ܛܝ̈ܡܐ ܢܘܟܪ̈ܝܐ ܘܫܪ̈ܛܐ: ܡܘܕܝ ܟܡܥܠܐ ܡܣܒ ܒܐܦ̈ܐ ܓܘ ܦܐܪ̈ܐ، ܘܡܘܕܝ ܟܥܒܕܚ

ܡܕܒܪܢܐ (guide)

ܡܐ ܐܝܬ ܓܘ ܐܗܐ ܦܐܬܐ (On this page)

ܩܪܝܒ ܟܠ ܒܘܚܪ̈ܢܐ ܕܓܘ ܣܐܝܛ – ܐܣܘܪܐ ܕܚܕ̈ܕܐ، t، ANOVA، ܪܝܓܪܫܢ – ܢܘܣ̈ܚܐ ܝܢܐ ܕܚܕ ܡܘܕܝܠ، ܡܘܕܝܠ ܣܪܛܢܝܐ (linear model)، ܘܡܛܠ ܗܕܟܐ ܐܝܬ ܠܗܘܢ ܐܢܝ ܫܪ̈ܛܐ ܓܢܝܗܝ ܘܐܢܝ ܒܥܠܕ̈ܒܒܐ ܓܢܝܗܝ. Field (2024، ܨܚܚܐ 6) ܟܩܪܐ ܠܐܗܐ "ܚܝܘܬܐ ܕܡܣܒ ܒܐܦ̈ܐ" (bias) ܥܡ ܬܪܝܢ ܪ̈ܫܐ: ܛܝ̈ܡܐ ܢܘܟܪ̈ܝܐ ܘܬܒܪܬܐ ܕܫܪ̈ܛܐ. ܦܐܬܐ ܟܡܦܫܩܐ ܡܘܕܝ ܟܡܢܟܐ ܟܠ ܪܝܫܐ – ܡܛܠ ܕܠܐ ܟܠ ܡܕܡ ܟܡܬܢܟܐ ܒܐܗܝ ܡܫܘܚܬܐ ܓܢܗ̇: ܫܘܥܪܐ ܒܓܢܗ ܣܓܝ ܓܗ̈ܐ ܛܒܐ ܝܠܗ، ܘܡܐ ܕܟܬܒܪ ܝܠܗ̇ ܛܥܝܘܬܐ ܬܩܝܢܬܐ ܘܥܡܗ̇ ܬܚܘܡܐ ܕܬܘܟܠܢܐ ܘܒܘܚܪܢܐ – ܟܡܛܟܣܐ ܠܫܪ̈ܛܐ ܠܦܘܬ ܚܫܝܚܘܬܐ (ܣܪܛܢܝܘܬܐ ܩܕܡܝܬܐ، ܢܘܪܡܠܝܘܬܐ ܐܚܪܝܬܐ)، ܟܡܚܘܝܐ ܐܝܟܢ ܟܡܫܬܘܕܥܚ ܥܩ̈ܬܐ ܓܘ ܨܘܪ̈ܬܐ ܘܓܘ ܡܢܝ̈ܢܐ، ܘܡܘܕܝ ܟܥܒܕܚ: ܐܘܪ̈ܚܬܐ ܚܣܝ̈ܢܬܐ، ܠܐ ܫܩܠܬܐ ܘܠܐ ܫܘܢܝܐ ܕܦܐܪܐ.

1. ܡܘܕܝ ܝܠܗ ܡܣܒ ܒܐܦ̈ܐ – ܘܡܘܕܝ ܒܚܬܝܬܘܬܐ ܟܡܬܢܟܐ

ܕܝܢܐ "ܕܡܣܒ ܒܐܦ̈ܐ" ܝܠܗ ܐܗܘ ܕܦܘܣܩܢܐ ܕܝܠܗ ܠܐ ܟܫܠܡ ܥܡ ܫܪܪܐ ܕܠܐ ܦܪܨܘܦܝܐ (objective)؛ ܘܗܕܟܐ ܓܘ ܣܛܐܛܝܣܛܝܩܐ – ܦܪܡܝ̈ܛܪܐ ܕܟܫܥܪܚ ܡܨܝ̈ܐ ܕܗܘܝ ܦܪ̈ܝܫܐ ܡܢ ܛܝ̈ܡܐ ܫܪܝܪ̈ܐ ܕܝܠܗܘܢ، ܘܒܘܚܪ̈ܢܐ ܡܨܝ̈ܐ ܕܛܥܝ (Field, 2024, Section 6.3). ܡܐ ܕܚܫܝܚܐ ܝܠܗ ܩܐ ܐܗܐ ܦܐܬܐ ܝܠܗ ܕ"ܡܣܒ ܒܐܦ̈ܐ" ܠܐ ܝܠܗ ܚܕ ܡܕܡ. Field ܟܦܪܫ ܠܗ ܠܦܘܬ ܡܐ ܕܒܥܝܚ ܡܢ ܡܘܕܝܠ: ܐܢ ܒܥܝܚ ܕܫܥܪܚ – ܡܫܘܥܪܢܐ ܕܠܐ ܡܣܒ ܒܐܦ̈ܐ ܝܠܗ ܐܗܘ ܕܒܡܨܥܝܬܐ، ܥܠ ܕܘ̈ܡܝܐ، ܟܡܛܐ ܠܛܝܡܐ ܕܟܢܫܐ ܟܠܢܝܐ؛ ܡܫܘܥܪܢܐ ܫܠܝܡܐ (consistent) ܟܩܪܒ ܠܗ ܟܡܐ ܕܕܘܡܝܐ ܟܪܒܐ؛ ܡܫܘܥܪܢܐ ܡܥܕܪܢܐ (efficient) ܝܠܗ ܐܗܘ ܕܐܝܬ ܠܗ ܫܘܚܠܦܐ ܙܥܘܪܐ ܡܢ ܟܠ ܒܝܢܝ ܓܘܒ̈ܝܐ. ܐܢ ܒܥܝܚ ܬܚܘܡܐ ܕܬܘܟܠܢܐ – ܡܐ ܕܒܚܝܪܐ ܝܠܗ ܟܣܝܘܬܐ (coverage) ܝܠܗ̇: ܬܚܘܡܐ ܕ-95% ܓܪܓ ܕܐܚܕ ܛܝܡܐ ܕܟܢܫܐ ܟܠܢܝܐ ܓܘ 95% ܡܢ ܕܘ̈ܡܝܐ، ܘܐܢ ܠܐ – ܐܝܬ ܠܗ ܡܣܒ ܒܐܦ̈ܐ. ܘܐܢ ܒܥܝܚ ܕܒܚܪܚ ܗܘܦܘܬܣܝܣ – ܒܘܚܪܢܐ ܕܠܐ ܡܣܒ ܒܐܦ̈ܐ ܟܢܛܪ ܡܢܬܐ ܕܛܥܝܘܬܐ ܕܙܢܐ I ܕܦܣܝܩܐ ܝܠܗ̇ (5%) ܘܡܢܬܐ ܕܛܥܝܘܬܐ ܕܙܢܐ II (20%). ܐܗܐ ܦܘܪܫܐ ܩܠܝܕܐ ܝܠܗ ܩܐ ܟܠ ܡܐ ܕܒܕ ܐܬܐ: ܣܓܝܐܐ ܡܢ ܬܒܪ̈ܬܐ ܟܫܒܩܝ ܠܫܘܥܪܐ ܬܪܝܨܐ ܘܟܡܢܟܝ ܠܛܥܝܘܬܐ ܬܩܝܢܬܐ – ܘܥܡܗ̇ ܠܬܚܘܡܐ ܕܬܘܟܠܢܐ ܘܠܒܘܚܪܢܐ.

