ܐܣܘܪ̈ܐ ܕܚܕ̈ܕܐ ܕ-Pearson ܘ-Spearman (Pearson and Spearman correlations)

ܡܚܫܒܢܐ (calculator)

ܛܥܢܐ ܕܝܗܝ̈ܒܬܐ (loading the data)

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

ܓܘܒܝܐ ܕܡܫܬܚܠܦ̈ܢܐ (Variable selection) ܘܙܢܐ ܕܐܣܘܪܐ ܕܚܕ̈ܕܐ (correlation)

ܡܕܒܪܢܐ (guide)

ܐܝܡܢ ܡܦܠܚܝܚ (When to use)؟

ܐܝܡܢ ܕܒܥܝܚ ܕܒܚܪܚ ܐܣܘܪܐ ܒܝܢܝ ܬܪܝܢ ܡܫܬܚܠܦ̈ܢܐ (variables): ܐܢ ܣܠܩܐ ܓܘ ܛܝܡܐ ܕܚܕ ܐܣܝܪܐ ܝܠܗ ܥܡ ܣܠܩܐ، ܝܢ ܥܡ ܢܚܬܐ، ܓܘ ܛܝܡܐ ܕܐܚܪܢܐ. Pearson ܒܥܐ ܬܪܝܢ ܡܫܬܚܠܦ̈ܢܐ ܟܡܝ̈ܝܐ (ܣܒܠܬܐ ܕܪܘ̈ܚܩܐ ܫܘ̈ܝܐ ܝܢ ܣܒܠܬܐ ܕܦܘܚܡܐ – interval or ratio)؛ Spearman ܦܐܝܐ ܝܠܗ ܐܦ ܐܝܡܢ ܕܚܕ ܡܢ ܡܫܬܚܠܦ̈ܢܐ ܡܫܝܚܐ ܝܠܗ ܒܣܒܠܬܐ ܕܛܟܣܐ (ordinal) – ܦܘܪܫܐ ܓܡܝܪܐ ܡܚܕܐ ܠܬܚܬ. ܬܪܘܝܗܝ ܟܣܐܡܝ ܚܙ̈ܝܬܐ ܚܐܪ̈ܬܐ (independent observations): ܟܠ ܣܕܪܐ ܓܘ ܝܗܝ̈ܒܬܐ ܝܠܗ ܡܫܬܘܬܦܢܐ (participant) ܐܚܪܢܐ، ