ܡܝܛܐ-ܐܢܐܠܝܣܝܣ

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 ܕܐܝܬ ܟܡܐ ܒܘܨ̈ܝܐ ܕܒܚܪܠܗܘܢ ܗܘ ܫܘܐܠܐ – ܗܘ ܥܒܕܐ (intervention) ܩܘܒܠ ܓܘܕܐ ܕܦܘܚܡܐ، ܗܘ ܐܣܘܪܐ ܒܝܢܝ ܬܪܝܢ ܡܫܬܚܠܦ̈ܢܐ – ܘܒܥܝܚ ܕܝܕܥܚ ܡܘܕܝ ܟܐܡܪܝ ܐܟܚܕܐ: ܡܘܕܝ ܝܠܗ̇ ܡܥܒܕܢܘܬܐ ܡܨܥܝܬܐ، ܟܡܐ ܚܬܝܬܐ ܝܠܗ̇، ܘܐܝܢ ܩܝܡܬܐ ܝܠܗ̇ ܒܝܢܝ ܒܘܨ̈ܝܐ. ܡܝܛܐ-ܐܢܐܠܝܣܝܣ (meta-analysis) ܟܥܒܕܐ ܐܗܐ ܒܡܨܥܝܬܐ ܡܬܩܠܬܐ ܕܪ̈ܒܘܝܬܐ ܕܡܥܒܕܢܘܬܐ (effect sizes)، ܕܓܘܗ̇ ܒܘܨܝܐ ܚܬܝܬܐ ܒܝܫ ܟܫܩܠ ܡܬܩܠܐ ܪܒܐ ܒܝܫ. ܚܠܦܐ ܝܕܝܥܐ – ܡܢܝܢܐ ܕܟܡܐ ܒܘܨ̈ܝܐ ܢܦܩܠܗܘܢ ܪ̈ܫܝܡܐ – ܛܥܝܐ ܝܠܗ: "ܡܢܝܢܐ ܕܩܠ̈ܐ" (vote counting) ܟܚܫܒ ܦܐܪܐ ܠܐ ܪܫܝܡܐ ܐܝܟ ܣܗܕܘܬܐ ܕܠܝܬ ܡܥܒܕܢܘܬܐ، ܐܦܢ ܕܡܨܐ ܕܢܦܩ ܡܢ ܚܝܠܐ ܣܛܐܛܝܣܛܝܩܝܐ (statistical power) ܢܚܝܬܐ، ܘ-Hedges ܘ-Olkin ܚܘܝܠܗܘܢ ܕܚܝܠܐ ܕܝܠܗ ܡܨܐ ܕܐܙܠ ܠܣܦܪ ܟܡܐ ܕܡܢܝܢܐ ܕܒܘܨ̈ܝܐ ܪܒܐ (ܐܝܟ ܕܡܬܝ̈ܬܐ ܝܢܐ ܓܘ Borenstein et al., 2009، ܦܐܬܐ 251-252). ܓܘ ܡܬܠܐ ܕܬܡܢ، ܚܡܫܐ ܒܘܨ̈ܝܐ ܕܟܠ ܚܕ ܡܢܝܗܝ ܠܐ ܝܠܗ ܪܫܝܡܐ (p = .265) ܟܡܬܟܢܫܝ ܠܡܥܒܕܢܘܬܐ ܪܫܝܡܬܐ (p = .013).

ܚܘܫܒܢܐ ܝܠܗ ܡܢܬܐ ܙܥܘܪܬܐ. ܩܕܡ ܕܡܛܝܚ ܠܗ ܐܝܬ ܫܘܐܠܐ ܡܚܕܕܐ، ܒܨܝܐ ܡܛܟܣܐ، ܡܫܘ̈ܚܬܐ ܕܡܥܠܬܐ (inclusion criteria) ܘܪܡܙܢܘܬܐ (coding) – Harrer ܘܚܒܪ̈ܘܗܝ (2021، ܦܐܬܐ 9-11) ܟܡܢܝ ܦܚ̈ܐ: "ܚܙܘܪ̈ܐ ܘܦܪ̈ܬܩܠܐ" (ܒܘܨ̈ܝܐ ܦܪ̈ܝܫܐ ܝܬܝܪ ܡܢ ܕܡܬܩܠܝ)، "garbage in, garbage out" (ܒܘܨ̈ܝܐ ܥܩܝ̈ܡܐ)، "file drawer" (ܒܘܨ̈ܝܐ ܕܠܐ ܦܪܝܣ̈ܐ ܝܢܐ)، ܘܢܝܫ̈ܐ ܕܒܨܘܝܐ – ܕܐܚܪܝܐ ܡܨܐ ܕܡܙܥܪ ܒܪܘܫܡܐ ܩܕܡܝܐ ܕܬܘܩܢܐ ܕܦܘܫܩܐ (pre-registration). ܡܝܛܐ-ܐܢܐܠܝܣܝܣ ܕܪܓܝܫܘܬܐ (sensitivity) ܘܝܚܝܕܝܘܬܐ (specificity) ܕܒܘܚܪ̈ܢܐ ܕܦܘܪܫܢܐ ܕܟܘܪܗܢܐ (diagnosis) ܣܢܝܩܐ ܝܠܗ̇ ܠܡܘܕ̈ܝܠܐ ܕܬܪܝܢ ܡܫܬܚܠܦ̈ܢܐ (bivariate)، ܕܟܡܬܩܠܝ ܬܪܘܝܗܝ ܐܟܚܕܐ (Macaskill et al., 2023, p. 203) – ܦܐܬܐ ܠܐ ܟܪܗܛܐ ܠܗܘܢ؛ ܩܐ ܒܘܚܪܢܐ ܚܕ – ܦܐܬܐ ܦܘܫܩܐ ROC.

ܪܒܘܬܐ ܕܡܥܒܕܢܘܬܐ (effect size)

ܡܨܥܝ̈ܬܐ ܓܘ ܬܪܬܝܢ ܓܘ̈ܕܐ. ܐܝܡܢ ܕܟܠ ܒܘܨ̈ܝܐ ܦܠܚܠܗܘܢ ܒܗܝ ܣܒܠܬܐ (scale) – ܡܨܝܐ ܕܡܬܩܠܚ ܦܘܪܫܢܐ ܓܘܠܡܝܐ ܕܡܨܥܝ̈ܬܐ، ܕܡܬܦܗܡܢܐ ܝܠܗ ܒܡܫܘ̈ܚܬܐ ܕܫܪܫܐ؛ ܐܝܡܢ ܕܦܠܚܠܗܘܢ ܒܡܐܢ̈ܐ ܦܪ̈ܝܫܐ – ܒܣ ܦܘܪܫܢܐ ܡܬܩܢܐ (standardized)، ܦܘܪܫܢܐ ܕܡܨܥܝ̈ܬܐ ܦܠܝܓܐ ܥܠ ܣܛܝܘܬܐ ܬܩܝܢܬܐ ܡܫܘܬܦܬܐ (pooled standard deviation؛ Borenstein et al., 2009, p. 25). ܠ-d "ܐܝܬ ܥܩܝܡܘܬܐ ܩܠܝܠܬܐ" (bias) ܓܘ ܕܘ̈ܡܝܐ ܙܥܘܪ̈ܐ، ܘܡܛܠ ܗܕܐ ܟܬܪܨܚ ܠܗ ܠ-g ܕ-Hedges (ܬܡܢ، ܦܐܬܐ 27). ܠܫܘܚܠܦܐ (variance) ܕ-g ܐܝܬ ܟܡܐ ܡܬܢܝ̈ܬܐ، ܘ-Borenstein ܘܚܒܪ̈ܘܗܝ ܓܢܒܝܗܝ ܟܡܥܗܕܝ ܕ"ܡ̈ܠܐ ܦܪ̈ܝܫܐ ܩܠܝܠ" ܝܗܝ̈ܒܐ ܝܢܐ ܒܝܕ ܟܬܘ̈ܒܐ ܦܪ̈ܝܫܐ (ܦܐܬܐ 28) – "ܐܦ ܐܗܐ ܘܐܦ ܐܗܐ": ܦܐܬܐ ܟܚܫܒܐ ܐܝܟ escalc ܓܘ metafor (ܬܘܪܨܐ ܚܬܝܬܐ، ܘܫܘܚܠܦܐ ܥܡ g²)، ܘܟܬܒܐ ܟܡܦܠܚ ܒܬܘܪܨܐ ܩܪܝܒܐ ܘܒܫܘܚܠܦܐ ܕ-d ܥܦܝܦܐ ܒ-J². ܦܘܪܫܢܐ ܙܥܘܪܐ ܛܒܐ ܝܠܗ ܐܠܐ ܓܘ ܕܘ̈ܡܝܐ ܙܥܘܪ̈ܐ ܣܓܝ؛ ܓܘ ܡܬܠܐ ܓܡܝܪܐ ܕܟܬܒܐ ܡܥܒܕܢܘܬܐ ܡܬܩܠܬܐ 0.3585 ܩܘܒܠ 0.3582. ܐܘܪܚܐ ܡܢ ܨܒܝܢܐ ܝܠܗ̇، ܐܠܐ ܣܢܝܩܐ ܝܠܗ̇ ܕܗܘܝܐ ܚܕܐ: ܐܢ ܥܠ ܡܢ ܣܦܪ ܟܐܡܪ ܕܓܘܕܐ ܕܢܣܝܘܢܐ ܛܒܐ ܝܠܗ ܒܝܫ، ܐܗܐ ܣܢܝܩܐ ܝܠܗ ܕܗܘܐ ܩܐ ܟܠ ܒܘܨ̈ܝܐ (ܬܡܢ، ܦܐܬܐ 25).

ܠܘ̈ܚܐ 2×2. ܦܘܚܡܐ ܕܣܘܟ̈ܢܐ (risk ratio) ܘܦܘܚܡܐ ܕܣܟܘ̈ܝܐ (odds ratio) ܡܚܘ̈ܝܢܐ ܢܣܒ̈ܝܐ ܝܢܐ، "ܢܣܒܐܝܬ ܠܐ ܪܓܝܫ̈ܐ ܠܦܘܪ̈ܫܢܐ ܓܘ ܡܢܬܐ ܕܫܬܐܣܐ" (base rate)؛ ܦܘܪܫܢܐ ܕܣܘܟ̈ܢܐ (risk difference) ܫܪܝܪܐ (absolute) ܝܠܗ – ܪܓܝܫܐ ܠܡܢܬܐ ܕܫܬܐܣܐ، ܐܠܐ ܒܥܕܢ̈ܐ "ܒܥܠ ܣܘܟܠܐ ܒܝܫ ܩܠܝܢܝܩܐܝܬ" (Borenstein et al., 2009, p. 38). ܦܘܚܡ̈ܐ ܡܬܦܫܩܝ ܓܘ ܠܘܓ ܘܡܬܕܥܪܝ ܠܡܚܘܝܢܘܬܐ (ܦܐܬܐ 39). ܐܝܡܢ ܕܐܝܬ ܓܘ ܒܘܨܝܐ ܩܠܝܬܐ (cell) ܕܣܦܪ، ܦܐܬܐ ܟܡܘܣܦܐ ܦܠܓܐ ܠܟܠ ܐܪܒܥ ܩܠ̈ܝܬܐ ܕܗܘ ܒܘܨܝܐ، ܐܝܟ escalc.

ܐܣܘܪ̈ܐ ܕܚܕ̈ܕܐ. ܫܘܚܠܦܐ (variance) ܕ-r ܬܠܝܐ ܝܠܗ ܒ-r ܓܢܒܗ، ܘܡܛܠ ܗܕܐ ܟܡܬܩܠܚ ܒܬܪ ܫܘܢܝܐ (transformation) z ܕ-Fisher ܘܟܕܥܪܚ ܠ-r ܩܐ ܡܚܘܝܢܘܬܐ (Borenstein et al., 2009, pp. 41-43).