2. ܛܝ̈ܡܐ ܢܘܟܪ̈ܝܐ – ܪܝܫܐ ܩܕܡܝܐ

ܛܝܡܐ ܢܘܟܪܝܐ ܝܠܗ ܡܢܝܢܐ ܕܦܪܝܫܐ ܝܠܗ ܒܣܓܝ ܡܢ ܝܗܝ̈ܒܬܐ ܐܚܪ̈ܢܐ. ܡܬܠܐ ܕ-Field (2024، ܦܣܩܐ 6.4) ܝܠܗ ܫܒܥܐ ܡܐܡܪ̈ܐ ܕܪܥܝܢܐ (reviews) ܩܕܡܝ̈ܐ ܥܠ ܡܦܩܬܐ ܩܕܡܝܬܐ ܕܟܬܒܐ ܕܝܠܗ ܓܘ Amazon: 2، 5، 4، 5، 5، 5، 5. ܡܨܥܝܬܐ 4.43؛ ܕܠܐ ܡܐܡܪܐ ܩܕܡܝܐ – 4.83. ܡܢܝܢܐ ܚܕ ܓܪܫܠܗ ܠܡܨܥܝܬܐ 0.4 ܠܬܚܬ، ܘܙܒܘܢܐ ܚܕܬܐ ܒܕ ܗܘܐ ܡܦܠܛ ܫܘܠܡܐ ܕܟܬܒܐ ܒܝܫܐ ܝܠܗ ܡܢ ܡܐ ܕܟܢܫܐ ܟܠܢܝܐ ܟܚܫܒ. ܓܘ ܡܘܕܝܠ ܥܡ ܡܢܒܝܢܐ – ܙܡܪܬܐ (concert) ܕܩܠܐ ܪܡܐ ܣܓܝ ܥܡ ܛܢܝܢܐ ܩܨܝܪܐ ܓܘ ܐܕ̈ܢܐ – ܛܝܡܐ ܢܘܟܪܝܐ ܦܫܛܠܗ ܠܣܪܛܐ ܕܪܝܓܪܫܢ: ܡܨܠܝܢܘܬܐ ܢܚܬܠܗ̇ ܡܢ 9.94 ܠ-6.01. ܐܠܐ ܢܘܩܙܐ ܚܫܝܚܬܐ ܕ-Field ܝܠܗ̇ ܕܛܝ̈ܡܐ ܢܘܟܪ̈ܝܐ ܟܡܢܟܝ ܒܣܓܝ ܒܙܘܕܐ ܠܛܥܝܘܬܐ ܡܢ ܠܫܘܥܪܐ: ܓܘ ܡܬܠܐ ܕܚܡܫܐ ܡܠܦ̈ܢܐ (1، 3، 4، 3، 2)، ܚܠܦܬܐ ܕ-4 ܒ-10 ܟܡܙܝܥܐ ܠܡܨܥܝܬܐ ܡܢ 2.6 ܠ-3.8، ܐܠܐ ܠܓܘܡܪܐ ܕܡܪ̈ܒܥܐ ܕܛܥܝܘܬܐ ܡܢ 5.2 ܠ-50.8 – 38.44 ܡܢܝܗܝ ܥܠ ܛܝܡܐ ܢܘܟܪܝܐ. ܥܠܬܐ: ܛܥ̈ܝܘܬܐ ܡܪ̈ܒܥܬܐ ܝܢܐ، ܘܣܛܝܘܬܐ ܪܒܬܐ ܟܡܬܪܒܥܐ. ܘܓܘܡܪܐ ܕܡܪ̈ܒܥܐ ܝܠܗ ܡܐ ܕܡܢܗ ܚܫܝܒ̈ܐ ܝܢܐ ܣܛܝܘܬܐ ܬܩܝܢܬܐ، ܛܥܝܘܬܐ ܬܩܝܢܬܐ، ܬܚܘܡܐ ܕܬܘܟܠܢܐ ܘܡܢܝܢܐ ܣܛܐܛܝܣܛܝܩܝܐ ܕܒܘܚܪܢܐ. ܛܝܡܐ ܢܘܟܪܝܐ ܚܕ – ܬܚܘܡܐ ܕܬܘܟܠܢܐ ܦܬܝܐ ܘܒܘܚܪܢܐ ܟܪܝܗܐ.

ܘܐܦܢ ܗܕܟܐ، Field ܓܠܝܐ ܝܠܗ: ܛܝ̈ܡܐ ܢܘܟܪ̈ܝܐ ܟܦܝܫܝ ܓܘ ܝܗܝ̈ܒܬܐ، ܐܠܐ ܐܢ ܐܝܬ ܣܗܕܘܬܐ ܚܝܠܬܢܬܐ ܕܐܢܝ ܠܐ ܝܢܐ ܡܢ ܟܢܫܐ ܟܠܢܝܐ ܕܚܫܝܚܐ ܝܠܗ ܩܐܠܢ. ܕܡܢܝܢܐ ܢܘܟܪܝܐ ܝܠܗ ܠܐ ܝܠܗ̇ ܥܠܬܐ ܕܫܩܠܚ ܠܗ. ܫܘܐܠܐ ܕܓܪܓ ܕܫܐܠܚ ܝܠܗ ܩܐ ܡܘܕܝ: ܐܢ ܙܡܪܬܐ ܕܩܠܐ ܪܡܐ ܚܠܨܠܗ̇ ܒܛܢܝܢܐ ܩܨܝܪܐ، ܘܐܬܝܕܥ ܕܐܗܐ ܒܪܢܫܐ ܝܚܝܕܝܐ ܝܠܗ ܕܛܡܡܠܗ ܐܕ̈ܢܘܗܝ (earplugs) – ܐܗܐ ܨܐ ܟܡܦܫܩ ܘܨܐ ܟܡܥܒܪ ܠܗ ܠܟܢܫܐ ܟܠܢܝܐ ܐܚܪܢܐ، ܘܡܨܝܚ ܕܡܦܩܚ ܠܗ، ܒܫܪܛܐ ܕܡܬܢܚ ܕܦܠܛܠܗ ܘܩܐ ܡܘܕܝ؛ ܘܛܒܐ ܝܠܗ ܕܦܣܩܚ ܢܡܘ̈ܣܐ ܕܡܦܩܬܐ ܡܢ ܩܕܡ، ܒܡܟܬܒܬ ܡܩܕܡܬܐ (preregistration). ܘܐܢ ܠܝܬ ܦܘܫܩܐ ܕܐܗܐ ܙܢܐ – ܓܘܒܝܐ ܡܩܕܡܐ ܝܠܗ ܕܛܝܡܐ ܢܘܟܪܝܐ ܟܡܚܘܐ ܫܘܚܠܦܐ ܟܝܢܝܐ، ܘܒܥܝܚ ܕܢܛܪܚ ܠܗ. Field ܟܡܘܣܦ ܙܘܗܪܐ ܥܠ "ܛܝ̈ܡܐ ܢܘܟܪ̈ܝܐ ܛܫܝ̈ܐ" (ܟܘܬܐ 6.5): ܠܐ ܡܢܝܢܐ ܪܚܝܩܐ ܘܝܚܝܕܝܐ، ܐܠܐ ܟܢܫܐ ܙܥܘܪܐ ܓܘܝܐ ܥܡ ܕܘܢ̈ܒܐ ܝܩܘܪ̈ܐ ܕܛܫܐ ܓܢܗ ܓܘ ܦܘܠܓܐ ܕܟܡܬܚܙܐ ܐܝܟ ܙܓܐ ܓܡܝܪܐ – ܦܘܠܓܐ ܢܘܪܡܠܝܐ ܡܚܠܛܐ (contaminated normal distribution) (Tukey, 1960, as cited in Field). ܗܘ ܟܡܢܦܚ ܠܫܘܥܪܐ ܕܫܘܚܠܦܐ ܘܟܡܢܚܬ ܠܚܝܠܐ ܣܛܐܛܝܣܛܝܩܝܐ ܕܒܘܚܪ̈ܢܐ، ܘܣܓܝ ܡܬܚܙܐ ܝܠܗ.

