐ ܟܫܚܠܦܝ ܩܠܝܠ ܠܦܘܬ ܓܘܒ̈ܝܐ ܕܓܘ ܟܘܬܐ، ܘܡܛܠ ܗܕܐ ܣܝܢܬܐܟܣ ܕܒܕ ܦܝܫܐ ܓܒܘܟܘܢ ܡܨܐ ܕܡܬܚܙܐ ܩܠܝܠ ܫܢܝܐ.

ܘܡܘܗܒܬܐ: ܣܝܢܬܐܟܣ ܟܓܠܐ ܕܟܝ SPSS ܦܗܡܠܗ ܟܠ ܡܫܬܚܠܦܢܐ. ܢܣܒܚ ܕܒܕܘܟܬܐ ܕܡܨܝܢܘܬܐ ܓܪܫܚ ܠܣܪܛܐ X ܡܫܬܚܠܦܢܐ ܕܕܝܢܐ – ܡܫܬܚܠܦܢܐ ܕܓܢ̈ܣܐ ܕܐܝܬ ܠܗ ܬܠܬܐ ܓܢ̈ܣܐ. SPSS ܠܐ ܒܕ ܟܠܐ ܠܗ، ܒܕ ܡܦܩ ܨܘܪܬܐ، ܘܐܗܐ ܝܠܗ ܡܐ ܕܒܕ ܡܬܚܙܐ ܓܘ Paste:

DATA: dat=col(source(s), name("dat"), unit.category())
GUIDE: axis(dim(1), label("dat"))
SCALE: cat(dim(1), include("1", "2", "3"))
SCALE: linear(dim(2), include(0))
ELEMENT: point(position(dat*trust))

ܬܪܬܝܢ ܡ̈ܠܐ ܕܟܓܠܝܢ ܝܢܐ unit.category() ܓܘ ܣܕܪܐ ܕ-DATA ܘ-cat ܓܘ ܣܕܪܐ ܕ-SCALE ܕܣܪܛܐ X – ܩܘܒܠ linear ܓܘ ܣܪܛܐ Y. ܝܥܢܝ ܚܕ ܣܪܛܐ ܕܓܢ̈ܣܐ ܝܠܗ ܘܐܚܪܢܐ ܡܬܡܫܚܢܐ، ܘܪܫܝܡܬܐ ܕ-include("1", "2", "3") ܓܠܝܐܝܬ ܟܡܢܝܐ ܬܠܬܐ ܓܢ̈ܣܐ. ܨܘܪܬܐ ܕܦܝܫܐ ܠܐ ܝܠܗ ܥܢܢܐ ܕܢܘܩ̈ܙܐ، ܐܠܐ ܬܠܬܐ ܣܕܪ̈ܐ ܙܩܝܦ̈ܐ، ܚܕ ܩܐ ܟܠ ܓܘܕܐ، ܘܠܐ ܡܨܝܚ ܕܩܪܝܚ ܡܢܗ ܡܓܡܐ ܝܢ ܕܡܦܐܚ ܥܡܗ ܣܪܛܐ ܕܪܝܓܪܫܢ (regression line) ܕܐܝܬ ܠܗ ܣܘܟܠܐ. ܐܗܐ ܝܠܗ ܒܚܬܝܬܘܬܐ ܡܐ ܕܬܚܘܝܠܗ ܓܘ ܦܣܩܐ ܕ-ܫܪ̈ܛܐ: ܐܡܢ ܕܡܫܬܚܠܦܢܐ ܡܦܫܩܢܐ ܕܓܢ̈ܣܐ ܝܠܗ، ܫܘܐܠܐ ܠܐ ܝܠܗ "ܐܝܬ ܡܓܡܐ ܣܠܩܢܐ؟" ܐܠܐ "ܡܨܥܝ̈ܬܐ ܦܪ̈ܝܫܐ ܝܢܐ ܒܝܢܝ ܓܘ̈ܕܐ؟" – ܘܩܐ ܐܗܐ ܫܘܐܠܐ ܦܐܝ̈ܐ ܝܢܐ boxplot ܘܦܘܚܡܐ ܕܡܨܥܝ̈ܬܐ، ܠܐ ܨܘܪܬܐ ܕܒܕܪܐ. (ܢܡܘܣܐ ܠܐ ܝܠܗ ܒܠܚܘܕ ܥܠ ܡܫܬܚܠܦܢܐ ܕܫܡܗ̈ܐ: ܐܦ ܡܫܬܚܠܦܢܐ ܕܛܟܣܐ (ordinal variable) ܕܐܝܬ ܠܗ ܩܠܝܠ ܛܝ̈ܡܐ، ܐܝܟ ܐܟܐ، ܒܕ ܝܗܒ ܣܕܪ̈ܐ ܘܠܐ ܥܢܢܐ.)

ܣܪܛܐ ܕܪܝܓܪܫܢ (regression line) ܟܡܬܘܣܦ ܒܚܬܝܬܘܬܐ ܐܝܟ ܕܬܚܘܝܠܗ ܠܥܠ، ܓܘ ܗܘ Chart Editor ܓܘܦܗ – ܬܪܬܝܢ ܐܘܪ̈ܚܬܐ ܟܦܓܥܝ ܐܟܡܐ. ܫܘܝܐ ܝܠܗ ܠܝܕܥܐ ܚܕ ܡܠܟܐ ܕ-Field ܓܘ ܐܗܐ ܨܝܪܐ: ܓܒ ܣܪܛܐ SPSS ܟܡܕܒܩ ܪܘܫܡܐ (label)، ܘܒܙܒ̈ܢܐ ܗܘ ܪܘܫܡܐ ܟܢܚܬ ܥܠ ܢܘܩ̈ܙܐ ܘܟܡܛܫܐ ܝܗܝ̈ܒܬܐ؛ ܓܘ ܐܗܐ ܡܐܪܐ ܦܫܝܛܐܝܬ ܟܛܦܚ ܠܗ ܓܘ ܟܘܬܐ ܕ-Properties. ܘܓܘ ܨܘܪܬܐ ܕܓܘ̈ܕܐ، ܒܬܪ ܡܘܣܦܬܐ ܕܣܪܛܐ، SPSS ܒܕ ܨܐܪ ܣܪܛܐ ܦܪܝܫܐ ܩܐ ܟܠ ܓܘܕܐ – ܘܦܘܚܡܐ ܒܝܢܝ ܡܨܠܝܢ̈ܘܬܐ (slopes) ܕܝܗܝ ܝܠܗ ܒܚܬܝܬܘܬܐ ܫܘܐܠܐ ܐܢ ܐܣܘܪܐ ܚܝܠܢܐ ܝܠܗ ܒܝܫ ܓܘ ܓܘܕܐ ܚܕܐ ܡܢ ܐܚܪܬܐ (ܦܣܩܐ 5.8.2).

ܩܪܝܢܐ ܕܡܦܩܢܐ (How to read the output)

ܠܐ ܐܝܟ ܠܘܚܐ ܕ-Correlations، ܕܟܡܚܘܝܐ ܡܢܝܢܐ ܡܫܘܬܦܐ ܕܐܣܘܪܐ ܕܚܕ̈ܕܐ (correlation coefficient) r ܓܘܦܗ، SPSS ܟܡܚܘܝܐ ܥܠ ܨܘܪܬܐ ܕܒܕܪܐ – ܓܘ ܙܘܝܬܐ ܕܝܠܗ، ܓܒ ܣܪܛܐ ܕܪܝܓܪܫܢ – ܡܢܝܢܐ ܡܫܘܬܦܐ ܕܦܣܩܬܐ (coefficient of determination)، ܐܝܟ ܟܬܝܒܬܐ "R Sq Linear = …". ܡܬܠܐ، ܓܘ ܨܘܪܬܐ ܕܒܕܪܐ ܕܬܚܘܡܠܢ ܗܫܐ – efficacy (X) ܩܘܒܠ trust (Y) ܓܘ ܦܐܝܠ ܕܝܗܝ̈ܒܬܐ ܕܐܗܐ ܦܐܬܐ (512 ܡܦܢܝ̈ܢܐ، ܒܬܪ ܫܩܠܬܐ ܙܘܓܢܝܬܐ (pairwise deletion) ܕܛܝ̈ܡܐ ܚܣܝ̈ܪܐ): R Sq Linear = .55، ܘ-N = 479.

ܩܐ ܕܕܥܪܚ ܡܢ R² ܠܡܢܝܢܐ ܡܫܘܬܦܐ ܕ-Pearson r، ܟܫܩܠܚ ܫܪܫܐ ܡܪܒܥܐ ܘܟܡܘܣܦܚ ܐܬܐ ܠܦܘܬ ܐܘܪܚܐ ܕܣܪܛܐ ܕܪܝܓܪܫܢ: ܐܟܐ √.55 ≈ .74، ܘܡܛܠ ܕܣܪܛܐ ܣܠܩܢܐ ܝܠܗ (ܡܨܠܝܢܘܬܐ ܥܠ ܡܢ ܨܦܪܐ) ܟܦܝܫܚ ܥܡ r = .74 – ܒܚܬܝܬܘܬܐ ܛܝܡܐ ܕܟܡܬܚܙܐ ܓܘ ܩܠܝܬܐ ܕܐܣܘܪܐ ܕܚܕ̈ܕܐ ܒܝܢܝ efficacy ܘ-trust ܓܘ ܠܘܚܐ ܕܐܣܘܪ̈ܐ ܕܚܕ̈ܕܐ (ܦܐܬܐ ܕܐܣܘܪ̈ܐ ܕܚܕ̈ܕܐ، ܠܘܚܐ ܕܐܣܘܪ̈ܐ ܕܚܕ̈ܕܐ ܒܝܢܝ ܚܡܫܐ ܡܫܬܚܠܦ̈ܢܐ ܕܚܣܝܢܘܬܐ)، ܘܐܣܘܪܐ ܚܝܠܢܐ ܡܢ ܟܠܗܘܢ ܡܢ ܒܝܢܝ ܥܣܪܐ ܙܘܓ̈ܐ ܐܟܡܐ. ܐܗܐ ܐܦ ܐܘܪܚܐ ܦܫܝܩܬܐ ܝܠܗ ܕܒܚܪܝܬܘܢ ܓܢܘܟܘܢ: ܐܢ ܚܫܒܠܘܟܘܢ ܡܢ ܩܕܡ ܐܣܘܪܐ ܕܚܕ̈ܕܐ ܕ-Pearson، ܡܪܒܥܐ ܕܝܠܗ ܓܪܓ ܕܗܘܐ ܫܘܝܐ ܠ-R² Linear ܕܟܡܚܘܝܐ ܨܘܪܬܐ.