ܐܣܘܪܐ ܕܚܕ̈ܕܐ ܡܢܬܢܝܐ (partial correlation) ܡܢ ܡܢܝܢܐ ܡܫܘܬܦܐ ܕܪܝܓܪܫܢ. ܓܘ ܒܘܨ̈ܝܐ ܕܡܕܒܪܢܘܬܐ (policy)، ܕܡܕܒܪܢܘܬܐ ܕܥܡܐ (public administration) ܘܕܝܕ̈ܥܬܐ ܕܟܢܫܐ ܣܓܝܐܐ ܡܢ ܡܫܟܚ̈ܢܘܬܐ (findings) ܟܐܬܝ ܐܝܟ ܡܢ̈ܝܢܐ ܡܫܘܬܦ̈ܐ ܕܪܝܓܪܫܢ، ܘ-Ringquist (2013، ܦܐܬܐ 104-105) ܟܡܩܘܒܠ ܕܡܦܠܚܚ ܒܗܘܢ ܓܘ ܪ̈ܒܘܝܬܐ ܕܡܥܒܕܢܘܬܐ ܡܢ ܫܪܒܬܐ ܕ-r: ܡܢ t ܕܡܢܝܢܐ ܡܫܘܬܦܐ ܟܚܫܒܚ r = t/√(t² + df) – ܐܣܘܪܐ ܕܚܕ̈ܕܐ ܡܢܬܢܝܐ ܒܝܢܝ ܡܢܒܝܢܐ (predictor) ܘܡܫܬܚܠܦܢܐ ܬܠܝܐ (dependent variable)، ܕܠܐ ܐܣܘܪܐ ܥܡ ܡܢܝܢܐ ܕܡܢܒ̈ܝܢܐ ܓܘ ܡܘܕܝܠ؛ ܥܩܝܡܘܬܐ (bias) ܙܥܘܪܬܐ ܕܟܢܦܩܐ ܡܢ ܡܢܝܢܐ ܕܡܢܒ̈ܝܢܐ "ܙܥܘܪܬܐ ܛܒܐ ܝܠܗ̇" ܓܘ ܣܓܝܐܐ ܡܢ ܚܠ̈ܝܬܐ (ܦܐܬܐ 105-106). ܐܬܐ ܝܠܗ ܕܡܢܝܢܐ ܡܫܘܬܦܐ، ܘܣܢܝܩܐ ܝܠܗ ܠܡܚܬܡܐ ܕܐܘܪܚܐ ܕܝܠܗ ܚܕܐ ܝܠܗ̇ ܓܘ ܟܠ ܒܘܨ̈ܝܐ (ܦܐܬܐ 137-138). ܒܘܨܝܐ ܕܬܢܠܗ ܒܣ ܟܘ̈ܟܒܐ (asterisks) – ܟܡܚܬܚ ܛܝܡܐ ܕܬܚܘܡܐ ܕ-t، ܘܐܣܘܪܐ ܕܟܢܦܩ ܝܠܗ ܬܚܘܡܐ ܬܚܬܝܐ (lower bound)؛ ܒܘܨܝܐ ܕܟܬܒܠܗ ܒܣ "ܠܐ ܪܫܝܡܐ" – ܓܒܝܐ ܝܠܗ ܕܡܚܬܚ r = 0 ܡܢ ܕܫܒܩܚ ܠܗ، ܡܛܠ ܕܫܒܩܬܐ "ܩܪܝܒ ܒܫܪܪܐ ܒܕ ܡܢܦܚܐ" ܡܥܒܕܢܘܬܐ ܡܨܥܝܬܐ (ܦܐܬܐ 108). "ܐܦ ܐܗܐ ܘܐܦ ܐܗܐ" ܓܘ ܫܘܚܠܦܐ: Ringquist ܟܡܦܠܚ ܒܫܘܚܠܦܐ ܥܡܝܐ ܕ-z ܕ-Fisher، 1/(n − 3) (ܦܐܬܐ 109)؛ ܦܐܬܐ ܟܚܫܒܐ ܐܝܟ escalc("ZPCOR") ܓܘ metafor، 1/(n − m − 2) ܥܡ m ܡܢܒ̈ܝܢܐ – ܦܘܪܫܢܐ ܙܥܘܪܐ ܝܠܗ ܓܘ ܕܘ̈ܡܝܐ ܪ̈ܒܐ.

ܡܥܒܕܢܘܬܐ ܕܚܫܝܒܬܐ ܡܢ ܩܕܡ. ܐܝܡܢ ܕܒܘܨ̈ܝܐ ܬܢܠܗܘܢ ܒܣ ܡܥܒܕܢܘܬܐ ܘܬܚܘܡܐ ܕܬܘܟܠܢܐ (confidence interval)، ܛܥܝܘܬܐ ܬܩܝܢܬܐ (standard error) ܝܠܗ̇ ܦܬܝܘܬܐ ܕܬܚܘܡܐ ܦܠܝܓܬܐ ܥܠ 2 × 1.96؛ ܩܐ ܦܘܚܡܐ (OR, RR, HR) – ܓܘ ܣܒܠܬܐ ܕܠܘܓ. ܩܐ g ܕܥܐܠܐ ܗܕܟܐ – ܛܒܐ ܝܠܗ ܕܡܚܬܡܚ ܕܬܘܪܨܐ ܩܐ ܥܩܝܡܘܬܐ (bias) ܡܢ ܩܕܡ ܥܒܝܕܐ ܝܠܗ، ܡܛܠ ܕܦܐܬܐ ܠܐ ܟܝܕܥܐ (Harrer et al., 2021, p. 105).

ܡܥܒܕܢܘܬܐ ܩܝܡܬܐ ܝܢ ܡܥܒܕ̈ܢܘܝܬܐ ܓܕܫܢ̈ܝܬܐ

ܓܘ ܡܘܕܝܠ ܕܡܥܒܕܢܘܬܐ ܩܝܡܬܐ (fixed effect) ܟܣܒܪܚ ܕܠܟܠ ܒܘܨ̈ܝܐ ܐܝܬ ܗܝ ܡܥܒܕܢܘܬܐ ܫܪܝܪܬܐ، ܘܦܪ̈ܝܫܐ ܝܢܐ ܒܣ ܒܛܥܝܘܬܐ ܕܓܘܒܝܐ ܕܕܘܡܝܐ (sampling error)؛ ܓܘ ܡܘܕܝܠ ܕܡܥܒܕ̈ܢܘܝܬܐ ܓܕܫܢ̈ܝܬܐ (random effects) – ܕܡܥܒܕܢܘܬܐ ܫܪܝܪܬܐ ܟܫܚܠܦܐ ܒܝܢܝ ܒܘܨ̈ܝܐ، ܘܢܝܫܐ ܝܠܗ ܡܨܥܝܬܐ ܕܦܘܠܓܐ ܕܡܥܒܕ̈ܢܘܝܬܐ (Borenstein et al., 2009, p. 77). ܡܥܒܕܢܘܬܐ ܩܝܡܬܐ ܦܐܝܐ ܝܠܗ̇ ܐܝܡܢ ܕܒܘܨ̈ܝܐ "ܫܘ̈ܝܐ ܝܢܐ ܡܢ ܓܢܒܐ ܕܥܒܕܐ" (functionally identical) ܘܢܝܫܐ ܠܐ ܝܠܗ ܕܡܦܫܛܚ ܚܬܡܬܐ ܠܒܪ ܡܢܗܘܢ – ܚܠܬܐ "ܢܕܝܪܬܐ ܢܣܒܐܝܬ"؛ ܐܝܡܢ ܕܒܘܨ̈ܝܐ ܥܒܝ̈ܕܐ ܝܢܐ ܒܝܕ ܒܨܘ̈ܝܐ ܦܪ̈ܝܫܐ ܘܟܢܝ̈ܫܐ ܝܢܐ ܡܢ ܟܬܒ̈ܐ (literature)، ܡܥܒܕ̈ܢܘܝܬܐ ܓܕܫܢ̈ܝܬܐ "ܡܬܩܒܠ̈ܢܝܬܐ ܝܢܐ ܒܝܫ ܓܘ ܣܓܝܐܐ ܕܥܕ̈ܢܐ" (ܦܐܬܐ 83-86). Harrer ܘܚܒܪ̈ܘܗܝ (2021، ܦܐܬܐ 101) ܟܡܘܣܦܝ ܕܓܘ ܝܕ̈ܥܬܐ ܕܟܢܫܐ "ܥܝܕܐ ܝܠܗ ܕܡܦܠܚܚ ܟܠ ܐܡܢ" ܒܡܥܒܕ̈ܢܘܝܬܐ ܓܕܫܢ̈ܝܬܐ، ܐܠܐ "ܐܦ ܐܗܐ ܘܐܦ ܐܗܐ": ܡܘܕܝܠ ܟܝܗܒ ܡܬܩܠܐ ܪܒܐ ܒܝܫ ܠܒܘܨ̈ܝܐ ܙܥܘܪ̈ܐ، ܕܒܥܕܢ̈ܐ ܥܩܝ̈ܡܐ ܝܢܐ ܒܝܫ – ܘܐܝܬ ܕܐܡܪܝ ܕܡܥܒܕܢܘܬܐ ܩܝܡܬܐ ܓܒܝܬܐ ܝܠܗ̇ ܒܥܕܢ̈ܐ (ܬܡܢ). ܐܦ ܟܬܒ̈ܐ ܠܦܘܬ ܣܘܟܠܐ (field) ܟܓܒܝ ܡܥܒܕ̈ܢܘܝܬܐ ܓܕܫܢ̈ܝܬܐ: Ringquist (2013، ܦܐܬܐ 33) – "ܟܠ ܐܡܢ"، ܐܠܐ ܐܢ ܐܝܬ ܣܒ̈ܒܐ ܚܝ̈ܠܢܐ ܣܓܝ ܕܣܒܪܚ ܡܥܒܕܢܘܬܐ ܩܝܡܬܐ، ܡܛܠ ܕܚܬ̈ܡܬܐ ܕܡܥܒܕܢܘܬܐ ܩܝܡܬܐ ܟܦܐܝܢ ܒܣ ܥܠ ܒܘܨ̈ܝܐ ܕܟܢܝ̈ܫܐ ܝܢܐ (ܦܐܬܐ 120-121)؛ Cooke (2024، ܦܐܬܐ 133) – ܒܘܨ̈ܝܐ ܕܝܕܥܬܐ ܕܢܦܫܐ (psychology) ܠܐ ܥܒܝ̈ܕܐ ܝܢܐ ܒܗܝ ܐܘܪܚܐ ܓܘ ܓܘ̈ܕܐ ܦܪ̈ܝܫܐ ܕܒܨܘ̈ܝܐ، ܘܡܛܠ ܗܕܐ "ܥܣܩܐ ܝܠܗ ܠܡܙܕܩܐ" ܡܥܒܕܢܘܬܐ ܩܝܡܬܐ. ܘ"ܐܦ ܐܗܐ ܘܐܦ ܐܗܐ": Kumar (2023، ܦܐܬܐ 112-113) ܟܟܬܒ ܕܐܗܘ ܓܢܒܗ ܟܓܒܐ ܡܥܒܕܢܘܬܐ ܩܝܡܬܐ ܗܕܟܡܐ ܕܫܘܚܠܦܐ ܠܐ ܝܠܗ ܣܓܝ، ܘܕܓܒܝܐ ܝܠܗ ܕܒܨܚ ܡܒܘ̈ܥܐ ܕܦܘܪܫܢܐ ܒܝܢܝ ܒܘܨ̈ܝܐ (heterogeneity) ܡܢ ܕܥܒܕܚ ܠܗܘܢ ܡܘܕܝܠ. ܦܐܬܐ ܟܡܚܘܝܐ ܬܪܘܝܗܝ؛ ܦܣܩܐ ܟܡܘܕܥܐ ܡܥܒܕ̈ܢܘܝܬܐ ܓܕܫܢ̈ܝܬܐ.

