ANOVA ܠܡܫܘ̈ܚܬܐ ܡܬܢ̈ܝܬܐ

ܛܥܢܐ ܕܝܗܝ̈ܒܬܐ (loading the data)

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

ܡܫܬܚܠܦ̈ܢܐ ܘܬܘܩ̈ܢܐ (Variables and settings)

ܐܝܡܢ ܡܦܠܚܝܚ (When to use)؟

ܐܝܡܢ ܕܗܢܝ ܡܫܬܘܬܦ̈ܢܐ ܟܡܥܕܪܝ ܠܟܠ ܡܨܥܝ̈ܬܐ: ܡܫܝܚ̈ܐ ܝܢܐ ܓܘ ܟܠ ܫܪ̈ܛܐ ܕܢܣܝܘܢܐ (experiment)، ܝܢ ܓܘ ܟܡܐ ܢܘܩ̈ܙܐ ܕܙܒܢܐ (Field, 2024, Section 15.2). ܡܬ̈ܠܐ: ܩܢܛܐ ܩܕܡ ܬܪܥܝܬܐ، ܓܘ ܫܘܠܡܐ ܕܝܠܗ̇ ܘܒܬܪ ܙܒܢܐ؛ ܙܒܢܐ ܕܦܘܢܝܐ ܓܘ ܬܠܬܐ ܫܪ̈ܛܐ ܕܩܠܐ؛ ܛܟܣܐ ܕܗܢܝ ܦܣܘ̈ܩܐ ܒܝܕ ܗܢܝ ܐܢܫ̈ܐ. ܐܝܡܢ ܕܐܝܬ ܨܐ ܓܘ̈ܕܐ ܦܪ̈ܝܫܐ – ܬܪܥܝܬܐ ܩܘܒܠ ܓܘܕܐ ܕܦܘܚܡܐ – ܬܘܩܢܐ ܡܚܠܛܐ ܝܠܗ: ܥܠܬܐ ܒܝܢܝ ܡܫܬܘܬܦ̈ܢܐ ܘܥܠܬܐ ܓܘ ܡܫܬܘܬܦ̈ܢܐ (ܬܡܢ، ܦܣܩܐ 16.2). ܒܣ ܬܪܬܝܢ ܡܫܘ̈ܚܬܐ – ܦܐܬܐ ܟܚܫܒܐ، ܐܠܐ ܒܘܚܪܢܐ t ܠܕܘ̈ܡܝܐ ܙܘܓܢ̈ܝܐ ܟܝܗܒ ܗܘ ܦܣܩܐ (F = t²; Gravetter & Wallnau, 2017, pp. 433-435) ܘܙܘܕܐ ܡܢ ܗܕܐ d ܘܬܚܘܡܐ ܕܬܘܟܠܢܐ (confidence interval) ܩܐ ܦܘܪܫܢܐ. ܓܘ̈ܕܐ ܦܪ̈ܝܫܐ ܓܘ ܟܠ ܫܪܛܐ – ܦܘܫܩܐ ܕܫܘܚܠܦܐ ܕܚܕ ܐܘܪܚܐ؛ ܟܡܐ ܥܠ̈ܠܬܐ ܒܝܢܝ ܡܫܬܘܬܦ̈ܢܐ – ܬܘܩܢܐ ܕܢܣܝ̈ܘܢܐ.

ܒܢܝܢܐ ܕܝܗܝ̈ܒܬܐ

ܒܢܝܢܐ ܦܬܝܐ (wide format)، ܐܝܟ ܓܘ SPSS: ܣܕܪܐ ܩܐ ܟܠ ܡܫܬܘܬܦܢܐ، ܥܡܘܕܐ ܩܐ ܟܠ ܡܫܘܚܬܐ (Field, 2024, Section 15.8.1). ܓܘ ܬܪܬܝܢ ܥܠ̈ܠܬܐ ܓܘ ܡܫܬܘܬܦ̈ܢܐ – ܥܡܘܕܐ ܩܐ ܟܠ ܚܘܠܛܐ (treatment combination)، ܒܛܟܣܐ ܕܓܘܗ ܥܠܬܐ ܬܪܝܢܝܬܐ ܟܫܚܠܦܐ ܒܥܓܠܐ: (1,1)، (1,2)، (1,3)، (2,1)... – ܐܝܟ ܪܫܝܡܬܐ ܓܘ ܟܘܬܐ ܕ-SPSS (ܬܡܢ، ܦܣܩܐ 15.14). ܦܐܬܐ ܟܡܚܘܐ ܠܬܚܬ ܪܫܝܡܬܐ ܐܝܢܐ ܥܡܘܕܐ ܦܠܝܓܬܐ ܝܠܗ̇ ܩܐ ܐܝܢܐ ܚܘܠܛܐ، ܘܫܡ̈ܗܐ ܐܝܟ absent_0, absent_4... ܦܪ̈ܝܩܐ ܝܢܐ ܒܓܢܗܘܢ ܠܫܡ̈ܗܐ ܕܕܪ̈ܓܐ. ܡܫܬܘܬܦܢܐ ܕܚܣܝܪܐ ܠܗ ܚܕ ܡܫܘܚܬܐ – ܠܐ ܥܠܝܠܐ ܝܠܗ ܒܟܠܗ (ܫܩܠܬܐ ܕܣܕܪܐ ܟܠܗ (listwise deletion)، ܐܝܟ SPSS)، ܘܦܐܬܐ ܟܡܬܢܐ ܟܡܐ ܡܫܬܘܬܦ̈ܢܐ ܫܒܝܩ̈ܐ ܝܢܐ.