3. ܫܪ̈ܛܐ – ܠܦܘܬ ܛܟܣܐ ܕܚܫܝܚܘܬܐ، ܠܐ ܠܦܘܬ ܛܟܣܐ ܕܒܓܘܗ ܟܡܠܦܝ ܠܗܘܢ

ܫܪܛܐ ܝܠܗ ܬܢܝܐ ܕܟܡܫܪܪ ܕܡܐ ܕܟܢܣܝܚ ܕܥܒܕܚ ܟܥܒܕ ܐܝܟ ܕܓܪܓ (Field, 2024, Section 6.5). ܐܘܪ̈ܚܬܐ ܣܛܐܛܝܣܛܝܩ̈ܝܬܐ ܒܥܕܢܐ ܫܚܝܡܐ ܡܚܘܝ̈ܐ ܝܢܐ ܐܝܟ ܒܘܚܪ̈ܢܐ ܦܪ̈ܝܫܐ ܥܡ ܫܪ̈ܛܐ ܕܝܠܗܘܢ، ܐܠܐ ܣܓܝܐܐ ܡܢܝܗܝ ܢܘܣ̈ܚܐ ܝܢܐ ܕܡܘܕܝܠ ܣܪܛܢܝܐ ܕܡܫܘܥܪܐ ܝܠܗ ܒܐܘܪܚܐ ܕܡܪ̈ܒܥܐ ܒܨܝܪ̈ܐ (least squares)، ܘܡܛܠ ܗܕܟܐ ܐܝܬ ܠܗܘܢ ܛܘܟܣܐ ܡܫܘܬܦܐ ܕܫܪ̈ܛܐ. Field ܟܡܛܟܣ ܠܗ ܠܦܘܬ ܚܫܝܚܘܬܐ: (1) ܣܪܛܢܝܘܬܐ ܘ-additivity؛ (2) ܛܝܡܐ ܡܣܟܝܐ ܕܛܥ̈ܝܘܬܐ ܨܦܪܐ – ܩܪܝܒ ܟܠܙܒܢ ܟܗܘܐ؛ (3) "ܛܥ̈ܝܘܬܐ ܐܣܦܝܪ̈ܝܬܐ" – ܫܘܝܘܬܐ ܕܫܘܚܠܦܐ (homoscedasticity) ܘܠܐ ܬܠܝܘܬܐ؛ (4) ܢܘܪܡܠܝܘܬܐ "ܕܡܕܡ". ܘܠܘܚܐ 6.1 ܕܝܠܗ ܟܡܘܣܦ ܡܐ ܕܟܠ ܫܪܛܐ ܟܙܒܢ: ܣܪܛܢܝܘܬܐ ܣܢܝܩܬܐ ܝܠܗ̇ ܩܐ ܟܠ ܡܕܡ؛ ܩܐ ܫܘܥܪܐ ܕܠܐ ܡܣܒ ܒܐܦ̈ܐ ܣܦܩܐ ܕܛܥ̈ܝܘܬܐ ܒܡܨܥܝܬܐ ܨܦܪܐ ܗܘܝܐ؛ ܩܐ ܫܘܥܪܐ ܛܒܐ ܡܢ ܟܠ – ܨܐ ܛܥ̈ܝܘܬܐ ܐܣܦܝܪ̈ܝܬܐ؛ ܩܐ ܛܥܝܘܬܐ ܬܩܝܢܬܐ ܕܠܐ ܡܣܒ ܒܐܦ̈ܐ – ܛܥ̈ܝܘܬܐ ܐܣܦܝܪ̈ܝܬܐ ܘܨܐ ܢܘܪܡܠܝܘܬܐ ܕܛܥ̈ܝܘܬܐ ܝܢ ܕܘܡܝܐ ܪܒܐ. ܬܚܘܡܐ ܕܬܘܟܠܢܐ ܘܒܘܚܪܢܐ ܟܝܪܬܝ ܫܪ̈ܛܐ ܕܛܥܝܘܬܐ ܬܩܝܢܬܐ.

ܣܪܛܢܝܘܬܐ ܘ-additivity. ܫܪܛܐ ܕܦܐܪܐ ܐܣܝܪܐ ܝܠܗ ܥܡ ܡܢܒ̈ܝܢܐ ܒܣܪܛܐ ܬܪܝܨܐ، ܘܕܟܡܐ ܡܢܒ̈ܝܢܐ ܟܥܒܕܝ ܒܓܘܡܪܐ. Field (2024، ܦܣܩܐ 6.6) ܟܡܩܝܡ ܠܗ ܠܥܠ ܡܢ ܟܠܗܘܢ: ܐܢ ܛܥܝܐ ܝܠܗ، ܡܘܕܝܠ ܟܡܬܚܘܐ ܠܥܠܡܐ ܠܐ ܬܪܝܨܐܝܬ – ܐܦ ܐܝܡܢ ܕܟܠ ܫܪ̈ܛܐ ܐܚܪ̈ܢܐ ܩܝܡ̈ܐ ܝܢܐ – ܘܠܝܬ ܣܘܟܠܐ ܕܡܦܫܩܚ ܡܢܝ̈ܢܐ ܡܫܘܬ̈ܦܐ ܝܢ ܕܙܕܥܚ ܥܠ ܪܫܝܡܘܬܐ. ܡܬܠܐ ܕܝܠܗ: ܩܪܝܬܐ ܕܫܘܢܪܐ ܟܠܒܐ. ܡܨܝܚ ܕܢܣܝܚ ܕܡܥܠܚ ܠܗ ܠܒܝܬܐ ܕܟܠܒܐ ܝܢ ܕܡܫܕܚ ܠܗ ܟܘܪܬܐ، ܐܠܐ ܗܘ ܒܕ ܦܐܫ ܫܘܢܪܐ. ܐܣܘܪܐ ܟܦܝܦܐ ܕܡܬܚܘܐ ܝܠܗ ܒܣܪܛܐ ܬܪܝܨܐ ܡܘܕܝܠ ܛܥܝܐ ܝܠܗ، ܠܐ ܡܘܕܝܠ ܥܡ ܥܩܬܐ.

ܫܘܝܘܬܐ ܕܫܘܚܠܦܐ (homoscedasticity). ܒܕܪܐ ܕܛܥ̈ܝܘܬܐ ܚܕܪ ܡܘܕܝܠ ܐܗܘ ܓܢܗ ܝܠܗ ܓܘ ܟܠ ܛܝ̈ܡܐ ܕܡܢܒܝܢܐ – ܥܢܢܐ ܕܝܗܝ̈ܒܬܐ ܡܩܒܠܐ ܝܠܗ ܠܣܪܛܐ، ܘܠܐ ܟܦܬܐ ܐܝܟ funnel (Field, 2024, Section 6.7.1). ܐܝܡܢ ܕܫܪܛܐ ܬܒܝܪܐ ܝܠܗ، ܫܘ̈ܥܪܐ ܕܡܢܝ̈ܢܐ ܡܫܘܬ̈ܦܐ ܟܦܝܫܝ ܕܠܐ ܡܣܒ ܒܐܦ̈ܐ – ܐܠܐ ܛܥ̈ܝܘܬܐ ܬܩܝ̈ܢܬܐ، ܬܚܘ̈ܡܐ ܕܬܘܟܠܢܐ ܘܒܘܚܪ̈ܢܐ ܠܐ ܝܢܐ ܚܬܝܬ̈ܐ، ܘܬܚܘ̈ܡܐ ܕܬܘܟܠܢܐ ܡܨܝ̈ܐ ܕܗܘܝ "ܠܐ ܚܬܝܬ̈ܐ ܒܓܘܢܐ ܪܚܝܩܐ" (Wilcox, 2010, as cited in Field, Section 6.7.2). ܐܗܐ ܟܐܡܪ: ܐܢ ܒܣ ܟܫܥܪܚ – ܠܐ ܒܝܫܐ ܝܠܗ؛ ܐܢ ܟܒܚܪܚ ܪܫܝܡܘܬܐ ܝܢ ܟܡܬܢܚ ܬܚܘܡܐ ܕܬܘܟܠܢܐ – ܚܫܝܚܐ ܝܠܗ، ܘܐܝܬ ܫܪܝܐ (ܦܣܩܐ 6). ܓܘ ܦܘܚܡܐ ܕܓܘ̈ܕܐ ܐܗܐ ܫܪܛܐ ܟܡܬܩܪܐ ܗܘܡܘܓܢܝܘܬܐ ܕܫܘܚܠ̈ܦܐ.

ܠܐ ܬܠܝܘܬܐ ܕܛܥ̈ܝܘܬܐ. ܛܥܝܘܬܐ ܓܘ ܡܢܒܝܢܘܬܐ ܕܡܫܬܘܬܦܢܐ ܚܕ ܠܐ ܝܠܗ̇ ܐܣܝܪܬܐ ܥܡ ܐܗܝ ܕܐܚܪܢܐ. ܡܬܠܐ ܕ-Field (2024، ܦܣܩܐ 6.7.3): Paul ܘ-Julie ܕܟܡܫܘܠܝ ܚܕ ܠܚܕ ܐܝܢܝ ܨܘܪ̈ܬܐ ܚܙܝܠܗܘܢ – ܦܘܢ̈ܝܐ، ܘܡܛܠ ܗܕܟܐ ܛܥ̈ܝܘܬܐ، ܠܐ ܝܢܐ ܠܐ ܬܠܝ̈ܐ. ܫܪܛܐ ܬܒܝܪܐ ܝܠܗ ܟܠܙܒܢ ܐܝܡܢ ܕܟܡܟܢܫܚ ܝܗܝ̈ܒܬܐ ܡܢ ܐܢܝ ܐܝܬܘ̈ܬܐ ܓܢܝܗܝ ܒܐܘܪܟܐ ܕܙܒܢܐ – ܡܫܘ̈ܚܬܐ ܡܬܢ̈ܝܬܐ، ܒܘܨܝܐ ܕܐܘܪܟܐ ܕܙܒܢܐ – ܡܛܠ ܕܦܘܢܝܐ ܕܒܪܢܫܐ ܓܘ ܙܒܢܐ ܚܕ ܐܣܝܪܐ ܝܠܗ ܥܡ ܦܘܢܝܐ ܕܝܠܗ ܓܘ ܙܒܢܐ ܐܚܪܢܐ؛ ܘܩܐ ܣܐܝܛ ܨܐ ܐܝܡܢ ܕܡܫܬܘܬܦ̈ܢܐ ܡܩܢ̈ܢܐ ܝܢܐ ܓܘ ܓܘ̈ܕܐ ܕܟܡܥܒܕܝ ܥܠܝܗܝ (ܒ̈ܢܝ ܒܝܬܐ، ܡܬ̈ܘܬܐ، ܣܕܪ̈ܐ ܕܡܕܪܫܬܐ). ܦܐܪ̈ܐ ܐܝܟ ܓܘ homoscedasticity – ܛܥܝܘܬܐ ܬܩܝܢܬܐ ܛܥܝܬܐ ܝܠܗ̇ – ܘܫܪܝܐ ܝܠܗ ܡܘܕܝܠ ܕܚܫܒ ܠܬܠܝܘܬܐ، ܠܐ ܐܘܪܚܐ ܕܡܪ̈ܒܥܐ ܒܨܝܪ̈ܐ ܫܚܝܡܬܐ.