ܠܒܪ ܡܢ ܪܒܘܬܐ ܕܐܣܘܪܐ، ܦܘܚܡܐ ܕܡܨܠܝܢܘܬܐ (slope) ܕܣܪܛܐ ܥܡ ܫܘܝܘܬܐ ܕܝܠܗ ܟܡܚܘܝܐ ܣܘܟܠܐ ܡܢܝܢܝܐ: ܓܘ ܐܗܐ ܕܘܡܝܐ (sample) ܫܘܝܘܬܐ ܕܣܪܛܐ ܝܠܗ Ý = 1.159 + 0.687X – ܝܥܢܝ، ܩܐ ܟܠ ܣܠܩܐ ܕܚܕ ܢܘܩܙܐ ܓܘ ܪܡܐ ܕ-efficacy، ܪܡܐ ܡܣܟܝܐ ܕ-trust ܟܣܠܩ ܒܩܘܪܒܐ 0.69 ܢܘܩ̈ܙܐ ܒܡܨܥܝܬܐ. ܢܘܩܙܐ ܕܦܣܩܬܐ (1.159)، ܛܝܡܐ ܡܣܟܝܐ ܐܡܢ ܕ-X = 0، ܣܓܝ ܙܒ̈ܢܐ ܠܝܬ ܠܗ ܣܘܟܠܐ ܫܪܝܪܐ ܐܡܢ ܕ-0 ܠܒܪ ܡܢ ܦܬܝܘܬܐ (range) ܕܛܝ̈ܡܐ ܕܐܬܚܙܝ ܒܥܒܕܐ ܓܘ ܣܒܠܬܐ ܕܡܫܘܚܬܐ.

ܡܢ ܨܘܪܬܐ ܠܪܝܓܪܫܢ: ܗܢܝ ܡܢܝ̈ܢܐ ܓܘܦܝܗܝ ܓܘ ܐܘܪܚܐ ܕ-Regression

ܨܘܪܬܐ ܕܒܕܪܐ ܟܡܚܘܝܐ R² ܘܣܪܛܐ، ܒܣ ܠܐ ܦܪ̈ܡܝܛܪܐ ܘܒܘܚܪ̈ܢܐ ܕܝܗܝ. ܗܢܝ ܡܢܝ̈ܢܐ ܓܘܦܝܗܝ ܕܡܚܫܒܢܐ (calculator) ܐܟܐ ܟܡܚܘܝܐ ܓܘ ܠܘܚܐ ܟܦܝܫܝ ܓܘ SPSS ܡܢ ܐܘܪܚܐ ܕܪܝܓܪܫܢ (regression): Analyze › Regression › Linear…، ܡܫܬܚܠܦܢܐ ܬܠܝܐ (dependent variable) ܠܩܘܦܬܐ ܕ-Dependent ܘܡܢܒܝܢܐ (predictor) ܠܩܘܦܬܐ ܕ-Independent(s) (Field, 2024, Section 9.7). ܡܦܩܢܐ (output) ܟܐܬܐ ܓܘ ܬܠܬܐ ܠܘ̈ܚܐ (ܦܣܩܐ 9.8)، ܘܛܒ ܝܠܗ ܠܝܕܥܐ ܐܝܟܐ ܟܠ ܛܝܡܐ ܕܝܠܢ ܝܬܝܒܐ ܝܠܗ – ܘܠܘܚܐ 1 ܕܐܗܐ ܦܐܬܐ ܡܢ ܗܫܐ ܟܡܚܘܝܐ ܟܠܗܘܢ (R² ܡܬܘܪܨܐ، ܛܥܝܘܬܐ ܬܩܝܢܬܐ ܕܫܘܥܪܐ (standard error of the estimate)، F، ܘ-b ܘ-a ܥܡ ܛܥܝ̈ܘܬܐ ܬܩܝܢ̈ܬܐ، t ܘܬܚܘ̈ܡܐ ܕܬܘܟܠܢܐ). ܩܐ ܪܝܓܪܫܢ ܥܡ ܒܝܫ ܡܢ ܚܕ ܡܢܒܝܢܐ – ܦܐܬܐ ܕܪܝܓܪܫܢ ܣܪܛܢܝܐ:

Field ܟܡܠܟ ܕܪܫܡܚ ܓܘ ܟܘܬܐ ܪܫܝܬܐ Bootstrap… ܘܕܒܥܚ ܬܚܘ̈ܡܐ ܕܬܘܟܠܢܐ (confidence intervals) ܕܙܢܐ BCa ܩܐ b: ܬܚܘܡܐ ܕܬܘܟܠܢܐ ܕ"ܠܐ ܟܡܛܐ ܠܨܦܪܐ" ܝܠܗ ܣܗܕܘܬܐ ܬܪܝܨܬܐ ܒܝܫ ܩܐ ܐܣܘܪܐ ܓܘ ܟܢܫܐ ܟܠܢܝܐ (population)، ܘܒܘܛܣܛܪܐܦ (bootstrap) ܠܐ ܟܡܣܬܡܟ ܥܠ ܫܪ̈ܛܐ (assumptions) ܕܢܘܪܡܠܝܘܬܐ ܘܕܫܘܝܘܬܐ ܕܫܘܚܠܦܐ (2024، ܦܣܩܐ 9.8.2). ܪܥܝܢܐ ܦܫܝܛܐ ܝܠܗ (Field & Wilcox, 2017, Section Adjusting standard errors): ܒܕܘܟܬܐ ܕܡܣܒܚ ܕܟܝ b ܗܘܐ ܡܬܦܠܓ ܓܘ ܕܘ̈ܡܝܐ ܡܬܢ̈ܝܐ، ܟܡܕܡܚ ܠܗ – ܟܓܒܚ ܡܢ ܝܗܝ̈ܒܬܐ ܓܘܦܝܗܝ، ܥܡ ܕܥܪܬܐ، ܕܘܡܝܐ ܚܕܬܐ ܒܪܒܘܬܐ ܕܩܕܡܝܐ، ܟܚܫܒܚ ܥܠܗ b، ܘܟܬܢܚ ܐܗܐ ܐܠܦ̈ܐ ܕܙܒ̈ܢܐ (ܡܠܟܐ ܡܩܒܠܐ: 2,000). ܛܝ̈ܡܐ ܕܟܬܚܡܝ 95% ܡܨܥ̈ܝܐ ܕܐܢܝ̈ ܐܠܦ̈ܐ ܕ-b ܝܢܐ ܬܚܘܡܐ ܕܬܘܟܠܢܐ (percentile)، ܘ-BCa ܢܘܣܚܐ ܝܠܗ ܕܟܬܪܨ ܐܦ ܩܐ ܠܐ ܫܘܝܘܬܐ (skewness). ܡܛܠ ܕܐܗܐ ܐܘܪܚܐ ܠܐ ܟܡܣܒܐ ܡܕܡ ܥܠ ܐܣܟܝܡܐ ܕܦܘܠܓܐ (distribution)، ܛܥܝ̈ܘܬܐ ܬܩܝܢ̈ܬܐ ܘܬܚܘ̈ܡܐ ܕܬܘܟܠܢܐ ܕܟܝܗܒ ܓܪܓ ܕܩܝܡܝ ܐܦ ܒܥܒܪܬܐ ܥܠ ܫܪ̈ܛܐ ܕܬܚܘܝܠܗܘܢ ܠܥܠ. ܘܠܫܘܠܡܐ، ܡܐܡܪܐ ܕ-Field & Wilcox (ibid., Section Discussion and recommendations) ܕܛܒ ܝܠܗ ܠܡܥܗܕܐ ܩܘܒܠ ܟܠ ܢܫ ܕܐܡܪ ܕ"ܪܝܓܪܫܢ ܐܘܪܚܐ ܚܣܝܢܬܐ ܝܠܗ": ܥܠ ܫܬܐܣܐ ܕܡܐܐ̈ ܕܒܘܨ̈ܝܐ ܡܢ ܚܡܫܝܢ ܫܢ̈ܐ ܐܚܪܝ̈ܐ، ܐܗܐ ܡܐܡܪܐ ܦܫܝܛܐܝܬ ܠܐ ܝܠܗ ܫܪܝܪܐ – ܘܐܢܝ̈ ܟܡܠܟܝ ܕܡܬܟܠܐ. ܦܘܫܐ ܕܐܘܪܚܐ – ܒܝܫ ܡܢ ܚܕ ܡܢܒܝܢܐ، ܡܚܘ̈ܝܢܐ ܕܒܘܚܪܢܐ، ܫܪ̈ܛܐ ܓܘ ܡܦܩܢܐ – ܟܡܦܪܫ ܠܗ ܦܐܬܐ ܕܪܝܓܪܫܢ ܣܪܛܢܝܐ (linear regression) ܓܘ ܣܐܝܛ.

ܡܪܘ̈ܚܢܘܝܬܐ: ܦܘܚܡܐ ܕܓܘ̈ܕܐ ܘܟܠ ܙܘܓ̈ܐ ܒܚܕ ܙܒܢܐ

ܦܘܚܡܐ ܕܓܘ̈ܕܐ ܓܘ ܚܕܐ ܨܘܪܬܐ – Overlay Scatter. ܐܡܢ ܕܒܥܝܚ ܕܡܚܘܚ ܟܡܐ ܙܘܓ̈ܐ ܕܡܫܬܚܠܦ̈ܢܐ (variables) ܐܟܚܕܐ، ܝܢ ܕܦܚܡܚ ܗܘ ܙܘܓܐ ܓܘܦܗ ܒܝܢܝ ܓܘ̈ܕܐ ܡܢܬܢ̈ܝܐ (subgroups) – ܡܬܠܐ، ܐܢ ܐܣܘܪܐ ܒܝܢܝ efficacy ܘ-trust ܕܡܝܐ ܝܠܗ ܒܚܝܠܗ ܓܘ ܓܘ̈ܕܐ ܕܝܢ̈ܝܐ ܦܪ̈ܝܫܐ – ܟܓܒܚ ܓܘ ܩܘܦܬܐ ܕ-Scatter/Dot ܠ-Overlay Scatter ܘܟܕܚܩܚ Define:

ܓܘ ܟܘܬܐ ܕ-Overlay Scatterplot ܟܪܫܡܚ ܓܘ ܪܫܝܡܬܐ ܕܡܫܬܚܠܦ̈ܢܐ (variables) ܬܪܝܢ ܡܫܬܚܠܦ̈ܢܐ ܒܚܕ ܙܒܢܐ ܘܟܡܫܢܚ ܠܗܘܢ ܠܪܫܝܡܬܐ ܕ-Y-X Pairs؛ ܟܠ ܣܕܪܐ ܓܘܗ ܙܘܓܐ ܝܠܗ، ܘܡܫܬܚܠܦܢܐ ܕܓܒܝܐ ܝܠܗ ܩܕܡܝܐ ܟܗܘܐ ܡܫܬܚܠܦܢܐ ܕ-Y ܕܙܘܓܐ. button ܕܓܐܪ̈ܐ (Swap Pair) ܟܡܚܠܦ ܒܝܢܝ Y ܘ-X ܕܙܘܓܐ ܪܫܝܡܐ – ܚܙܝܡܘܢ (Note) ܕܓܘ ܡܬܠܐ ܕܩܡ ܐܦܢ efficacy ܝܠܗ Y ܘ-trust ܘ-belonging ܝܢܐ X، ܗܘܦܟܐ ܕܡܬܠܐ ܪܫܝܐ ܕܦܐܬܐ. ܩܐ ܕܦܠܓܚ ܨܘܪܬܐ ܠܨܘܪ̈ܬܐ ܙܥܘܪ̈ܬܐ ܠܦܘܬ ܓܘܕܐ، ܟܡܫܢܚ ܡܫܬܚܠܦܢܐ ܕܓܢ̈ܣܐ (categorical variable) ܠܩܘܦܬܐ ܕ-Columns (ܨܘܪ̈ܬܐ ܙܥܘܪ̈ܬܐ ܚܕܐ ܓܒ ܐܚܪܬܐ) ܝܢ Rows (ܚܕܐ ܬܚܘܬ ܐܚܪܬܐ) ܕܓܘ Panel by – ܐܟܐ ܡܫܬܚܠܦܢܐ ܕܕܝܢܐ (dat):

ܡܦܩܢܐ (output) ܝܠܗ ܬܠܬܐ ܨܘܪ̈ܬܐ ܙܥܘܪ̈ܬܐ ܚܕܐ ܓܒ ܐܚܪܬܐ – ܥܠܡ̈ܝܐ، ܡܫܠܡܢܝ̈ܐ ܘܕܝܢܝ̈ܐ-ܚܪܕ̈ܝܐ – ܘܓܘ ܟܠ ܚܕܐ ܡܢܝܗܝ ܬܪܝܢ ܣܕܪ̈ܐ ܕܢܘܩ̈ܙܐ ܒܓܘܢ̈ܐ ܦܪ̈ܝܫܐ، ܠܦܘܬ ܡܦܫܩܢܐ (legend) ܕܠܓܒܐ ܝܡܝܢܐ: efficacy ܩܘܒܠ trust ܘ-efficacy ܩܘܒܠ belonging. ܣܪ̈ܛܐ ܡܫܘܬܦ̈ܐ ܝܢܐ ܩܐ ܟܠ ܨܘܪ̈ܬܐ ܙܥܘܪ̈ܬܐ، ܘܡܛܠ ܗܕܐ ܡܨܝܚ ܕܦܚܡܚ ܒܝܢܝ ܕܝܗܝ ܬܪܝܨܐܝܬ:

ܐܦ ܐܟܐ ܣܪ̈ܛܐ ܕܪܝܓܪܫܢ (regression lines) ܠܐ ܟܡܬܚܙܝܐ ܡܢ ܓܢܗܘܢ: ܟܦܬܚܚ ܨܘܪܬܐ ܓܘ Chart Editor ܘܟܓܒܚ Elements › Fit Line at Subgroups – ܘܗܝܓܝ ܟܦܝܫ ܣܪܛܐ ܦܪܝܫܐ ܩܐ ܟܠ ܣܕܪܐ ܓܘ ܟܠ ܨܘܪܬܐ ܙܥܘܪܬܐ، ܘܓܘ ܡܦܫܩܢܐ ܕܠܓܒܐ ܝܡܝܢܐ R² Linear ܕܟܠ ܣܪܛܐ (Pallant, 2020, p. 305):

ܬܪܝܢ ܡܠܟ̈ܐ ܕ-Gelman & Hill (2007، ܦܐܬܐ 555) ܩܐ ܨܘܪܬܐ ܐܝܟ ܐܗܐ. ܩܕܡܝܐ – ܥܠ ܐܬܘ̈ܬܐ: ܩܐ ܬܪܬܝܢ-ܬܠܬܐ ܓܘ̈ܕܐ ܟܓܒܚ ܐܬܘ̈ܬܐ ܕܦܪ̈ܝܫܐ ܝܢܐ ܠܥܝܢܐ – ܚܘܕܪܐ ܦܬܝܚܐ ܩܘܒܠ ܚܘܕܪܐ ܡܠܝܐ، ܠܐ ܐܬܘ̈ܬܐ M ܘ-F – ܡܛܠ ܕܐܬܐ ܝܠܗ ܐܘܪܚܐ ܕܒܗ ܨܘܪܬܐ ܟܐܡܪܐ "ܟܠ ܢܘܩܙܐ ܡܫܬܘܬܦܢܐ ܝܠܗ ܡܢ ܐܗܐ ܓܘܕܐ"؛ ܪܒܘܬܐ ܕܐܬܐ، ܒܣ، ܩܪܝܒܐܝܬ ܠܐ ܡܨܝܐ ܕܡܚܘܝܐ ܡܫܬܚܠܦܢܐ ܡܬܡܫܚܢܐ (continuous variable). ܬܪܝܢܐ – ܬܫܥܝܬܐ ܡܢ ܥܒܕܐ ܕܝܗܝ: ܨܪܠܗܘܢ ܨܘܪܬܐ ܕܩܕܡ-ܘܒܬܪ ܥܡ ܣܪ̈ܛܐ ܕܪܝܓܪܫܢ ܦܪ̈ܝܫܐ ܩܐ ܓܘ̈ܕܐ ܕ-treatment ܘܕܦܘܚܡܐ، ܘܒܬܪ ܕܚܙܠܗܘܢ ܨܘܪܬܐ ܥܡ ܣܪ̈ܛܐ ܡܩܒܠ̈ܐ ܒܠܚܘܕ ܦܗܡܠܗܘܢ ܕܣܪ̈ܛܐ ܠܐ ܡܩܒܠ̈ܐ – ܝܥܢܝ ܥܒܕܐ ܕܚܕ̈ܕܐ (interaction) ܒܝܢܝ treatment ܘܡܫܘܚܬܐ ܕ"ܩܕܡ" – ܐܢܝ̈ ܝܢܐ ܡܘܕܝܠ ܫܪܝܪܐ، ܘܐܗܐ ܐܬܚܙܝܠܗ ܐܝܟ ܫܪܪܐ ܪܫܝܐ ܕܝܗܝ̈ܒܬܐ. "ܣܪ̈ܛܐ ܘܢܘܩ̈ܙܐ ܐܟܚܕܐ ܟܡܚܘ̈ܝܢ ܐܗܐ ܒܓܠܝܘܬܐ ܣܓܝ ܒܝܫ ܡܢ ܟܠ ܟܢܘܫܝܐ ܡܢܝܢܝܐ" (ܗܘ ܕܘܟܬܐ). ܐܗܐ ܝܠܗ ܒܚܬܝܬܘܬܐ ܡܐ ܕܨܘܪܬܐ ܕ-Overlay ܥܡ Fit Line at Subgroups ܟܡܨܝܐ ܕܒܚܪܐ: ܐܢ ܡܨܠܝܢ̈ܘܬܐ (slopes) ܕܡ̈ܝܐ ܝܢܐ.

ܗܕܟܐ ܡܨܝܚ ܕܦܢܚ ܓܘ ܚܕܐ ܨܘܪܬܐ ܥܠ ܬܪܝܢ ܫܘܐ̈ܠܐ ܕܩܐܠܗܘܢ ܡܬܒܢܝܐ ܝܠܗ. ܐܝܢܐ ܡܢ ܬܪܝܢ ܐܣܘܪ̈ܐ ܚܝܠܢܐ ܝܠܗ ܒܝܫ؟ ܓܒ ܥܠܡ̈ܝܐ، efficacy ܐܣܝܪܐ ܝܠܗ ܥܡ trust (R² = .554) ܒܝܫ ܡܢ ܥܡ belonging (.460)، ܘܓܒ ܕܝܢܝ̈ܐ-ܚܪܕ̈ܝܐ ܦܘܪܫܢܐ ܕܡܝܐ ܝܠܗ (.506 ܩܘܒܠ .404) – ܐܠܐ ܓܒ ܡܫܠܡܢܝ̈ܐ ܬܪܘܝܗܝ ܩܪܝܒܐܝܬ ܫܘ̈ܝܐ ܝܢܐ (.525 ܘ-.536). ܘܐܢ ܐܣܘܪܐ ܕܡܝܐ ܝܠܗ ܒܝܢܝ ܓܘ̈ܕܐ؟ ܐܣܘܪܐ efficacy-trust ܩܝܡܐ ܝܠܗ ܒܝܫ ܒܬܠܬܝܗܝ (.51-.55)، ܘܐܣܘܪܐ efficacy-belonging ܟܫܚܠܦ ܒܝܫ (.40-.54). ܚܙܝܡܘܢ (Note) ܕܡܢܝ̈ܢܐ ܓܘ ܡܦܫܩܢܐ ܝܢܐ R² ܘܠܐ r: ܦܘܪܫܢܐ ܒܝܢܝ .554 ܘ-.460 ܝܠܗ ܦܘܪܫܢܐ ܒܝܢܝ r = .74 ܘ-r = .68. ܘܙܘܗܪܐ ܕܟܢܒܥ ܬܪܝܨܐܝܬ ܡܢ ܦܣܩܐ ܕ-ܫܪ̈ܛܐ – ܐܫܬܐ ܐܣܟܝ̈ܡܐ ܘܡܪܝܡܢܘܬܐ (leverage): ܐܡܢ ܕܓܘܕܐ ܙܥܘܪܬܐ ܝܠܗ – ܐܝܟ ܕܝܢܝ̈ܐ-ܚܪܕ̈ܝܐ ܓܘ ܐܗܐ ܕܘܡܝܐ، ܕܨܘܪܬܐ ܙܥܘܪܬܐ ܕܝܗܝ ܓܠܝܐܝܬ ܪܩܝܩܬܐ ܝܠܗ – ܬܪܝܢ-ܬܠܬܐ ܢܘܩ̈ܙܐ ܥܡ ܡܪܝܡܢܘܬܐ ܪܡܬܐ ܣܦܩܝ ܩܐ ܕܡܨܠܝ ܣܪܛܐ ܕܝܗܝ ܠܟܠ ܓܒܐ، ܘܡܛܠ ܗܕܐ ܟܦܚܡܚ ܡܨܠܝܢ̈ܘܬܐ ܒܝܢܝ ܓܘ̈ܕܐ ܒܬܪ ܕܒܚܪܚ ܟܡܐ ܡܫܬܘܬܦ̈ܢܐ ܐܝܬ ܓܘ ܟܠ ܚܕܐ ܒܠܚܘܕ، ܘܐܢ ܦܘܪܫܢܐ ܚܫܝܚܐ ܝܠܗ – ܟܒܚܪܚ ܠܗ ܒܒܘܚܪܢܐ ܘܠܐ ܒܥܝܢܐ.

ܕܚܩܐ ܥܠ Paste ܓܘ ܟܘܬܐ ܕ-Overlay Scatterplot ܟܢܛܪ ܬܚܘܡܐ ܐܝܟ ܣܝܢܬܐܟܣ (syntax) – ܘܗܘ ܩܨܝܪܐ ܘܓܠܝܐ ܝܠܗ ܒܝܫ ܡܢ ܟܘܬܐ ܓܘܦܗ:

GRAPH
  /SCATTERPLOT(OVERLAY)=trust belonging WITH efficacy efficacy (PAIR)
  /PANEL COLVAR=dat COLOP=CROSS
  /MISSING=LISTWISE.

ܗܕܟܐ ܟܩܪܝܚ ܠܗ: OVERLAY – ܟܡܐ ܙܘܓ̈ܐ ܥܠ ܗܢܝ ܣܪ̈ܛܐ ܓܘܦܝܗܝ؛ ܩܕܡ WITH ܡܫܬܚܠܦ̈ܢܐ ܕ-X ܘܒܬܪܗ ܡܫܬܚܠܦ̈ܢܐ ܕ-Y، ܠܦܘܬ ܛܟܣܐ، ܘ-(PAIR) ܟܦܩܕ ܕܡܙܘܓ ܠܗܘܢ ܚܕ-ܥܡ-ܚܕ – ܩܕܡܝܐ ܥܡ ܩܕܡܝܐ، ܬܪܝܢܐ ܥܡ ܬܪܝܢܐ (ܘܠܐ ܟܠ ܚܕ ܥܡ ܟܠ ܚܕ). ܐܟܐ: trust ܥܡ efficacy ܘ-belonging ܥܡ efficacy – ܬܘܒ ܟܚܙܚ ܕ-efficacy ܝܠܗ Y. /PANEL COLVAR=dat ܝܠܗ ܦܘܠܓܐ ܠܥܡܘ̈ܕܐ ܠܦܘܬ ܕܝܢܐ (ROWVAR ܗܘܐ ܦܠܓ ܠܣܕܪ̈ܐ)، ܘ-/MISSING=LISTWISE – ܐܝܟ ܓܘ ܨܘܪܬܐ ܝܚܝܕܝܬܐ – ܟܫܒܩ ܡܫܬܘܬܦܢܐ (participant) ܕܚܣܝܪܐ ܠܗ ܛܝܡܐ ܓܘ ܟܠ ܚܕ ܡܢ ܡܫܬܚܠܦ̈ܢܐ ܕܓܘ ܦܘܩܕܢܐ؛ ܓܘ ܨܘܪܬܐ ܕܟܡܐ ܙܘܓ̈ܐ ܐܗܐ ܚܫܝܚܐ ܝܠܗ، ܡܛܠ ܕܡܫܬܘܬܦܢܐ ܕܚܣܝܪܐ ܠܗ belonging ܒܠܚܘܕ ܒܕ ܓܐܒܐ ܐܦ ܡܢ ܙܘܓܐ efficacy-trust. ܐܢ ܒܥܝܚ ܫܩܠܬܐ ܙܘܓܢܝܬܐ (pairwise deletion)، ܟܡܚܠܦܚ ܠ-/MISSING=VARIABLEWISE.

ܚܙܝܬܐ ܥܠ ܟܠ ܙܘܓ̈ܐ ܒܚܕ ܙܒܢܐ – Matrix Scatter. ܩܐ ܕܒܚܪܚ ܒܚܕ ܙܒܢܐ ܟܠ ܙܘܓ̈ܐ ܕܡܫܬܚܠܦ̈ܢܐ (variables) – ܡܬܠܐ ܒܝܢܝ ܚܡܫܐ ܡܫܬܚܠܦ̈ܢܐ ܕܚܣܝܢܘܬܐ (resilience) – ܟܡܦܠܚܚ Matrix Scatter: ܟܡܫܢܚ ܟܠ ܡܫܬܚܠܦ̈ܢܐ ܠܪܫܝܡܬܐ ܕ-Matrix Variables ܘܟܩܒܠܚ. ܟܠ ܩܠܝܬܐ ܓܘ ܡܐܛܪܝܟܣ ܨܘܪܬܐ ܕܒܕܪܐ (scatter plot) ܝܠܗ ܕܚܕ ܙܘܓܐ، ܗܕܟܐ ܕܡܐܛܪܝܟܣ ܟܠܗ ܟܩܐܡ ܩܘܒܠ ܡܐܛܪܝܟܣ ܕܐܣܘܪ̈ܐ ܕܚܕ̈ܕܐ (correlation matrix) ܕܓܘ ܦܐܬܐ ܕܐܣܘܪ̈ܐ ܕܚܕ̈ܕܐ، ܩܠܝܬܐ ܩܘܒܠ ܡܢܝܢܐ – ܘܟܡܚܘܝܐ ܡܐ ܕܡܢܝܢܐ ܠܐ ܡܨܐ: ܐܢ ܚܕ ܡܢ ܙܘܓ̈ܐ ܟܦܝܦܐ ܝܠܗ، ܘܐܢ ܓܘ ܚܕ ܡܢܝܗܝ ܝܬܝܒܐ ܝܠܗ ܚܙܝܬܐ (observation) ܕܟܢܓܕܐ ܣܪܛܐ. ܡܛܠ ܗܕܐ ܫܘܝܐ ܝܠܗ ܕܚܙܚ ܓܘܗ ܩܕܡ ܚܘܫܒܢܐ ܕܐܣܘܪ̈ܐ ܕܚܕ̈ܕܐ ܘܠܐ ܒܬܪܗ. ܘܝܘܬܪܢܐ ܕܝܠܗ ܒܠܚܘܕ: ܡܫܬܘܬܦܢܐ (participant) ܕܒܠܝܩܐ ܝܠܗ ܓܘ ܚܕܐ ܩܠܝܬܐ ܡܨܝܚ ܕܒܨܚ ܠܗ ܓܘ ܩܠ̈ܝܬܐ ܐܚܪ̈ܢܝܬܐ، ܘܕܚܙܚ ܐܢ ܢܘܟܪܝܐ ܝܠܗ ܓܘ ܟܠ ܡܫܬܚܠܦ̈ܢܐ ܝܢ ܓܘ ܚܕ ܙܘܓܐ ܒܠܚܘܕ – Cohen, Cohen, West & Aiken (2003، ܦܐܬܐ 115-116) ܟܡܚܘܝ ܐܗܐ ܒܒܠܩܐ ܕܗܘ ܡܫܬܘܬܦܢܐ ܓܘܦܗ ܓܘ ܟܠ ܩܠ̈ܝܬܐ.

ܓܘ ܟܘܬܐ ܕ-Scatterplot Matrix ܟܡܫܢܚ ܠܪܫܝܡܬܐ ܕ-Matrix Variables ܟܠ ܡܫܬܚܠܦ̈ܢܐ (variables) ܕܒܥܝܚ ܕܚܙܚ – ܐܟܐ ܚܡܫܐ ܡܫܬܚܠܦ̈ܢܐ ܕܚܣܝܢܘܬܐ. ܦܘܫܐ ܕܩܘܦ̈ܬܐ ܝܕܝܥ̈ܐ ܝܢܐ ܡܢ ܨܘܪܬܐ ܝܚܝܕܝܬܐ: Set Markers by ܩܐ ܨܒܥܐ ܠܦܘܬ ܓܘܕܐ، Label Cases by ܩܐ ܪܘ̈ܫܡܐ، ܘ-Panel by ܩܐ ܦܘܠܓܐ:

ܡܦܩܢܐ (output) ܡܨܝܕܬܐ ܝܠܗ ܕ-5×5 ܩܠ̈ܝܬܐ. ܣܪܛܐ ܡܨܠܝܢܐ ܣܦܝܩܐ ܝܠܗ – ܡܫܬܚܠܦܢܐ ܩܘܒܠ ܓܢܗ ܠܐ ܝܠܗ ܡܥܠܝܢܐ – ܘܟܠ ܩܠܝܬܐ ܐܚܪܬܐ ܨܘܪܬܐ ܕܒܕܪܐ ܝܠܗ ܕܚܕ ܙܘܓܐ: ܡܫܬܚܠܦܢܐ ܕܣܕܪܐ ܥܠ ܣܪܛܐ Y، ܡܫܬܚܠܦܢܐ ܕܥܡܘܕܐ ܥܠ ܣܪܛܐ X. ܬܪܝܢ ܦܠ̈ܓܐ ܕܡܨܝܕܬܐ ܨܘܪ̈ܬܐ ܕܡܚܙܝܬܐ ܝܢܐ – ܩܠܝܬܐ "ܡܕܒܪܢܘܬܐ ܩܘܒܠ efficacy" ܠܥܠ ܡܢ ܣܪܛܐ ܡܨܠܝܢܐ ܗܝ ܨܘܪܬܐ ܓܘܦܗ ܝܠܗ ܐܝܟ "efficacy ܩܘܒܠ ܡܕܒܪܢܘܬܐ" ܠܬܚܬ ܡܢܗ، ܒܣܪ̈ܛܐ ܡܚܘܠܦ̈ܐ – ܘܡܛܠ ܗܕܐ ܣܦܩ ܕܚܙܚ ܓܘ ܦܠܓܐ ܚܕ – ܥܕܡܐ ܕܡܘܣܦܚ ܣܪ̈ܛܐ ܕܪܝܓܪܫܢ (regression lines): ܓܘ ܟܠ ܩܠܝܬܐ ܣܪܛܐ ܝܠܗ ܕܡܫܬܚܠܦܢܐ ܕܣܕܪܐ ܥܠ ܡܫܬܚܠܦܢܐ ܕܥܡܘܕܐ، ܘܡܛܠ ܗܕܐ ܣܪ̈ܛܐ ܓܘ ܬܪܬܝܢ ܩܠ̈ܝܬܐ ܬܐܘ̈ܡܐ ܠܐ ܝܢܐ ܨܘܪ̈ܬܐ ܕܡܚܙܝܬܐ، ܐܠܐ ܬܪܝܢ ܣܪ̈ܛܐ ܦܪ̈ܝܫܐ، Y ܥܠ X ܘ-X ܥܠ Y (ܚܙܝܡܘܢ ܘܡܘܕܝ ܟܗܘܐ ܐܡܢ ܕܡܚܠܦܚ ܣܪ̈ܛܐ). ܠܦܘܬ Cohen, Cohen, West & Aiken (2003، ܦܐܬܐ 115) ܐܗܐ ܝܠܗ ܝܘܬܪܢܐ ܪܫܝܐ ܕܡܐܛܪܝܟܣ ܥܠ ܠܘܚܐ ܕܐܣܘܪ̈ܐ ܕܚܕ̈ܕܐ: ܠܘܚܐ ܟܡܚܘܝܐ ܐܘܪܚܐ ܘܚܝܠܐ ܕܐܣܘܪܐ ܣܪܛܢܝܐ (linear) ܒܠܚܘܕ، ܐܠܐ ܡܐܛܪܝܟܣ ܟܓܠܐ ܐܦ ܐܣܘܪ̈ܐ ܠܐ ܣܪܛܢ̈ܝܐ، ܕܓܘ ܠܘܚܐ ܦܫܝܛܐܝܬ ܟܡܬܚܙܝ ܐܝܟ ܐܣܘܪܐ ܕܚܕ̈ܕܐ ܢܡܘܟܐ. ܘܬܘܒ ܡܨܝܕܬܐ ܝܕܝܥܬܐ: ܟܠ ܡܫܬܚܠܦ̈ܢܐ ܡܨܥܝ̈ܬܐ ܝܢܐ ܕܦܣܘ̈ܩܐ (items) ܒܫܘ̈ܪܐ ܕܦܠܓܐ ܢܘܩܙܐ، ܘܡܛܠ ܗܕܐ ܢܘܩ̈ܙܐ ܛܟܝܣ̈ܐ ܝܢܐ ܒܣܕܪ̈ܐ ܘܒܥܡܘ̈ܕܐ، ܘܚܕ ܢܘܩܙܐ ܟܡܚܘܝܐ ܣܓܝ ܡܫܬܘܬܦ̈ܢܐ:

ܘܐܝܟ ܓܘ ܟܠ ܨܘܪܬܐ ܕܒܕܪܐ، ܣܪܛܐ ܕܪܝܓܪܫܢ (regression line) ܟܡܬܘܣܦ ܒܬܘܪܨܐ: Chart Editor ܘܗܝܓܝ Elements › Fit Line at Total – ܚܕ ܥܒܕܐ ܕܟܡܘܣܦ ܣܪܛܐ ܩܐ ܟܠ ܩܠ̈ܝܬܐ ܒܚܕ ܙܒܢܐ:

ܡܘܕܝ ܟܚܙܚ ܐܟܐ ܒܚܕܐ ܚܙܝܬܐ؟ ܟܠ ܥܣܪܐ ܐܣܘܪ̈ܐ ܥܠ ܡܢ ܨܦܪܐ ܘܓܠܝ̈ܐ ܝܢܐ – ܟܠ ܣܪ̈ܛܐ ܣܠܩ̈ܢܐ ܝܢܐ ܘܐܦ ܚܕ ܥܢܢܐ ܠܐ ܟܦܐܦ – ܘܡܛܠ ܗܕܐ Pearson ܦܐܝܐ ܝܠܗ ܩܐ ܟܠܗܘܢ؛ ܐܗܐ ܝܠܗ ܒܚܬܝܬܘܬܐ ܠܘܚܐ ܓܪܦܝܐ ܕܡܐܛܪܝܟܣ ܕܐܣܘܪ̈ܐ ܕܚܕ̈ܕܐ (correlation matrix) ܕܓܘ ܦܐܬܐ ܕܐܣܘܪ̈ܐ ܕܚܕ̈ܕܐ (ܐܟܡܐ: r ܒܝܢܝ .62 ܘ-.74). ܡܐ ܕܥܣܩܐ ܝܠܗ ܠܚܙܝܐ ܓܘ ܡܨܝܕܬܐ ܐܝܟ ܐܗܐ ܝܢܐ ܦܘܪ̈ܫܢܐ ܒܚܝܠܐ ܒܝܢܝ ܙܘܓ̈ܐ: ܐܠܝܨܘܬܐ ܟܡܛܫܝܐ ܠܗܘܢ، ܘܦܘܚܡܐ ܟܥܒܕܚ ܠܗ ܥܡ ܡܢܝ̈ܢܐ. ܒܣ، ܥܠ ܫܘܐܠܐ ܚܫܝܚܐ ܒܝܫ – ܐܢ ܐܝܬ ܙܘܓܐ ܕܟܥܒܕ ܫܢܝܐ ܡܢ ܐܚܪ̈ܢܐ، ܒܐܣܟܝܡܐ ܟܦܝܦܐ ܝܢ ܥܡ ܢܘܩ̈ܙܐ ܢܘܟܪ̈ܝܐ – ܡܐܛܪܝܟܣ ܟܡܦܢܐ ܛܒ ܒܝܫ ܡܢ ܟܠ ܠܘܚܐ. ܐܦ ܐܟܐ Paste ܟܢܛܪ ܣܝܢܬܐܟܣ (syntax)، ܘܐܦ ܐܟܐ /MISSING=LISTWISE: ܡܫܬܘܬܦܢܐ ܕܚܣܝܪܐ ܠܗ ܛܝܡܐ ܓܘ ܚܕ ܡܢ ܚܡܫܐ ܡܫܬܚܠܦ̈ܢܐ ܟܓܐܒܐ ܡܢ ܟܠ ܥܣܪܝܢ ܩܠ̈ܝܬܐ، ܘܡܛܠ ܗܕܐ N ܓܘ ܟܠ ܩܠܝܬܐ ܙܥܘܪܐ ܝܠܗ ܡܢ ܗܘ ܕܨܘܪܬܐ ܝܚܝܕܝܬܐ ܕܗܘ ܙܘܓܐ ܓܘܦܗ:

GRAPH
  /SCATTERPLOT(MATRIX)=leadership efficacy readiness belonging trust
  /MISSING=LISTWISE.

ܬܘܢܝܐ ܕܡܫܟܚ̈ܢܘܬܐ (reporting the results)

ܬܘܢܝܐ ܥܠ ܨܘܪܬܐ ܕܒܕܪܐ (scatter plot) ܣܓܝ ܙܒ̈ܢܐ ܟܥܐܠ ܓܘܗ ܨܘܪܬܐ ܓܘܦܗ (ܥܡ ܣܪܛܐ ܕܪܝܓܪܫܢ)، ܘܓܒܗ – ܒܡ̈ܠܐ – ܐܘܪܚܐ ܕܐܣܘܪܐ ܘܚܝܠܐ ܕܝܠܗ، ܡܢܝܢܐ ܡܫܘܬܦܐ ܕܦܣܩܬܐ (coefficient of determination)، ܘܒܙܒ̈ܢܐ ܐܦ ܫܘܝܘܬܐ ܕܣܪܛܐ. ܐܡܢ ܕܨܘܪܬܐ ܕܒܕܪܐ ܟܐܙܠܐ ܥܡ ܚܘܫܒܢܐ ܕܐܣܘܪܐ ܕܚܕ̈ܕܐ (correlation)، ܐܝܟ ܐܟܐ، ܡܥܝܕܐ ܝܠܗ ܕܡܬܢܐ ܬܪܘܝܗܝ ܐܟܚܕܐ: ܨܘܪܬܐ ܐܝܟ ܣܡܟܐ ܕܚܙܝܬܐ، ܘܐܣܘܪܐ ܕܚܕ̈ܕܐ ܐܝܟ ܟܢܘܫܝܐ ܡܢܝܢܝܐ. ܨܘܪܬܐ ܓܘܦܗ ܟܡܬܩܢܚ ܠܗ ܐܝܟ "ܨܘܪܬܐ" (Figure) ܠܦܘܬ ܢܡܘ̈ܣܐ ܕ-APA: ܡܢܝܢܐ ܕܨܘܪܬܐ ܠܥܠ، ܪܫܐ ܡܚܘܝܢܐ ܒܐܬܘ̈ܬܐ ܡܨܠ̈ܝܬܐ، ܣܪ̈ܛܐ ܥܡ ܫܡܗ̈ܐ ܕܡܫܬܚܠܦ̈ܢܐ، ܘܠܬܚܬ ܡܢ ܨܘܪܬܐ ܡܥܝܪܢܘܬܐ ܕܟܡܦܫܩܐ ܡܘܕܝ ܟܡܚܘܝܐ ܟܠ ܢܘܩܙܐ ܘܡܘܕܝ ܝܠܗ ܣܪܛܐ – ܒܚܬܝܬܘܬܐ ܐܝܟ ܨܘܪܬܐ ܕܒܕܪܐ ܕܡܬܠܐ ܓܘ ܡܕܒܪܢܐ (guide)، ܕܓܘܗ ܟܠ ܢܘܩܙܐ ܡܫܬܘܬܦܢܐ ܝܠܗ ܘܣܪ̈ܛܐ ܕܪܝܓܪܫܢ ܡܦܫܩ̈ܐ ܝܢܐ ܓܘ ܡܥܝܪܢܘܬܐ (American Psychological Association [APA], 2020, Sections 7.22-7.28; Section 7.36, Figure 7.15).

ܨܘܪܬܐ، ܠܘܚܐ ܘܡܐܡܪ̈ܐ ܕܬܘܢܝܐ (report sentences) ܒܐܗܐ ܐܣܟܝܡܐ – r ܘ-R² ܒܬܪܬܝܢ ܡܢܝ̈ܢܐ ܕܠܐ ܨܦܪܐ ܩܕܡܝܐ، b ܘ-a ܥܡ ܨܦܪܐ ܩܕܡܝܐ، ܬܚܘ̈ܡܐ ܕܬܘܟܠܢܐ ܩܐ r ܘܩܐ b (Field, 2024, Section 9.14) – ܡܚܫܒܢܐ (calculator) ܕܐܗܐ ܦܐܬܐ ܟܡܦܩ ܠܗܘܢ ܡܢ ܓܢܗ ܡܢ ܦܐܝܠ ܕܝܗܝ̈ܒܬܐ، ܘܡܨܝܚ ܕܡܚܬܚ ܠܗܘܢ ܐܝܟ ܦܐܝܠ ܕ-Word؛ ܨܘܪܬܐ ܓܘܦܗ ܟܡܬܢܣܚܐ ܡܢ ܡܚܙܝܢܐ، ܘܡܥܝܪܢܘܬܐ ܕܨܘܪܬܐ – ܡܢ ܠܘܚܐ ܕܡܦܩܢܐ.