ܚܘܫܒܐ: ܦܘܪܩܐ ܕܫܘܚܠܦܐ

ܫܘܚܠܦܐ (variance) ܟܠܢܝܐ ܟܡܬܦܠܓ ܠܫܘܚܠܦܐ ܒܝܢܝ ܫܪ̈ܛܐ ܘܠܫܘܚܠܦܐ ܓܘ ܫܪ̈ܛܐ، ܘܗܝܕܝܟ – ܘܐܗܐ ܝܠܗ ܦܘܪܫܢܐ – ܫܘܚܠܦܐ ܓܘ ܫܪ̈ܛܐ ܟܡܬܦܪܩ ܬܘܒ: ܡܢܬܐ ܡܢܗ ܝܠܗ̇ ܦܘܪ̈ܫܢܐ ܩܝ̈ܡܐ ܒܝܢܝ ܡܫܬܘܬܦ̈ܢܐ، ܘܗܝ ܡܦܩܬܐ ܝܠܗ̇ ܡܢ ܛܥܝܘܬܐ (Gravetter & Wallnau, 2017, pp. 420-424). ܡܐ ܕܦܝܫ – ܥܒܕܐ ܕܚܕ̈ܕܐ (interaction) ܒܝܢܝ ܫܪ̈ܛܐ ܘܡܫܬܘܬܦ̈ܢܐ – ܝܠܗ ܬܚܬܝܬܐ ܕ-F. ܓܘ ܡܬܠܐ ܕܬܡܢ: SS ܒܝܢܝ ܫܪ̈ܛܐ 84، ܒܝܢܝ ܡܫܬܘܬܦ̈ܢܐ 66 ܘܛܥܝܘܬܐ 22، ܘ-F(2, 10) = 19.09 (ܬܡܢ، ܦܐܬܐ 426) – ܦܐܬܐ ܟܝܗܒ ܗܢܝ ܡܢܝ̈ܢܐ. ܡܛܠ ܗܕܐ ܬܘܩܢܐ ܓܘ ܡܫܬܘܬܦ̈ܢܐ ܪܓܝܫܐ ܝܠܗ ܝܬܝܪ: ܓܘ ܡܬܠܐ ܡܢܝܢܝܐ ܕ-Gravetter ܘ-Wallnau ܗܢܝ ܦܘܪ̈ܫܢܐ ܟܝܗܒܝ F ܕ-1.91 ܓܘ ܓܘ̈ܕܐ ܦܪ̈ܝܫܐ ܘ-11 ܓܘ ܡܫܘ̈ܚܬܐ ܡܬܢ̈ܝܬܐ (ܬܡܢ، ܦܐ̈ܬܐ 430-431). ܓܘ ܬܘܩܢܐ ܥܡ ܬܪܬܝܢ ܥܠ̈ܠܬܐ ܓܘ ܡܫܬܘܬܦ̈ܢܐ ܩܐ ܟܠ ܡܥܒܕܢܘܬܐ (effect) ܐܝܬ ܛܥܝܘܬܐ ܕܝܠܗ̇ – ܥܒܕܐ ܕܚܕ̈ܕܐ ܕܡܥܒܕܢܘܬܐ ܥܡ ܡܫܬܘܬܦ̈ܢܐ (Maxwell et al., 2018, p. 673).

ܐܣܦܝܪܝܘܬܐ ܘܬܘܪܨܐ ε

ܒܘܚܪܢܐ ܕܚܕ ܡܫܬܚܠܦܢܐ (univariate) ܟܣܡܟ ܥܠ ܐܣܦܝܪܝܘܬܐ (sphericity): ܕܫܘܚܠܦܐ ܕܦܘܪܫܢܐ ܒܝܢܝ ܟܠ ܬܪܬܝܢ ܡܫܘ̈ܚܬܐ ܫܘܝܐ ܝܠܗ (Maxwell et al., 2018, p. 627; Field, 2024, Section 15.5.1). ܓܘ ܬܪܬܝܢ ܡܫܘ̈ܚܬܐ ܐܝܬ ܚܕ ܦܘܪܫܢܐ، ܘܫܪܛܐ ܒܟܠ ܙܒܢ ܩܝܡܐ ܝܠܗ (Maxwell et al., 2018, p. 628). ܓܘ ܡܫܘ̈ܚܬܐ ܒܐܘܪܟܐ ܕܙܒܢܐ ܣܓܝ ܓܐ̈ܝܐ ܬܒܝܪܐ ܝܠܗ – ܡܫܘ̈ܚܬܐ ܩܪܝ̈ܒܬܐ ܐܣܝܪ̈ܬܐ ܝܢܐ ܝܬܝܪ ܡܢ ܪ̈ܚܝܩܬܐ – ܘܗܝܕܝܟ ܡܢܬܐ ܕܛܥܝܘܬܐ ܕܙܢܐ I ܡܨܝܐ ܕܡܛܝܐ ܠ-.10 ܝܢ .15 ܒܕܘܟܬ .05 (ܬܡܢ، ܦܐ̈ܬܐ 629-630).

ܦܘܫܪܐ: ܕܥܦܦܚ ܕܪ̈ܓܐ ܕܚܐܪܘܬܐ (degrees of freedom) ܕܒܘܚܪܢܐ ܒ-ε، ܫܘܥܪܐ ܕܟܡܝܘܬܐ ܕܣܛܝܘܬܐ ܡܢ ܐܣܦܝܪܝܘܬܐ – 1 ܐܝܡܢ ܕܩܝܡܬܐ ܝܠܗ̇، ܘܥܕܡܐ 1/(k − 1) ܓܘ ܣܛܝܘܬܐ ܪܒܬܐ ܡܢ ܟܠ (ibid., p. 630; Field, 2024, Sections 15.5.2, 15.5.4). F ܓܢܒܗ ܠܐ ܟܫܚܠܦ، ܒܣ p. ܐܪܒܥܐ ܓܘܒ̈ܝܐ، ܡܢ ܚܐܪܐ ܥܕܡܐ ܢܛܘܪܐ: ܕܠܐ ܬܘܪܨܐ، Huynh-Feldt، Greenhouse-Geisser ܘܬܚܘܡܐ ܬܚܬܝܐ. Maxwell ܘܚܒܪ̈ܘܗܝ "ܟܚܫܒܝ ܕܠܐ ܐܝܬ ܠܢ ܕܡܦܠܚܚ ܡܢ ܡܬܘܡ" ܒܒܘܚܪܢܐ ܕܠܐ ܬܘܪܨܐ (2018، ܦܐܬܐ 632)، ܡܘܥܕܢܘܬܐ ܟܠܢܝܬܐ ܕܝܠܗܘܢ ܝܠܗ̇ Greenhouse-Geisser، ܡܛܠ ܕ-Huynh-Feldt ܡܨܐ ܕܠܐ ܢܛܪ ܡܢܬܐ ܕܛܥܝܘܬܐ (ܬܡܢ، ܦܐܬܐ 634)، ܘܬܚܘܡܐ ܬܚܬܝܐ ܢܛܘܪܐ ܝܬܝܪ ܡܢ ܡܫܘܚܬܐ ܝܠܗ (ܬܡܢ). Field (2024، ܦܣܩܐ 15.5.4) ܟܡܝܬܐ ܨܐ ܢܡܘܣܐ ܡܦܪܣܐ – Huynh-Feldt ܐܝܡܢ ܕܫܘܥܪܐ ܠܥܠ ܡܢ .75 ܝܠܗ – ܘܓܘܒܝܐ ܕܫܩܠܚ ܡܨܥܝܬܐ ܕܬܪܘܝܗܝ. ܦܐܬܐ ܟܬܢܐ ܠܦܘܬ Greenhouse-Geisser، ܘܡܨܝܚ ܕܓܒܚ ܐܚܪܢܐ.

Mauchly: ܒܘܚܪܢܐ ܕܪܫܝܡܘܬܐ (significance) ܩܐ ܫܪܛܐ ܕܐܣܦܝܪܝܘܬܐ. Field ܟܡܘܥܕ ܕܠܐ ܣܡܟܚ ܥܠܗ: ܗܘ ܬܠܝܐ ܝܠܗ ܒܪܒܘܬܐ ܕܕܘܡܝܐ (sample size) – ܓܘ ܕܘܡܝܐ ܪܒܐ ܪܫܝܡܐ ܝܠܗ ܐܦ ܓܘ ܣܛܝܘܬܐ ܙܥܘܪܬܐ ܛܒܐ، ܘܓܘ ܙܥܘܪܐ ܠܐ ܪܫܝܡܐ ܝܠܗ ܐܦ ܓܘ ܪܒܬܐ – ܘܡܛܠ ܗܕܐ ܒܨܒܝܢܐ ܝܠܗ ܕܬܪܨܚ ܒܟܠ ܙܒܢ ܠܦܘܬ ε (2024، ܦܣܩܐ 15.5.2). ܐܦ Maxwell ܘܚܒܪ̈ܘܗܝ ܟܟܬܒܝ ܕܐܝܬ ܠܗ "ܛܝܡܐ ܩܠܝܠܐ ܐܝܟ ܒܘܚܪܢܐ ܩܕܡܝܐ" (2018، ܦܐܬܐ 629). ܦܐܬܐ ܟܡܚܘܐ ܠܗ ܡܛܠ ܕ-SPSS ܟܡܚܘܐ ܠܗ.

ܐܘܪܚܐ ܕܣܓܝ ܡܫܬܚܠܦ̈ܢܐ

ܐܘܪܚܐ ܐܚܪܬܐ، ܕܠܐ ܟܣܡܟܐ ܥܠ ܐܣܦܝܪܝܘܬܐ ܒܟܠܗ̇: ܕܡܫܚܠܦܚ k ܡܫܘ̈ܚܬܐ ܠ-k − 1 ܡܫܬܚܠܦ̈ܢܐ ܕܦܘܪܫܢܐ ܘܕܒܚܪܚ ܐܢ ܟܠ ܡܨܥܝ̈ܬܐ ܕܝܠܗܘܢ ܨܦܪܐ ܝܢܐ – ܦܘܫܩܐ ܕܫܘܚܠܦܐ ܕܣܓܝ ܡܫܬܚܠܦ̈ܢܐ (multivariate؛ Maxwell et al., 2018, pp. 728, 741; Field, 2024, Section 15.5.4). SPSS ܟܛܒܥ ܐܪܒܥܐ ܒܘܚܪ̈ܢܐ: Pillai، Wilks، Hotelling ܘ-Roy. ܓܘ ܡܥܒܕܢܘܬܐ ܕܓܘ ܡܫܬܘܬܦ̈ܢܐ ܕܟܝܬܐ ܐܢܝ ܒܟܠ ܙܒܢ ܫܘ̈ܝܐ ܝܢܐ (Maxwell et al., 2018, pp. 832-833)؛ ܐܝܡܢ ܕܦܪ̈ܝܫܐ ܝܢܐ، Pillai ܚܣܝܢܐ ܝܠܗ ܝܬܝܪ ܡܢ ܟܠ (ܬܡܢ، ܦܐܬܐ 829). Pallant (2020، ܨܚܚܐ 18) ܒܟܠ ܙܒܢ ܟܩܪܝܐ ܒܘܚܪܢܐ ܕܣܓܝ ܡܫܬܚܠܦ̈ܢܐ.

ܡܘܕܝ ܒܨܒܝܢܐ ܝܠܗ؟ ܒܘܚܪܢܐ ܕܣܓܝ ܡܫܬܚܠܦ̈ܢܐ ܚܬܝܬܐ ܝܠܗ ܐܝܡܢ ܕܦܘܠܓܐ (distribution) ܢܘܪܡܠܝܐ ܝܠܗ، ܐܠܐ ܟܪܝܗܐ ܝܠܗ ܓܘ ܕܘ̈ܡܝܐ ܙܥܘܪ̈ܐ، ܘܠܐ ܡܨܝܢܐ ܝܠܗ ܐܝܡܢ ܕܐܝܬ ܒܨܘܪܐ ܡܫܬܘܬܦ̈ܢܐ ܡܢ ܡܫܘ̈ܚܬܐ (Maxwell et al., 2018, pp. 775-777). ܢܡܘܣܐ ܕ-Algina ܘ-Keselman (1997, as cited in Maxwell et al., 2018, p. 776): ܕܣܓܝ ܡܫܬܚܠܦ̈ܢܐ ܐܝܡܢ ܕܐܝܬ ܥܕܡܐ 4 ܡܫܘ̈ܚܬܐ، ε ≤ .90 ܘܒܨܘܪܐ ܕܨܘܪܐ k + 15 ܡܫܬܘܬܦ̈ܢܐ، ܝܢ 5-8 ܡܫܘ̈ܚܬܐ، ε ≤ .85 ܘܒܨܘܪܐ ܕܨܘܪܐ k + 30؛ ܐܢ ܠܐ – ܕܚܕ ܡܫܬܚܠܦܢܐ ܥܡ ܬܘܪܨܐ. ܢܡܘܣܐ ܟܡܚܘܐ ܠ-ε ܓܘ ܟܢܫܐ ܟܠܢܝܐ (population)، ܘܓܘܒܝܐ ܠܦܘܬ ܫܘܥܪܐ ܡܢ ܕܘܡܝܐ "ܡܨܐ ܕܗܘܐ ܥܩܬܢܝܐ" (ܬܡܢ). ܓܘ ܟܢܘܫܝܐ Maxwell ܘܚܒܪ̈ܘܗܝ ܟܝܗܒܝ ܠܐܘܪܚܐ ܕܣܓܝ ܡܫܬܚܠܦ̈ܢܐ "ܝܬܝܪܘܬܐ ܩܠܝܠܬܐ" (ܬܡܢ، ܦܐܬܐ 778). "ܩܪܝܢܐ ܕܦܐܪܐ" ܓܘ ܡܦܩܢܐ ܟܚܫܒ ܢܡܘܣܐ ܥܠ ܝܗܝ̈ܒܬܐ ܕܝܘܟܘܢ.