ܡܘܕܝ ܠܐ ܥܒܕܚ: ܫܘܪܝܐ ܒܡܥܒܕܢܘܬܐ ܩܝܡܬܐ ܘܫܚܠܦܐ ܠܡܥܒܕ̈ܢܘܝܬܐ ܓܕܫܢ̈ܝܬܐ ܐܢ ܒܘܚܪܢܐ ܕܦܘܪܫܢܐ ܒܝܢܝ ܒܘܨ̈ܝܐ (heterogeneity) ܪܫܝܡܐ ܝܠܗ – "ܣܢܝܩܐ ܝܠܗ ܕܡܬܪܚܩܚ ܡܢ ܗܕܐ ܒܚܝܠܐ"، ܡܛܠ ܕܓܘܒܝܐ ܬܠܝܐ ܝܠܗ ܒܦܗܡܐ ܐܢ ܒܘܨ̈ܝܐ ܡܫܘܬܦ̈ܐ ܝܢܐ ܓܘ ܚܕܐ ܡܥܒܕܢܘܬܐ، ܘܒܘܚܪܢܐ ܟܪܝܗܐ ܝܠܗ (Borenstein et al., 2009, p. 84)؛ ܡܘܕܝܠ ܡܬܓܒܐ ܝܠܗ "ܓܘ ܕܪܓܐ ܕܬܘܩܢܐ" (Kumar, 2023, p. 36). ܘܦܘܪܫܢܐ ܐܚܪܢܐ: ܓܘ ܡܥܒܕ̈ܢܘܝܬܐ ܓܕܫܢ̈ܝܬܐ ܬܚܘܡܐ ܕܬܘܟܠܢܐ (confidence interval) ܟܠ ܐܡܢ ܦܬܝܐ ܝܠܗ ܒܝܫ، ܘܠܐ ܟܙܥܪ ܠܣܦܪ ܐܦ ܥܡ ܒܘܨ̈ܝܐ ܪ̈ܒܐ ܣܓܝ – ܡܛܠ ܕܡܢܝܢܐ ܕܒܘܨ̈ܝܐ، ܠܐ ܪܒܘܬܐ ܕܝܠܗܘܢ، ܟܡܚܕܕ ܚܬܝܬܘܬܐ ܕܡܨܥܝܬܐ (ܦܐܬܐ 80-81). ܐܝܡܢ ܕܐܝܬ ܩܠܝܠ ܣܓܝ ܒܘܨ̈ܝܐ، ܫܘܥܪܐ ܕܫܘܚܠܦܐ ܒܝܢܝ ܒܘܨ̈ܝܐ ܠܐ ܝܠܗ ܚܬܝܬܐ، ܘ"ܟܠ ܚܕ ܡܢ ܓܘܒ̈ܝܐ ܐܝܬܠܗ ܥܩܬܐ" (ܦܐܬܐ 84).

ܫܘܥܪܐ ܕ-τ² ܘ-Knapp-Hartung

ܫܘܥܪܐ. ܫܘܚܠܦܐ ܒܝܢܝ ܒܘܨ̈ܝܐ، τ²، ܡܨܝܐ ܕܡܫܬܥܪ ܒܟܡܐ ܐܘܪ̈ܚܬܐ. DerSimonian-Laird ܝܠܗ ܕܣܓܝ ܡܬܦܠܚ ܘܓܘܒܝܐ ܡܩܕܡܐ (default) ܓܘ ܬܘܟܢܝ̈ܬܐ ܥܬܝܩ̈ܬܐ، ܐܠܐ "ܡܨܐ ܕܗܘܐ ܥܩܝܡܐ، ܝܬܝܪ ܐܝܡܢ ܕܡܢܝܢܐ ܕܒܘܨ̈ܝܐ ܙܥܘܪܐ ܝܠܗ ܘܦܘܪܫܢܐ ܒܝܢܝ ܒܘܨ̈ܝܐ ܪܡܐ ܝܠܗ". ܦܘܩܕ̈ܢܐ ܕ-Harrer ܘܚܒܪ̈ܘܗܝ (2021، ܦܐܬܐ 102-103)، "ܐܦ ܐܗܐ ܘܐܦ ܐܗܐ": REML ܩܐ ܡܥܒܕ̈ܢܘܝܬܐ ܡܬܡܫܚ̈ܢܝܬܐ ܐܝܟ ܢܘܩܙܐ ܕܫܘܪܝܐ (ܘܐܗܐ ܝܠܗ ܓܘܒܝܐ ܡܩܕܡܐ ܕ-metafor)؛ Paule-Mandel ܩܐ ܡܥܒܕ̈ܢܘܝܬܐ ܕܬܪܝܢ ܛܝ̈ܡܐ (binary)؛ ܘ-DerSimonian-Laird ܐܝܡܢ ܕܒܥܝܚ ܕܐܚܪ̈ܢܐ ܡܬܢܝ ܦܐܪܐ ܐܦ ܠܒܪ ܡܢ R. "ܠܝܬ ܢܡܘ̈ܣܐ ܕܦܪܙܠܐ"، ܘܦܘܪ̈ܫܢܐ ܓܘ ܣܓܝܐܐ ܕܥܕ̈ܢܐ ܙܥܘܪ̈ܐ ܝܢܐ – ܛܒܐ ܝܠܗ ܕܪܗܛܚ ܬܘܒ ܥܡ ܫܘܥܪܐ ܐܚܪܢܐ ܘܚܙܝܚ ܐܢ ܦܘܫܩܐ ܟܫܚܠܦ. ܦܐܬܐ ܟܫܒܩܐ ܬܠܬܝܗܝ.

Knapp-Hartung. ܬܚܘܡܐ ܕܬܘܟܠܢܐ (confidence interval) ܥܡܝܐ ܠܐ ܟܚܙܐ ܠܐ ܫܪܝܪܘܬܐ ܕܫܘܥܪܐ ܕ-τ². ܬܘܪܨܐ ܕ-Knapp ܘ-Hartung (ܘܒܫܡܗ ܓܡܝܪܐ HKSJ) ܟܚܫܒ ܛܥܝܘܬܐ ܬܩܝܢܬܐ ܐܚܪܬܐ ܘܟܡܦܠܚ ܒܦܘܠܓܐ t ܥܡ k − 1 ܕܪ̈ܓܐ ܕܚܐܪܘܬܐ (degrees of freedom)؛ ܓܘ simulations ܐܗܘ "ܟܦܠܚ ܣܓܝ ܛܒ ܒܝܫ" ܡܢ ܒܘܚܪܢܐ ܕ-Wald ܓܘ ܡܢ̈ܝܢܐ ܕܒܘܨ̈ܝܐ ܕܡܬܚܙܝܢ ܒܫܪܝܪܘܬܐ، ܘܓܘ ܒܘܚܪܢܐ ܕ-689 ܡܝܛܐ-ܐܢܐܠܝܣ̈ܝܣ ܕ-Cochrane، ܪܘܒܥܐ ܡܢ ܡܫܟܚ̈ܢܘܬܐ ܪ̈ܫܝܡܬܐ ܒܐܘܪܚܐ ܥܡܝܬܐ ܠܐ ܗܘܘ ܪ̈ܫܝܡܐ ܥܡܗ (Stijnen et al., 2021, p. 51). Harrer ܘܚܒܪ̈ܘܗܝ (2021، ܦܐܬܐ 104) ܟܚܙܝ ܠܗ "ܓܘ ܣܓܝܐܐ ܕܥܕ̈ܢܐ ܡܬܦܗܡܢܐ"، ܘܟܡܥܗܕܝ ܕܐܝܬ ܕܐܡܪܝ ܕܓܘ ܚܠ̈ܝܬܐ ܢܕܝܪ̈ܬܐ ܕܡܥܒܕ̈ܢܘܝܬܐ ܫܘ̈ܝܬܐ ܣܓܝ (homogeneous) ܐܗܘ ܪܟܝܟܐ ܝܬܝܪܐ ܝܠܗ. ܦܐܬܐ ܟܡܚܘܝܐ ܬܪܝܢ ܬܚܘ̈ܡܐ ܚܕ ܓܢܒ ܚܕ.

ܦܘܪܫܢܐ ܒܝܢܝ ܒܘܨ̈ܝܐ ܘܬܚܘܡܐ ܕܡܢܒܝܢܘܬܐ

ܐܪܒܥܐ ܡܚܘ̈ܝܢܐ، ܘܠܟܠ ܚܕ ܐܝܬ ܦܘܠܚܢܐ (Borenstein et al., 2009, pp. 119-122; Harrer et al., 2021, pp. 140-150): Q ܘ-p ܕܝܠܗ ܟܒܚܪܝ ܐܢ ܐܝܬ ܫܘܚܠܦܐ ܫܪܝܪܐ ܒܟܠ – ܐܠܐ ܪܓܝܫ̈ܐ ܝܢܐ ܠܡܢܝܢܐ ܕܒܘܨ̈ܝܐ ܘܠܪܒܘܬܐ ܕܝܠܗܘܢ؛ τ² ܘ-τ – ܫܘܚܠܦܐ (variance) ܘܣܛܝܘܬܐ ܬܩܝܢܬܐ (standard deviation) ܕܡܥܒܕ̈ܢܘܝܬܐ ܫܪ̈ܝܪܬܐ، ܒܡܫܘ̈ܚܬܐ ܕܡܥܒܕܢܘܬܐ؛ I² – ܡܢܬܐ ܕܒܕܪܐ ܚܙܝܐ ܕܫܪܝܪܐ ܝܠܗ ܘܠܐ ܛܥܝܘܬܐ ܕܓܘܒܝܐ ܕܕܘܡܝܐ (sampling error)، "ܦܘܚܡܐ ܕܐܬܐ ܠܩܠܐ" (signal-to-noise) ܒܝܢܝ 0% ܘ-100%. ܬܚܘ̈ܡܐ ܕ-Higgins ܘܚܒܪ̈ܘܗܝ – 25%، 50%، 75% ܩܐ ܢܚܝܬܐ، ܡܨܥܝܐ ܘܪܡܐ – "ܕܙܒܢܐ ܝܢܐ" (Borenstein et al., 2009, p. 119)، ܘ-I² ܠܐ ܟܐܡܪ ܟܡܐ ܡܥܒܕ̈ܢܘܝܬܐ ܡܒܕܪ̈ܐ ܝܢܐ: I² ܩܪܝܒ ܠ-100% ܡܨܐ ܕܐܬܐ ܡܢ ܡܥܒܕ̈ܢܘܝܬܐ ܓܘ ܦܬܝܘܬܐ (range) ܥܨܝܪܬܐ ܕܡܫܥܪ̈ܐ ܝܢܐ ܒܚܬܝܬܘܬܐ ܪܒܬܐ (ܬܡܢ). ܐܦ I² ܬܠܝܐ ܝܠܗ ܒܚܬܝܬܘܬܐ ܕܒܘܨ̈ܝܐ – ܓܘ ܒܘܨ̈ܝܐ ܪ̈ܒܐ ܣܓܝ ܟܐܙܠ ܠ-100% (Harrer et al., 2021, p. 149). ܐܦ ܟܬܒ̈ܐ ܦܪ̈ܝܫܐ ܝܢܐ ܓܘ ܬܚܘ̈ܡܐ: Kumar (2023، ܦܐܬܐ 42) ܟܡܝܬܐ ܦܬܝ̈ܘܬܐ ܕܥܒܪ̈ܢ ܥܠ ܚܕ̈ܕܐ ܕ-Cochrane – 0%-40% ܢܚܝܬܐ، 30%-60% ܡܨܥܝܐ، 50%-90% ܪܒܐ، 75%-100% ܪܡܐ ܣܓܝ – ܘܟܡܙܗܪ ܕ-I² ܥܩܝܡܐ ܝܠܗ ܐܝܡܢ ܕܐܝܬ ܩܠܝܠ ܒܘܨ̈ܝܐ. ܘܐܝܡܢ ܕܦܘܪܫܢܐ ܒܝܢܝ ܒܘܨ̈ܝܐ ܪܡܐ ܝܠܗ ܣܓܝ، ܡܕܡ ܩܕܡܝܐ ܠܒܘܚܪܢܐ ܝܠܗ ܛܥܝ̈ܘܬܐ ܕܟܬܝܒܬܐ ܓܘ ܝܗܝ̈ܒܬܐ (ܬܡܢ، ܦܐܬܐ 43).

ܬܚܘ̈ܡܐ ܕܬܘܟܠܢܐ ܩܐ ܦܘܪܫܢܐ ܒܝܢܝ ܒܘܨ̈ܝܐ. "ܠܐ ܫܪܝܪܘܬܐ ܚܕܪ τ² ܝܢ I² ܓܘ ܣܓܝܐܐ ܕܥܕ̈ܢܐ ܪܒܬܐ ܝܠܗ̇ ܣܓܝ"، ܘܡܛܠ ܗܕܐ "ܛܥܝܘܬܐ ܒܕ ܗܘܝܐ" ܦܘܫܩܐ ܕܫܘܥܪܐ ܕܣܦܪ ܐܝܟ ܣܗܕܘܬܐ ܕܫܠܡܘܬܐ (consistency)، ܐܠܐ ܐܢ ܬܚܘܡܐ ܟܡܦܠܛ ܛܝ̈ܡܐ ܪ̈ܒܐ (Borenstein et al., 2009, p. 122). ܦܐܬܐ ܟܚܫܒܐ ܬܚܘ̈ܡܐ ܒܐܘܪܚܐ ܕ-Q-profile، ܐܝܟ metafor ܘ-meta (Harrer et al., 2021, pp. 148-149)؛ ܠ-Borenstein ܘܚܒܪ̈ܘܗܝ (2009، ܦܐܬܐ 122-125) ܐܝܬ ܡܬܢܝܬܐ ܦܫܝܛܬܐ ܒܝܫ، ܘܐܗܐ ܝܠܗ ܕܘܟܬܐ ܐܚܪܬܐ ܕܓܘܗ̇ ܬܘܟܢܝ̈ܬܐ ܦܪ̈ܝܫܐ ܝܢܐ.

ܬܚܘܡܐ ܕܡܢܒܝܢܘܬܐ (prediction interval). ܬܚܘܡܐ ܕܬܘܟܠܢܐ ܟܐܡܪ ܟܡܐ ܚܬܝܬܐ ܝܠܗ̇ ܡܨܥܝܬܐ؛ ܬܚܘܡܐ ܕܡܢܒܝܢܘܬܐ – ܐܝܟܐ ܡܣܟܝܐ ܝܠܗ̇ ܕܢܦܠܐ ܡܥܒܕܢܘܬܐ ܫܪܝܪܬܐ ܓܘ ܒܘܨܝܐ ܚܕܬܐ، ܘܡܛܠ ܗܕܐ "ܬܪܬܝܢ ܡܫܘ̈ܚܬܐ ܠܐ ܡܨܝ ܕܡܬܚܠܦܝ" (Borenstein et al., 2009, p. 131). ܟܡܐ ܕܡܢܝܢܐ ܕܒܘܨ̈ܝܐ ܟܪܒܐ، ܬܚܘܡܐ ܕܬܘܟܠܢܐ ܟܙܥܪ ܠܣܦܪ، ܘܬܚܘܡܐ ܕܡܢܒܝܢܘܬܐ ܠܐ – ܟܡܩܪܒ ܠܒܕܪܐ ܫܪܝܪܐ (ܦܐܬܐ 132-133). ܐܢ ܟܠܗ ܥܠ ܡܢ ܣܦܪ ܝܠܗ، ܥܒܕܐ (intervention) ܡܣܟܝܐ ܝܠܗ ܕܡܘܬܪ ܐܦ ܓܘ ܚܠ̈ܝܬܐ ܐܚܪ̈ܢܐ؛ ܐܢ ܐܝܬ ܓܘܗ ܣܦܪ – ܒܨܝܪ ܫܪܝܪܐ (Harrer et al., 2021, p. 150). ܡܬܢܝܬܐ – "ܐܦ ܐܗܐ ܘܐܦ ܐܗܐ": Higgins ܘܚܒܪ̈ܘܗܝ (ܐܝܟ ܕܡܬܝ̈ܬܐ ܝܢܐ ܓܘ Borenstein et al., 2009، ܦܐܬܐ 130) ܟܡܦܠܚܝ ܒ-t ܥܡ k − 2 ܕܪ̈ܓܐ ܕܚܐܪܘܬܐ، ܘܐܗܐ ܝܠܗ ܡܐ ܕܦܐܬܐ ܟܡܘܕܥܐ؛ Harrer ܘܚܒܪ̈ܘܗܝ (2021، ܦܐܬܐ 150) – k − 1؛ ܘ-predict ܓܘ metafor – ܦܘܠܓܐ ܢܘܪܡܠܝܐ (ܡܚܘܝܐ ܝܠܗ ܓܘ ܩܘܦܣܐ ܕܩܪܝܢܐ). Cooke (2024، ܦܐܬܐ 165) – ܕܠܐ ܟܡܘܕܥ ܒܟܠ τ² (ܦܐܬܐ 137) – ܟܡܩܘܒܠ ܕ"ܬܚܘ̈ܡܐ ܕܡܢܒܝܢܘܬܐ ܡܬܬܢܝ ܟܠ ܐܡܢ".

ܓܘ̈ܕܐ ܡܢܬܢ̈ܝܐ

ܦܘܫܩܐ ܕܓܘ̈ܕܐ ܡܢܬܢ̈ܝܐ (subgroups) ܟܫܐܠ ܐܢ ܡܥܒܕܢܘܬܐ ܦܪܝܫܬܐ ܝܠܗ̇ ܒܝܢܝ ܙ̈ܢܐ ܕܒܘܨ̈ܝܐ – ܬܘܟܢܝܬܐ ܝܚܝܕܝܬܐ ܩܘܒܠ ܕܓܘܕܐ، ܬܘܢܝܐ ܕܢܦܫܐ ܩܘܒܠ ܫܘܥܪܐ ܕܡܗܝܪܐ. ܓܘ ܟܠ ܓܘܕܐ – ܡܝܛܐ-ܐܢܐܠܝܣܝܣ ܥܡܝܬܐ، ܘܒܬܪ ܟܦܚܡܚ ܫܘ̈ܥܪܐ ܕܓܘ̈ܕܐ ܒܒܘܚܪܢܐ Q، ܐܝܟ ܕܟܠ ܓܘܕܐ ܚܕ ܒܘܨܝܐ ܪܒܐ ܝܠܗ (Harrer et al., 2021, pp. 184-185). ܫܘܐܠܐ ܦܬܝܚܐ – "ܐܦ ܐܗܐ ܘܐܦ ܐܗܐ" – ܝܠܗ ܐܢ ܣܢܝܩܐ ܝܠܗ ܕܡܫܥܪܚ τ² ܦܪܝܫܐ ܓܘ ܟܠ ܓܘܕܐ ܝܢ ܚܕ ܡܫܘܬܦܐ: ܦܪܝܫܐ، ܐܝܡܢ ܕܡܣܟܝܚ ܕܒܕܪܐ ܦܪܝܫܐ ܝܠܗ ܒܝܢܝ ܓܘ̈ܕܐ؛ ܡܫܘܬܦܐ، ܐܝܡܢ ܕܣܒܪܚ ܕܕܡܝܐ ܝܠܗ، ܘܐܦ ܐܝܡܢ ܕܓܘ ܓܘܕܐ ܐܝܬ ܚܡܫܐ ܒܘܨ̈ܝܐ ܝܢ ܒܨܝܪ، ܡܛܠ ܕܬܡܢ ܫܘܥܪܐ ܦܪܝܫܐ ܠܐ ܝܠܗ ܚܬܝܬܐ (Borenstein et al., 2009, pp. 162-163). ܦܐܬܐ ܟܚܫܒܐ ܬܪܘܝܗܝ: ܒܘܚܪܢܐ Q_between ܥܡ τ² ܦܪܝܫܐ، ܘܡܘܕܝܠ ܡܚܠܛܐ (mixed) ܥܡ τ² ܡܫܘܬܦܐ (Q_M، ܘܡܢܬܐ ܕܫܘܚܠܦܐ ܡܦܫܩܐ R²؛ ܦܐܬܐ 179).

ܬܠܬܐ ܙܘܗܪ̈ܐ (Harrer et al., 2021, pp. 188-190): ܚܝܠܐ ܣܛܐܛܝܣܛܝܩܝܐ (statistical power) ܢܚܝܬܐ ܝܠܗ، ܘܢܡܘܣܐ ܡܩܘܒܠܐ ܝܠܗ ܠܐ ܒܨܝܪ ܡܢ 10 ܒܘܨ̈ܝܐ؛ ܠܐ ܐܝܬܘܬܐ ܕܦܘܪܫܢܐ ܪܫܝܡܐ ܠܐ ܝܠܗ ܚܘܝܐ ܕܓܘ̈ܕܐ ܫܘ̈ܝܐ ܝܢܐ؛ ܘܦܘܫܩܐ "ܕܚܙ̈ܝܬܐ ܒܠܚܘܕ ܝܠܗ" (observational) – ܐܦ ܐܝܡܢ ܕܟܠ ܒܘܨ̈ܝܐ ܢܣܝ̈ܘܢܐ ܡܛܟܣ̈ܐ ܝܢܐ، ܓܘ̈ܕܐ ܡܨܝ ܕܦܪ̈ܝܫܐ ܗܘܝ ܓܘ ܡܫܬܚܠܦ̈ܢܐ ܐܚܪ̈ܢܐ (ܘܐܦ Borenstein et al., 2009، ܦܐܬܐ 209). ܘܦܚܐ ܐܚܪܢܐ: ܦܘܠܓܐ ܠܦܘܬ ܝܗܒܬܐ ܟܢܝܫܬܐ (aggregate)، ܐܝܟ ܥܘܡܪܐ ܡܨܥܝܐ ܕܡܫܬܘܬܦ̈ܢܐ، ܟܓܠܐ ܠ"ܥܩܝܡܘܬܐ ܐܩܘܠܘܓܝܬܐ" (ecological bias) – ܐܣܘܪܐ ܒܝܢܝ ܒܘܨ̈ܝܐ ܠܐ ܝܠܗ ܐܣܘܪܐ ܒܝܢܝ ܒܢܝ̈ ܐܢܫܐ (Harrer et al., 2021, p. 189). Cooke (2024، ܦܐܬܐ 146) ܟܡܩܘܒܠ ܚܡܫܐ ܒܘܨ̈ܝܐ ܠܐ ܒܨܝܪ ܓܘ ܟܠ ܓܘܕܐ؛ Kumar (2023، ܦܐܬܐ 57) ܟܡܝܬܐ ܥܝܕܐ ܩܠܝܢܝܩܝܐ ܕܓܘܗ p ܙܥܘܪܐ ܡܢ .10 ܓܘ ܒܘܚܪܢܐ ܕܦܘܪܫܢܐ ܒܝܢܝ ܓܘ̈ܕܐ ܡܢ ܩܕܡ ܡܬܚܫܒ ܪܫܝܡܐ، ܡܛܠ ܕܒܘܚܪܢܐ ܟܪܝܗܐ ܝܠܗ. ܘ-Ringquist (2013، ܦܐܬܐ 142) ܟܓܒܐ meta-regression – ܚܕ ܡܘܕܝܠ ܥܡ ܡܫܬܚܠܦܢܐ ܕܓܘܕܐ ܐܝܟ ܡܢܒܝܢܐ – ܥܠ ܡܝܛܐ-ܐܢܐܠܝܣ̈ܝܣ ܦܪ̈ܝܫܐ ܩܐ ܟܠ ܓܘܕܐ، ܕ"ܚܝܠܐ ܕܝܠܗܘܢ ܒܨܝܪ ܝܠܗ"؛ ܐܗܐ ܝܠܗ ܚܬܝܬܐܝܬ ܐܘܪܚܐ ܬܪܝܢܝܬܐ ܓܘ ܦܐܬܐ (τ² ܡܫܘܬܦܐ).

