ܒܘܚܪܢܐ t ܠܕܘ̈ܡܝܐ ܙܘܓܢ̈ܝܐ

ܛܥܢܐ ܕܝܗܝ̈ܒܬܐ (loading the data)

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

ܓܘܒܝܐ ܕܬܪܬܝܢ ܡܫܘ̈ܚܬܐ

ܐܝܡܢ ܡܦܠܚܝܚ (When to use)؟

ܐܡܢ ܕܠܟܠ ܡܫܬܘܬܦܢܐ (participant) ܐܝܬ ܬܪܬܝܢ ܡܫܘ̈ܚܬܐ ܡܢ ܚܕ ܙܢܐ ܘܫܘܐܠܐ ܝܠܗ ܐܢ ܡܨܥܝܬܐ (mean) ܫܚܠܦܠܗ̇: ܗܝ̇ ܦܢܩܝܬܐ ܕܫܘܐ̈ܠܐ (questionnaire) ܩܕܡ ܡܥܠܬܐ (intervention) ܘܒܬܪܗ̇، ܬܪܝܢ ܫܪ̈ܛܐ ܕܟܠ ܡܫܬܘܬܦܢܐ ܥܒܪܠܗ ܒܓܘܝܗܘܢ، ܬܪܝܢ ܦܣܘ̈ܩܐ (items) ܓܘ ܗܝ̇ ܣܒܠܬܐ ܕܗܢܝ ܐܢܫ̈ܐ ܛܟܣܠܗܘܢ – ܝܢ ܙܘܓ̈ܐ ܡܦܐ̈ܝܐ، ܕܓܘܝܗܘܢ ܟܠ ܡܫܬܘܬܦܢܐ ܓܘ ܓܘܕܐ ܚܕ ܡܦܐܝܐ ܝܠܗ ܚܕ-ܠܚܕ ܥܡ ܡܫܬܘܬܦܢܐ ܓܘ ܓܘܕܐ ܐܚܪܢܐ (ܬܐܡ̈ܐ، ܙܘܓ̈ܐ ܕܓܘܪܐ، ܝܢ ܦܐܝܘܬܐ ܠܦܘܬ ܥܘܡܪܐ ܘܕܟܪܐ/ܢܩܒܬܐ). Pallant (2020، ܨܚܚܐ 17) ܟܬܚܡܐ: ܓܘܕܐ ܚܕ ܕܡܫܬܘܬܦ̈ܢܐ، ܬܪܝܢ ܟܢܫ̈ܐ ܕܡܢܝ̈ܢܐ ܥܠ ܗܘ ܡܫܬܚܠܦܢܐ ܡܬܡܫܚܢܐ (continuous) – ܘܡܫܬܚܠܦܢܐ ܠܐ ܬܠܝܐ (independent variable) ܕܓܢ̈ܣܐ ܚܕ ܥܡ ܬܪܝܢ ܕܪ̈ܓܐ (ܙܒܢܐ 1 / ܙܒܢܐ 2). Field (2024، ܦܣܩܐ 10.5) ܟܡܝܬܐ "ܡܟܝܢܐ ܕܚܘܠܛܢܐ": ܒܘܚܪܢܐ t ܠܙܘܓܢ̈ܝܐ، ܒܘܚܪܢܐ t ܬܠܝܐ، ܒܘܚܪܢܐ ܠܡܫܘ̈ܚܬܐ ܡܬܢ̈ܝܬܐ، ܒܘܚܪܢܐ ܠܙܘܓ̈ܐ ܡܦܐ̈ܝܐ – ܟܠܗܘܢ ܗܘ ܒܘܚܪܢܐ ܝܢܐ. Gravetter ܘ-Wallnau (2017، ܦܐ̈ܬܐ 336-338) ܟܩܪܝ ܠܬܪܝܢ ܬܘܩ̈ܢܐ – ܡܫܘ̈ܚܬܐ ܡܬܢ̈ܝܬܐ ܘܙܘܓ̈ܐ ܡܦܐ̈ܝܐ – ܒܫܡܐ ܡܫܘܬܦܐ related-samples designs، ܘܟܡܚܝܠܝ ܕܐܢܝ ܫܘ̈ܝܐ ܝܢܐ ܣܛܐܛܝܣܛܝܩܐܝܬ: ܝܗܝ̈ܒܬܐ ܙܘܓ̈ܐ ܕܡܢܝ̈ܢܐ ܝܢܐ، ܘܡܐ ܕܡܒܘܚܪܐ ܝܠܗ ܦܘܪܫܢܐ ܓܘ ܟܠ ܙܘܓܐ.

ܚܕܝܘܬܐ ܕܡܒܘܚܪܐ ܝܠܗ̇ ܦܘܪܫܢܐ ܝܠܗ ܓܘ ܡܫܬܘܬܦܢܐ (ܝܢ ܓܘ ܙܘܓܐ) – ܘܡܛܠ ܗܕܐ ܐܗܐ ܒܘܚܪܢܐ ܦܪܝܫܐ ܝܠܗ ܡܢ ܒܘܚܪܢܐ t ܠܕܘ̈ܡܝܐ ܠܐ ܬܠܝ̈ܐ، ܕܓܘܗ ܟܠ ܓܘܕܐ ܡܪܟܒܐ ܝܠܗ ܡܢ ܐܢܫ̈ܐ ܐܚܪ̈ܢܐ. ܝܬܝܪ ܡܢ ܬܪܬܝܢ ܡܫܘ̈ܚܬܐ ܕܗܢܝ ܡܫܬܘܬܦ̈ܢܐ – ܦܘܫܩܐ ܕܫܘܚܠܦܐ (analysis of variance) ܠܡܫܘ̈ܚܬܐ ܡܬܢ̈ܝܬܐ (Pallant, Chapter 18; Gravetter & Wallnau, Chapter 13)، ܓܘ ܦܐܬܐ ANOVA ܠܡܫܘ̈ܚܬܐ ܡܬܢ̈ܝܬܐ، ܠܐ ܣܕܪܐ ܕܒܘܚܪ̈ܢܐ t ܙܘܓܢ̈ܝܐ؛ ܐܡܢ ܕܦܘܪ̈ܫܢܐ ܟܬܒܪܝ ܒܩܫܝܘܬܐ ܫܪܛܐ ܕܢܘܪܡܠܝܘܬܐ (normality) ܓܘ ܕܘܡܝܐ ܙܥܘܪܐ – ܒܘܚܪܢܐ ܕ-Wilcoxon (Pallant, 2020, Chapter 16; Gravetter & Wallnau, Appendix E)، ܓܘ ܦܐܬܐ ܕܝܠܗ. ܡܢܝܢܐ ܕܣܒܠܬܐ ܕܦܣܘ̈ܩܐ ܣܓܝ̈ܐܐ (multi-item scale؛ ܡܨܥܝܬܐ ܕܦܣܘ̈ܩܐ، ܦܐܬܐ ܐܠܦܐ ܕ-Cronbach ܘܡܢܝܢܐ ܕܣܒܠܬܐ) ܟܡܬܚܫܒ ܐܝܟ ܡܫܬܚܠܦܢܐ ܕܪܘ̈ܚܩܐ ܫܘ̈ܝܐ ܠܦܘܬ ܥܝܕܐ ܕܣܐܝܛ (ܦܐܬܐ ܡܫܬܚܠܦ̈ܢܐ ܘܕܪ̈ܓܐ ܕܡܫܘܚܬܐ)، ܘܡܛܠ ܗܕܐ ܦܐܝܐ ܝܠܗ ܐܝܟ ܡܫܘܚܬܐ؛ ܦܣܘܩܐ ܕ-Likert ܝܚܝܕܝܐ – ܠܐ.