ܬܘܩܢܐ ܡܚܠܛܐ

ܐܝܡܢ ܕܐܝܬ ܨܐ ܥܠܬܐ ܒܝܢܝ ܡܫܬܘܬܦ̈ܢܐ، ܐܝܬ ܬܪܝܢ ܙܢ̈ܝܐ ܕܒܘܚܪ̈ܢܐ (Maxwell et al., 2018, pp. 691-693). ܡܥܒܕܢܘܬܐ ܒܝܢܝ ܡܫܬܘܬܦ̈ܢܐ ܒܚܝܪܬܐ ܝܠܗ̇ ܩܘܒܠ ܫܘܚܠܦܐ ܒܝܢܝ ܡܫܬܘܬܦ̈ܢܐ ܓܘ ܓܘ̈ܕܐ – ܗܝ ܫܘܝܐ ܝܠܗ̇ ܠܦܘܫܩܐ ܕܫܘܚܠܦܐ ܕܚܕ ܐܘܪܚܐ ܥܠ ܡܨܥܝܬܐ ܕܟܠ ܡܫܬܘܬܦܢܐ، ܘܐܣܦܝܪܝܘܬܐ ܠܐ ܟܡܛܝܐ ܠܗ̇ (ܬܡܢ، ܦܐ̈ܬܐ 692، 706). ܡܥܒܕܢܘܬܐ ܓܘ ܡܫܬܘܬܦ̈ܢܐ ܘܥܒܕܐ ܕܚܕ̈ܕܐ ܥܡ ܓܘܕܐ ܒܚܝܪ̈ܐ ܝܢܐ ܩܘܒܠ ܥܒܕܐ ܕܚܕ̈ܕܐ ܕܥܠܬܐ ܓܘ ܡܫܬܘܬܦ̈ܢܐ ܥܡ ܡܫܬܘܬܦ̈ܢܐ ܓܘ ܓܘ̈ܕܐ. ܥܒܕܐ ܕܚܕ̈ܕܐ ܒܥܡܝܘܬܐ ܝܠܗ ܫܘܐܠܐ: ܐܝܬܘ ܫܘܢܝܐ ܒܐܘܪܟܐ ܕܙܒܢܐ ܦܪܝܫܐ ܝܠܗ ܓܘ ܬܪܥܝܬܐ ܘܓܘ ܓܘܕܐ ܕܦܘܚܡܐ؟ ܟܬܢܚ ܥܠܗ ܩܕܡܝܐ (Pallant, 2020, Chapter 20).

ܫܪܛܐ ܙܘܕܐ: ܕܡܐܛܪܝܟ̈ܣܐ ܕܫܘܚܠܦܐ ܡܫܘܬܦܐ (covariance) ܕܡܫܘ̈ܚܬܐ ܫܘ̈ܝܐ ܝܢܐ ܓܘ ܓܘ̈ܕܐ. ܒܘܚܪ̈ܢܐ ܚܣܝܢ̈ܐ ܝܢܐ ܠܬܒܪܐ ܕܝܠܗ ܐܝܡܢ ܕܓܘ̈ܕܐ ܫܘ̈ܝܐ ܝܢܐ ܒܪܒܘܬܐ (Maxwell et al., 2018, p. 704). SPSS ܟܒܚܪ ܠܗ ܒ-Box's M؛ Pallant (2020، ܨܚܚܐ 20) ܟܡܩܪܒܐ ܕܩܪܚ ܠܗ ܒ-α = .001 ܡܛܠ ܕܪܓܝܫܐ ܝܠܗ ܣܓܝ، ܘ-Maxwell ܘܚܒܪ̈ܘܗܝ (2018، ܦܐܬܐ 840) ܟܚܫܒܝ ܕܦܐܝܕܐ ܥܒܕܢܝܬܐ ܕܝܠܗ ܩܠܝܠܬܐ ܝܠܗ̇. ܦܐܬܐ ܟܡܚܘܐ ܠܗ ܘܠ-Levene ܩܐ ܟܠ ܡܫܘܚܬܐ.

ܣܘܩܒ̈ܠܐ، ܦܘܚܡ̈ܐ ܙܘܓܢ̈ܝܐ ܘ-simple effects

ܒܘܚܪܢܐ F ܟܐܡܪ ܕܐܝܬ ܦܘܪܫܢܐ، ܠܐ ܐܝܟܐ. ܬܠܬܐ ܐܘܪ̈ܚܬܐ ܕܡܬܡܢܥܚ – ܘܟܓܒܚ ܚܕܐ ܠܦܘܬ ܫܘܐܠܐ (Field, 2024, Sections 15.9.5, 15.15.3):

ܣܘܩܒ̈ܠܐ ܬܘܩܢ̈ܐ – ܫܘܐ̈ܠܐ ܬܚܝܡ̈ܐ ܡܢ ܩܕܡ: ܢܛܝܘܬܐ ܣܪܛܢܝܬܐ ܝܢ ܡܪܒܥܝܬܐ ܒܐܘܪܟܐ ܕܙܒܢܐ (ܦܘܠܝܢܘܡܝܐܠ، ܓܘܒܝܐ ܡܩܕܡܐ ܕ-SPSS)، ܟܠ ܫܪܛܐ ܩܘܒܠ ܫܪܛܐ ܕܫܬܐܣܐ (ܦܫܝܛܐ)، ܝܢ ܟܠ ܕܪܓܐ ܩܘܒܠ ܕܒܬܪܗ (ܡܬܢܝܐ) (ܬܡܢ، ܦܣܩܐ 15.8.2). ܗܪܟܐ ܣܢܝܩ ܝܠܗ ܕܟܠ ܣܘܩܒܠܐ ܒܚܝܪܐ ܗܘܐ ܥܡ ܛܥܝܘܬܐ ܕܝܠܗ – ܫܘܚܠܦܐ ܕܡܢܝ̈ܢܐ ܕܣܘܩܒܠܐ – ܘܠܐ ܥܡ ܛܥܝܘܬܐ ܡܫܘܬܦܬܐ، ܕܟܣܡܟܐ ܥܠ ܐܣܦܝܪܝܘܬܐ؛ ܣܘܩܒ̈ܠܐ ܪܓܝܫ̈ܐ ܝܢܐ ܠܬܒܪܐ ܕܐܣܦܝܪܝܘܬܐ ܣܓܝ ܝܬܝܪ ܡܢ ܒܘܚܪܢܐ ܟܠܢܝܐ (Maxwell et al., 2018, pp. 638-639). ܗܟܢܐ ܦܐܬܐ، ܘܗܟܢܐ SPSS.