4. ܢܘܪܡܠܝܘܬܐ – ܫܪܛܐ ܕܒܨܝܪ ܚܫܝܚܐ ܝܠܗ ܡܢ ܟܠ، ܘܒܨܝܪ ܦܗܝܡܐ ܡܢ ܟܠ

Field (2024، ܦܣܩܐ 6.8) ܟܫܪܐ ܕܐܗܐ ܫܪܛܐ ܡܨܐ ܕܗܘܐ ܡܕܡ ܕܒܨܝܪ ܦܗܝܡܐ ܝܠܗ ܡܢ ܟܠ ܓܘ ܣܛܐܛܝܣܛܝܩܐ، ܘܟܫܩܠ ܥܠ ܓܢܗ ܡܢܬܐ ܡܢ ܚܘܒܬܐ. ܛܥܝܘܬܐ ܕܣܓܝ ܡܬܚܙܝܐ: ܚܫܒܬܐ ܕ"ܫܪܛܐ ܕܢܘܪܡܠܝܘܬܐ" ܟܐܡܪ ܕܝܗܝ̈ܒܬܐ ܓܪܓ ܕܦܠܝܓ̈ܐ ܗܘܝ ܢܘܪܡܠܐܝܬ. ܠܐ. ܡܐ ܕܓܪܓ ܕܗܘܐ ܢܘܪܡܠܝܐ ܝܢܐ ܛܥ̈ܝܘܬܐ ܕܡܘܕܝܠ، ܘܒܝܚܝܕܝܘܬܐ – ܦܘܠܓܐ ܕܓܘܒܝܐ ܕܕܘܡܝܐ (sampling distribution) ܕܫܘܥܪܐ: ܩܐ ܝܕܥܬܐ ܕܛܥܝܘܬܐ ܬܩܝܢܬܐ ܟܡܦܠܚܚ ܒܢܘܣܚܐ (formula) ܕܬܪܝܨܐ ܝܠܗ ܐܝܡܢ ܕܫܘ̈ܥܪܐ ܦܠܝ̈ܓܐ ܝܢܐ ܢܘܪܡܠܐܝܬ ܥܠ ܕܘ̈ܡܝܐ؛ ܐܢ ܠܐ – ܛܥܝܘܬܐ ܬܩܝܢܬܐ، ܬܚܘܡܐ ܕܬܘܟܠܢܐ ܘܒܘܚܪܢܐ ܠܐ ܝܢܐ ܚܬܝܬ̈ܐ. ܫܓܘܫܝܐ ܟܐܬܐ ܡܢ ܕܐܢ ܦܐܪܐ ܢܘܪܡܠܝܐ ܝܠܗ، ܨܐ ܛܥ̈ܝܘܬܐ ܒܕ ܗܘܝ، ܘܡܛܠ ܗܕܟܐ ܦܐܪܐ ܟܡܦܠܚ ܐܝܟ ܚܠܦܐ ܕܡܕܡ ܕܚܫܝܚܐ ܝܠܗ.

ܘܬܠܬܐ ܣܒ̈ܒܐ ܕܡܛܠܬܝܗܝ ܐܗܐ ܝܠܗ ܫܪܛܐ ܕܒܨܝܪ ܚܫܝܚܐ ܝܠܗ ܡܢ ܟܠ (Field, 2024, Section 6.8.3): ܫܘܥܪܐ ܠܐ ܟܒܥܐ ܢܘܪܡܠܝܘܬܐ – ܐܘܪܚܐ ܕܡܪ̈ܒܥܐ ܒܨܝܪ̈ܐ ܟܝܗܒܐ ܫܘܥܪܐ ܕܠܐ ܡܣܒ ܒܐܦ̈ܐ ܕܟܡܙܥܪ ܛܥܝܘܬܐ ܐܦ ܐܝܡܢ ܕܛܥ̈ܝܘܬܐ ܠܐ ܝܢܐ ܢܘܪܡܠ̈ܝܐ؛ ܢܘܪܡܠܝܘܬܐ ܒܣ ܟܥܒܕܐ ܠܗ "ܛܒܐ ܡܢ ܟܠ". ܓܘ ܕܘܡܝܐ ܪܒܐ ܢܘܪܡܠܝܘܬܐ ܠܐ ܟܡܫܚܠܦܐ ܡܕܡ – ܢܡܘܣܐ ܕܬܚܘܡܐ ܡܨܥܝܐ ܟܡܫܪܪ ܕܦܘܠܓܐ ܕܓܘܒܝܐ ܕܕܘܡܝܐ ܒܕ ܗܘܐ ܢܘܪܡܠܝܐ ܕܠܐ ܐܣܘܪܐ ܥܡ ܐܣܟܝܡܐ ܕܟܢܫܐ ܟܠܢܝܐ. ܘܓܘ ܕܘܡܝܐ ܙܥܘܪܐ ܟܒܚܪܚ ܫܪ̈ܟܐ ܕܡܘܕܝܠ: ܐܢ ܢܘܪܡܠ̈ܝܐ ܝܢܐ، ܡܨܝܚ ܕܐܙܠܚ ܠܩܕܡ. ܟܡܐ ܪܒܐ ܝܠܗ "ܪܒܐ"؟ ܛܝܡܐ ܡܩܒܠܐ ܝܠܗ 30، ܐܠܐ ܠܝܬ ܦܘܢܝܐ ܦܫܝܛܐ (ܟܘܬܐ 6.4): ܓܘ ܦܘܠ̈ܓܐ ܥܡ ܕܘܢ̈ܒܐ ܩܠܝ̈ܠܐ ܐܦ 20 ܣܦܩܐ ܝܠܗ؛ ܥܡ ܕܘܢ̈ܒܐ ܝܩܘܪ̈ܐ – ܕܓܘܝܗܝ ܛܝ̈ܡܐ ܢܘܟܪ̈ܝܐ ܣܓܝ ܡܬܚܙܝܢ – ܡܨܐ ܕܣܢܝܩ 100 ܘܐܦ 160، ܘܥܡ ܥܩܝܡܘܬܐ ܘܓܒܢܘܬܐ ܣܓܝ̈ܐܬܐ – ܒܙܘܕܐ ܡܢ ܗܕܟܐ. ܘܡܢ ܐܟܐ ܫܘܠܡܐ ܡܥܒܕܢܝܐ ܕ-Field: ܓܘ ܕܘܡܝܐ ܪܒܐ، ܛܝ̈ܡܐ ܢܘܟܪ̈ܝܐ ܝܢܐ ܙܕܥܬܐ ܕܚܝܦܐ ܒܙܘܕܐ ܡܢ ܢܘܪܡܠܝܘܬܐ.