ܗܘܢܐ: ܦܘܪ̈ܫܢܐ، ܠܐ ܡܢܝ̈ܢܐ

ܕܪܓܐ ܩܕܡܝܐ ܝܠܗ ܚܘܫܒܢܐ ܩܐ ܟܠ ܡܫܬܘܬܦܢܐ ܕܦܘܪܫܢܐ ܒܝܢܝ ܬܪܬܝܢ ܡܫܘ̈ܚܬܐ – D (Gravetter & Wallnau, 2017, pp. 339-340, Equation 11.1). ܡܢ ܐܟܐ ܘܠܩܕܡ ܒܘܚܪܢܐ ܠܐ ܟܚܙܐ ܡܢܝ̈ܢܐ ܫܪܫܝ̈ܐ ܐܠܐ ܒܣ ܦܘܪ̈ܫܢܐ: ܡܨܥܝܬܐ (mean) ܕܝܠܗܘܢ، M_D، ܫܘܥܪܐ ܝܠܗ̇ ܕܡܥܒܕܢܘܬܐ؛ ܣܛܝܘܬܐ ܬܩܝܢܬܐ (standard deviation) ܕܝܠܗܘܢ، s_D، ܟܐܡܪܐ ܗܠ ܟܡܐ ܡܥܒܕܢܘܬܐ ܡܬܢܝܬܐ ܝܠܗ̇ ܒܝܢܝ ܡܫܬܘܬܦ̈ܢܐ. ܫܘܐܠܐ ܝܠܗ ܐܢ ܡܨܥܝܬܐ ܕܦܘܪ̈ܫܢܐ ܓܘ ܟܢܫܐ ܟܠܢܝܐ (population)، μ_D، ܨܦܪܐ ܝܠܗ̇. Field (2024، ܦܣܩܐ 10.5.2، ܫܘܝ̈ܘܬܐ 10.6-10.7): t ܝܠܗ ܡܨܥܝܬܐ ܕܦܘܪ̈ܫܢܐ ܡܦܠܓܐ ܥܠ ܛܥܝܘܬܐ ܬܩܝܢܬܐ (standard error) ܕܦܘܪ̈ܫܢܐ (s_D/√N) – "ܐܬܐ ܡܦܠܓܐ ܥܠ ܚܘܠܛܢܐ ܕܣܪܝܩܐ": ܦܘܪܫܢܐ ܚܙܝܐ ܩܘܒܠ ܡܐ ܕܡܬܩܒܠܐ ܝܠܗ ܕܫܩܠܚ ܡܢ ܬܪܝܢ ܓܘܒ̈ܝܐ ܕܓܕܫܐ ܡܢ ܗܘ ܟܢܫܐ ܟܠܢܝܐ. ܕܪ̈ܓܐ ܕܚܐܪܘܬܐ: df = n − 1، ܐܡܢ ܕܚܕܝܘܬܐ ܙܘܓܐ ܝܠܗ (Gravetter & Wallnau, pp. 341-342).

ܩܐ ܡܘܕܝ ܬܘܩܢܐ ܙܘܓܢܝܐ ܚܝܠܢܐ ܝܬܝܪ ܝܠܗ. Gravetter ܘ-Wallnau (ܦܐ̈ܬܐ 353-354، ܠܘܚܐ 11.4) ܟܡܚܘܝ ܐܗܐ ܥܠ ܗܢܝ ܡܢܝ̈ܢܐ ܚܬܝܬܐܝܬ: ܬܠܬܐ ܡܫܬܘܬܦ̈ܢܐ، ܦܘܪܫܢܐ ܡܨܥܝܐ ܕ-5 ܢܘܩ̈ܙܐ. ܐܝܟ ܒܘܚܪܢܐ ܠܠܐ ܬܠܝ̈ܐ – ܫܘܚܠܦܐ (variance) ܓܘ ܟܠ ܫܪܛܐ ܟܥܒܥܒ ܦܘܪ̈ܫܢܐ ܪ̈ܒܐ ܒܝܢܝ ܐܢܫ̈ܐ (Bill 33، John 18)، ܛܥܝܘܬܐ ܬܩܝܢܬܐ 5.77، t = 0.87، ܠܐ ܪܫܝܡܐ. ܐܝܟ ܡܫܘ̈ܚܬܐ ܡܬܢ̈ܝܬܐ – ܦܘܪ̈ܫܢܐ ܒܝܢܝ ܐܢܫ̈ܐ ܟܓܢܒܝ ܓܘ ܦܘܪ̈ܫܢܐ (ܟܠ ܚܕ ܢܚܬܠܗ ܒܟܡܐ ܢܘܩ̈ܙܐ)، ܛܥܝܘܬܐ ܬܩܝܢܬܐ 1.15، t = −4.35، ܪܫܝܡܐ. ܟܠ ܡܫܬܘܬܦܢܐ ܟܦܠܚ ܐܝܟ ܓܘܕܐ ܕܦܘܚܡܐ ܕܓܢܗ. Field (ܦܣܩܐ 10.9.4) ܟܟܬܒ ܗܘ ܚܘܫܒܐ ܒܐܘܪܚܐ ܕܐܣܘܪܐ ܕܚܕ̈ܕܐ ܕܓܘ ܠܘܚܐ 2: ܐܝܟܡܐ ܕܡܫܘ̈ܚܬܐ ܐܣܝܪ̈ܐ ܝܬܝܪ ܝܢܐ، ܣܛܝܘܬܐ ܬܩܝܢܬܐ ܕܦܘܪ̈ܫܢܐ ܙܥܘܪܬܐ ܝܬܝܪ ܝܠܗ̇ ܘܒܘܚܪܢܐ ܪܓܝܫܐ ܝܬܝܪ ܝܠܗ.

ܩܪܝܢܐ ܕܡܦܩܢܐ (How to read the output)

ܬܠܬܐ ܠܘ̈ܚܐ (tables) ܐܢܝ ܝܢܐ ܬܠܬܐ ܠܘ̈ܚܐ ܕ-SPSS (Pallant, 2020, Chapter 17; Field, 2024, Section 10.9.4):

ܠܘܚܐ 1 – ܣܛܐܛܝܣܛܝܩܐ ܡܚܘܝܢܝܬܐ ܕܬܪܬܝܢ ܡܫܘ̈ܚܬܐ (Paired Samples Statistics): ܡܨܥܝܬܐ، N، ܣܛܝܘܬܐ ܬܩܝܢܬܐ ܘܛܥܝܘܬܐ ܬܩܝܢܬܐ ܕܟܠ ܡܫܘܚܬܐ، ܥܠ ܡܫܬܘܬܦ̈ܢܐ ܕܐܝܬܠܗܘܢ ܬܪܘܝܗܝ. Pallant ܟܫܪܝܐ ܠܐܟܐ "ܕܪܓܐ 2": ܒܬܪ ܕܡܫܟܚܐ ܝܠܗ ܦܘܪܫܢܐ ܪܫܝܡܐ، ܓܘ ܐܗܐ ܠܘܚܐ ܟܚܙܚ ܠܐܝܢܐ ܐܘܪܚܐ – ܐܝܢܐ ܡܫܘܚܬܐ ܪܡܬܐ ܝܬܝܪ ܝܠܗ̇. Field ܟܡܥܝܪ ܕܡܢܝ̈ܢܐ ܕܠܐܟܐ ܫܘ̈ܝܐ ܝܢܐ ܠܡܢܝ̈ܢܐ ܕܗܢܝ ܝܗܝ̈ܒܬܐ ܓܘ ܬܘܩܢܐ ܠܐ ܬܠܝܐ؛ ܡܐ ܕܟܫܚܠܦ ܠܘܚܐ 3 ܝܠܗ.