ܦܘܚܡ̈ܐ ܙܘܓܢ̈ܝܐ – ܟܠ ܙܘܓܐ ܕܡܫܘ̈ܚܬܐ، ܥܡ ܬܘܪܨܐ ܕ-Bonferroni (Bonferroni correction). ܓܘ ܡܫܘ̈ܚܬܐ ܡܬܢ̈ܝܬܐ ܐܗܐ ܝܠܗ̇ ܡܘܥܕܢܘܬܐ، ܘܠܐ Tukey، ܕܠܐ ܟܢܛܪ ܡܢܬܐ ܕܛܥܝܘܬܐ ܐܝܡܢ ܕܠܝܬ ܐܣܦܝܪܝܘܬܐ (Maxwell et al., 2018, pp. 757-758; Field, 2024, Section 15.5.3).

Simple effects – ܐܝܡܢ ܕܐܝܬ ܥܒܕܐ ܕܚܕ̈ܕܐ: ܡܥܒܕܢܘܬܐ ܕܚܕ ܥܠܬܐ ܓܘ ܟܠ ܕܪܓܐ ܕܐܚܪܬܐ – ܠܡܬܠܐ، ܫܘܢܝܐ ܒܐܘܪܟܐ ܕܙܒܢܐ ܓܘ ܬܪܥܝܬܐ ܒܦܪܝܫܘܬܐ ܘܓܘ ܓܘܕܐ ܕܦܘܚܡܐ ܒܦܪܝܫܘܬܐ (Field, 2024, Section 15.15.3). ܟܠ ܡܥܒܕܢܘܬܐ ܕܐܗܐ ܙܢܐ ܒܘܚܪܢܐ ܙܘܕܐ ܝܠܗ̇؛ Field ܟܡܘܥܕ ܕܦܪܩܚ ܥܒܕܐ ܕܚܕ̈ܕܐ ܒܩܠܝܠ ܒܘܚܪ̈ܢܐ ܟܡܐ ܕܡܨܝܐ ܘܕܬܪܨܚ ܠܡܢܝܢܐ ܕܝܠܗܘܢ (ܬܡܢ).

ܪ̈ܒܘܬܐ ܕܡܥܒܕܢܘܬܐ

SPSS ܟܛܒܥ ܐܝܬܐ ܡܪܒܥܐ ܡܢܬܢܝܐ (partial eta squared): SS_{ܡܥܒܕܢܘܬܐ}/(SS_{ܡܥܒܕܢܘܬܐ} + SS_ܛܥܝܘܬܐ) – ܦܘܪ̈ܫܢܐ ܒܝܢܝ ܡܫܬܘܬܦ̈ܢܐ ܠܐ ܝܢܐ ܓܘ ܬܚܬܝܬܐ (Gravetter & Wallnau, 2017, p. 427). ܡܛܠ ܗܕܐ ܗܝ ܪܒܬܐ ܝܠܗ̇، ܘܠܐ ܡܨܝܐ ܕܡܬܦܚܡܐ ܥܡ ܐܝܬܐ ܡܪܒܥܐ ܕܒܘܨܝܐ ܒܝܢܝ ܡܫܬܘܬܦ̈ܢܐ. Maxwell ܘܚܒܪ̈ܘܗܝ (2018، ܦܐ̈ܬܐ 634-635) ܟܓܒܝ ܐܘܡܝܓܐ ܡܪܒܥܐ (omega squared) ܕܟܡܦܝܫܐ ܫܘܚܠܦܐ ܒܝܢܝ ܡܫܬܘܬܦ̈ܢܐ ܓܘ ܬܚܬܝܬܐ، ܐܝܟ ܓܘ ܒܘܨܝܐ ܒܝܢܝ ܡܫܬܘܬܦ̈ܢܐ – "ܟܡܬܚܙܐ ܒܨܒܝܢܐ ܕܠܐ ܡܛܥܝܚ ܡܢܗ" (ܬܡܢ، ܦܐܬܐ 635) – ܘܗܝ ܟܫܥܪܐ ܟܢܫܐ ܟܠܢܝܐ ܘܠܐ ܕܘܡܝܐ. ܓܘ ܡܬܠܐ ܕ-McCarthy ܬܡܢ: ω² = .04 (ܬܡܢ)، ܐܝܡܢ ܕܐܝܬܐ ܡܪܒܥܐ ܡܢܬܢܝܐ ܕܗܢܝ ܝܗܝ̈ܒܬܐ ܝܠܗ̇ .22. ܦܐܬܐ ܟܡܚܘܐ ܬܪܘܝܗܝ، ܘܐܘܡܝܓܐ ܡܪܒܥܐ – ܓܘ ܬܘܩ̈ܢܐ ܕܐܝܬ ܠܗ̇ ܫܘܝܘܬܐ ܓܘ ܟܬܒܐ (ܚܕ ܝܢ ܬܪܬܝܢ ܥܠ̈ܠܬܐ ܓܘ ܡܫܬܘܬܦ̈ܢܐ، ܝܢ ܚܕܐ ܥܡ ܥܠܬܐ ܒܝܢܝ ܡܫܬܘܬܦ̈ܢܐ؛ ܬܡܢ، ܫܘܝ̈ܘܬܐ 11.35، 12.6 ܘ-12.22-12.24). ܩܐ ܣܘܩܒܠܐ ܘܦܘܚܡܐ ܙܘܓܢܝܐ ܡܨܝܚ ܕܚܫܒܚ d (ܒܘܚܪܢܐ t ܠܕܘ̈ܡܝܐ ܙܘܓܢ̈ܝܐ).