ܐܡܢ ܕܪܝܓܪܫܢ ܝܠܗ ܡܕܡ ܪܫܝܐ. ܐܢ ܣܘܥܪܢܐ ܓܘ ܥܒܕܐ ܥܠ ܡܘܕܝܠ (model) ܝܠܗ ܘܠܐ ܥܠ ܐܣܘܪܐ ܕܚܕ̈ܕܐ، Field (2024، ܦܣܩܐ 9.14) ܟܬܚܡ ܩܠܝܠܘܬܐ ܩܐ ܬܘܢܝܐ: b ܥܡ ܛܥܝܘܬܐ ܬܩܝܢܬܐ (standard error) ܘܬܚܘܡܐ ܕܬܘܟܠܢܐ (confidence interval) ܕܝܠܗ (ܛܒ ܒܝܫ ܒܘܛܣܛܪܐܦ)، ܛܝܡܐ ܕ-p (p-value) ܚܬܝܬܐ، ܡܢܝܢܐ ܡܫܘܬܦܐ ܡܬܩܢܐ β، ܘ-R² – ܘܛܒ ܝܠܗ ܐܦ ܡܢܝܢܐ ܩܝܡܐ (intercept)، ܩܐ ܕܩܪܘܝܐ ܡܨܐ ܕܥܒܕ ܬܘܒ ܫܘܝܘܬܐ. ܠܦܘܬ ܢܡܘ̈ܣܐ ܕ-APA (APA, 2020, Section 6.36)، ܛܝ̈ܡܐ ܕܠܐ ܡܨܝ ܕܣܠܩܝ ܠܥܠ ܡܢ 1 – β، R² ܘ-p – ܟܡܬܟܬܒܝ ܕܠܐ ܨܦܪܐ ܩܕܡ ܢܘܩܙܐ (.55 ܘܠܐ 0.55)؛ b ܘܡܢܝܢܐ ܩܝܡܐ، ܕܡܨܝ، ܟܡܬܟܬܒܝ ܥܡ ܨܦܪܐ. ܛܥܝܘܬܐ ܬܩܝܢܬܐ ܘܬܚܘܡܐ ܕܬܘܟܠܢܐ ܕ-b ܠܐ ܝܢܐ ܓܘ ܠܘܚܐ ܕܐܗܐ ܦܐܬܐ – ܟܡܦܩܚ ܠܗܘܢ ܓܘ ܐܘܪܚܐ ܕܪܝܓܪܫܢ (ܚܙܝܡܘܢ ܡܢ ܨܘܪܬܐ ܠܪܝܓܪܫܢ). ܘܒܢܘܣܚܐ ܩܠܝܠܐ: ܡܥܒܕܢܘܬܐ ܡܫܘܥܪܬܐ (b)، ܛܥܝܘܬܐ ܬܩܝܢܬܐ ܕܝܠܗ ܘܛܝܡܐ ܕ-p – ܘܓܒܝܗܝ ܡܐܡܪܐ ܕܟܡܦܫܩ ܡܘܕܝ ܡܢܝܢܐ ܡܫܘܬܦܐ ܟܐܡܪ، ܩܐ ܕܟܠ ܩܪܘܝܐ ܦܗܡ؛ ܘܐܡܢ ܕܪܝܓܪܫܢ ܦܫܝܛܐ ܝܠܗ، ܨܘܪܬܐ ܕܒܕܪܐ ܥܡ ܣܪܛܐ ܝܠܗ ܐܘܪܚܐ ܛܒܬܐ ܒܝܫ ܩܐ ܡܚܘܝܐ ܕܦܐܪܐ.

ܘܕܟܝ ܟܥܒܕܚ ܐܗܐ ܒ-R؟

ܗܝ ܨܘܪܬܐ ܓܘܦܗ ܒܚܬܝܬܘܬܐ – ܢܘܩ̈ܙܐ، ܣܪܛܐ ܕܪܝܓܪܫܢ، ܪܫܐ ܡܨܠܝܐ ܘܡܥܝܪܢܘܬܐ ܕܨܘܪܬܐ – ܟܦܝܫܐ ܓܘ R ܒܚܕ ܣܩܪܝܦܬ (script)، ܥܡ ܚܙܡܐ ܕܓܪܦܝܩܐ ggplot2. ܥܝ̈ܕܐ ܐܝܟ ܚܕ̈ܕܐ ܝܢܐ ܥܡ ܦܣܩܐ ܕ-R ܓܘ ܦܘܫܐ ܕܦܐܬ̈ܐ ܕܣܐܝܛ: ܦܐܝܠ UTF-8، ܟܠ ܣܕܪܐ ܕܡܥܝܪܢܘܬܐ ܟܡܫܪܐ ܒܚܕܐ ܡܠܬܐ ܕܣܘܪܝܬ، ܫܡܗ̈ܐ ܩܨܝܪ̈ܐ ܒܐܢܓܠܝܙܝܐ ܩܐ ܫܘܝܘܬܐ (efficacy = מסוגלות، trust = אמון)، ܘܣܒܝܒܘܬܐ ܕ-UTF-8 ܩܐ ܫܡܗ̈ܐ ܥܒܪ̈ܝܐ (ܓܘ Windows: Sys.setlocale("LC_ALL", "Hebrew") ܝܢ R 4.2 ܘܠܥܠ). ܣܩܪܝܦܬ ܒܢܝܐ ܝܠܗ ܒܐܪܒܥܐ ܡܢܘ̈ܬܐ: ܡܢܝ̈ܢܐ، ܨܘܪܬܐ، ܢܛܘܪܬܐ، ܘܣܪ̈ܛܐ ܦܬܝ̈ܐ ܕܬܘܟܠܢܐ. ܪܗܛܐ ܝܠܗ ܐܝܟ ܕܐܝܬܘܗܝ ܥܠ ܦܐܝܠ ܕܡܬܠܐ (sample data file) ܕܦܐܬܐ (DATA_scatter_example_heb.xlsx، ܓܠܝܘܢܐ "נתונים") ܓܘ R 4.3.3، ܘܦܐܪ̈ܐ – ܐܝܟ ܚܕ̈ܕܐ ܥܡ ܠܘܚܐ 1 ܘܡܐܡܪ̈ܐ ܕܬܘܢܝܐ – ܟܬܝܒ̈ܐ ܝܢܐ ܓܘ ܡܥܝܪ̈ܢܘܬܐ. ܚܠܦܘܢ ܐܘܪܚܐ ܕܦܐܝܠ ܘܫܡܗ̈ܐ ܕܡܫܬܚܠܦ̈ܢܐ ܒܕܝܘܟܘܢ؛ ܓܘ R ܟܟܬܒܚ ܓܘ ܐܘܪܚܐ ܕܦܐܝܠ ܣܪܛܐ ܡܨܠܝܐ ܦܫܝܛܐ (/).

# ܨܘܪܬܐ ܕܒܕܪܐ ܘܣܪܛܐ ܕܪܝܓܪܫܢ – ܦܪܘܦܣܘܪ ܣܛܐܛ. ܐܗܐ ܦܐܝܠ ܢܛܝܪܐ ܝܠܗ ܒ-UTF-8؛ ܟܠ ܣܕܪܐ ܕܡܥܝܪܢܘܬܐ ܟܡܫܪܐ ܒܚܕܐ ܡܠܬܐ ܕܣܘܪܝܬ
# ܚܕ ܙܒܢܐ ܒܠܚܘܕ، ܐܢ ܚܙ̈ܡܐ ܠܐ ܝܢܐ ܡܬܩܢ̈ܐ: install.packages(c("readxl", "ggplot2", "ragg"))
library(readxl)    # ܩܪܝܢܐ ܕܐܩܣܠ
library(ggplot2)   # ܓܪܦܝܩܐ

# ܛܥܢܐ: ܛܘܦܣܐ ܬܩܝܢܐ – ܣܕܪܐ = ܡܫܬܘܬܦܢܐ، ܥܡܘܕܐ = ܡܫܬܚܠܦܢܐ؛ ܓܠܝܘܢܐ "נתונים"
d <- read_excel("C:/Rdata/DATA_scatter_example_heb.xlsx", sheet = "נתונים")
d <- d[, c("מסוגלות", "אמון")]
names(d) <- c("efficacy", "trust")          # ܫܡܗ̈ܐ ܩܨܝܪ̈ܐ ܒܐܢܓܠܝܙܝܐ ܩܐ ܫܘܝܘܬܐ

# --- 1. ܡܢܝ̈ܢܐ (ܐܝܟ ܚܕ̈ܕܐ ܥܡ ܠܘܚܐ 1 ܕܦܐܬܐ) ---
cor.test(d$efficacy, d$trust)               # ܦܐܪܐ: r = .738, t(477) = 23.90, p < .001, ܬܚܘܡܐ ܕܬܘܟܠܢܐ [.695, .776]
cor.test(d$efficacy, d$trust, method = "spearman", exact = FALSE)   # ܦܐܪܐ: rho = .728
fit <- lm(trust ~ efficacy, data = d)       # ܣܪܛܐ ܕܪܝܓܪܫܢ: trust ܥܠ efficacy (ܫܩܠܬܐ ܙܘܓܢܝܬܐ ܡܢ ܓܢܗ)
summary(fit)                                # ܦܐܪܐ: a = 1.159 (SE .096), b = 0.687 (SE .029, t = 23.90), s = 0.715, R² = .545, ܡܬܘܪܨܐ .544, F(1, 477) = 571.4
confint(fit)                                # ܬܚܘ̈ܡܐ ܕܬܘܟܠܢܐ 95%: a [0.970, 1.349], b [0.631, 0.744]
nobs(fit)                                   # ܦܐܪܐ: N = 479 – ܚܙ̈ܝܬܐ ܥܡ ܛܝܡܐ ܬܪܝܨܐ ܓܘ ܬܪܘܝܗܝ ܡܫܬܚܠܦ̈ܢܐ

# --- 2. ܨܘܪܬܐ ---
p <- ggplot(d, aes(x = efficacy, y = trust)) +
  geom_point(colour = "#5B63B0", alpha = 0.55, size = 2.2) +
  geom_smooth(method = "lm", se = FALSE, colour = "#37716D", linewidth = 0.9) +
  labs(x = "ܡܨܝܢܘܬܐ", y = "ܬܘܟܠܢܐ",
       title = "ܨܘܪܬܐ 1",
       subtitle = "ܬܘܟܠܢܐ ܐܝܟ ܦܘܢܩܣܝܘܢ ܕܡܨܝܢܘܬܐ",
       caption = paste0("ܡܥܝܪܢܘܬܐ. ܟܠ ܢܘܩܙܐ ܟܡܚܘܝܐ ܚܕ ܡܫܬܘܬܦܢܐ، ܠܦܘܬ ܛܝ̈ܡܐ ܕܝܠܗ ܓܘ ܡܨܝܢܘܬܐ (ܣܪܛܐ ܦܫܝܛܐ) ܘܓܘ ܬܘܟܠܢܐ (ܣܪܛܐ ܙܩܝܦܐ).\n",
                        "ܣܪܛܐ ܝܠܗ ܣܪܛܐ ܕܪܝܓܪܫܢ ܣܪܛܢܝܐ ܕܬܘܟܠܢܐ ܥܠ ܡܨܝܢܘܬܐ. N = ", nobs(fit),
                        " ܚܙ̈ܝܬܐ ܥܡ ܛܝܡܐ ܬܪܝܨܐ ܓܘ ܬܪܘܝܗܝ ܡܫܬܚܠܦ̈ܢܐ.")) +
  theme_minimal(base_size = 13) +
  theme(plot.title = element_text(face = "bold"),
        plot.subtitle = element_text(face = "italic"),
        plot.caption = element_text(hjust = 1, size = 10),
        panel.grid.minor = element_blank())
p