ܠܘܚܐ 2 – ܐܣܘܪܐ ܕܚܕ̈ܕܐ (Paired Samples Correlations): ܐܣܘܪܐ ܕܚܕ̈ܕܐ ܕ-Pearson (Pearson correlation) ܒܝܢܝ ܬܪܬܝܢ ܡܫܘ̈ܚܬܐ ܥܡ p. ܓܘ Field (ܦܣܩܐ 10.9.4) ܐܝܗܘ ܪܡܐ ܘܪܫܝܡܐ ܝܠܗ ܓܘ ܡܬܠܐ ܕܓܘܠܬܐ ܕܓܢܒܘܬܐ ܡܢ ܥܝ̈ܢܐ (invisibility cloak؛ r = .806, p = .002) – ܐܝܟ ܕܡܣܟܝܐ ܗܘܐ، ܩܐ ܕܬܪܬܝܢ ܡܫܘ̈ܚܬܐ ܐܬܝܠܗܝ ܡܢ ܗܢܝ ܐܢܫ̈ܐ ܘܐܢܫ̈ܐ ܡܬܢ̈ܝܐ ܝܢܐ ܥܡ ܓܢܗܘܢ. ܓܘ Pallant (ܨܚܚܐ 17) r = .862 ܒܝܢܝ ܙܕܥܬܐ ܡܢ ܣܛܐܛܝܣܛܝܩܐ ܓܘ ܙܒܢܐ 1 ܘܓܘ ܙܒܢܐ 2. ܐܣܘܪܐ ܕܚܕ̈ܕܐ ܢܚܝܬܐ ܠܐ ܝܠܗ ܛܥܝܘܬܐ، ܐܠܐ ܟܐܡܪ ܕܬܘܩܢܐ ܙܘܓܢܝܐ ܩܪܝܒ ܠܐ ܟܡܘܬܪ ܡܕܡ (Gravetter & Wallnau, p. 354) – ܘܒܥܕ̈ܢܐ ܕܙܘܓܐ ܓܘ ܦܐܝܠ ܛܥܝܐ ܝܠܗ.

ܠܘܚܐ 3 – ܦܘܪ̈ܫܢܐ (Paired Samples Test): ܡܨܥܝܬܐ ܕܦܘܪ̈ܫܢܐ (M_D؛ ܩܕܡܝܬܐ ܒܨܝܪ ܬܪܝܢܝܬܐ، ܐܝܟ ܓܘ SPSS)، ܣܛܝܘܬܐ ܬܩܝܢܬܐ ܕܦܘܪ̈ܫܢܐ، ܛܥܝܘܬܐ ܬܩܝܢܬܐ ܕܝܠܗܘܢ، ܬܚܘܡܐ ܕܬܘܟܠܢܐ (confidence interval) 95% ܩܐ ܦܘܪܫܢܐ، ܘܒܬܪܗ t، df ܘ-p ܕܬܪܝܢ ܕܘܢ̈ܒܐ. Pallant (ܨܚܚܐ 17، "ܕܪܓܐ 1"): ܩܕܡܝܐ ܟܚܙܚ ܒܥܡܘܕܐ ܕ-Sig. (2-tailed) – ܙܥܘܪܐ ܡܢ .05، ܐܝܬ ܦܘܪܫܢܐ ܪܫܝܡܐ؛ ܟܟܬܒܚ t، df ܘܦܘܪܫܢܐ ܥܡ ܬܚܘܡܐ ܕܬܘܟܠܢܐ. Field (ܦܣܩܐ 10.9.4) ܟܦܪܩ ܡܢܝ̈ܢܐ: t = −1.25/0.329 = −3.804، df = N − 1 = 11، p = .003 – "ܒܣ 0.3% ܣܟܘܝܐ ܩܐ t ܗܕܟܐ ܐܢ ܡܨܥܝܬܐ ܕܦܘܪ̈ܫܢܐ ܓܘ ܟܢܫܐ ܟܠܢܝܐ ܨܦܪܐ ܝܠܗ̇". ܐܬܐ ܕ-t ܘܕܦܘܪܫܢܐ ܬܠܐ ܝܠܗ ܒܣ ܒܛܟܣܐ ܕܓܒܝܠܘܟܘܢ: ܐܢ ܡܫܘܚܬܐ ܬܪܝܢܝܬܐ ܪܡܬܐ ܝܠܗ̇، ܦܘܪܫܢܐ ܬܚܘܬ ܨܦܪܐ ܝܠܗ. ܬܚܘܡܐ ܕܬܘܟܠܢܐ. ܦܬܝܘܬܐ (range) ܕܓܘܗ̇، ܒܕܪܓܐ ܕܬܘܟܠܢܐ 95%، ܐܝܬ ܡܨܥܝܬܐ ܕܦܘܪ̈ܫܢܐ ܓܘ ܟܢܫܐ ܟܠܢܝܐ (Gravetter & Wallnau, pp. 348-349, Equation 11.5): ܐܡܢ ܕܟܥܒܥܒ ܨܦܪܐ ܒܘܚܪܢܐ ܠܐ ܪܫܝܡܐ ܝܠܗ، ܘܒܗܦܟܐ – ܗܘ ܦܘܣܩܢܐ ܒܬܪܬܝܢ ܠܫܢ̈ܐ. ܐܝܟܡܐ ܕܕܘܡܝܐ ܙܥܘܪܐ ܝܠܗ، ܬܚܘܡܐ ܦܬܝܐ ܝܠܗ، ܘܡܛܠ ܗܕܐ ܐܝܗܘ ܬܚܘܝܬܐ ܝܠܗ ܕܦܘܠܓ ܪܥܝܢܐ (uncertainty) ܘܠܐ ܡܚܘܝܢܐ ܕܟܝܐ ܕܪܒܘܬܐ ܕܡܥܒܕܢܘܬܐ (ܦܐܬܐ 349).