ܩܪܝܢܐ ܕܡܦܩܢܐ (How to read the output)

ܠܘ̈ܚܐ ܒܛܟܣܐ ܕ-SPSS: ܡܨܥܝ̈ܬܐ؛ ܐܣܦܝܪܝܘܬܐ (Mauchly ܘ-ε)؛ ܒܘܚܪ̈ܢܐ ܓܘ ܡܫܬܘܬܦ̈ܢܐ ܠܦܘܬ ܬܘܪܨܐ ܕܓܒܝܐ ܝܠܗ؛ ܠܘܚܐ ܕܟܦܚܡܐ p ܓܘ ܐܪܒܥܐ ܐܘܪ̈ܚܬܐ؛ ܒܘܚܪ̈ܢܐ ܕܣܓܝ ܡܫܬܚܠܦ̈ܢܐ؛ ܓܘ ܬܘܩܢܐ ܡܚܠܛܐ – ܒܘܚܪܢܐ ܒܝܢܝ ܡܫܬܘܬܦ̈ܢܐ، Levene ܘ-Box's M؛ ܣܘܩܒ̈ܠܐ؛ ܡܨܥܝ̈ܬܐ ܕܣܦܪܐ (marginal means)؛ ܦܘܚܡ̈ܐ ܙܘܓܢ̈ܝܐ؛ simple effects؛ ܘܨܘܪܬܐ. ܟܩܪܚ ܩܕܡܝܐ ܥܒܕܐ ܕܚܕ̈ܕܐ، ܒܬܪܗ ܡܥܒܕ̈ܢܘܝܬܐ ܪ̈ܫܝܬܐ (main effects). "ܩܪܝܢܐ ܕܦܐܪܐ" ܟܡܚܘܐ ܡܐ ܕܣܢܝܩ ܝܠܗ ܓܘ ܗܘܝܐ ܕܝܘܟܘܢ – ܟܡܝܘܬܐ ܕܣܛܝܘܬܐ ܡܢ ܐܣܦܝܪܝܘܬܐ، ܕܚܕ ܡܫܬܚܠܦܢܐ ܝܢ ܕܣܓܝ ܡܫܬܚܠܦ̈ܢܐ، ܘܥܒܕܐ ܕܚܕ̈ܕܐ.

ܫܪ̈ܛܐ

ܫܪ̈ܛܐ (assumptions) ܕܦܘܫܩܐ ܕܫܘܚܠܦܐ ܥܡܝܐ – ܠܐ ܬܠܝܘܬܐ ܒܝܢܝ ܡܫܬܘܬܦ̈ܢܐ، ܢܘܪܡܠܝܘܬܐ (normality؛ ܝܚܝܕܐܝܬ ܓܘ ܕܘܡܝܐ ܙܥܘܪܐ) ܘܫܘܝܘܬܐ ܕܫܘܚܠ̈ܦܐ – ܘܙܘܕܐ ܚܕ: "ܗܘܡܘܓܢܝܘܬܐ ܕܫܘܚܠܦܐ ܡܫܘܬܦܐ"، ܗܢܘ ܕܡܫܬܘܬܦ̈ܢܐ ܟܢܛܪܝ ܒܩܪܝܒܘܬܐ ܕܘܟܬܐ ܢܣܝܒܬܐ ܕܝܠܗܘܢ ܒܝܢܝ ܫܪ̈ܛܐ (Gravetter & Wallnau, 2017, p. 428). ܒܢܘܣܚܐ ܚܬܝܬܐ – ܐܣܦܝܪܝܘܬܐ (ܠܥܠ). ܓܘ ܬܘܩܢܐ ܡܚܠܛܐ – ܐܦ ܡܐܛܪܝܟ̈ܣܐ ܫܘ̈ܝܐ ܒܝܢܝ ܓܘ̈ܕܐ (Maxwell et al., 2018, p. 704). ܐܝܡܢ ܕܫܪ̈ܛܐ ܠܐ ܩܝܡܝ: ܒܘܚܪܢܐ ܚܣܝܢܐ (robust) ܥܠ ܡܨܥܝ̈ܬܐ ܓܙܝܙ̈ܬܐ (trimmed means؛ rmanova ܓܘ ܨܪܪܐ WRS2 ܓܘ R؛ Field, 2024، ܦܣܩܐ 15.10)، ܒܘܚܪܢܐ ܕ-Friedman ܐܝܟ ܦܘܫܪܐ ܐܚܪܝܐ (ܬܡܢ، ܦܣܩܐ 15.7)، ܝܢ ܡܘܕܝܠ ܕܣܓܝ ܕܪ̈ܓܐ (multilevel؛ ܬܡܢ، ܦܣܩܐ 15.5.4).

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

Analyze → General Linear Model → Repeated Measures: ܟܬܚܡܚ ܥܠܬܐ ܓܘ ܡܫܬܘܬܦ̈ܢܐ ܘܡܢܝܢܐ ܕܕܪ̈ܓܐ، ܟܣܝܡܚ ܥܡܘ̈ܕܐ ܠܦܘܬ ܛܟܣܐ، ܘܟܡܘܣܦܚ ܥܠܬܐ ܒܝܢܝ ܡܫܬܘܬܦ̈ܢܐ ܐܢ ܐܝܬ (Field, 2024, Sections 15.8, 16.5; Pallant, 2020, Chapters 18, 20). ܓܘ Options – ܬܚܘܝ̈ܬܐ، ܪܒܘܬܐ ܕܡܥܒܕܢܘܬܐ، ܘܓܘ ܬܘܩܢܐ ܡܚܠܛܐ ܒܘܚܪ̈ܢܐ ܕܗܘܡܘܓܢܝܘܬܐ؛ ܓܘ EM Means – ܦܘܚܡܐ ܕܡܥܒܕ̈ܢܘܝܬܐ ܪ̈ܫܝܬܐ ܥܡ Bonferroni. ܠܘܚܐ ܕܣܢܝܩ ܝܠܗ: Tests of Within-Subjects Effects، ܓܘ ܣܕܪܐ ܕ-Greenhouse-Geisser (Field, 2024, Section 15.9). ܦܐܬܐ ܟܡܚܬܐ ܣܝܢܬܐܟܣ ܡܛܝܒܐ (GLM ... /WSFACTOR). PSPP ܠܐ ܟܪܗܛ ܡܫܘ̈ܚܬܐ ܡܬܢ̈ܝܬܐ ܓܘ GLM، ܘܡܛܠ ܗܕܐ ܣܝܢܬܐܟܣ ܠܐ ܒܚܝܪܐ ܝܠܗ ܓܘܗ.