# --- 3. ܢܛܘܪܬܐ ܩܐ ܥܒܕܐ: 300 dpi، ܡܫܩܠܢܐ AGG (ܐܬܘ̈ܬܐ ܣܘܪ̈ܝܝܐ ܘܢܘܩ̈ܙܐ ܬܪ̈ܝܨܐ) ---
ggsave("C:/Rdata/scatter_trust_efficacy.png", p, width = 7, height = 4.5, dpi = 300, device = ragg::agg_png)

# --- 4. ܣܪ̈ܛܐ ܦܬܝ̈ܐ ܕܬܘܟܠܢܐ: Mean ܩܘܒܠ Individual (ܐܝܟ ܓܘ ܨܘܪܬܐ ܕܦܐܬܐ ܐܡܢ ܕܪܫܡܚ ܬܪܘܝܗܝ) ---
# ܦܘܫܩܐ: Mean – ܬܚܘܡܐ ܕܬܘܟܠܢܐ 95% ܩܐ ܣܪܛܐ ܓܘܦܗ: se = TRUE ܓܘ geom_smooth (ܓܘܒܝܐ ܡܩܕܡܐ ܕܝܠܗ)؛ Individual – ܬܚܘܡܐ ܕܡܢܒܝܢܘܬܐ 95% ܩܐ ܡܫܬܘܬܦܢܐ ܝܚܝܕܝܐ: predict(interval = "prediction")
grid <- data.frame(efficacy = seq(min(d$efficacy, na.rm = TRUE), max(d$efficacy, na.rm = TRUE), length.out = 100))
pred <- cbind(grid, predict(fit, newdata = grid, interval = "prediction", level = 0.95))
pred[c(1, 50, 100), ]                        # ܡܬܠܐ x = 3: ŷ = 3.22، ܬܚܘܡܐ ܕܡܢܒܝܢܘܬܐ [1.81, 4.62]؛ ܦܬܝܘܬܐ ܕܣܪܛܐ ܦܬܝܐ ܟܪܒܐ ܩܠܝܠ ܓܘ ܣܦܪ̈ܐ

p_ci <- ggplot(d, aes(x = efficacy, y = trust)) +
  geom_ribbon(data = pred, aes(x = efficacy, ymin = lwr, ymax = upr), inherit.aes = FALSE, fill = "#A7D6D5", alpha = 0.35) +   # Individual
  geom_point(colour = "#5B63B0", alpha = 0.55, size = 2.2) +
  geom_smooth(method = "lm", se = TRUE, level = 0.95, colour = "#37716D", fill = "#37716D", alpha = 0.35, linewidth = 0.9) +  # Mean
  labs(x = "ܡܨܝܢܘܬܐ", y = "ܬܘܟܠܢܐ",
       title = "ܨܘܪܬܐ 2",
       subtitle = "ܬܘܟܠܢܐ ܐܝܟ ܦܘܢܩܣܝܘܢ ܕܡܨܝܢܘܬܐ، ܥܡ ܣܪ̈ܛܐ ܦܬܝ̈ܐ ܕܬܘܟܠܢܐ",
       caption = paste0("ܡܥܝܪܢܘܬܐ. ܟܠ ܢܘܩܙܐ ܟܡܚܘܝܐ ܚܕ ܡܫܬܘܬܦܢܐ؛ N = ", nobs(fit), " ܚܙ̈ܝܬܐ ܥܡ ܛܝܡܐ ܬܪܝܨܐ ܓܘ ܬܪܘܝܗܝ ܡܫܬܚܠܦ̈ܢܐ.\n",
                        "ܣܪܛܐ ܝܠܗ ܣܪܛܐ ܕܪܝܓܪܫܢ ܣܪܛܢܝܐ ܕܬܘܟܠܢܐ ܥܠ ܡܨܝܢܘܬܐ.\n",
                        "ܣܪܛܐ ܦܬܝܐ ܚܫܘܟܐ – ܬܚܘܡܐ ܕܬܘܟܠܢܐ 95% ܩܐ ܣܪܛܐ (Mean)؛ ܒܗܝܪܐ – ܬܚܘܡܐ ܕܡܢܒܝܢܘܬܐ 95% ܩܐ ܡܫܬܘܬܦܢܐ ܝܚܝܕܝܐ (Individual).")) +
  theme_minimal(base_size = 13) +
  theme(plot.title = element_text(face = "bold"),
        plot.subtitle = element_text(face = "italic"),
        plot.caption = element_text(hjust = 1, size = 10),
        panel.grid.minor = element_blank())
p_ci

ggsave("C:/Rdata/scatter_trust_efficacy_ci.png", p_ci, width = 7, height = 4.5, dpi = 300, device = ragg::agg_png)

ܡܘܕܝ ܟܗܘܐ ܓܘ ܟܠ ܡܢܬܐ. ܓܘ ܡܢܬܐ 1 cor.test ܟܝܗܒ r، ܕܪ̈ܓܐ ܕܚܐܪܘܬܐ (degrees of freedom)، p ܘܬܚܘܡܐ ܕܬܘܟܠܢܐ (confidence interval) (ܒܫܘܢܝܐ ܕ-Fisher – ܗܘ ܬܚܘܡܐ ܓܘܦܗ ܕܓܘ ܠܘܚܐ 1)، ܘܒܗܝ ܦܘܢܩܣܝܘܢ ܓܘܦܗ ܥܡ method = "spearman" – r_s؛ lm ܟܫܥܪ ܣܪܛܐ، summary ܟܛܒܥ ܡܢܝܢܐ ܩܝܡܐ (intercept) ܘܡܨܠܝܢܘܬܐ (slope) ܥܡ ܛܥܝ̈ܘܬܐ ܬܩܝܢ̈ܬܐ، t ܘ-p ܕܝܗܝ، ܛܥܝܘܬܐ ܬܩܝܢܬܐ ܕܫܘܥܪܐ (Residual standard error)، R² ܘ-F – ܓܘ ܝܗܝ̈ܒܬܐ ܕܡܬܠܐ 1.159 ܘ-0.687، s = 0.715، R² = .545، ܒܚܬܝܬܘܬܐ ܣܕܪ̈ܐ ܕܠܘܚܐ 1 ܕܟܡܦܩ ܡܚܫܒܢܐ (calculator)؛ confint ܟܝܗܒ ܬܚܘ̈ܡܐ ܕܬܘܟܠܢܐ ܕܡܢܝ̈ܢܐ ܡܫܘܬܦ̈ܐ، ܘ-nobs ܟܡܕܥܪ N = 479. ܓܘ ܡܢܬܐ 2 geom_point ܟܨܐܪ ܢܘܩ̈ܙܐ (ܒܫܦܝܘܬܐ، ܡܛܠ ܕܓܘ ܣܒܠܬܐ ܕ-Likert ܣܓܝ ܡܫܬܘܬܦ̈ܢܐ ܝܬܝܒ̈ܐ ܝܢܐ ܥܠ ܢܘܩܙܐ ܚܕ ܒܚܬܝܬܘܬܐ، ܘܗܕܟܐ ܟܚܙܚ ܐܝܟܐ ܥܢܢܐ ܐܠܝܨܐ ܝܠܗ)، geom_smooth(method = "lm", se = FALSE) ܟܡܘܣܦ ܣܪܛܐ ܕܪܝܓܪܫܢ ܕܠܐ ܣܪܛܐ ܦܬܝܐ، ܘ-labs ܟܝܗܒ ܠܨܘܪܬܐ ܡܢܘ̈ܬܐ ܕ-APA: ܡܢܝܢܐ، ܪܫܐ ܡܨܠܝܐ (subtitle ܥܡ face = "italic")، ܫܡܗ̈ܐ ܕܡܫܬܚܠܦ̈ܢܐ ܥܠ ܣܪ̈ܛܐ، ܘܡܥܝܪܢܘܬܐ ܕܨܘܪܬܐ ܓܘ caption – ܡܘܕܝ ܟܡܚܘܝܐ ܟܠ ܢܘܩܙܐ، ܡܘܕܝ ܝܠܗ ܣܪܛܐ ܘܪܒܘܬܐ ܕܕܘܡܝܐ (sample size)، ܡܫܘܝܐ ܠܓܒܐ ܝܡܝܢܐ ܒ-hjust = 1. ܡܢܬܐ 3 ܟܢܛܪ ܦܐܝܠ ܕ-PNG ܒ-300 dpi ܒܪܒܘܬܐ ܩܝܡܬܐ، ܘܐܗܐ ܝܠܗ ܢܘܣܚܐ ܕܟܥܐܠ ܠܥܒܕܐ – ܠܐ ܡܦܩܬܐ ܡܢ ܟܘܬܐ ܕ-Plots، ܕܟܢܛܪ ܒܚܬܝܬܘܬܐ ܕܡܚܙܝܢܐ ܘܒܪܒܘܬܐ ܕܟܘܬܐ.

ܬܪܝܢ "ܙܘܗܪ̈ܐ" ܠܐ ܝܢܐ ܛܥܝܘܬܐ. ܒܬܪ ܟܠ ܪܗܛܐ ܟܡܬܛܒܥ Removed 33 rows containing missing values: 512 ܡܫܬܘܬܦ̈ܢܐ (participants) ܓܘ ܦܐܝܠ ܒܨܝܪ 479 ܥܡ ܛܝܡܐ ܬܪܝܨܐ ܓܘ ܬܪܘܝܗܝ ܡܫܬܚܠܦ̈ܢܐ – R ܦܫܝܛܐܝܬ ܟܡܘܕܥ ܥܠ ܫܩܠܬܐ ܙܘܓܢܝܬܐ (pairwise deletion)، ܗܝ ܐܘܪܚܐ ܓܘܦܗ ܕܐܚܕܝ SPSS ܘܡܚܫܒܢܐ ܕܦܐܬܐ. ܠܝܬ ܣܢܝܩܘܬܐ ܕܥܒܕܚ ܡܕܡ. ܛܝ̈ܡܐ ܚܣܝ̈ܪܐ ܟܡܬܫܩܠܝ ܡܢ ܓܢܗܘܢ ܓܘ ܟܠ ܬܠܬܐ ܕܪ̈ܓܐ – cor.test، lm ܘܨܘܪܬܐ – ܘܡܛܠ ܗܕܐ ܡܢܝ̈ܢܐ ܐܝܟ ܚܕ̈ܕܐ ܝܢܐ ܥܡ ܗܢܝ ܕܓܘ ܠܘܚܐ: r(477) = .738, p < .001.