ܪܒܘܬܐ ܕܡܥܒܕܢܘܬܐ (effect size)

ܪܫܝܡܘܬܐ (significance) ܠܐ ܝܠܗ̇ ܪܒܘܬܐ: ܓܘ ܕܘܡܝܐ (sample) ܪܒܐ ܐܦ ܫܘܢܝܐ ܙܥܘܪܐ ܒܣܓܝ ܟܦܠܛ ܪܫܝܡܐ (Field, 2024, Section 3.7.3). ܠܘܚܐ ܟܛܒܥ ܬܠܬܐ ܡܚܘ̈ܝܢܐ، ܩܐ ܕܬܠܬܐ ܡܒܘ̈ܥܐ ܟܡܘܕܥܝ ܡܚܘ̈ܝܢܐ ܦܪ̈ܝܫܐ – ܘܦܐܬܐ ܟܡܚܘܝܐ ܟܠܗܘܢ:

ܡܘܢܐ ܝܠܗ ܦܘܪܫܢܐ ܓܘ ܥܒܕܐ: d_z ܟܡܫܘܚ ܡܬܢܝܘܬܐ ܕܫܘܢܝܐ ܓܘ ܐܢܫ̈ܐ، ܘܡܛܠ ܗܕܐ ܬܠܐ ܝܠܗ ܒܐܣܘܪܐ ܕܚܕ̈ܕܐ – ܐܣܘܪܐ ܪܡܐ ܟܡܙܥܪ ܣܛܝܘܬܐ ܬܩܝܢܬܐ ܕܦܘܪ̈ܫܢܐ ܘܟܡܪܒܐ ܠܗ؛ d ܬܪܝܨܐ ܘܐܝܬܐ ܡܪܒܥܐ ܩܪܝܒ̈ܐ ܝܬܝܪ ܝܢܐ ܠܡܐ ܕܗܘܐ ܡܬܩܒܠܐ ܓܘ ܬܘܩܢܐ ܠܐ ܬܠܝܐ. ܩܘܛܝܐ ܕ"ܩܪܝܢܐ ܕܦܐܪܐ" ܕܓܘ ܡܦܩܢܐ ܟܡܚܘܝܐ ܬܠܬܝܗܘܢ ܘܟܐܡܪܐ ܐܢ ܐܢܝ ܟܡܫܥܝ ܗܝ̇ ܬܫܥܝܬܐ. Gravetter ܘ-Wallnau (ܦܐ̈ܬܐ 350-351، ܨܘܪ̈ܬܐ 11.3-11.4) ܟܡܚܘܝ: ܗܘ ܦܘܪܫܢܐ ܡܨܥܝܐ ܕ-2 ܢܘܩ̈ܙܐ ܥܡ s = 2 ܡܥܒܕܢܘܬܐ ܪܒܬܐ ܘܪܫܝܡܬܐ ܝܠܗ̇، ܘܥܡ s = 6 – ܐܡܢ ܕܡܢܬܐ ܟܣܠܩܝ ܘܡܢܬܐ ܟܢܚܬܝ – ܠܐ ܪܫܝܡܬܐ ܝܠܗ̇: "ܫܘܚܠܦܐ ܪܒܐ ܟܡܥܡܛ ܨܘܪ̈ܬܐ".

ܫܪ̈ܛܐ ܘܙܘܗܪ̈ܐ (Assumptions and warnings)

ܬܪܝܢ ܫܪ̈ܛܐ (assumptions؛ Gravetter & Wallnau, 2017, p. 346): ܚܙ̈ܝܬܐ (observations) ܓܘ ܟܠ ܫܪܛܐ ܠܐ ܬܠܝ̈ܬܐ ܝܢܐ ܚܕܐ ܒܚܕܐ (ܐܢܫ̈ܐ ܦܪ̈ܝܫܐ)، ܘܦܘܠܓܐ (distribution) ܕܦܘܪ̈ܫܢܐ ܓܘ ܟܢܫܐ ܟܠܢܝܐ ܢܘܪܡܠܝܐ ܝܠܗ. Field (2024، ܦܣܩܐ 10.9.2) ܟܡܚܬܬ: ܡܐ ܕܐܝܬܠܗ ܐܪܙܐ ܝܠܗ ܦܘܠܓܐ ܕܦܘܪ̈ܫܢܐ، ܠܐ ܡܢܝ̈ܢܐ ܒܓܢܒܗܘܢ – "ܡܨܝܐ ܕܬܪܬܝܢ ܡܫܘ̈ܚܬܐ ܠܐ ܢܘܪܡܠܝ̈ܐ ܓܠܝܐܝܬ ܝܗܒܝ ܦܘܪ̈ܫܢܐ ܕܦܠܝܓܝ ܫܦܝܪܐܝܬ"؛ ܡܛܠ ܗܕܐ ܐܢ ܟܒܚܪܚ ܢܘܪܡܠܝܘܬܐ (normality)، ܟܚܫܒܚ ܥܡܘܕܐ ܕܦܘܪܫܢܐ ܘܟܒܚܪܚ ܠܗ (ܦܐܬܐ ܣܓܝܐܘ̈ܬܐ ܘܣܛܐܛܝܣܛܝܩܐ ܡܚܘܝܢܝܬܐ؛ ܛܝ̈ܡܐ ܢܘܟܪ̈ܝܐ – ܦܐܬܐ ܛܝ̈ܡܐ ܢܘܟܪ̈ܝܐ ܘܫܪ̈ܛܐ). Pallant (ܨܚܚܐ 17) ܘ-Gravetter ܘ-Wallnau (ܦܐܬܐ 346) ܫܠܝܡܝ ܝܢܐ ܕܓܘ ܕܘܡܝܐ ܕ-30 ܙܘܓ̈ܐ ܘܠܥܠ ܬܘܒܪܐ ܠܐ ܟܡܙܝܥ؛ ܓܘ ܕܘܡܝܐ ܙܥܘܪܐ ܥܡ ܦܘܪ̈ܫܢܐ ܠܐ ܢܘܪܡܠܝ̈ܐ – Wilcoxon، ܝܢ ܬܚܘ̈ܡܐ ܕܬܘܟܠܢܐ ܒ-bootstrap (Field, Section 10.9.5) ܘܒܘܚܪܢܐ t ܚܣܝܢܐ (Yuen) – ܕܠܝܬ ܓܘ ܦܐܬܐ.

ܙܘܓܐ ܓܪܓ ܕܗܘܐ ܬܪܝܨܐ. ܣܕܪܐ ܡܫܬܘܬܦܢܐ ܝܠܗ: ܬܪܬܝܢ ܡܫܘ̈ܚܬܐ ܓܘ ܗܘ ܣܕܪܐ ܕܗܘ ܐܢܫܐ ܝܢܐ (ܝܢ ܕܗܘ ܙܘܓܐ ܡܦܐܝܐ). ܦܐܝܠ ܕܡܛܟܣܐ ܝܠܗ ܡܢ ܪܝܫ ܒܥܡܘܕܐ ܚܕ ܒܠܚܘܕ ܟܚܪܒ ܙܘܓܐ ܕܠܐ ܚܕ ܡܘܕܥܢܘܬܐ ܕܛܥܝܘܬܐ – ܐܣܘܪܐ ܕܚܕ̈ܕܐ ܓܘ ܠܘܚܐ 2 ܝܠܗ ܒܘܚܪܢܐ ܕܚܘܠܡܢܐ: ܐܣܘܪܐ ܩܪܝܒ ܠܨܦܪܐ ܒܝܢܝ "ܩܕܡ" ܘ"ܒܬܪ" ܕܗܝ̇ ܦܢܩܝܬܐ ܕܫܘܐ̈ܠܐ ܩܪܝܒ ܟܠ ܙܒܢܐ ܥܣܩܘܬܐ ܕܝܗܝ̈ܒܬܐ ܝܠܗ̇.