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

ܐܘܪܚܐ ܩܪܝܒܬܐ ܠ-SPSS: ܡܘܕܝܠ ܕܣܓܝ ܡܫܬܚܠܦ̈ܢܐ (lm ܥܡ ܡܐܛܪܝܟܣ ܕܦܘܢܝܐ) ܘ-car::Anova ܥܡ idata ܘ-idesign – ܟܝܗܒ ܒܘܚܪ̈ܢܐ ܕܣܓܝ ܡܫܬܚܠܦ̈ܢܐ، ܕܚܕ ܡܫܬܚܠܦܢܐ، Mauchly ܘܬܘܪ̈ܨܐ؛ emmeans – ܡܨܥܝ̈ܬܐ ܕܣܦܪܐ ܘܦܘܚܡ̈ܐ. ܬܪܝܢ ܦܘܪ̈ܫܢܐ ܙܥܘܪ̈ܐ ܡܢ SPSS: Mauchly ܓܘ R ܐܝܬ ܓܘܗ ܗܕܡܐ ܕܛܟܣܐ ܬܪܝܢܐ، ܘ-Huynh-Feldt ܓܘ ܨܪܪܐ car ܚܫܝܒܐ ܝܠܗ ܒܬܘܪܨܐ ܐܚܪܢܐ ܐܝܡܢ ܕܐܝܬ ܓܘ̈ܕܐ. ܣܩܪܝܦܬ (script) ܕܠܬܚܬ ܪܗܛܐ ܝܠܗ ܐܝܟ ܕܐܝܬܘܗܝ ܥܠ ܦܐܝܠ ܕܡܬܠܐ (ܛܝ̈ܡܐ ܓܘ ܡܥܝܪ̈ܢܘܬܐ).

# ANOVA ܠܡܫܘ̈ܚܬܐ ܡܬܢ̈ܝܬܐ ܓܘ R – ܦܐܝܠ ܕܡܬܠܐ ܕܦܐܬܐ (36 ܬܠܡܝ̈ܕܐ، ܬܪܥܝܬܐ/ܦܘܚܡܐ × ܬܠܬܐ ܡܫܘ̈ܚܬܐ ܕܩܢܛܐ ܕܒܘܚܪ̈ܢܐ)
library(car)       # ܦܘܩܕܢܐ Anova ܥܠ ܡܘܕܝܠ ܕܣܓܝ ܡܫܬܚܠܦ̈ܢܐ
library(emmeans)   # ܡܨܥܝ̈ܬܐ ܕܣܦܪܐ ܘܦܘܚܡ̈ܐ
options(contrasts = c("contr.sum", "contr.poly"))   # ܡܚܝܒܐ ܝܠܗ ܩܐ Type III

d <- data.frame(group = factor(c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2), labels = c("program", "control")),
                pre = c(46, 53, 34, 59, 59, 50, 39, 39, 41, 61, 38, 79, 60, 59, 68, 75, 55, 43, 38, 51, 48, 44, 56, 51, 64, 51, 44, 60, 60, 61, 33, 48, 45, 39, 52, 32),
                post = c(48, 34, 39, 48, 53, 42, 32, 27, 25, 41, 44, 65, 54, 59, 51, 67, 39, 38, 40, 46, 47, 59, 45, 54, 64, 55, 55, 64, 50, 56, 30, 39, 46, 43, 50, 30),
                followup = c(34, 45, 27, 42, 55, 43, 41, 42, 40, 55, 45, 67, 55, 57, 51, 70, 44, 36, 37, 51, 53, 52, 54, 64, 78, 50, 49, 62, NA, 53, 37, 53, 47, 47, 51, 30))
d <- na.omit(d)                                     # ܫܩܠܬܐ ܕܣܕܪܐ ܟܠܗ: ܟܦܝܫܝ 35
fit <- lm(cbind(pre, post, followup) ~ group, data = d)
idata <- data.frame(time = factor(1:3))
av <- Anova(fit, idata = idata, idesign = ~ time, type = 3)
summary(av, multivariate = TRUE)
# ܙܒܢܐ (time): F(2, 66) = 5.94, GG eps = .94
# ܥܒܕܐ ܕܚܕ̈ܕܐ (group:time): F(2, 66) = 9.46, p (GG) = .0003
# ܐܘܪܚܐ ܕ-Pillai ܩܐ ܥܒܕܐ ܕܚܕ̈ܕܐ: V = .42, F(2, 32) = 11.50

ml <- list(time = c("pre", "post", "followup"))
pairs(emmeans(fit, ~ time | group, mult.name = "time", mult.levs = ml), adjust = "bonferroni")
# ܓܘ ܬܪܥܝܬܐ: pre - post = 8.44 (p = .0001)

ܬܘܢܝܐ ܕܡܫܟܚ̈ܢܘܬܐ (reporting the results)

ܟܬܢܚ ܬܘܩܢܐ، ܐܝܢܐ ܬܘܪܨܐ ܥܒܝܕܐ ܝܠܗ ܘ-ε، ܘܩܐ ܟܠ ܡܥܒܕܢܘܬܐ F ܥܡ ܕܪ̈ܓܐ ܕܚܐܪܘܬܐ ܡܬܘܪ̈ܨܐ (ܠܡܬܠܐ F(1.60, 11.19))، p ܘܪܒܘܬܐ ܕܡܥܒܕܢܘܬܐ (effect size) – ܘܟܐܡܪܚ ܐܝܢܐ (Field, 2024, Section 15.12). ܐܝܡܢ ܕܟܬܢܚ ܒܘܚܪܢܐ ܕܣܓܝ ܡܫܬܚܠܦ̈ܢܐ – Pillai (V) ܘ-F ܕܝܠܗ (ܬܡܢ؛ Pallant, 2020، ܨܚܚܐ 18 – ܬܡܢ Wilks). ܡܨܥܝ̈ܬܐ ܘܣܛܝ̈ܘܬܐ ܬܩܝܢ̈ܬܐ – ܓܘ ܠܘܚܐ. ܓܘ ܬܘܩܢܐ ܡܚܠܛܐ – ܥܒܕܐ ܕܚܕ̈ܕܐ ܩܕܡܝܐ (Pallant, 2020, Chapter 20). ܦܐܬܐ ܟܟܬܒܐ ܦܣܩܐ ܕܐܗܐ ܙܢܐ ܒܣܘܪܝܬ ܘܒܐܢܓܠܝܙܝܐ.

ܛܥܝ̈ܘܬܐ ܕܡܬܚܙܝܢ ܣܓܝ (Common mistakes)

ܦܘܫܩܐ ܕܡܫܘ̈ܚܬܐ ܡܬܢ̈ܝܬܐ ܐܝܟ ܕܐܢ ܗܘܘ ܓܘ̈ܕܐ ܦܪ̈ܝܫܐ – ܦܘܪ̈ܫܢܐ ܒܝܢܝ ܡܫܬܘܬܦ̈ܢܐ ܟܦܝܫܝ ܓܘ ܛܥܝܘܬܐ، ܘܒܘܚܪܢܐ ܟܡܘܒܕ ܣܓܝܐܘܬܐ ܕܝܬܝܪܘܬܐ ܕܝܠܗ (Gravetter & Wallnau, 2017, pp. 430-431).