ܡܣܒ ܒܐܦ̈ܐ ܕܡܦܪܣܢܘܬܐ

ܒܘܨ̈ܝܐ ܥܡ ܡܥܒܕ̈ܢܘܝܬܐ ܪ̈ܒܬܐ ܘܪ̈ܫܝܡܬܐ ܟܡܬܦܪܣܝ ܒܝܫ، ܘܡܛܠ ܗܕܐ ܡܝܛܐ-ܐܢܐܠܝܣܝܣ ܕܟܡܬܬܟܠܐ ܥܠ ܟܬܒ̈ܐ ܦܪ̈ܝܣܐ ܡܨܝܐ ܕܡܫܥܪܐ ܝܬܝܪܐ (Borenstein et al., 2009, p. 277). funnel plot ܟܡܚܘܝܐ ܟܠ ܒܘܨܝܐ ܠܦܘܬ ܡܥܒܕܢܘܬܐ ܘܛܥܝܘܬܐ ܬܩܝܢܬܐ ܕܝܠܗ؛ ܕܠܐ ܥܩܝܡܘܬܐ ܢܘܩ̈ܙܐ ܟܡܬܒܕܪܝ ܫܘܝܐܝܬ ܚܕܪ ܡܨܥܝܬܐ، ܘܒܘܨ̈ܝܐ ܙܥܘܪ̈ܐ ܕܚܣܝ̈ܪܐ ܝܢܐ ܓܘ ܚܕ ܓܢܒܐ ܝܢܐ ܐܬܐ ܕܙܘܗܪܐ. ܒܘܚܪܢܐ ܕ-Egger ܟܒܚܪ ܠܐ ܫܘܝܘܬܐ (asymmetry) ܒܪܝܓܪܫܢ (Harrer et al., 2021, pp. 236-238)، ܘTrim-and-Fill ܟܡܫܠܡ ܒܘܨ̈ܝܐ "ܚܣܝ̈ܪܐ" ܗܕܟܡܐ ܕ-funnel ܫܘܝܐ ܗܘܐ ܘܟܚܫܒ ܫܘܥܪܐ ܡܬܘܪܨܐ (Borenstein et al., 2009, p. 286).

ܐܠܐ – ܘܐܗܐ ܝܠܗ ܪܝܫܝܐ – ܬܪܝܢ ܐܘܪ̈ܚܬܐ ܟܡܫܟܚܝ "ܡܥܒܕܢܘܬܐ ܕܒܘܨ̈ܝܐ ܙܥܘܪ̈ܐ" (small-study effect)، ܠܐ ܡܣܒ ܒܐܦ̈ܐ ܕܡܦܪܣܢܘܬܐ: ܡܥܒܕܢܘܬܐ ܡܨܝܐ ܕܗܘܝܐ ܪܒܬܐ ܒܝܫ ܓܘ ܒܘܨ̈ܝܐ ܙܥܘܪ̈ܐ ܡܛܠ ܣܒ̈ܒܐ ܫܪ̈ܝܪܐ (ܟܢܫܐ ܟܠܢܝܐ ܦܪܝܫܐ، ܚܬܝܬܘܬܐ ܦܪܝܫܬܐ، ܛܝܒܘܬܐ ܦܪܝܫܬܐ)، ܝܢ ܒܓܕܫܐ (Borenstein et al., 2009, p. 291; Harrer et al., 2021, pp. 235-236). ܡܛܠ ܗܕܐ ܟܟܬܒܚ "ܐܢ ܠܐ ܫܘܝܘܬܐ ܢܦܝܩܬܐ ܝܠܗ̇ ܡܢ ܥܩܝܡܘܬܐ، ܦܘܫܩܐ ܟܣܗܕ ܕ…". ܒܘܚܪ̈ܢܐ ܟܪܝܗ̈ܐ ܝܢܐ، ܘܡܩܘܒܠܐ ܝܠܗ ܕܡܪܗܛܚ ܠܗܘܢ ܒܣ ܐܝܡܢ ܕܐܝܬ ܠܐ ܒܨܝܪ ܡܢ 10 ܒܘܨ̈ܝܐ (Sterne et al., 2011، ܐܝܟ ܕܡܬܝ̈ܬܐ ܝܢܐ ܓܘ Harrer et al., 2021، ܦܐܬܐ 242)، ܘܡܛܠ ܗܕܐ ܠܐ ܐܝܬܘܬܐ ܕܠܐ ܫܘܝܘܬܐ ܪܫܝܡܬܐ ܠܐ ܟܡܚܬܡܐ ܫܘܝܘܬܐ (Borenstein et al., 2009, p. 291). Trim-and-Fill "ܠܐ ܟܝܗܒ ܦܐܪ̈ܐ ܡܗܝܡܢ̈ܐ ܐܝܡܢ ܕܦܘܪܫܢܐ ܒܝܢܝ ܒܘܨ̈ܝܐ ܪܒܐ ܝܠܗ"، ܘܓܘ ܣܓܝܐܐ ܕܥܕ̈ܢܐ ܠܐ ܟܬܪܨ ܣܦܩ (Harrer et al., 2021, pp. 243, 282)؛ ܘܠܝܬ ܐܘܪܚܐ ܕܟܦܠܚܐ ܛܒ ܐܝܡܢ ܕ-I² ܚܕܪ 75% ܝܠܗ (ܬܡܢ، ܦܐܬܐ 282). ܐܘܪ̈ܚܬܐ ܚܕ̈ܬܐ ܒܝܫ – PET-PEESE، p-curve، ܡܘܕ̈ܝܠܐ ܕܓܘܒܝܐ (selection models) – ܠܝܬ ܓܘ ܦܐܬܐ، ܘ"ܗܠ ܗܫܐ ܠܝܬ ܙܟܝܐ ܓܠܝܐ" (ܬܡܢ، ܦܐܬܐ 281). ܐܘܪܚܐ ܛܒܬܐ ܡܢ ܟܠܗ: ܒܨܝܐ ܕܒܘܨ̈ܝܐ ܕܠܐ ܦܪܝܣ̈ܐ ܝܢܐ (ܬܡܢ).

"ܐܦ ܐܗܐ ܘܐܦ ܐܗܐ" ܥܠ Trim-and-Fill: Borenstein ܘܚܒܪ̈ܘܗܝ (2009، ܦܐܬܐ 286) ܟܡܚܘܝܝ ܠܗ ܐܝܟ ܐܘܪܚܐ ܠܫܘܥܪܐ ܕܡܥܒܕܢܘܬܐ ܡܬܘܪܨܬܐ، ܘ-Ringquist (2013، ܦܐܬܐ 256) ܠܐ ܟܡܩܘܒܠ ܠܗ ܒܟܠ ܓܘ ܒܘܨ̈ܝܐ ܕܡܕܒܪܢܘܬܐ (policy) ܘܕܡܕܒܪܢܘܬܐ ܕܥܡܐ – ܐܝܡܢ ܕܐܝܬ ܫܘܚܠܦܐ ܫܪܝܪܐ ܒܝܢܝ ܡܥܒܕ̈ܢܘܝܬܐ ܐܗܘ ܟܙܥܪ ܣܓܝ ܡܥܒܕܢܘܬܐ ܡܨܥܝܬܐ. ܐܦ ܒܘܚܪܢܐ ܕ-Egger ܟܗܘܐ ܪܟܝܟܐ ܝܬܝܪܐ ܐܝܡܢ ܕܦܘܪܫܢܐ ܒܝܢܝ ܒܘܨ̈ܝܐ ܪܒܐ ܝܠܗ، ܘܡܢܬܐ ܕܦܐܪ̈ܐ ܐܝܓܒ̈ܝܐ ܛܥ̈ܝܐ (false positives) ܓܘܗ ܡܨܝܐ ܕܡܩܪܒܐ ܠ-100% ܓܘ ܡܝܛܐ-ܐܢܐܠܝܣ̈ܝܣ ܪ̈ܒܐ ܘܦܪ̈ܝܫܐ (Peters et al., 2006، ܐܝܟ ܕܡܬܝ̈ܬܐ ܝܢܐ ܓܘ Ringquist, 2013، ܦܐܬܐ 249). ܡܩܘܒܠܘܬܐ ܕܬܡܢ: ܒܨܝܐ ܓܡܝܪܐ ܐܦ ܓܘ ܡܘܕ̈ܥܢܘܝܬܐ ܕܡܠܟܘܬܐ ܘܓܘ ܟܬܒ̈ܐ ܕܠܐ ܦܪܝܣ̈ܐ ܝܢܐ (grey literature)، ܘܡܫܬܚܠܦܢܐ "ܦܪܝܣܐ / ܠܐ ܦܪܝܣܐ" ܐܝܟ ܓܘܕܐ ܡܢܬܢܝܐ (ܦܐܬܐ 265-266).

ܝܕܥܬܐ ܕܢܦܫܐ، ܒܘܨܝܐ ܩܠܝܢܝܩܝܐ، ܡܕܒܪܢܘܬܐ

ܝܕܥܬܐ ܕܢܦܫܐ (psychology). Cooke (2024) ܟܟܬܒ ܩܐ ܝܕ̈ܘܥܐ ܕܢܦܫܐ، ܘܟܡܩܪܒ ܬܪܝܢ ܪ̈ܒܘܝܬܐ ܕܡܥܒܕܢܘܬܐ: r ܡܢ ܒܘܨ̈ܝܐ ܕܫܘܐ̈ܠܐ (survey) ܘ-d (ܓܘ ܦܐܬܐ – g) ܡܢ ܢܣܝ̈ܘܢܐ ܘܥܒ̈ܕܐ (interventions؛ ܦܐܬܐ 1، 75). ܬܪܝܢ ܙܘܗܪ̈ܐ ܥܡܠܢ̈ܝܐ: r = .5 ܝܠܗ ܐܣܘܪܐ ܕܚܕ̈ܕܐ ܪܒܐ، ܐܠܐ d = .5 ܝܠܗ ܡܥܒܕܢܘܬܐ ܡܨܥܝܬܐ – ܘܣܓܝܐܐ ܡܢ d ܓܘ ܝܕܥܬܐ ܕܢܦܫܐ ܟܦܝܫܝ ܒܝܢܝ −0.50 ܘ-+0.50، ܗܕܟܐ ܕܐܢ ܣܓܝܐܐ ܡܢ ܛܝ̈ܡܐ ܕܝܘܟܘܢ ܪ̈ܒܐ ܝܢܐ – "ܛܒܐ ܝܠܗ ܕܒܚܪܚ ܚܘܫܒ̈ܢܐ" (ܦܐܬܐ 26، 29)؛ ܘܦܘܪܫܢܐ ܒܝܢܝ ܒܘܨ̈ܝܐ (heterogeneity) ܝܠܗ ܢܡܘܣܐ، ܠܐ ܢܘܟܪܝܐ (ܦܐܬܐ 135). ܐܝܡܢ ܕܒܘܨܝܐ ܬܢܠܗ ܟܡܐ ܡܫܘ̈ܚܬܐ ܝܢ ܟܡܐ ܙܒ̈ܢܐ، ܚܕ ܡܢ ܐܘܪ̈ܚܬܐ ܝܠܗ̇ ܕܓܒܚ ܝܢ ܕܥܒܕܚ ܡܨܥܝܬܐ ܡܢ ܩܕܡ، ܘܐܘܪ̈ܚܬܐ ܕܣܓܝ ܕܪ̈ܓܐ (multilevel) ܟܫܒܩܝ ܠܡܥܠܬܐ ܕܟܠܗܘܢ (ܦܐܬܐ 167-169) – ܐܢܝ ܦܐܬܐ ܠܐ ܟܪܗܛܐ. ܪܘܫܡܐ ܩܕܡܝܐ ܓܘ PROSPERO ܘܬܘܢܝܐ ܠܦܘܬ PRISMA (ܦܐܬܐ 46-47).