ܛܝ̈ܡܐ ܚܣܝ̈ܪܐ (missing values). ܡܫܬܘܬܦܢܐ ܕܚܣܝܪܐ ܝܠܗ̇ ܚܕܐ ܡܢ ܬܪܬܝܢ ܡܫܘ̈ܚܬܐ ܠܐ ܥܠܝܠܐ ܝܠܗ ܟܠܗ – ܠܝܬܠܗ ܦܘܪܫܢܐ (/MISSING=ANALYSIS، ܓܘܒܝܐ ܡܩܕܡܐ ܕ-SPSS)؛ ܦܐܬܐ ܟܡܘܕܥܐ ܟܡܐ ܢܦܠܠܗܘܢ. ܓܘ ܩܕܡ-ܒܬܪ ܐܗܐ ܢܦܠܬܐ ܝܠܗ̇ (attrition): ܐܢ ܐܢܝ ܕܢܦܠܠܗܘܢ ܦܪ̈ܝܫܐ ܝܢܐ ܡܢ ܐܢܝ ܕܦܝܫܠܗܘܢ، ܦܘܚܡܐ ܡܨܠܝܐ ܝܠܗ. ܡܘܢܐ ܕܥܒܕܚ ܥܡ ܚܣܝ̈ܪܐ – ܦܐܬܐ ܛܝ̈ܡܐ ܚܣܝ̈ܪܐ.

ܛܟܣܐ، ܙܒܢܐ ܘܡܪܓܠܢܘܬܐ. Gravetter ܘ-Wallnau (ܦܐ̈ܬܐ 354-355): ܒܨܝܪܘܬܐ ܕܡܫܘ̈ܚܬܐ ܡܬܢ̈ܝܬܐ ܝܠܗ̇ ܕܥܠ̈ܠܬܐ ܕܟܫܚܠܦܝ ܥܡ ܙܒܢܐ – ܪܓܫܐ ܕܢܦܫܐ، ܚܘܠܡܢܐ، ܐܐܪ – ܘܢܣܝܘܢܐ ܓܘ ܡܫܘܚܬܐ ܩܕܡܝܬܐ (ܡܥܒܕܢܘܬܐ ܕܡܪܓܠܢܘܬܐ، ܡܥܒܕܢܘܬܐ ܕܛܟܣܐ) ܡܨܝ ܕܫܚܠܦܝ ܡܢܝܢܐ ܬܪܝܢܝܐ ܕܠܐ ܐܣܘܪܐ ܥܡ ܐܣܝܘܬܐ. ܐܣܝܘܬܐ ܕܬܘܩܢܐ: ܫܘܝܘܬܐ ܕܛܟܣܐ (counterbalancing) – ܦܠܓܐ ܕܡܫܬܘܬܦ̈ܢܐ ܒܛܟܣܐ ܐ-ܒ ܘܦܠܓܐ ܒ-ܐ؛ ܐܡܢ ܕܡܣܟܝ̈ܐ ܝܢܐ ܡܥܒܕ̈ܢܘܝܬܐ ܚܝܠܢ̈ܝܬܐ ܕܙܒܢܐ ܝܢ ܕܛܟܣܐ، ܬܘܩܢܐ ܠܐ ܬܠܝܐ ܛܒܐ ܝܬܝܪ ܝܠܗ. Pallant (ܨܚܚܐ 17، "ܙܘܗܪܐ"): ܦܘܪܫܢܐ ܪܫܝܡܐ ܩܕܡ-ܒܬܪ ܠܐ ܝܠܗ ܚܘܘܝܐ ܕܡܥܠܬܐ ܥܒܕܠܗ̇ ܠܗ – ܥܒܪܬܐ ܕܙܒܢܐ ܘܓܕܫ̈ܐ ܐܚܪ̈ܢܐ ܡܨܝ ܕܡܦܫܩܝ ܠܗ؛ ܓܘܕܐ ܕܦܘܚܡܐ (control group) ܕܠܐ ܩܒܠܠܗ ܡܥܠܬܐ ܗܘܐ ܡܛܝܒ ܬܘܩܢܐ.

ܬܚܘ̈ܡܐ ܕܬܘܟܠܢܐ ܕܓܘ ܨܘܪܬܐ. Field (ܦܣܩܐ 10.9.2) ܟܙܗܪ: ܬܚܘ̈ܡܐ ܕܬܘܟܠܢܐ (confidence intervals) ܕܟܠ ܡܫܘܚܬܐ ܒܦܪܝܫܘܬܐ ܟܛܥܝ ܡܢ ܙܘܓܐ، ܘܓܘ ܡܫܘ̈ܚܬܐ ܡܬܢ̈ܝܬܐ ܡܨܝ ܕܥܒܪܝ ܚܕ ܥܠ ܚܕ ܐܦ ܐܡܢ ܕܦܘܪܫܢܐ ܪܫܝܡܐ ܝܠܗ ܒܣܓܝ (ܐܝܗܘ ܟܡܩܪܒ ܬܘܪܨܐ ܠܦܘܬ ܡܨܥܝܬܐ ܕܡܫܬܘܬܦܢܐ). ܨܘܪܬܐ ܓܘ ܦܐܬܐ ܟܡܚܘܝܐ ܐܢܝ ܐܝܟ ܬܚܘܝܬܐ ܕܟܠ ܡܫܘܚܬܐ؛ ܬܚܘܡܐ ܕܦܣܩ ܝܠܗ ܬܚܘܡܐ ܕܬܘܟܠܢܐ ܩܐ ܦܘܪܫܢܐ ܕܓܘ ܠܘܚܐ 3.

ܡܘܕܝ ܠܐ ܟܚܫܒܐ ܐܗܐ ܦܐܬܐ. ܬܚܘܡܐ ܕܬܘܟܠܢܐ ܩܐ d (SPSS 27 ܘܠܥܠ ܟܛܒܥ ܠܗ – Field، ܦܣܩܐ 10.9.6)، bootstrap ܘܒܘܚܪܢܐ t ܚܣܝܢܐ (Yuen – Field, Section 10.9.5)، ܒܘܚܪܢܐ ܕܚܕ ܕܘܢܒܐ (Gravetter & Wallnau، ܦܐ̈ܬܐ 345-346، ܡܬܠܐ 11.3 – ܐܘܪܚܐ ܕܬܪܝܢ ܕܪ̈ܓܐ)، ܦܘܫܩܐ ܕܫܘܚܠܦܐ ܠܡܫܘ̈ܚܬܐ ܡܬܢ̈ܝܬܐ، Bayes factor (Field, Section 10.9.7)، ܘܟܡܐ ܙܘܓ̈ܐ ܒܕܚܝܬܐ ܚܕܐ (SPSS ܟܝܗܒ؛ ܠܐܟܐ ܙܘܓܐ ܚܕ ܓܘ ܟܠ ܙܒܢܐ – ܘܐܡܢ ܕܟܡܪܗܛܚ ܟܡܐ، ܟܠ ܒܘܚܪܢܐ ܛܥܝܢܐ ܝܠܗ ܣܘܟܢܐ ܕ-5% ܕܛܥܝܘܬܐ ܕܙܢܐ I). ܚܠܦܐ ܠܐ ܦܪܡܝܛܪܝܐ، Wilcoxon ܠܕܘ̈ܡܝܐ ܙܘܓܢ̈ܝܐ – ܓܘ ܦܐܬܐ ܕܝܠܗ.