5. ܐܝܟܢ ܟܒܚܪܚ – ܨܘܪ̈ܬܐ ܩܕܡ ܡܢܝ̈ܢܐ، ܡܢܝ̈ܢܐ ܩܕܡ ܒܘܚܪ̈ܢܐ

ܛܝ̈ܡܐ ܢܘܟܪ̈ܝܐ ܟܚܙܚ ܓܘ ܝܗܝ̈ܒܬܐ؛ ܬܒܪ̈ܬܐ ܕܫܪ̈ܛܐ – ܓܘ ܫܪ̈ܟܐ ܕܡܘܕܝܠ، ܘܒܩܘܪܒܐ ܩܕܡܝܐ ܐܦ ܓܘ ܦܐܪܐ ܒܓܢܗ (Field, 2024, Section 6.9). ܡܬܠܐ ܕ-Field: ܡܢܝ̈ܢܐ ܕܕܟܝܘܬܐ (hygiene) ܕ-810 ܡܫܬܘܬܦ̈ܢܐ ܓܘ ܥܐܕܐ ܕܡܘܣܝܩܝ ܕ-metal، ܒܣܒܠܬܐ ܕ-0 ܗܠ 4، ܓܘ ܬܠܬܐ ܝܘܡ̈ܬܐ. ܨܘܪܬܐ ܕܒܕܪܐ، ܗܝܣܛܘܓܪܡ ܘܨܘܪܬܐ ܕܩܘܛܝܐ (boxplot) ܟܠܗܘܢ ܟܡܚܘܝ ܗܘܝܐ ܚܕ ܪܚܝܩܐ ܡܢ ܟܠܗܘܢ – ܡܢܝܢܐ 20.02 ܓܘ ܝܘܡܐ ܩܕܡܝܐ، ܓܘ ܣܒܠܬܐ ܕܟܡܫܠܡܐ ܒ-4. ܟܕܥܪܚ ܠܪܫܝܡܬܐ ܫܪܫܝܬܐ: 2.02، ܛܥܝܘܬܐ ܕܟܬܒܬܐ. ܐܗܐ ܝܠܗ ܝܘܠܦܢܐ ܩܕܡܝܐ: ܛܝܡܐ ܢܘܟܪܝܐ ܩܕܡ ܟܠ ܡܕܡ ܫܘܐܠܐ ܝܠܗ ܥܠ ܝܗܝܒܬܐ، ܘܒܣ ܒܬܪܟܐ ܫܘܐܠܐ ܣܛܐܛܝܣܛܝܩܝܐ. ܓܘ ܣܐܝܛ: ܡܢ SPSS ܠܐܩܣܠ ܟܡܙܗܪ ܥܠ ܛܝ̈ܡܐ ܠܒܪ ܡܢ ܬܚܘܡܐ ܕܡܦܫܩܢܐ ܟܡܬܚܡ، ܘܡܚܫܒܢܐ ܕܣܓܝܐܘ̈ܬܐ ܘܣܛܐܛܝܣܛܝܩܐ ܡܚܘܝܢܝܬܐ ܟܡܚܘܐ ܛܝܡܐ ܬܚܬܝܐ، ܛܝܡܐ ܥܠܝܐ ܘܨܘܪܬܐ ܩܐ ܟܠ ܡܫܬܚܠܦܢܐ – ܬܡܢ ܟܫܪܚ.

ܡܢܝ̈ܢܐ z (ܟܘܬܐ 6.6): ܟܡܫܚܠܦܚ ܠܡܢܝ̈ܢܐ z ܘܟܦܚܡܚ ܥܡ ܡܐ ܕܡܣܟܝܚ ܓܘ ܦܘܠܓܐ ܢܘܪܡܠܝܐ – ܩܪܝܒ 5% ܠܥܠ ܡܢ 1.96 ܒܛܝܡܐ ܫܪܝܪܐ، 1% ܠܥܠ ܡܢ 2.58، ܘܩܪܝܒ ܚܕ ܠܐ ܠܥܠ ܡܢ 3.29. ܓܘ ܡܬܠܐ ܕ-Field: 6.8% ܠܥܠ ܡܢ 1.96 (ܩܘܒܠ 5%)، 2.3% ܠܥܠ ܡܢ 2.58 (ܩܘܒܠ 1%)، 0.8% ܠܥܠ ܡܢ 3.29 – "ܩܪܝܒ ܡܐ ܕܡܣܟܝܚ". ܨܘܪܬܐ ܕܩܘܛܝܐ ܟܡܪܫܡܐ ܛܝ̈ܡܐ ܢܘܟܪ̈ܝܐ ܘܗܘ̈ܝܐ ܪܚܝ̈ܩܐ ܥܡ ܡܢܝܢܐ ܕܣܕܪܐ. ܨܘܪܬܐ Q-Q ܟܦܚܡܐ ܝܗܝ̈ܒܬܐ ܥܡ ܣܪܛܐ ܡܨܠܝܐ (diagonal) ܕܦܘܠܓܐ ܢܘܪܡܠܝܐ – ܢܘܩ̈ܙܐ ܥܠ ܣܪܛܐ: ܢܘܪܡܠܝܐ؛ ܟܦܦܐ ܠܥܠ: ܥܩܝܡܘܬܐ ܠܥܠ ܡܢ ܨܦܪܐ (ܦܣܩܐ 6.9.4-6.9.5). ܠܟܠܗܘܢ ܐܢܝ – ܡܢܝ̈ܢܐ z، ܗܝܣܛܘܓܪܡ، Q-Q، ܥܩܝܡܘܬܐ ܘܓܒܢܘܬܐ ܥܡ ܛܥ̈ܝܘܬܐ ܬܩܝ̈ܢܬܐ، ܘܨܐ ܬܪܝܢ ܒܘܚܪ̈ܢܐ ܕܓܘ ܦܣܩܐ ܕܒܬܪܗ̇، ܥܡ ܡܬܩܠܐ ܠܦܘܬ ܪܒܘܬܐ ܕܕܘܡܝܐ – ܟܡܦܩ ܡܚܫܒܢܐ ܕܒܘܚܪܢܐ ܕܢܘܪܡܠܝܘܬܐ، ܩܐ ܟܠ ܕܘܡܝܐ ܝܢ ܠܦܘܬ ܓܘܕܐ. ܥܩܝܡܘܬܐ ܘܓܒܢܘܬܐ: SPSS ܟܝܗܒ ܛܝ̈ܡܐ ܕܒܓܘܝܗܝ ܨܦܪܐ ܢܘܪܡܠܝܐ ܝܠܗ؛ ܥܩܝܡܘܬܐ ܠܥܠ ܡܢ ܨܦܪܐ ܟܓܪܫܐ ܠܡܨܥܝܬܐ ܠܥܠ ܡܢ ܛܝܡܐ ܡܨܥܝܐ، ܘܡܛܠ ܗܕܟܐ ܡܨܥܝܬܐ ܪܒܬܐ ܡܢ ܛܝܡܐ ܡܨܥܝܐ ܐܬܐ ܝܠܗ̇ ܕܥܩܝܡܘܬܐ ܠܥܠ ܡܢ ܨܦܪܐ؛ ܓܒܢܘܬܐ ܠܥܠ ܡܢ ܨܦܪܐ – ܕܘܢ̈ܒܐ ܝܩܘܪ̈ܐ. ܓܘ ܡܬܠܐ: ܝܘܡܐ 1 ܫܘܝܐ ܝܠܗ ܒܬܪܝܢ ܓܢܒ̈ܐ (ܥܩܝܡܘܬܐ ܩܪܝܒ ܨܦܪܐ)، ܝܘܡ̈ܬܐ 2-3 ܒܥܩܝܡܘܬܐ ܕܩܪܝܒ 1 – ܒܙܘܕܐ ܐܢܫ̈ܐ ܥܡ ܡܢܝ̈ܢܐ ܢܚܝ̈ܬܐ، "ܐܢܫ̈ܐ ܗܘܝܠܗܘܢ ܒܙܘܕܐ ܣܪ̈ܝܚܐ ܟܡܐ ܕܥܐܕܐ ܐܙܠܗ ܠܩܕܡ".