ܒܘܨܝܐ ܩܠܝܢܝܩܝܐ. Kumar (2023) ܟܟܬܒ ܩܐ ܒܨܘ̈ܝܐ ܩܠܝܢܝܩ̈ܝܐ: ܡܝܛܐ-ܐܢܐܠܝܣܝܣ ܕܢܣܝ̈ܘܢܐ ܡܛܟܣ̈ܐ (controlled trials) ܓܘ ܪܫܐ ܕܕܪ̈ܓܐ ܕܣܗܕ̈ܘܬܐ (ܦܐܬܐ 1-2)، ܘܬܘܢܝܐ ܠܦܘܬ PRISMA (ܦܐܬܐ 1، 3). ܩܐ ܦܐܪܐ ܕܬܪܝܢ ܛܝ̈ܡܐ – ܦܘܚܡܐ ܕܣܘܟ̈ܢܐ ܝܢ ܦܘܚܡܐ ܕܣܟܘ̈ܝܐ ܩܐ ܡܬܩܠܢܘܬܐ، ܡܛܠ ܕܩܝ̈ܡܐ ܝܢܐ ܒܝܫ ܒܝܢܝ ܡܢ̈ܘܬܐ ܕܫܬܐܣܐ ܦܪ̈ܝܫܐ، ܘܦܘܪܫܢܐ ܕܣܘܟ̈ܢܐ ܩܐ ܡܚܘܝܐ ܕܝܘܬܪܢܐ ܩܠܝܢܝܩܝܐ (ܦܐܬܐ 29)؛ ܩܐ ܦܐܪܐ ܡܬܡܫܚܢܐ – ܦܘܪܫܢܐ ܕܡܨܥܝ̈ܬܐ ܐܝܡܢ ܕܟܠ ܒܘܨ̈ܝܐ ܡܫܚܠܗܘܢ ܒܗܝ ܣܒܠܬܐ، ܘܦܘܪܫܢܐ ܡܬܩܢܐ ܒܣ ܐܝܡܢ ܕܠܐ (ܦܐܬܐ 27-28). ܛܥܝ̈ܘܬܐ ܕܐܗܘ ܣܓܝ ܟܡܚܙܐ: ܛܥܝ̈ܘܬܐ ܕܟܬܝܒܬܐ ܘܫܘܚܠܦܐ ܕܡܢ̈ܝܢܐ، ܛܥܝܘܬܐ ܬܩܝܢܬܐ ܕܡܨܥܝܬܐ ܕܥܠܝܠܬܐ ܝܠܗ̇ ܒܕܘܟܬܐ ܕܣܛܝܘܬܐ ܬܩܝܢܬܐ، ܘܗܘ ܒܘܨܝܐ ܬܪܝܢ ܓܗ̈ܐ (ܦܐܬܐ 108-109). ܠܦܘܬ ܚܘܫܒܐ ܕܝܠܗ ܣܢܝܩܐ ܝܠܗ ܠܐ ܒܨܝܪ ܡܢ 10 ܒܘܨ̈ܝܐ ܩܐ ܚܬܡܬܐ ܬܪܝܨܬܐ (ܦܐܬܐ 109) – ܬܒܥܬܐ ܩܫܝܬܐ ܡܢ ܡܐ ܕܡܩܘܒܠܐ ܝܠܗ، ܕ-Borenstein ܘܚܒܪ̈ܘܗܝ (2009، ܦܐܬܐ 84) ܟܟܬܒܝ ܠܗ̇ ܒܐܘܪܚܐ ܐܚܪܬܐ: ܥܡ ܩܠܝܠ ܒܘܨ̈ܝܐ ܟܠ ܓܘܒ̈ܝܐ ܐܝܬܠܗܘܢ ܥܩܬܐ.

ܡܕܒܪܢܘܬܐ ܘܡܕܒܪܢܘܬܐ ܕܥܡܐ (policy and public administration). Ringquist (2013) ܟܟܬܒ ܩܐ ܒܘܨܝܐ ܕܓܘܗ ܣܓܝܐܐ ܡܢ ܒܘܨ̈ܝܐ ܕܚܙ̈ܝܬܐ ܝܢܐ (observational)، ܡܥܒܕ̈ܢܘܝܬܐ ܟܐܬܝ ܡܢ ܪܝܓܪܫ̈ܢܐ (ܐܣܘܪܐ ܕܚܕ̈ܕܐ ܡܢܬܢܝܐ – ܚܙܝܡܘܢ "ܪܒܘܬܐ ܕܡܥܒܕܢܘܬܐ")، ܘܦܘܪܫܢܐ ܒܝܢܝ ܒܘܨ̈ܝܐ ܝܠܗ ܢܡܘܣܐ (ܦܐܬܐ 18، 33). ܡܢܝܢܐ ܕܒܘܨ̈ܝܐ ܪ̈ܫܝܡܐ ܟܡܛܥܐ ܝܬܝܪ ܬܡܢ: ܥܣܪܝܢ ܒܘܨ̈ܝܐ ܥܡ ܚܝܠܐ ܕ-.50 ܟܦܠܓܝ ܦܠܓܐ-ܦܠܓܐ، ܘܚܬܡܬܐ ܕ"ܣܗܕ̈ܘܬܐ ܦܠܝܓ̈ܐ ܝܢܐ" – "ܛܥܝܬܐ ܝܠܗ̇" (ܦܐܬܐ 24). ܡܛܠ ܗܕܐ ܠܦܘܬ ܚܘܫܒܐ ܕܝܠܗ meta-regression ܝܠܗ "ܢܘܩܙܐ ܪܝܫܝܐ" (ܦܐܬܐ 20)؛ ܒܘܨܝܐ ܓܘ ܣܓܝܐܐ ܕܥܕ̈ܢܐ ܟܝܗܒ ܟܡܐ ܡܥܒܕ̈ܢܘܝܬܐ، ܘܬܠܝܘܬܐ ܒܝܢܝܗܝ ܣܢܝܩܐ ܝܠܗ̇ ܠܬܘܪܨܐ (ܦܐܬܐ 150-151) – ܬܪܝܢ ܥܒ̈ܕܐ ܕܦܐܬܐ ܠܐ ܟܥܒܕܐ. ܡܐ ܕܦܐܬܐ ܟܝܗܒܐ: ܓܘ̈ܕܐ ܡܢܬܢ̈ܝܐ ܠܦܘܬ ܡܫܬܚܠܦܢܐ ܕܒܘܨܝܐ (ܣܘܟܠܐ، ܙܢܐ ܕܬܘܟܢܝܬܐ، ܦܪܝܣܐ / ܠܐ ܦܪܝܣܐ) ܓܘ ܡܘܕܝܠ ܡܫܘܬܦܐ، ܐܝܟ meta-regression ܥܡ ܚܕ ܡܢܒܝܢܐ ܕܓܢ̈ܣܐ.

ܩܪܝܢܐ ܕܡܦܩܢܐ (How to read the output)

ܠܘܚܐ 1 – ܒܘܨ̈ܝܐ: ܩܐ ܟܠ ܒܘܨܝܐ – ܪܒܘܬܐ ܕܡܥܒܕܢܘܬܐ، ܬܚܘܡܐ ܕܬܘܟܠܢܐ، ܛܥܝܘܬܐ ܬܩܝܢܬܐ ܘܡܬܩܠܐ ܓܘ ܬܪܝܢ ܡܘܕ̈ܝܠܐ. ܨܘܪܬܐ 1 – ܨܘܪܬܐ ܕܥܒܐ (forest plot): ܗܢܝ ܒܘܨ̈ܝܐ ܓܘ ܨܘܪܬܐ، ܥܡ ܡܪܒܥܐ ܡܣܠܝܐ (diamond) ܩܐ ܟܠ ܡܥܒܕܢܘܬܐ ܡܬܩܠܬܐ ܘܣܪܛܐ ܩܐ ܬܚܘܡܐ ܕܡܢܒܝܢܘܬܐ. ܠܘܚܐ 2 – ܡܥܒܕܢܘܬܐ ܡܬܩܠܬܐ: ܡܥܒܕܢܘܬܐ ܩܝܡܬܐ، ܡܥܒܕ̈ܢܘܝܬܐ ܓܕܫܢ̈ܝܬܐ، ܘܡܥܒܕ̈ܢܘܝܬܐ ܓܕܫܢ̈ܝܬܐ ܥܡ Knapp-Hartung. ܠܘܚܐ 3 – ܦܘܪܫܢܐ ܒܝܢܝ ܒܘܨ̈ܝܐ: Q، τ²، τ، I² ܘ-H² ܥܡ ܬܚܘ̈ܡܐ ܕܬܘܟܠܢܐ، ܘܬܚܘܡܐ ܕܡܢܒܝܢܘܬܐ.

ܐܝܡܢ ܕܓܒܚ ܓܘܕܐ ܡܢܬܢܝܐ – ܠܘܚܐ ܕܓܘ̈ܕܐ ܡܢܬܢ̈ܝܐ ܥܡ ܫܘܥܪܐ ܓܘ ܟܠ ܓܘܕܐ ܒܬܪܬܝܢ ܐܘܪ̈ܚܬܐ ܘܒܘܚܪ̈ܢܐ ܕܦܘܪܫܢܐ ܓܘ ܡܥܝܪܢܘܬܐ. ܡܢ ܬܠܬܐ ܒܘܨ̈ܝܐ ܘܠܥܠ – funnel plot ܘܠܘܚܐ ܕܡܥܒܕܢܘܬܐ ܕܒܘܨ̈ܝܐ ܙܥܘܪ̈ܐ (Egger، Trim-and-Fill)، ܘܒܕܚܩܐ – ܫܒܩܬܐ ܕܟܠ ܒܘܨܝܐ ܒܕܘܪܗ (leave-one-out): ܐܢ ܫܒܩܬܐ ܕܚܕ ܒܘܨܝܐ ܟܫܢܝܐ ܨܘܪܬܐ، ܐܗܘ ܡܥܒܕܢܐ ܝܠܗ ܝܬܝܪ (Harrer et al., 2021, p. 156).

ܫܪ̈ܛܐ ܘܙܘܗܪ̈ܐ (Assumptions and warnings)

ܚܕܐ ܡܥܒܕܢܘܬܐ ܡܢ ܚܕ ܒܘܨܝܐ. ܟܠ ܚܘܫܒܢܐ ܟܣܒܪ ܕܟܠ ܣܕܪܐ ܕܘܡܝܐ (sample) ܠܐ ܬܠܝܐ ܝܠܗ. ܒܘܨܝܐ ܕܬܢܠܗ ܟܡܐ ܦܐܪ̈ܐ ܥܠ ܗܢܝ ܡܫܬܘܬܦ̈ܢܐ (ܟܡܐ ܣܒ̈ܠܬܐ، ܟܡܐ ܙܒ̈ܢܐ ܕܡܫܘܚܬܐ) ܠܐ ܝܠܗ ܟܡܐ ܒܘܨ̈ܝܐ – ܡܥܠܬܐ ܕܟܠܗܘܢ "ܒܕ ܡܡܛܝܐ ܠܫܘ̈ܥܪܐ ܛܥ̈ܝܐ ܕܫܘܚܠܦܐ" (Borenstein et al., 2009, p. 215)؛ ܟܓܒܚ ܚܕ ܦܐܪܐ ܠܦܘܬ ܢܡܘܣܐ ܕܡܚܕܕܐ ܝܠܗ ܡܢ ܩܕܡ، ܝܢ ܟܡܦܠܚܚ ܒܐܘܪ̈ܚܬܐ ܩܐ ܒܢܝ̈ܢܐ ܡܪܟ̈ܒܐ (ܬܡܢ، ܡܢܬܐ 5)، ܕܠܝܬ ܓܘ ܦܐܬܐ. ܓܘ̈ܕܐ ܡܢܬܢ̈ܝܐ ܠܐ ܬܠܝ̈ܐ ܓܘ ܒܘܨܝܐ (ܡܬܠܐ: ܝܠܘ̈ܕܐ ܘܓܘܪ̈ܐ) ܡܨܝܐ ܕܡܥܠܚ ܐܝܟ ܬܪܝܢ ܣܕܪ̈ܐ (ܬܡܢ).