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

ܡܥܝܪܢܘܬܐ ܕܢܘܣ̈ܚܐ. ܐܘܪܚܐ ܩܝܡܬܐ ܝܠܗ̇؛ ܡܢ ܢܘܣܚܐ 27 ܕܝܠܘܓ ܐܝܬ ܓܘܗ Estimate effect sizes ܘܟܛܒܥ ܠܘܚܐ Paired Samples Effect Sizes ܥܡ Cohen's d ܘܬܚܘܡܐ ܕܬܘܟܠܢܐ، ܘܓܘܗ ܐܦ ܓܘܒܝܐ ܕܡܬܩܢܢܐ (Standardizer): ܣܛܝܘܬܐ ܬܩܝܢܬܐ ܕܦܘܪ̈ܫܢܐ (d_z، ܓܘܒܝܐ ܡܩܕܡܐ)، ܬܪܝܨܬܐ ܩܐ ܐܣܘܪܐ ܕܚܕ̈ܕܐ (d ܕ-Field، ܦܣܩܐ 10.9.3)، ܝܢ ܡܨܥܝܬܐ ܕܫܘܚܠ̈ܦܐ. Pallant (2020، ܠܦܘܬ ܢܘܣܚܐ 26) ܟܟܬܒܐ ܕ-SPSS "ܠܐ ܟܝܗܒ ܪܒܘܬܐ ܕܡܥܒܕܢܘܬܐ ܩܐ ܒܘܚܪ̈ܢܐ t" ܘܟܚܫܒܐ ܐܝܬܐ ܡܪܒܥܐ ܒܐܝܕܐ. ܓܘ ܢܘܣ̈ܚܐ ܥܬܝ̈ܩܐ – ܫܩܘܠܘܢ ܣܕܪܐ ܕ-/ES ܡܢ ܣܝܢܬܐܟܣ.

ܐܘܪܚܐ (Pallant, 2020, Chapter 17; Field, 2024, Section 10.9.3): Analyze › Compare Means › Paired-Samples T Test… – ܟܪܫܡܚ ܬܪܝܢ ܡܫܬܚܠܦ̈ܢܐ (ܩܕܡܝܐ، ܘܒܬܪܗ ܥܡ Ctrl ܬܪܝܢܝܐ) ܘܟܥܒܪܚ ܠܗܘܢ ܐܟܚܕܐ ܠܩܘܛܝܐ Paired Variables؛ ܛܟܣܐ ܟܦܣܩ ܐܘܪܚܐ ܕܦܘܪܫܢܐ (Variable1 − Variable2). ܡܨܝܚ ܕܡܘܣܦܚ ܙܘܓ̈ܐ ܐܚܪ̈ܢܐ ܓܘ ܗܘ ܕܝܠܘܓ. Options… – ܕܪܓܐ ܕܬܚܘܡܐ ܕܬܘܟܠܢܐ (95%) ܘܥܒܕܐ ܥܡ ܚܣܝ̈ܪܐ؛ Bootstrap… – ܬܚܘ̈ܡܐ ܕܬܘܟܠܢܐ BCa ܕܠܐ ܟܡܣܡܝ ܢܘܪܡܠܝܘܬܐ (Field, Section 10.9.5). ܣܝܢܬܐܟܣ:

T-TEST PAIRS=עמדות_ציון WITH עמדות_ציון_2 (PAIRED)
  /ES DISPLAY(TRUE) STANDARDIZER(SD)
  /CRITERIA=CI(.9500)
  /MISSING=ANALYSIS.

ܩܪܝܢܐ ܕܡܦܩܢܐ. Paired Samples Statistics = ܠܘܚܐ 1 (Mean, N, Std. Deviation, Std. Error Mean)؛ Paired Samples Correlations = ܠܘܚܐ 2 (N, Correlation, Sig.؛ ܓܘ SPSS 27 ܘܠܥܠ Two-Sided p)؛ Paired Samples Test = ܠܘܚܐ 3 – ܬܚܘܬ Paired Differences: Mean, Std. Deviation, Std. Error Mean, 95% Confidence Interval of the Difference (Lower, Upper)، ܘܒܬܪܗ t, df, Sig. (2-tailed) (ܓܘ 27 ܘܠܥܠ One-Sided p ܘ-Two-Sided p – ܟܡܘܕܥܚ ܕܬܪܝܢ ܓܢ̈ܒܐ)؛ Paired Samples Effect Sizes – ܣܕܪܐ ܕ-Cohen's d، ܥܡܘܕܐ ܕ-Point Estimate، ܐܝܗܘ ܝܠܗ d_z ܕܓܘ ܡܥܝܪܢܘܬܐ ܕܠܘܚܐ (Hedges' correction – ܠܝܬ ܓܘ ܦܐܬܐ). ܩܦܬܘܪܐ "ܡܚܬܬܐ ܕܣܝܢܬܐܟܣ SPSS" ܓܘ ܡܦܩܢܐ ܟܒܢܐ ܛܥܢܐ، ܟܬܒܐ ܕܪ̈ܡܙܐ (ܐܢ ܗܘܐ ܡܦܫܩܢܐ) ܘܦܘܩܕܢܐ T-TEST PAIRS ܥܠ ܙܘܓܐ ܕܓܒܝܐ ܝܠܗ.

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

ܓܘ R ܫܬܐܣܝܐ t.test(x, y, paired = TRUE) ܟܝܗܒ ܠܘܚܐ 3 (ܦܘܪܫܢܐ x − y)، ܘ-cor.test(x, y) ܠܘܚܐ 2. R ܡܢ ܓܢܗ ܟܛܥܐ ܡܢ ܣܕܪ̈ܐ ܕܓܘܝܗܘܢ ܚܕܐ ܡܢ ܡܫܘ̈ܚܬܐ ܚܣܝܪܐ ܝܠܗ̇ (ܥܡ paired = TRUE ܟܫܩܠ ܙܘܓܐ). d_z، d ܬܪܝܨܐ ܘ-η² ܚܫܝ̈ܒܐ ܝܢܐ ܒܐܝܕܐ ܡܢ ܡܥܠܝ̈ܬܐ ܕܓܘ ܡܕܒܪܢܐ (guide). ܣܩܪܝܦܬ (script) ܪܗܝܛܐ ܝܠܗ ܐܝܟ ܕܐܝܬܘܗܝ ܥܠ ܦܐܝܠ ܕܡܬܠܐ ܘܝܗܒܠܗ ܛܝ̈ܡܐ ܕܠܘ̈ܚܐ (ܓܘ ܡܥܝܪ̈ܢܘܬܐ). ܢܡܘܣܐ ܕܣܐܝܛ ܩܐ ܣܘܪܝܬ ܓܘ R: ܦܐܝܠ UTF-8، ܟܠ ܣܕܪܐ ܕܡܥܝܪܢܘܬܐ ܟܫܪܐ ܒܡܠܬܐ ܕܣܘܪܝܬ، ܘܐܬܪܐ ܕ-UTF-8 ܩܐ ܫܡ̈ܗܐ ܥܒܪ̈ܝܐ (ܓܘ Windows: R 4.2 ܘܠܥܠ، ܝܢ Sys.setlocale('LC_ALL', 'Hebrew')).