ܘܒܘܚܪ̈ܢܐ ܕܪܫܝܡܘܬܐ ܩܐ ܢܘܪܡܠܝܘܬܐ – ܠܐ. Field (ܟܘܬܐ 6.7) ܟܡܟܣܐ Kolmogorov-Smirnov، Shapiro-Wilk ܘ-Levene "ܒܝܚܝܕܝܘܬܐ ܡܛܠ ܕܐܢܫ̈ܐ ܟܡܣܟܝ ܕܚܙܝ ܠܗܘܢ ܓܘ ܟܬ̈ܒܐ ܕܫܘܪܝܐ، ܘܠܐ ܡܛܠ ܕܐܢܝ ܚܘܫܒܐ ܛܒܐ ܝܢܐ": ܓܘ ܕܘܡܝܐ ܪܒܐ ܐܢܝ ܪܫܝ̈ܡܐ ܝܢܐ ܐܦ ܩܐ ܣܛܝ̈ܘܬܐ ܙܥܘܪ̈ܐ ܘܕܠܐ ܐܝܩܪܐ – ܒܚܬܝܬܘܬܐ ܐܝܡܢ ܕܢܘܪܡܠܝܘܬܐ ܠܐ ܟܡܫܚܠܦܐ ܡܕܡ؛ ܓܘ ܕܘܡܝܐ ܙܥܘܪܐ ܠܝܬ ܠܗܘܢ ܚܝܠܐ ܕܡܫܟܚܝ ܬܒܪ̈ܬܐ – ܒܚܬܝܬܘܬܐ ܐܝܡܢ ܕܗܝ ܟܡܫܚܠܦܐ. ܓܘ ܡܬܠܐ، K-S ܥܠ ܝܘܡܐ 1 (N = 810) ܩܪܝܒ ܪܫܝܡܐ ܝܠܗ (p = .097) ܐܦܢ ܕܗܝܣܛܘܓܪܡ ܢܘܪܡܠܝܐ ܝܠܗ ܬܡܝܗܐܝܬ. ܡܠܟܐ: ܓܘ ܕܘܡܝܐ ܪܒܐ – ܠܐ ܡܦܠܚܬܐ ܒܓܘܝܗܝ، ܘܠܐ ܙܕܥܬܐ ܥܠ ܢܘܪܡܠܝܘܬܐ ܒܟܠܗ؛ ܓܘ ܕܘܡܝܐ ܙܥܘܪܐ – ܚܙܝܬܐ ܐܢ ܪܫܝ̈ܡܐ ܝܢܐ، ܘܠܐ ܢܝܚܘܬܐ ܐܢ ܠܐ. ܘܩܐ ܟܠ ܕܘ̈ܡܝܐ: ܨܘܪܬܐ. ܣܪܛܢܝܘܬܐ ܘܫܘܝܘܬܐ ܕܫܘܚܠܦܐ ܟܒܚܪܚ ܐܟܚܕܐ ܓܘ ܨܘܪܬܐ ܚܕܐ – ܫܪ̈ܟܐ ܡܬܩ̈ܢܐ ܩܘܒܠ ܛܝ̈ܡܐ ܡܢܒ̈ܝܐ (ܨܘܪܬܐ 1): ܥܢܢܐ ܫܘܝܐ – ܛܒܐ؛ funnel – heteroscedasticity؛ ܩܫܬܐ – ܠܐ ܣܪܛܢܝܐ. ܥܡ ܡܢܒܝܢܐ ܝܚܝܕܝܐ، ܨܘܪܬܐ ܕܒܕܪܐ ܫܚܝܡܬܐ ܩܘܪܒܐ ܡܩܒܠܢܐ ܝܠܗ̇.

ܘܛܝ̈ܡܐ ܚܣܝ̈ܪܐ، ܒܐܘܪܚܐ (Field, 2024، ܡܠܟܐ 6.1): ܫܩܠܬܐ ܕܣܕܪܐ ܟܠܗ (listwise deletion) ܟܡܦܩܐ ܡܫܬܘܬܦܢܐ ܡܢ ܟܠ ܦܘܫܩܐ ܐܢ ܚܣܝܪܐ ܝܠܗ ܠܗ ܛܝܡܐ ܚܕ؛ ܫܩܠܬܐ ܙܘܓܢܝܬܐ (pairwise deletion) ܟܡܦܩܐ ܠܗ ܒܣ ܡܢ ܦܘܫܩ̈ܐ ܕܛܝܡܐ ܚܣܝܪܐ ܐܣܝܪܐ ܝܠܗ ܒܓܘܝܗܝ – ܡܐܛܪܝܟܣ ܕܐܣܘܪ̈ܐ ܕܚܕ̈ܕܐ ܓܘ ܣܐܝܛ ܟܥܒܕܐ ܗܕܟܐ، ܘܟܡܬܢܝܐ N ܩܐ ܟܠ ܙܘܓܐ. ܚܠܦܬܐ ܕܚܣܝܪܐ ܒܡܨܥܝܬܐ ܕܡܫܬܚܠܦܢܐ – ܕ-SPSS ܚܠܐ ܓܗ̈ܐ ܟܡܩܪܒ – ܟܡܙܥܪܐ ܣܛܝܘܬܐ ܬܩܝܢܬܐ ܘܛܥܝܘܬܐ ܬܩܝܢܬܐ، ܡܛܠ ܕܩܐ ܟܠ ܛܝܡܐ ܕܡܚܘܠܦܐ ܝܠܗ ܠܝܬ ܪܘܚܩܐ ܡܢ ܡܨܥܝܬܐ، ܘܥܡ ܛܝ̈ܡܐ ܚܣܝ̈ܪܐ ܣܓܝ̈ܐܐ ܟܒܪܐ ܦܐܪ̈ܐ "ܪܫܝ̈ܡܐ" ܕܐܢܝ ܦܐܪܐ ܕܚܠܦܬܐ ܝܢܐ. ܒܦܪܝܣܘܬܐ – ܓܘ ܦܐܬܐ ܛܝ̈ܡܐ ܚܣܝ̈ܪܐ.

6. ܡܘܕܝ ܟܥܒܕܚ – ܚܣܝܢܘܬܐ ܒܕܘܟܬ ܫܩܠܬܐ ܘܫܘܢܝܐ

ܐܘܪܚܐ ܬܫܥܝܬܝܬܐ ܗܘܐ ܒܘܚܪ̈ܢܐ ܠܐ ܦܪܡܝܛܪ̈ܝܐ (non-parametric)، ܕܟܡܫܚܠܦܝ ܡܢܝ̈ܢܐ ܠܕܪ̈ܓܐ ܕܛܟܣܐ – ܘܟܡܘܒܕܝ ܡܥܠܘܡܘܬܐ – ܘܟܡܟܣܝ ܙܢ̈ܐ ܡܚܕܕ̈ܐ ܕܬܘܩ̈ܢܐ (Field, 2024, Section 6.10). ܐܘܪܚܐ ܛܒܬܐ ܡܢ ܟܠ ܐܕܝܘܡ، ܠܦܘܬ Field، ܝܠܗ̇ ܫܘܥܪܐ ܕܦܪܡܝ̈ܛܪܐ، ܛܥ̈ܝܘܬܐ ܬܩܝ̈ܢܬܐ، ܬܚܘ̈ܡܐ ܕܬܘܟܠܢܐ ܘ-p ܒܐܘܪ̈ܚܬܐ ܕܠܝܬ ܠܗܘܢ ܡܣܒ ܒܐܦ̈ܐ ܒܐܝܬܘܬܐ ܕܛܝ̈ܡܐ ܢܘܟܪ̈ܝܐ ܘܬܒܪ̈ܬܐ – ܐܘܪ̈ܚܬܐ ܚܣܝ̈ܢܬܐ (robust methods):