ܩܘܪܒܐ ܢܘܪܡܠܝܐ. ܦܘܫܩܐ ܟܚܫܒ ܛܥܝ̈ܘܬܐ ܬܩܝ̈ܢܬܐ ܐܝܟ ܝܕܝ̈ܥܬܐ ܘܡܥܒܕ̈ܢܘܝܬܐ ܐܝܟ ܕܐܝܬܠܗܘܢ ܦܘܠܓܐ ܢܘܪܡܠܝܐ (normal distribution) – ܩܘܪܒܐ ܕܛܒܐ ܝܠܗ ܒܝܫ ܓܘ ܕܘ̈ܡܝܐ ܪ̈ܒܐ ܘܓܘ ܣܒ̈ܠܬܐ ܦܐܝ̈ܬܐ (ܠܘܓ ܩܐ ܦܘܚܡ̈ܐ، z ܕ-Fisher ܩܐ ܐܣܘܪ̈ܐ ܕܚܕ̈ܕܐ)؛ ܓܘ ܒܘܨ̈ܝܐ ܙܥܘܪ̈ܐ ܣܓܝ ܝܢ ܓܘ ܓܕܫ̈ܐ ܢܕܝܪ̈ܐ ܐܘܪ̈ܚܬܐ ܚܬܝ̈ܬܐ ܓܒܝ̈ܬܐ ܝܢܐ (Stijnen et al., 2021, p. 43)، ܕܠܝܬ ܓܘ ܦܐܬܐ.

ܡܘܕܝ ܠܐ ܟܚܫܒܐ ܐܗܐ ܦܐܬܐ. meta-regression ܥܡ ܡܢܒܝܢܐ ܡܬܡܫܚܢܐ، ܡܘܕ̈ܝܠܐ ܕܣܓܝ ܕܪ̈ܓܐ (multilevel) ܘܕܣܓܝ ܡܫܬܚܠܦ̈ܢܐ (multivariate)، network meta-analysis، ܐܘܪ̈ܚܬܐ ܕ-Mantel-Haenszel ܘ-Peto ܩܐ ܠܘ̈ܚܐ 2×2، ܒܘܚܪܢܐ ܕ-Peters، PET-PEESE، p-curve ܘܡܘܕ̈ܝܠܐ ܕܓܘܒܝܐ (selection models)، ܘܡܝܛܐ-ܐܢܐܠܝܣܝܣ ܕܒܘܚܪ̈ܢܐ ܕܦܘܪܫܢܐ ܕܟܘܪܗܢܐ. ܬܚܘ̈ܡܐ: 2 ܒܘܨ̈ܝܐ ܠܐ ܒܨܝܪ (3 ܩܐ ܬܚܘܡܐ ܕܡܢܒܝܢܘܬܐ ܘܩܐ ܒܘܚܪ̈ܢܐ ܕܒܘܨ̈ܝܐ ܙܥܘܪ̈ܐ)؛ ܒܘܨ̈ܝܐ ܥܡ ܩܠܝܬܐ ܚܣܝܪܬܐ ܓܘ ܥܡܘ̈ܕܐ ܓܒܝ̈ܐ – ܠܐ ܥܠܝܠ̈ܐ ܝܢܐ، ܘܦܐܬܐ ܟܡܘܕܥܐ.

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

ܓܘ ܢܘ̈ܣܚܐ ܚܕ̈ܬܐ ܕ-SPSS Statistics ܐܝܬ ܪܫܝܡܬܐ ܕܡܝܛܐ-ܐܢܐܠܝܣܝܣ (Analyze › Meta Analysis)، ܠܦܘܬ ܙܢܐ ܕܝܗܝ̈ܒܬܐ – ܐܗܐ ܝܠܗ ܡܘܕܥܢܘܬܐ ܟܠܢܝܬܐ ܥܠ ܬܘܟܢܝܬܐ، ܕܠܐ ܝܠܗ̇ ܒܚܝܪܬܐ ܐܟܐ. PSPP، ܚܠܦܐ ܕܡܓܢ، ܠܐ ܐܝܬ ܓܘܗ ܡܝܛܐ-ܐܢܐܠܝܣܝܣ. ܡܛܠ ܗܕܐ ܦܐܬܐ ܟܡܦܩܐ ܒܕܘܟܬܐ ܕܣܝܢܬܐܟܣ SPSS ܣܩܪܝܦܬ R ܥܡ ܝܗܝ̈ܒܬܐ ܥܠܝ̈ܠܬܐ ܓܘܗ، ܕܟܡܬܢܐ ܡܦܩܢܐ ܒܨܪܪܐ metafor – ܘܐܗܘ ܪܗܛܐ ܝܠܗ ܓܘ R ܥܠ ܦܐܝܠ ܕܡܬܠܐ.

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

ܨܪܪܐ metafor (Viechtbauer, 2010): escalc ܟܚܫܒܐ ܪܒܘܬܐ ܕܡܥܒܕܢܘܬܐ ܘܫܘܚܠܦܐ ܩܐ ܟܠ ܒܘܨܝܐ، rma ܟܪܗܛܐ ܡܘܕܝܠ (method – ܫܘܥܪܐ؛ test = "knha" – Knapp-Hartung؛ mods – ܡܢܒ̈ܝܢܐ)، confint ܟܝܗܒܐ ܬܚܘ̈ܡܐ ܕܬܘܟܠܢܐ ܩܐ ܦܘܪܫܢܐ ܒܝܢܝ ܒܘܨ̈ܝܐ، ܘ-forest، funnel، regtest، trimfill ܘ-leave1out – ܐܚܪ̈ܢܐ. Harrer ܘܚܒܪ̈ܘܗܝ (2021) ܟܡܠܦܝ ܗܘ ܚܘܡܪܐ ܒܨܪܪܐ meta. ܦܐܬܐ ܒܚܝܪܬܐ ܝܠܗ̇ ܩܘܒܠ metafor ܓܘ ܟܠ ܡܢ̈ܝܢܐ ܕܡܦܩܢܐ، ܘܣܩܪܝܦܬ ܕܠܬܚܬ ܪܗܛܐ ܝܠܗ ܐܝܟ ܕܐܝܬܘܗܝ ܥܠ ܦܐܝܠ ܕܡܬܠܐ (ܛܝ̈ܡܐ ܓܘ ܡܥܝܪ̈ܢܘܬܐ).

# ܡܝܛܐ-ܐܢܐܠܝܣܝܣ – ܦܪܘܦܣܘܪ ܣܛܐܛ. ܐܗܐ ܦܐܝܠ ܢܛܝܪܐ ܝܠܗ ܒ-UTF-8؛ ܟܠ ܣܕܪܐ ܕܡܥܝܪܢܘܬܐ ܟܫܪܐ ܒܡܠܬܐ ܕܣܘܪܝܬ
library(readxl)    # ܩܪܝܢܐ ܕܐܩܣܠ
library(metafor)   # ܡܝܛܐ-ܐܢܐܠܝܣܝܣ (Viechtbauer, 2010)

# ܛܥܢܐ: ܣܕܪܐ = ܒܘܨܝܐ؛ ܓܠܝܘܢܐ "Data"
d <- read_excel("C:/Rdata/DATA_meta_example_eng.xlsx", sheet = "Data")
d <- d[complete.cases(d[, c("mean_mentor", "sd_mentor", "n_mentor", "mean_control", "sd_control", "n_control")]), ]   # 17 ܡܢ 18

# ܪܒܘܬܐ ܕܡܥܒܕܢܘܬܐ: g ܕ-Hedges (mentoring ܒܨܝܪ ܦܘܚܡܐ) ܘܫܘܚܠܦܐ ܕܝܠܗ
d <- escalc(measure = "SMD", m1i = mean_mentor, sd1i = sd_mentor, n1i = n_mentor,
            m2i = mean_control, sd2i = sd_control, n2i = n_control, data = d)

# ܡܥܒܕ̈ܢܘܝܬܐ ܓܕܫܢ̈ܝܬܐ (REML)، ܘܓܢܒܝܗܝ ܡܥܒܕܢܘܬܐ ܩܝܡܬܐ ܘ-Knapp-Hartung
re <- rma(yi, vi, data = d, method = "REML", slab = study)
re                                                      # g = 0.48 [0.34, 0.62]; Q(16) = 36.07, p = .003; I² = 51.8%
rma(yi, vi, data = d, method = "FE")                    # ܡܥܒܕܢܘܬܐ ܩܝܡܬܐ: g = 0.49 [0.40, 0.58]
rma(yi, vi, data = d, method = "REML", test = "knha")   # Knapp-Hartung: [0.34, 0.62], t(16) = 7.35
confint(re)                                             # τ² = 0.042 [0.005, 0.111]; I² [11.3%, 74.1%]

# ܬܚܘܡܐ ܕܡܢܒܝܢܘܬܐ ܠܦܘܬ Higgins ܘܚܒܪ̈ܘܗܝ – t ܥܡ k − 2 ܕܪ̈ܓܐ ܕܚܐܪܘܬܐ (predict ܟܡܦܠܚ ܒܦܘܠܓܐ ܢܘܪܡܠܝܐ)
c(re$b) + c(-1, 1) * qt(.975, re$k - 2) * sqrt(re$tau2 + re$se^2)   # ܬܚܘܡܐ: [0.02, 0.94]

# ܨܘܪܬܐ ܕܥܒܐ ܘ-funnel plot
forest(re, addpred = TRUE)
funnel(re)

# ܓܘ̈ܕܐ ܡܢܬܢ̈ܝܐ ܠܦܘܬ ܐܣܟܝܡܐ (1 = ܕܓܘܕܐ، 2 = ܝܚܝܕܝܬܐ): τ² ܦܪܝܫܐ، ܘܒܘܚܪܢܐ Q ܒܝܢܝ ܫܘ̈ܥܪܐ ܕܓܘ̈ܕܐ
sub <- lapply(split(d, d$format), function(x) rma(yi, vi, data = x, method = "REML"))
sub                                                     # ܕܓܘܕܐ: g = 0.39 [0.23, 0.55]؛ ܝܚܝܕܝܬܐ: g = 0.57 [0.35, 0.80]
rma(sapply(sub, coef), sapply(sub, vcov), method = "FE")   # Q ܒܝܢܝ: Q(1) = 1.67, p = .196
rma(yi, vi, mods = ~ factor(format), data = d, method = "REML", control = list(threshold = 1e-10))   # τ² ܡܫܘܬܦܐ: QM(1) = 1.54, p = .214؛ R² = 16.0% (ܕܠܐ control: 15.9%، ܟܠܝܬܐ ܡܩܕܡܬܐ)

# ܡܥܒܕܢܘܬܐ ܕܒܘܨ̈ܝܐ ܙܥܘܪ̈ܐ: ܒܘܚܪܢܐ ܕ-Egger ܘ-Trim-and-Fill
regtest(rma(yi, vi, data = d, method = "FE"), model = "lm")   # ܡܢܝܢܐ ܩܝܡܐ (intercept) ܕ-Egger: t(15) = -0.24, p = .812
trimfill(re)                                            # ܠܐ ܡܘܣܦ̈ܐ ܝܢܐ ܒܘܨ̈ܝܐ
leave1out(re)                                           # ܫܒܩܬܐ ܕܟܠ ܒܘܨܝܐ ܒܕܘܪܗ

ܬܘܢܝܐ ܕܡܫܟܚ̈ܢܘܬܐ (reporting the results)