# ܒܘܚܪܢܐ t ܠܕܘ̈ܡܝܐ ܙܘܓܢ̈ܝܐ – ܦܪܘܦܣܘܪ ܣܛܐܛ. ܐܗܐ ܦܐܝܠ ܢܛܝܪܐ ܝܠܗ ܒ-UTF-8؛ ܟܠ ܣܕܪܐ ܕܡܥܝܪܢܘܬܐ ܟܫܪܐ ܒܡܠܬܐ ܕܣܘܪܝܬ
library(readxl)   # ܩܪܝܢܐ ܕܐܩܣܠ

# ܛܥܢܐ: ܛܘܦܣܐ ܬܩܝܢܐ – ܣܕܪܐ = ܡܫܬܘܬܦܢܐ، ܥܡܘܕܐ = ܡܫܬܚܠܦܢܐ؛ ܓܠܝܘܢܐ "נתונים"
d <- read_excel("C:/Rdata/DATA_tpaired_example_heb.xlsx", sheet = "נתונים")
ok <- complete.cases(d[["עמדות_ציון"]], d[["עמדות_ציון_2"]])   # ܒܣ ܡܫܬܘܬܦ̈ܢܐ ܥܡ ܬܪܬܝܢ ܡܫܘ̈ܚܬܐ (113 ܡܢ 120)
x <- d[["עמדות_ציון"]][ok]; y <- d[["עמדות_ציון_2"]][ok]

# ܠܘܚܐ 1 – ܣܛܐܛܝܣܛܝܩܐ ܕܬܪܬܝܢ ܡܫܘ̈ܚܬܐ
rbind(ראשונה = c(n = length(x), M = mean(x), SD = sd(x)), שנייה = c(n = length(y), M = mean(y), SD = sd(y)))
# ܦܐܪܐ: ראשונה n 113, M 3.262, SD 0.754؛ שנייה n 113, M 3.412, SD 0.731

# ܠܘܚܐ 2 – ܐܣܘܪܐ ܕܚܕ̈ܕܐ ܒܝܢܝ ܡܫܘ̈ܚܬܐ
cor.test(x, y)                       # r = .852, p < .001

# ܠܘܚܐ 3 – ܒܘܚܪܢܐ t ܠܙܘܓܢ̈ܝܐ (ܦܘܪܫܢܐ = x − y)
t.test(x, y, paired = TRUE)          # t = -3.94, df = 112, p < .001، ܦܘܪܫܢܐ -0.150، ܬܚܘܡܐ ܕܬܘܟܠܢܐ [-0.226, -0.075]

# ܪܒܘܬܐ ܕܡܥܒܕܢܘܬܐ: dz، d ܬܪܝܨܐ ܩܐ ܐܣܘܪܐ، ܘܐܝܬܐ ܡܪܒܥܐ = t²/(t² + df)
D <- x - y; r <- cor(x, y)
mean(D) / sd(D)                                         # dz = -0.370
mean(D) / (sd(D) / sqrt(2 * (1 - r)))                   # d ܬܪܝܨܐ = -0.202
tt <- t.test(x, y, paired = TRUE); unname(tt$statistic^2 / (tt$statistic^2 + tt$parameter))   # ܐܝܬܐ ܡܪܒܥܐ = .122

ܬܘܢܝܐ ܕܡܫܟܚ̈ܢܘܬܐ (reporting the results)

ܟܡܘܕܥܚ ܡܫܟܚܢܘܬܐ ܘܒܬܪܗ̇ ܣܛܐܛܝܣܛܝܩܐ: ܡܨܥܝܬܐ (mean) ܘܣܛܝܘܬܐ ܬܩܝܢܬܐ (standard deviation؛ ܝܢ ܛܥܝܘܬܐ ܬܩܝܢܬܐ) ܕܟܠ ܡܫܘܚܬܐ، t ܥܡ ܕܪ̈ܓܐ ܕܚܐܪܘܬܐ ܓܘ ܩܘܫ̈ܬܐ، p ܚܬܝܬܐ، ܦܘܪܫܢܐ ܥܡ ܬܚܘܡܐ ܕܬܘܟܠܢܐ، ܘܪܒܘܬܐ ܕܡܥܒܕܢܘܬܐ (Field, 2024, Section 10.10; Gravetter & Wallnau, 2017, p. 349; American Psychological Association [APA], 2020, Section 6.43). ܡܬܠܐ ܕ-Pallant (2020، ܨܚܚܐ 17): "ܡܫܟܚܐ ܝܠܗ̇ ܢܚܬܬܐ ܪܫܝܡܬܐ ܣܛܐܛܝܣܛܝܩܐܝܬ ܓܘ ܡܢܝ̈ܢܐ ܕ-FOST ܡܢ ܙܒܢܐ 1 (M = 40.17, SD = 5.16) ܠܙܒܢܐ 2 (M = 37.5, SD = 5.15)، t(29) = 5.39, p < .001 (ܕܬܪܝܢ ܕܘܢ̈ܒܐ). ܢܚܬܬܐ ܡܨܥܝܬܐ ܗܘܝܐ 2.67، ܥܡ ܬܚܘܡܐ ܕܬܘܟܠܢܐ 95% ܡܢ 1.66 ܗܠ 3.68. ܐܝܬܐ ܡܪܒܥܐ (.50) ܚܘܝܠܗ ܪܒܘܬܐ ܕܡܥܒܕܢܘܬܐ ܪܒܬܐ." ܡܬܠܐ ܕ-Field (ܦܣܩܐ 10.10.1)، ܥܠ ܗܢܝ ܝܗܝ̈ܒܬܐ ܐܝܟ ܬܘܩܢܐ ܙܘܓܢܝܐ: "ܦܘܪܫܢܐ، −1.25، BCa 95% CI [−1.75, −0.75]، ܪܫܝܡܐ ܗܘܐ، t(11) = −3.80, p = .003، ܘܚܘܝܠܗ ܡܥܒܕܢܘܬܐ ܕ-d = 0.68 [−1.19, −0.18]". Gravetter ܘ-Wallnau (ܦܐܬܐ 349): "ܫܘܢܝܐ ܡܢ ܡܠܬܐ ܡܨܥܝܬܐ ܠܨܘܚܝܬܐ ܙܥܪܠܗ ܟܐܒܐ ܕܡܬܪܓܫ ܒܡܨܥܝܬܐ ܒ-M = 2.00 ܢܘܩ̈ܙܐ، SD = 2.00. ܡܥܒܕܢܘܬܐ ܪܫܝܡܬܐ ܗܘܝܐ، t(8) = −3.00, p = .017, r² = 0.529" – ܘܐܡܢ ܕ-p ܚܬܝܬܐ ܐܝܬܠܗ ܡܢ ܡܚܫܒܢܐ، ܟܡܘܕܥܚ ܠܗ ܘܠܐ p < .05.