ܓܙܙܬܐ (trimming): ܟܫܩܠܚ ܡܢܬܐ ܩܝܡܬܐ ܡܢ ܟܠ ܪܝܫܐ – 5%، 10%، 20% – ܘܟܚܫܒܚ ܡܨܥܝܬܐ ܓܙܝܙܬܐ؛ ܓܘ ܪܝܫܐ ܐܚܪܢܐ ܕܣܒܠܬܐ ܐܝܬ ܛܝܡܐ ܡܨܥܝܐ، ܕܝܠܗ ܓܙܙܬܐ ܕܟܠ ܡܕܡ ܠܒܪ ܡܢ ܡܨܥܬܐ (ܦܣܩܐ 6.10.5). ܓܙܙܬܐ ܠܦܘܬ ܣܛܝ̈ܘܬܐ ܬܩܝ̈ܢܬܐ ("ܫܩܠܬܐ ܕܟܠ ܡܐ ܕܠܥܠ ܡܢ 2.5 ܣܛܝ̈ܘܬܐ ܬܩܝ̈ܢܬܐ") ܚܘܫܒܐ ܒܝܫܐ ܝܠܗ (ܟܘܬܐ 6.8): ܡܨܥܝܬܐ ܘܣܛܝܘܬܐ ܬܩܝܢܬܐ ܒܓܢܝܗܝ ܢܦܝܚ̈ܐ ܝܢܐ ܒܝܕ ܛܝ̈ܡܐ ܢܘܟܪ̈ܝܐ، ܘܡܛܠ ܗܕܟܐ ܛܝ̈ܡܐ ܢܘܟܪ̈ܝܐ ܟܡܥܠܝ ܡܣܒ ܒܐܦ̈ܐ ܓܘ ܡܫܘܚܬܐ (criterion) ܕܓܪܓ ܕܦܠܚܐ ܒܓܘܝܗܝ – ܓܘ ܡܬܠܐ ܕ-Field ܢܡܘܣܐ ܠܐ ܫܩܠܠܗ ܚܕ ܡܢܝܢܐ ܓܘ ܣܒܠܬܐ 0-10، ܡܛܠ ܕܬܚܘܡܐ ܦܠܛܠܗ ܠܒܪ ܡܢ ܬܚܘ̈ܡܐ ܕܣܒܠܬܐ. Winsorization: ܒܕܘܟܬ ܫܩܠܬܐ، ܟܡܚܠܦܚ ܡܢܝ̈ܢܐ ܕܠܒܪ ܡܢ ܬܚܘܡܐ ܒܛܝܡܐ ܕܬܚܘܡܐ (ܦܣܩܐ 6.10.6). ܟܡܪܓܫ ܐܝܟ ܢܟܠܐ؟ Field: ܐܢ ܡܢܝܢܐ ܠܐ ܟܡܚܘܐ ܠܕܘܡܝܐ ܘܟܡܥܠܐ ܡܣܒ ܒܐܦ̈ܐ ܓܘ ܡܘܕܝܠ، ܛܒܐ ܝܠܗ ܡܢ ܬܘܢܝܐ ܕܡܘܕܝܠ ܥܡ ܡܣܒ ܒܐܦ̈ܐ. ܢܟܠܐ ܝܠܗ ܠܐ ܦܘܠܚܢܐ ܒܪ̈ܚܝܩܐ ܐܝܡܢ ܕܟܡܥܠܝ ܡܣܒ ܒܐܦ̈ܐ ܩܐ ܛܝܒܘܬܐ ܕܗܘܦܘܬܣܝܣ، ܝܢ ܫܘܚܠܦܐ ܕܡܢܝ̈ܢܐ ܒܐܘܪܚܐ ܛܟܣܢܝܬܐ ܡܢ ܥܠܬܐ ܐܚܪܬܐ ܠܒܪ ܡܢ ܒܨܪܬܐ ܕܡܣܒ ܒܐܦ̈ܐ. ܛܥ̈ܝܘܬܐ ܬܩܝ̈ܢܬܐ ܚܣܝ̈ܢܬܐ ܩܐ heteroscedasticity (HC3 ܝܢ HC4): ܟܫܥܪܚ ܛܥܝܘܬܐ ܬܩܝܢܬܐ ܡܢ ܫܪ̈ܟܐ ܕܠܐ ܡܢܚܬܐ ܕܫܘܝܘܬܐ ܕܫܘܚܠܦܐ (ܦܣܩܐ 6.10.7). Bootstrap: ܟܚܫܒܚ ܠܕܘܡܝܐ ܐܝܟ ܟܢܫܐ ܟܠܢܝܐ، ܟܓܒܚ ܡܢܗ ܥܡ ܕܥܪܬܐ 1,000-2,000 ܓܗ̈ܐ، ܟܚܫܒܚ ܫܘܥܪܐ ܓܘ ܟܠ ܓܘܒܝܐ، ܘܡܢ ܦܘܠܓܐ ܕܫܘ̈ܥܪܐ ܟܡܦܩܚ ܬܚܘܡܐ ܕܬܘܟܠܢܐ (ܕܕܪ̈ܓܐ ܡܢ ܡܐܐ) ܘܛܥܝܘܬܐ ܬܩܝܢܬܐ – ܕܠܐ ܡܢܚܬܐ ܕܡܕܡ ܥܠ ܐܣܟܝܡܐ ܕܦܘܠܓܐ ܕܓܘܒܝܐ ܕܕܘܡܝܐ (Efron & Tibshirani, 1993; Field, 2024, Section 6.10.8). ܓܘ SPSS ܐܝܬ ܩܐ ܐܗܐ button ܓܘ ܣܓܝܐܐ ܡܢ ܦܘܠܚ̈ܢܐ؛ Field ܟܡܪܫܡ ܕܦܐܪ̈ܐ ܩܠܝܠ ܦܪ̈ܝܫܐ ܝܢܐ ܓܘ ܟܠ ܪܗܛܐ ܡܛܠ ܕܓܘܒܝܐ ܓܕܫܢܝܐ ܝܠܗ – ܘܓܘ ܣܐܝܛ، ܒܗܦܟܐ، bootstrap ܟܪܗܛ ܥܡ ܙܪܥܐ ܩܝܡܐ، ܗܕܟܐ ܕܐܗܝ ܡܥܠܬܐ ܓܢܗ̇ ܟܠܙܒܢ ܟܝܗܒܐ ܐܗܘ ܬܚܘܡܐ ܓܢܗ (ܚܙܝܡܘܢ ܫܪܝܪܘܬܐ ܒܝܢܝ ܪܡܙ̈ܢܐ).

ܘܠܐ ܫܘܢܝܐ (transformation) ܕܦܐܪܐ (Field, 2024، ܦܣܩܐ 6.10.3 – "ܠܐ ܥܒܕܝܬܘܢ ܐܗܐ"). ܠܘܓܪܝܬܡ ܝܢ ܫܪܫܐ ܩܐ "ܢܘܪܡܠܢܘܬܐ" ܕܡܫܬܚܠܦܢܐ ܕܦܐܪܐ: ܢܘܪܡܠܝܘܬܐ ܠܐ ܝܠܗ̇ ܚܫܝܚܬܐ ܓܘ ܕܘܡܝܐ ܪܒܐ، ܩܐ heteroscedasticity ܐܝܬ ܫܪ̈ܝܐ ܚܣܝ̈ܢܐ، ܘܫܘܢܝܐ ܟܒܪܐ ܥܩ̈ܬܐ ܚܕ̈ܬܬܐ. Field ܟܡܝܬܐ ܡܢ Glass ܘܐܚܪ̈ܢܐ (1972): ܛܘܒܐ ܕܫܘܢܝ̈ܐ ܕܢܘܪܡܠܢܘܬܐ "ܢܚܝܬܐ ܝܠܗ، ܘܩܠܝܠ ܓܗ̈ܐ ܟܫܘܝ ܠܥܡܠܐ"، ܘܐܪܒܥܐ ܢܘܩ̈ܙܐ ܕ-Games (1984): ܓܘ ܕܘܡܝܐ ܕܠܥܠ ܡܢ 30 ܩܪܝܒ، ܦܘܠܓܐ ܕܓܘܒܝܐ ܕܕܘܡܝܐ ܢܘܪܡܠܝܐ ܝܠܗ ܡܢ ܓܢܗ؛ ܫܘܢܝܐ ܟܡܫܚܠܦ ܗܘܦܘܬܣܝܣ – ܠܘܓܪܝܬܡ ܟܦܚܡܐ ܡܨܥܝ̈ܬܐ ܓܐܘܡܛܪ̈ܝܬܐ، ܠܐ ܐܪܝܬܡܛܝ̈ܩܝܬܐ، ܘܟܡܫܚ ܒܢܝܢܐ (construct) ܐܚܪܢܐ ܡܢ ܐܗܘ ܕܡܫܝܚܐ ܗܘܐ؛ ܥܣܩܐ ܝܠܗ ܕܦܣܩܚ ܥܠ ܢܘܪܡܠܝܘܬܐ ܓܘ ܕܘܡܝܐ ܙܥܘܪܐ؛ ܘܫܘܢܝܐ "ܛܥܝܐ" ܡܨܐ ܕܡܢܟܐ ܒܙܘܕܐ ܡܢ ܦܘܫܩܐ ܕܝܗܝ̈ܒܬܐ ܓܠܡ̈ܝܐ (raw). ܡܕܡ ܝܚܝܕܝܐ ܕܠܒܪ ܡܢ ܢܡܘܣܐ: "ܬܪܨܬܐ" ܕܐܣܘܪܐ ܟܦܝܦܐ – ܫܘܢܝܐ ܕܡܢܒܝܢܐ ܗܕܟܐ ܕܡܘܕܝܠ ܣܪܛܢܝܐ ܡܬܚܘܐ ܠܐܣܘܪܐ ܬܪܝܨܐܝܬ – ܘܐܗܐ ܫܪܛܐ ܕܣܪܛܢܝܘܬܐ ܝܠܗ، ܕܚܫܝܚܐ ܝܠܗ ܡܢ ܟܠ.

7. ܐܝܟܢ ܟܡܬܢܚ

ܦܘܠܚܢܐ ܒܛܝ̈ܡܐ ܢܘܟܪ̈ܝܐ ܘܒܫܪ̈ܛܐ ܡܢܬܐ ܝܠܗ ܕܨܚܚܐ ܕܐܘܪܚܐ ܝܢ ܕܫܘܪܝܐ ܕܦܐܪ̈ܐ، ܘܟܡܬܢܚ ܠܗ ܐܝܟ ܦܘܣ̈ܩܢܐ، ܠܐ ܐܝܟ ܥܠ̈ܠܬܐ ܕܡܙܕܕܩܢܘܬܐ: ܐܝܢܝ ܒܘܚܪ̈ܢܐ ܥܒܝܕ̈ܐ ܝܢܐ (ܨܘܪ̈ܬܐ، ܡܢܝ̈ܢܐ z، ܥܩܝܡܘܬܐ ܘܓܒܢܘܬܐ – ܠܐ ܒܣ "ܝܗܝ̈ܒܬܐ ܦܠܝܓ̈ܐ ܝܢܐ ܢܘܪܡܠܐܝܬ")؛ ܟܡܐ ܗܘ̈ܝܐ ܡܦܝܩ̈ܐ ܝܢܐ، ܠܦܘܬ ܐܝܢܐ ܢܡܘܣܐ، ܐܢ ܦܣܝܩܐ ܗܘܐ ܡܢ ܩܕܡ، ܘܡܘܕܝ ܝܠܗ ܦܐܪܐ ܥܡ ܘܕܠܐ؛ ܐܝܢܐ ܐܘܪܚܐ ܚܣܝܢܬܐ ܦܠܝܚܬܐ ܝܠܗ̇ – "ܬܚܘ̈ܡܐ ܕܬܘܟܠܢܐ ܚܫܝܒ̈ܐ ܝܢܐ ܒ-bootstrap ܕܕܪ̈ܓܐ ܡܢ ܡܐܐ، 2,000 ܓܘܒ̈ܝܐ" ܝܢ "ܛܥ̈ܝܘܬܐ ܬܩܝ̈ܢܬܐ HC3" – ܘܩܐ ܡܘܕܝ؛ ܘܐܢ ܐܝܬ ܡܫܘ̈ܚܬܐ ܡܬܢ̈ܝܬܐ – ܐܝܢܐ ܡܘܕܝܠ ܚܫܒܠܗ ܠܬܠܝܘܬܐ. ܦܐܪܐ ܕܫܚܠܦܠܗ ܒܓܘܢܐ ܪܝܫܝܐ ܥܡ ܡܦܩܬܐ ܕܗܘܝܐ ܚܕ ܡܫܟܚܢܘܬܐ ܝܠܗ̇ ܒܓܢܗ̇، ܘܟܡܬܢܚ ܠܗ. Field ܟܡܥܗܕ (ܡܥܝܪܢܘܬܐ ܬܚܬܝܬܐ ܕܦܣܩܐ 6.10.6) ܕܛܝ̈ܡܐ ܢܘܟܪ̈ܝܐ ܚܫܝ̈ܚܐ ܝܢܐ ܒܓܢܝܗܝ: ܐܢ ܠܐ ܟܡܚܘܝ ܠܟܢܫܐ ܟܠܢܝܐ، ܫܘܐܠܐ ܩܐ ܡܘܕܝ ܦܪ̈ܝܫܐ ܝܢܐ ܡܨܐ ܕܗܘܐ ܫܘܐܠܐ ܕܒܘܨܝܐ ܕܒܬܪܗ.

ܛܥܝ̈ܘܬܐ ܕܡܬܚܙܝܢ ܣܓܝ (Common mistakes)

"ܝܗܝ̈ܒܬܐ ܓܪܓ ܕܦܠܝܓ̈ܐ ܗܘܝ ܢܘܪܡܠܐܝܬ." ܠܐ ܝܗܝ̈ܒܬܐ – ܛܥ̈ܝܘܬܐ، ܘܒܝܚܝܕܝܘܬܐ ܦܘܠܓܐ ܕܓܘܒܝܐ ܕܕܘܡܝܐ؛ ܘܓܘ ܕܘܡܝܐ ܪܒܐ ܐܦ ܐܗܐ ܠܐ. ܡܢܒܝܢܐ ܕܬܪܝܢ ܛܝ̈ܡܐ "ܠܐ ܢܘܪܡܠܝܐ" ܠܐ ܝܠܗ ܥܩܬܐ ܒܟܠܗ.

K-S ܥܠ 800 ܡܫܬܘܬܦ̈ܢܐ. ܒܕ ܗܘܐ ܪܫܝܡܐ ܐܦ ܥܠ ܦܘܠܓܐ ܩܪܝܒ ܓܡܝܪܐ، ܘܒܕ ܡܫܕܪ ܠܘܟܘܢ ܕܬܪܨܝܬܘܢ ܡܐ ܕܠܐ ܝܠܗ ܬܒܝܪܐ. ܓܘ ܕܘܡܝܐ ܪܒܐ – ܨܘܪ̈ܬܐ ܘܒܣ.

ܫܩܠܬܐ ܕܛܝܡܐ ܢܘܟܪܝܐ ܡܛܠ ܕܗܘ "ܟܡܒܝܫ". ܛܝܡܐ ܢܘܟܪܝܐ ܟܦܐܫ ܐܠܐ ܐܢ ܡܚܘܝܐ ܝܠܗ ܕܠܐ ܝܠܗ ܡܢ ܟܢܫܐ ܟܠܢܝܐ. ܣܗܕܘܬܐ ܝܠܗ̇ ܥܠܬܐ (ܛܡܡܬܐ ܕܐܕ̈ܢܐ، ܛܥܝܘܬܐ ܕܟܬܒܬܐ)، ܠܐ ܪܘܚܩܐ ܡܢ ܡܨܥܝܬܐ.

ܓܙܙܬܐ ܠܦܘܬ ܣܛܝ̈ܘܬܐ ܬܩܝ̈ܢܬܐ. ܢܡܘܣܐ ܚܫܝܒܐ ܝܠܗ ܡܢ ܡܨܥܝܬܐ ܘܡܢ ܣܛܝܘܬܐ ܬܩܝܢܬܐ – ܕܬܪܘܝܗܝ ܢܦܝܚ̈ܐ ܝܢܐ ܒܝܕ ܛܝ̈ܡܐ ܢܘܟܪ̈ܝܐ ܕܒܥܝܚ ܕܦܠܚܚ ܒܓܘܝܗܝ. ܟܓܙܙܚ ܠܦܘܬ ܡܢܘ̈ܬܐ ܒܡܐܐ.

ܠܘܓܪܝܬܡ ܥܠ ܦܐܪܐ "ܩܐ ܢܘܪܡܠܢܘܬܐ". ܟܡܫܚܠܦ ܗܘܦܘܬܣܝܣ ܘܒܢܝܢܐ ܡܫܝܚܐ، ܘܒܥܕܢܐ ܫܚܝܡܐ ܠܐ ܟܫܘܐ ܠܥܡܠܐ. ܫܘܢܝܐ ܢܛܝܪܐ ܝܠܗ ܩܐ ܬܪܨܬܐ ܕܡܢܒܝܢܐ.

ܒܘܚܪܢܐ ܕܢܘܪܡܠܝܘܬܐ ܘܛܥܝܬܐ ܕܣܪܛܢܝܘܬܐ. ܫܪܛܐ ܕܠܥܠ ܡܢܗ ܠܝܬ. ܩܫܬܐ ܓܘ ܨܘܪܬܐ ܕܫܪ̈ܟܐ – ܡܘܕܝܠ ܛܥܝܐ ܝܠܗ، ܘܚܕ ܬܘܪܨܐ ܕܢܘܪܡܠܝܘܬܐ ܠܐ ܒܕ ܡܥܕܪ.

ܚܠܦܬܐ ܕܚܣܝ̈ܪܐ ܒܡܨܥܝܬܐ. ܟܡܙܥܪܐ ܛܥܝܘܬܐ ܬܩܝܢܬܐ ܘܟܒܪܐ ܪܫܝܡܘܬܐ ܕܓܠܬܐ. ܫܩܠܬܐ ܙܘܓܢܝܬܐ، ܝܢ ܐܘܪ̈ܚܬܐ ܕܡܠܝܐ ܕܛܝ̈ܡܐ ܚܣܝ̈ܪܐ (imputation) ܣܡܝܟ̈ܬܐ ܥܠ ܡܘܕܝܠ – ܓܘ ܦܐܬܐ ܛܝ̈ܡܐ ܚܣܝ̈ܪܐ.

t ܠܠܐ ܬܠܝ̈ܐ ܥܠ ܡܫܘ̈ܚܬܐ ܡܬܢ̈ܝܬܐ. ܐܢܝ ܐܢܫ̈ܐ ܓܢܝܗܝ ܬܪܝܢ ܓܗ̈ܐ – ܛܥ̈ܝܘܬܐ ܬܠܝ̈ܬܐ ܝܢܐ، ܛܥܝܘܬܐ ܬܩܝܢܬܐ ܛܥܝܬܐ ܝܠܗ̇. ܒܘܚܪܢܐ ܩܐ ܕܘ̈ܡܝܐ ܙܘܓܢ̈ܝܐ ܝܢ ܡܘܕܝܠ ܩܐ ܡܫܘ̈ܚܬܐ ܡܬܢ̈ܝܬܐ.

ܪܫܝܡܬܐ ܕܒܘܚܪܢܐ – ܩܕܡ ܪܗܛܐ ܕܒܘܚܪܢܐ

ܡܒܘ̈ܥܐ

Efron, B., & Tibshirani, R. J. (1993). An introduction to the bootstrap. Chapman & Hall. https://doi.org/10.1007/978-1-4899-4541-9

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