ܡܨܝܕܬܐ ܕܣܘܪܝܬ – ܘܕܟܝ ܟܥܒܪܚ ܥܠܗ. ܓܘ ܪܗܛܐ ܩܕܡܝܐ ܡܨܐ ܕܗܘܐ ܕܣܘܪܝܬ ܓܘ ܨܘܪܬܐ ܡܬܚܙܝܐ ܛܒ، ܒܣ ܢܘܩ̈ܙܐ ܓܘ ܡܥܝܪܢܘܬܐ ܕܨܘܪܬܐ ܒܕ ܡܬܚܠܛܝ: ܢܘܩܙܐ ܐܚܪܝܐ ܒܕ ܫܘܪ ܠܓܒܐ ܣܡܠܐ ܕܣܕܪܐ، ܘ-N = 479 ܒܕ ܐܙܠ ܠܕܘܟܬܐ ܠܐ ܬܪܝܨܬܐ ܓܘ ܡܐܡܪܐ (ܗܕܟܐ ܗܘܝܠܗ ܐܦ ܓܘ ܪܗܛܐ ܕܒܘܚܪܢܐ ܕܦܐܬܐ، ܓܘ ܣܒܝܒܘܬܐ ܕ-Linux ܕܠܐ ܐܗܐ ܡܫܩܠܢܐ). ܐܗܐ ܠܐ ܝܠܗ ܥܘܩܬܐ ܓܘ ܪܡܙܐ، ܐܠܐ ܓܘ ܡܫܩܠܢܐ ܓܪܦܝܐ ܕܒܗ RStudio ܟܨܐܪ ܐܝܟ ܓܘܒܝܐ ܡܩܕܡܐ (default): ܗܘ ܟܡܛܟܣ ܐܬܘ̈ܬܐ ܣܘܪ̈ܝܝܐ ܡܢ ܝܡܝܢܐ ܠܣܡܠܐ، ܒܣ ܟܡܣܒܐ ܕܐܘܪܚܐ ܫܬܐܣܝܬܐ ܕܣܕܪܐ ܡܢ ܣܡܠܐ ܠܝܡܝܢܐ ܝܠܗ، ܘܡܛܠ ܗܕܐ ܟܠ ܡܐ ܕܠܐ ܝܠܗ ܐܬܐ ܣܘܪܝܝܬܐ – ܢܘܩܙܐ، ܩܘܠܦ̈ܐ، ܡܢܝܢܐ ܠܛܝܢܝܐ – ܟܢܦܠ ܓܘ ܕܘܟܬܐ ܠܐ ܬܪܝܨܬܐ. ܪ̈ܫܐ ܘܪܘ̈ܫܡܐ ܕܣܪ̈ܛܐ ܕܚܕܐ-ܬܪܬܝܢ ܡ̈ܠܐ ܠܐ ܟܡܬܚܒܠܝ؛ ܡܐܡܪܐ ܓܡܝܪܐ ܥܡ ܢܘܩ̈ܙܐ – ܐܝܢ. ܦܘܫܪܐ ܝܠܗ ܡܫܩܠܢܐ ܓܪܦܝܐ ܕܟܡܦܠܚ ܒܬܪܝܨܘܬܐ ܐܠܓܘܪܝܬܡ ܕܬܪܝܢ ܐܘܪ̈ܚܬܐ ܕ-Unicode، AGG، ܕܟܐܬܐ ܓܘ ܚܙܡܐ ragg، ܓܘ ܬܪܬܝܢ ܕܘܟ̈ܝܬܐ: ܓܘ ܦܐܝܠ – ܐܗܐ ܝܠܗ ܐܪܓܘܡܢܬ device = ragg::agg_png ܓܘ ܣܕܪܐ ܕ-ggsave ܕܓܘ ܣܩܪܝܦܬ؛ ܘܓܘ ܟܘܬܐ ܕ-Plots – ܚܕ ܙܒܢܐ، ܓܘ ܬܘܩ̈ܢܐ: Tools › Global Options › General › Graphics › Backend: AGG، ܘܗܝܓܝ Apply ܘ-OK:

ܘܬܘܒ ܬܪܝܢ ܢܡܘ̈ܣܐ ܙܥܘܪ̈ܐ ܩܐ ܣܘܪܝܬ ܓܘ R: ܟܢܛܪܚ ܦܐܝܠ ܕܣܩܪܝܦܬ ܒܪܡܙܢܘܬܐ (encoding) UTF-8 (ܓܘ RStudio: File › Save with Encoding) – ܐܢ ܠܐ، ܐܬܘ̈ܬܐ ܣܘܪ̈ܝܝܐ ܡܨܝ ܕܗܘܝ ܢܘܩ̈ܙܐ ܝܢ ܡܪ̈ܒܥܐ؛ ܘܐܡܢ ܕܦܠܓܚ ܡܥܝܪܢܘܬܐ ܐܪܝܟܬܐ ܠܟܡܐ ܣܕܪ̈ܐ ܒ-\n، ܟܡܫܪܚ ܟܠ ܣܕܪܐ ܒܡܠܬܐ ܕܣܘܪܝܬ ܘܠܐ ܒܐܬܐ ܠܛܝܢܝܬܐ ܝܢ ܒܡܢܝܢܐ – ܣܕܪܐ ܕܟܡܫܪܐ ܒ-N = 479 ܒܕ ܡܬܛܟܣ ܐܝܟ ܣܕܪܐ ܠܛܝܢܝܐ، ܘܢܘܩܙܐ ܕܝܠܗ ܒܕ ܥܪܩ ܬܘܒ.

ܣܪ̈ܛܐ ܦܬܝ̈ܐ ܕܬܘܟܠܢܐ – ܚܘܝܐ ܚܝܐ ܕ-Mean ܩܘܒܠ Individual

ܡܢܬܐ 4 ܕܣܩܪܝܦܬ (script) ܟܨܐܪ ܬܪܝܢ ܣܪ̈ܛܐ ܦܬܝ̈ܐ ܕܬܚܘܝܠܗܘܢ ܓܘ ܦܣܩܐ tab ܕ-Fit Line – ܘܡܨܝܚ ܕܚܙܚ ܒܥܝ̈ܢܐ ܕܝܢ ܩܡܘܕܝ ܦܘܪܫܢܐ ܒܝܢܝ ܕܝܗܝ ܚܫܝܚܐ ܝܠܗ. ܣܪܛܐ ܦܬܝܐ ܕ-Mean ܒܥܝܐ ܚܕܐ ܡܠܬܐ: se = TRUE ܓܘ geom_smooth (ܒܥܒܕܐ ܐܗܐ ܝܠܗ ܓܘܒܝܐ ܡܩܕܡܐ ܕܝܠܗ – ܫܩܠܬܐ ܕ-se = FALSE ܣܦܩܐ)، ܘܐܗܐ ܝܠܗ ܬܚܘܡܐ ܕܬܘܟܠܢܐ (confidence interval) 95% ܩܐ ܣܪܛܐ ܓܘܦܗ. ܣܪܛܐ ܦܬܝܐ ܕ-Individual ܠܐ ܝܠܗ ܒܢܝܐ ܓܘ ggplot2، ܘܡܛܠ ܗܕܐ ܟܚܫܒܚ ܠܗ ܬܪܝܨܐܝܬ ܡܢ ܡܘܕܝܠ (model): predict(fit, newdata, interval = "prediction") ܟܡܕܥܪ ܩܐ ܟܠ ܛܝܡܐ ܕ-X ܡܢܒܝܢܘܬܐ ܘܬܚܘ̈ܡܐ ܕܬܚܘܡܐ ܕܡܢܒܝܢܘܬܐ (prediction interval) ܩܐ ܡܫܬܘܬܦܢܐ ܝܚܝܕܝܐ، ܘ-geom_ribbon ܟܨܐܪ ܠܗܘܢ ܐܝܟ ܣܪܛܐ ܦܬܝܐ. ܬܪܝܢ ܣܪ̈ܛܐ ܦܬܝ̈ܐ ܨܝܪ̈ܐ ܝܢܐ ܒܗܘ ܪܡܐ ܕܬܘܟܠܢܐ ܓܘܦܗ، 95%، ܘܥܡ ܗܕܐ:

ܣܪܛܐ ܦܬܝܐ ܕ-Mean ܩܪܝܒܐܝܬ ܟܡܬܒܠܥ ܓܘ ܣܪܛܐ: ܥܡ 479 ܡܫܬܘܬܦ̈ܢܐ (participants) ܛܒ ܟܝܕܥܚ ܐܝܟܐ ܣܪܛܐ ܡܨܥܝܐ ܟܥܒܪ، ܘܓܘ ܕܘܡܝܐ ܪܒܐ ܒܝܫ ܗܘܐ ܟܡܬܟܢܫ ܠܨܦܪܐ. ܣܪܛܐ ܦܬܝܐ ܕ-Individual ܟܡܬܦܫܛ ܥܠ ܬܪܝܢ-ܬܠܬܐ ܢܘܩ̈ܙܐ ܓܘ ܣܒܠܬܐ (scale) – ܡܛܠ ܕܐܦ ܒܕܪܐ ܕܡܫܬܘܬܦ̈ܢܐ ܚܕܪ ܣܪܛܐ ܥܠܝܠܐ ܝܠܗ ܓܘܗ، σ ܕܗܘ ܦܣܩܐ، ܕܠܐ ܟܓܐܒܐ ܒܚܕ ܪܒܘܬܐ ܕܕܘܡܝܐ. ܘܬܪܘܝܗܝ، ܐܢ ܛܒ ܚܙܚ، ܩܛܝ̈ܢܐ ܝܢܐ ܝܬܝܪ ܚܕܪ ܡܨܥܝܬܐ (mean) ܕ-X ܘܟܡܬܦܬܝ ܩܠܝܠ ܠܣܦܪ̈ܐ – ܐܣܟܝܡܐ ܕܫܥܬܐ ܕܚܠܐ. ܡܥܝܪܢܘܬܐ ܕܨܘܪܬܐ ܕܓܘ ܪܡܙܐ ܓܠܝܐܝܬ ܟܐܡܪܐ ܡܘܕܝ ܟܡܚܘܝܐ ܟܠ ܣܪܛܐ ܦܬܝܐ ܘܒܐܝܢܐ ܪܡܐ ܕܬܘܟܠܢܐ، ܐܝܟ ܕܟܒܥܐ APA (2020، ܦܣܩܐ 7.28) – ܘܐܗܐ ܝܠܗ ܥܠܬܐ ܕܓܘ ܨܚܚܐ ܕܡܫܟܚ̈ܢܘܬܐ (results chapter) ܣܓܝ ܙܒ̈ܢܐ ܟܡܬܢܚ Mean ܒܠܚܘܕ: ܫܘܐܠܐ ܐܟܡܐ ܝܠܗ "ܐܝܟܐ ܐܣܘܪܐ ܟܥܒܪ"، ܠܐ "ܐܝܟܐ ܡܫܬܘܬܦܢܐ ܚܕܬܐ ܒܕ ܢܦܠ".

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