ܢܡܘ̈ܣܐ ܕܐܣܟܝܡܐ (APA, 2020, Section 6.36): t، ܦܘܪܫܢܐ ܘ-d ܥܡ ܨܦܪܐ ܩܕܡ ܢܘܩܙܐ (ܡܨܝ ܕܣܠܩܝ ܠܥܠ ܡܢ 1)، p، r ܘ-η² ܕܠܐ (ܠܐ ܡܨܝ). ܡܐܡܪ̈ܐ ܕܬܘܢܝܐ (report sentences) ܕܓܘ ܡܦܩܢܐ ܒܢܝ̈ܐ ܝܢܐ ܗܕܟܐ، ܒܣܘܪܝܬ ܘܒܐܢܓܠܝܙܝܐ، ܥܡ d_z؛ ܐܢܐ ܕܟܡܘܕܥ d ܬܪܝܨܐ ܕ-Field ܝܢ ܐܝܬܐ ܡܪܒܥܐ – ܟܡܚܠܦ ܡܚܘܝܢܐ ܡܢ ܡܥܝܪܢܘܬܐ ܕܠܘܚܐ ܘܟܐܡܪ ܐܝܢܐ ܡܚܘܝܢܐ ܝܠܗ.

ܛܥܝ̈ܘܬܐ ܕܡܬܚܙܝܢ ܣܓܝ (Common mistakes)

ܒܘܚܪܢܐ ܠܠܐ ܬܠܝ̈ܐ ܥܠ ܡܫܘ̈ܚܬܐ ܡܬܢ̈ܝܬܐ. ܩܕܡ-ܒܬܪ ܕܗܢܝ ܐܢܫ̈ܐ ܟܬܒܪ ܠܐ ܬܠܝܘܬܐ؛ ܒܘܚܪܢܐ ܠܠܐ ܬܠܝ̈ܐ ܥܠ ܗܢܝ ܝܗܝ̈ܒܬܐ ܐܦ ܟܡܘܒܕ ܝܘܬܪܢܐ ܕܙܘܓܐ – t = 0.87 ܒܕܘܟܬܐ ܕ-−4.35 ܓܘ ܡܬܠܐ ܕ-Gravetter ܘ-Wallnau (ܦܐ̈ܬܐ 353-354).

ܒܘܚܪܢܐ ܙܘܓܢܝܐ ܥܠ ܐܢܫ̈ܐ ܦܪ̈ܝܫܐ. ܒܗܦܟܐ: ܬܪܬܝܢ ܓܘ̈ܕܐ ܦܪ̈ܝܫܐ ܕܡܕܒ̈ܩܐ ܝܢܐ ܚܕ ܓܢܒ ܚܕ ܓܘ ܥܡܘ̈ܕܐ ܕ"ܩܕܡ" ܘ"ܒܬܪ" ܠܐ ܝܢܐ ܙܘܓ̈ܐ؛ ܦܘܪ̈ܫܢܐ ܕܠܐ ܣܘܟܠܐ ܝܢܐ. ܠܫܘܐܠܐ "ܡܢܝܢܐ ܐܝܬ ܓܘ ܣܕܪܐ" ܐܝܬ ܦܘܢܝܐ ܚܕ – ܗܘ ܡܫܬܘܬܦܢܐ (ܝܢ ܗܘ ܙܘܓܐ ܡܦܐܝܐ).

ܦܘܫܩܐ ܕܫܘܢܝܐ ܐܝܟ ܥܠܬܢܘܬܐ (causality). ܕܠܐ ܓܘܕܐ ܕܦܘܚܡܐ (control group)، ܙܒܢܐ ܕܥܒܪܠܗ، ܓܕܫ̈ܐ ܐܚܪ̈ܢܐ ܘܡܪܓܠܢܘܬܐ ܦܘܫܩ̈ܐ ܚܠܝ̈ܦܐ ܝܢܐ (Pallant, 2020, Chapter 17; Gravetter & Wallnau, 2017, p. 354).

ܬܘܢܝܐ ܕ-d ܕܠܐ ܐܡܪܬܐ ܐܝܢܐ. d_z ܘ-d ܬܪܝܨܐ ܡܨܝ ܕܗܘܝ ܦܪ̈ܝܫܐ ܬܪܝܢ ܚܕ̈ܐ ܥܠ ܗܢܝ ܝܗܝ̈ܒܬܐ (−0.37 ܩܘܒܠ −0.20 ܓܘ ܦܐܝܠ ܕܡܬܠܐ)؛ ܟܡܚܘܚ ܡܬܩܢܢܐ، ܘܠܐ ܟܦܚܡܚ d_z ܥܡ d ܕܬܘܩܢܐ ܠܐ ܬܠܝܐ.

ܒܘܚܪܢܐ ܕܢܘܪܡܠܝܘܬܐ (normality) ܕܡܫܘ̈ܚܬܐ ܒܕܘܟܬܐ ܕܦܘܪ̈ܫܢܐ. ܫܪܛܐ ܥܠ ܦܘܪ̈ܫܢܐ ܝܠܗ (Field, 2024, Section 10.9.2).

ܦܘܫܩܐ ܕ"ܠܐ ܪܫܝܡܐ" ܐܝܟ "ܠܝܬ ܫܘܢܝܐ". ܬܚܘܡܐ ܕܬܘܟܠܢܐ (confidence interval) ܕܟܥܒܥܒ ܨܦܪܐ ܟܐܡܪ ܕܫܘܢܝܐ ܫܪܝܪܐ ܡܨܐ ܕܗܘܐ ܬܚܘܬ ܨܦܪܐ، ܠܥܠ ܡܢ ܨܦܪܐ ܝܢ ܨܦܪܐ – ܠܐ ܕܐܝܗܘ ܨܦܪܐ ܝܠܗ. ܟܡܘܕܥܚ d_z ܘܬܚܘܡܐ.

ܣܕܪܐ ܕܒܘܚܪ̈ܢܐ t ܥܠ ܬܠܬܐ ܡܫܘ̈ܚܬܐ ܘܠܥܠ. ܬܠܬܐ ܙܒ̈ܢܐ ܦܘܫܩܐ ܕܫܘܚܠܦܐ ܠܡܫܘ̈ܚܬܐ ܡܬܢ̈ܝܬܐ ܝܠܗ (ANOVA ܠܡܫܘ̈ܚܬܐ ܡܬܢ̈ܝܬܐ)، ܠܐ ܬܠܬܐ ܒܘܚܪ̈ܢܐ t.

ܡܒܘ̈ܥܐ

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

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

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

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

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

Student (1908)، Yuen (1974) ܘ-Stephens، Atkins ܘ-Kingston (2009) – ܐܝܟ ܕܡܬܝ̈ܬܐ ܝܢܐ ܓܘ Field (2024) ܘܓܘ Gravetter ܘ-Wallnau (2017). ܠܦܘܬ ܢܡܘܣܐ ܕܣܐܝܛ (site rule)، ܓܘ ܪܫܝܡܬܐ ܕܡܒܘ̈ܥܐ (reference list) ܟܡܬܚܙܝ ܒܣ ܡܒܘ̈ܥܐ ܕܩܪܝ̈ܐ ܝܢܐ ܓܘ ܫܪܫܐ ܕܝܗܝ. Field (2024) ܘ-Pallant (2020) ܒܢܘܣܚܐ ܕܝܓܝܛܠܝܐ ܕܪܕܝܐ (reflowable) – ܡܬܝܬܐ ܠܦܘܬ ܦܣܩܐ ܘܨܚܚܐ؛ Gravetter ܘ-Wallnau (2017)، Cohen (1988) ܘ-APA (2020) – ܠܦܘܬ ܦܐܬܐ ܘܦܣܩܐ ܕܡܦܩܬܐ ܛܒܝܥܬܐ.