ܩܪܝܢܐ ܕܣܕܪܐ ܕܠܐ ܬܘܪܨܐ – "Sphericity Assumed" – ܕܠܐ ܒܘܚܪܢܐ ܕܐܣܦܝܪܝܘܬܐ (Maxwell et al., 2018, p. 632).

ܦܣܩܐ ܥܠ ܬܘܪܨܐ ܠܦܘܬ Mauchly – ܒܘܚܪܢܐ ܬܠܝܐ ܝܠܗ ܒܪܒܘܬܐ ܕܕܘܡܝܐ؛ ܟܬܪܨܚ ܠܦܘܬ ε (Field, 2024, Section 15.5.2).

ܓܘܒܝܐ ܒܝܢܝ Greenhouse-Geisser ܘ-Huynh-Feldt ܒܬܪ ܕܚܙܝܚ ܐܝܢܐ ܪܫܝܡܐ ܝܠܗ – Field (2024، ܦܣܩܐ 15.9.3) ܟܡܚܘܐ ܐܝܟܢܐ ܓܘ ܗܢܝ ܝܗܝ̈ܒܬܐ ܚܕ ܟܝܗܒ .063 ܘܐܚܪܢܐ .048؛ ܦܣܩܐ ܐܝܬ ܠܗ ܕܗܘܐ ܦܣܝܩܐ ܡܢ ܩܕܡ، ܘܡܐ ܕܣܢܝܩ ܝܠܗ ܪܒܘܬܐ ܕܡܥܒܕܢܘܬܐ ܝܠܗ̇.

Tukey ܝܢ ܣܘܩܒ̈ܠܐ ܥܡ ܛܥܝܘܬܐ ܡܫܘܬܦܬܐ – ܬܪܘܝܗܝ ܟܣܡܟܝ ܥܠ ܐܣܦܝܪܝܘܬܐ؛ Bonferroni ܘܛܥܝܘܬܐ ܦܪܝܫܬܐ ܩܐ ܟܠ ܣܘܩܒܠܐ (Maxwell et al., 2018, pp. 639, 757-758).

ܦܘܚܡܐ ܕܐܝܬܐ ܡܪܒܥܐ ܡܢܬܢܝܐ ܡܢ ܡܫܘ̈ܚܬܐ ܡܬܢ̈ܝܬܐ ܥܡ ܕܒܘܨܝܐ ܒܝܢܝ ܡܫܬܘܬܦ̈ܢܐ – ܬܚܬܝ̈ܬܐ ܦܪ̈ܝܫܐ ܝܢܐ (Gravetter & Wallnau, 2017, p. 427; Maxwell et al., 2018, p. 635).

ܫܩܠܬܐ ܕܥܠܬܢܘܬܐ (causality) ܡܢ ܫܘܢܝܐ ܒܐܘܪܟܐ ܕܙܒܢܐ ܕܠܐ ܓܘܕܐ ܕܦܘܚܡܐ – ܡܥܒܕ̈ܢܘܝܬܐ ܕܛܟܣܐ ܐܝܟ ܬܡܪܢܐ، ܡܪܝܪܘܬܐ ܘܠܐܘܬܐ ܡܨܝ ܕܡܦܫܩܝ ܠܗ (Field, 2024, Section 1.6.5; Gravetter & Wallnau, 2017, p. 430)؛ ܓܘ ܫܪ̈ܛܐ – ܕܫܘܝܚ ܛܟܣܐ ܒܦܣܐ (Field، ܬܡܢ؛ ܦܐܬܐ ܡܫܬܚܠܦ̈ܢܐ، ܣܒ̈ܠܬܐ ܘܬܘܩ̈ܢܐ ܕܒܘܨܝܐ).

ܡܒܘ̈ܥܐ

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

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.

Maxwell, S. E., Delaney, H. D., & Kelley, K. (2018). Designing experiments and analyzing data: A model comparison perspective (3rd ed.). Routledge.

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

Algina ܘ-Keselman (1997) – ܐܝܟ ܕܡܬܝ̈ܬܐ ܝܢܐ ܓܘ Maxwell ܘܚܒܪ̈ܘܗܝ (2018)؛ Girden (1992) ܘܐܚܪ̈ܢܐ – ܐܝܟ ܕܡܬܝ̈ܬܐ ܝܢܐ ܓܘ Field (2024). 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؛ Maxwell ܘܚܒܪ̈ܘܗܝ (2018) ܘ-Gravetter ܘ-Wallnau (2017) – ܠܦܘܬ ܦܐܬܐ ܛܒܝܥܬܐ. ܥܝ̈ܕܐ ܕܣܐܝܛ (site conventions): ܒܢܝܢܐ ܦܬܝܐ ܘܫܩܠܬܐ ܕܣܕܪܐ ܟܠܗ ܐܝܟ SPSS؛ Greenhouse-Geisser ܐܝܟ ܓܘܒܝܐ ܡܩܕܡܐ (default) ܓܘ ܬܘܢܝܐ؛ Huynh-Feldt ܒܫܘܝܘܬܐ ܫܪܫܝܬܐ ܐܝܟ SPSS؛ Type III ܘܡܨܥܝ̈ܬܐ ܕܣܦܪܐ ܕܠܐ ܡܬܩܠܢܘܬܐ (unweighted)؛ ܬܪܝܢ ܡܢܝ̈ܢܐ ܒܬܪ ܢܘܩܙܐ ܓܘ ܠܘ̈ܚܐ. ܚܘܫܒܢܐ ܡܫܪܪܐ ܝܠܗ ܩܘܒܠ R 4.3.3 (car, emmeans) ܘܩܘܒܠ ܡܢܝ̈ܢܐ ܛܒܝ̈ܥܐ: ܓܘ Maxwell ܘܚܒܪ̈ܘܗܝ – ܠܘ̈ܚܐ 11.5، 12.1، 12.7 ܘ-12.15 (ܥܡ 12.5، 12.19 ܘܫܘܥ̈ܪܐ ܕ-ε)، 13.2 ܘ-14.9؛ ܓܘ Gravetter ܘ-Wallnau – ܠܘܚܐ 13.2 ܘܡܦܩܢܐ ܕ-SPSS ܓܘ ܨܘܪܬܐ 13.4؛ ܘܒܦܘܚܡܐ ܥܡ ܡܦܩ̈ܢܐ ܕ-SPSS ܓܘ Field (2024) ܘ-Pallant (2020).