ܟܬܢܚ ܡܘܕܝܠ ܘܫܘܥܪܐ ܕ-τ² ܘܐܢ Knapp-Hartung ܥܒܝܕܐ ܝܠܗ – Harrer ܘܚܒܪ̈ܘܗܝ (2021، ܦܐܬܐ 104) ܟܝܗܒܝ ܢܘܣܚܐ ܕܡܬܠܐ: "ܡܛܠ ܕܡܣܟܝܢ ܗܘܝܚ ܠܦܘܪܫܢܐ ܪܒܐ ܒܝܢܝ ܒܘܨ̈ܝܐ، ܡܘܕܝܠ ܕܡܥܒܕ̈ܢܘܝܬܐ ܓܕܫܢ̈ܝܬܐ ܡܬܦܠܚ ܝܠܗ… ܫܘܥܪܐ REML ܡܬܦܠܚ ܝܠܗ ܩܐ ܚܘܫܒܢܐ ܕ-τ²… ܘܬܘܪ̈ܨܐ ܕ-Knapp-Hartung ܩܐ ܚܘܫܒܢܐ ܕܬܚܘܡܐ ܕܬܘܟܠܢܐ". ܘܒܬܪ ܗܕܐ: ܡܢܝܢܐ ܕܒܘܨ̈ܝܐ ܘܕܡܫܬܘܬܦ̈ܢܐ؛ ܡܥܒܕܢܘܬܐ ܡܬܩܠܬܐ ܥܡ ܬܚܘܡܐ ܕܬܘܟܠܢܐ؛ Q، τ² ܘ-I² ܥܡ ܬܚܘ̈ܡܐ ܕܬܘܟܠܢܐ، ܘܬܚܘܡܐ ܕܡܢܒܝܢܘܬܐ (Harrer et al., 2021, p. 150)؛ ܓܘ̈ܕܐ ܡܢܬܢ̈ܝܐ ܘܒܘܚܪ̈ܢܐ ܕܥܩܝܡܘܬܐ – ܐܝܟ ܕܬܘܩܢܐ ܝܠܗ ܡܢ ܩܕܡ. ܨܘܪܬܐ ܕܥܒܐ (forest plot) ܝܠܗ̇ ܡܢܬܐ ܡܩܘܒܠܬܐ ܓܘ ܬܘܢܝܐ. ܦܣܩܐ ܕܦܐܬܐ ܟܒܢܝܐ ܝܠܗ̇ ܢܘܩܙܐ ܕܫܘܪܝܐ.

ܛܥܝ̈ܘܬܐ ܕܡܬܚܙܝܢ ܣܓܝ (Common mistakes)

ܡܢܝܢܐ ܕܒܘܨ̈ܝܐ ܪ̈ܫܝܡܐ ܒܕܘܟܬܐ ܕܡܬܩܠܢܘܬܐ ܕܡܥܒܕ̈ܢܘܝܬܐ (Borenstein et al., 2009, pp. 251-252).

ܓܘܒܝܐ ܕܡܘܕܝܠ ܠܦܘܬ ܒܘܚܪܢܐ ܕܦܘܪܫܢܐ ܒܝܢܝ ܒܘܨ̈ܝܐ (Borenstein et al., 2009, p. 84; Harrer et al., 2021, p. 145).

ܩܪܝܢܐ ܕ-I² ܐܝܟ ܡܚܘܝܢܐ ܕܒܕܪܐ، ܝܢ I² ܕܣܦܪ ܐܝܟ ܣܗܕܘܬܐ ܕܫܠܡܘܬܐ (Borenstein et al., 2009, pp. 119, 122) – ܘܛܥܝܢܘܬܐ ܕܬܚܘܡܐ ܕܡܢܒܝܢܘܬܐ.

ܡܬܩܠܢܘܬܐ ܕܦܘܪܫܢܐ ܓܘܠܡܝܐ ܕܡܨܥܝ̈ܬܐ ܒܝܢܝ ܒܘܨ̈ܝܐ ܕܦܠܚܠܗܘܢ ܒܣܒ̈ܠܬܐ ܦܪ̈ܝܫܐ (Borenstein et al., 2009, p. 25)، ܝܢ ܚܘܠܛܐ ܕܐܘܪ̈ܚܬܐ – ܒܘܨܝܐ ܕܓܘܗ ܡܢܝܢܐ ܪܡܐ ܒܝܫܐ ܝܠܗ ܥܡ ܒܘܨܝܐ ܕܓܘܗ ܛܒܐ ܝܠܗ.

ܡܥܠܬܐ ܕܟܡܐ ܡܥܒܕ̈ܢܘܝܬܐ ܡܢ ܗܘ ܒܘܨܝܐ ܐܝܟ ܕܗܘܘ ܒܘܨ̈ܝܐ ܦܪ̈ܝܫܐ (Borenstein et al., 2009, p. 215).

ܦܣܩܐ ܕ"ܠܝܬ ܡܣܒ ܒܐܦ̈ܐ ܕܡܦܪܣܢܘܬܐ" ܡܛܠ ܕܒܘܚܪܢܐ ܕ-Egger ܠܐ ܗܘܐ ܪܫܝܡܐ، ܝܢ ܕ"ܐܝܬ" ܡܛܠ ܕܗܘܐ (Borenstein et al., 2009, p. 291).

ܦܘܫܩܐ ܕܓܘ̈ܕܐ ܡܢܬܢ̈ܝܐ ܐܝܟ ܥܠܬܢܘܬܐ (causality)، ܝܢ ܦܘܪܫܢܐ ܠܐ ܪܫܝܡܐ ܐܝܟ ܫܘܝܘܬܐ (Harrer et al., 2021, pp. 188-190).

ܪܘܫܡܐ ܕܡܥܒܕܢܘܬܐ ܐܝܟ "ܙܥܘܪܬܐ" ܝܢ "ܪܒܬܐ" ܠܦܘܬ ܬܚܘ̈ܡܐ ܕ-Cohen ܕܠܐ ܚܠܬܐ (context) – "ܓܘܒܝܐ ܐܚܪܝܐ" (Ellis, 2010, p. 42).

ܬܘܢܝܐ ܕ-z ܕ-Fisher ܐܝܟ ܕܗܘܐ r. ܡܬܠܐ ܕ-Cooke (2024، ܦܐܬܐ 102-105) ܟܡܘܕܥ r = 0.546 [0.416, 0.676] – ܐܠܐ ܐܗܢܐ ܛܝ̈ܡܐ ܕ-z ܝܢܐ: ܒܕܘܪܐ ܠܒܣܬܪܐ ܐܣܘܪܐ ܕܚܕ̈ܕܐ ܝܠܗ r = .50 [.39, .59]، ܘܠܦܘܬ ܬܚܘ̈ܡܐ ܕܓܘ ܟܬܒܐ ܓܢܒܗ (ܦܐܬܐ 24) – ܡܨܥܝܐ ܘܠܐ ܪܒܐ. ܦܐܬܐ ܟܠ ܐܡܢ ܟܕܥܪܐ ܠܒܣܬܪܐ.

ܡܥܠܬܐ ܕܛܥܝܘܬܐ ܬܩܝܢܬܐ ܕܡܨܥܝܬܐ ܒܕܘܟܬܐ ܕܣܛܝܘܬܐ ܬܩܝܢܬܐ (Kumar, 2023, pp. 108-109) – ܡܥܒܕܢܘܬܐ ܟܡܬܢܦܚܐ، ܘܦܘܪܫܢܐ ܒܝܢܝ ܒܘܨ̈ܝܐ ܟܣܠܩ.

ܫܒܩܬܐ ܕܒܘܨ̈ܝܐ ܕܬܢܠܗܘܢ ܒܣ "ܠܐ ܪܫܝܡܐ" – ܐܗܐ ܟܢܦܚ ܡܥܒܕܢܘܬܐ ܡܨܥܝܬܐ (Ringquist, 2013, p. 108).

ܡܒܘ̈ܥܐ

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

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Cooke, R. (2024). Meta-analysis for psychologists. Palgrave Macmillan. https://doi.org/10.1007/978-3-031-73773-2

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Harrer, M., Cuijpers, P., Furukawa, T. A., & Ebert, D. D. (2021). Doing meta-analysis with R: A hands-on guide. Chapman & Hall/CRC. https://doi.org/10.1201/9781003107347

Kumar, A. (2023). Meta-analysis in clinical research: Principles and procedures. Springer. https://doi.org/10.1007/978-981-99-2370-0

Macaskill, P., Takwoingi, Y., Deeks, J. J., & Gatsonis, C. (2023). Understanding meta-analysis. In J. J. Deeks, P. M. Bossuyt, M. M. Leeflang, & Y. Takwoingi (Eds.), Cochrane handbook for systematic reviews of diagnostic test accuracy (pp. 203-248). Wiley.

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Hedges ܘ-Olkin (1980)، Higgins ܘܚܒܪ̈ܘܗܝ، ܘ-Duval ܘ-Tweedie (2000) – ܐܝܟ ܕܡܬܝ̈ܬܐ ܝܢܐ ܓܘ Borenstein ܘܚܒܪ̈ܘܗܝ (2009)؛ Sterne ܘܚܒܪ̈ܘܗܝ (2011)، Schwarzer ܘܚܒܪ̈ܘܗܝ (2015)، Pustejovsky ܘ-Rodgers (2019) ܘ-van Aert ܘܚܒܪ̈ܘܗܝ (2016) – ܐܝܟ ܕܡܬܝ̈ܬܐ ܝܢܐ ܓܘ Harrer ܘܚܒܪ̈ܘܗܝ (2021). Peters ܘܚܒܪ̈ܘܗܝ (2006) – ܐܝܟ ܕܡܬܝ̈ܬܐ ܝܢܐ ܓܘ Ringquist (2013). ܠܦܘܬ ܢܡܘܣܐ ܕܣܐܝܛ (site rule)، ܓܘ ܪܫܝܡܬܐ ܕܡܒܘ̈ܥܐ (reference list) ܟܡܬܚܙܝ ܒܣ ܡܒܘ̈ܥܐ ܕܩܪܝ̈ܐ ܝܢܐ ܓܘ ܫܪܫܐ ܕܝܗܝ؛ ܡܬ̈ܝܬܐ ܠܦܘܬ ܦܐܬܐ ܛܒܝܥܬܐ. ܡܢ ܟܬܒ̈ܐ ܓܘ folder ܕܡܝܛܐ-ܐܢܐܠܝܣܝܣ، Cooper ܘܚܒܪ̈ܘܗܝ (2019)، Cheung (2015) ܘ-Chen ܘ-Peace (2021) ܠܐ ܝܢܐ ܡܬܝ̈ܬܐ ܓܘ ܦܐܬܐ – ܡ̈ܠܐ ܕܓܘܗܘܢ (ܟܢܘܫܝܐ ܦܬܝܐ ܕܒܘܨ̈ܝܐ، SEM، Stata) ܠܒܪ ܡܢ ܬܚܘܡܐ ܕܝܠܗ̇ ܝܢܐ. ܡܢ ܢܘܣܚܐ 2 – ܐܦ ܬܠܬܐ ܟܬܒ̈ܐ ܠܦܘܬ ܣܘܟܠܐ: Cooke (2024) ܩܐ ܝܕܥܬܐ ܕܢܦܫܐ، Kumar (2023) ܩܐ ܒܘܨܝܐ ܩܠܝܢܝܩܝܐ ܘ-Ringquist (2013) ܩܐ ܡܕܒܪܢܘܬܐ ܘܡܕܒܪܢܘܬܐ ܕܥܡܐ. ܚܘܫܒܢܐ ܓܘ ܦܐܬܐ ܒܚܝܪܐ ܝܠܗ ܩܘܒܠ R 4.3.3 ܘܨܪܪܐ metafor 4.4 (escalc، rma، confint، predict، regtest، trimfill، leave1out)، ܘܩܘܒܠ ܡܬ̈ܠܐ ܚܫܝܒ̈ܐ ܓܘ ܨܚ̈ܚܐ 14 ܘ-17 ܕ-Borenstein ܘܚܒܪ̈ܘܗܝ (2009) ܘܬܪܝܢ ܡܬ̈ܠܐ ܕ-Cooke (2024، ܠܘ̈ܚܐ 7.3 ܘ-10.1).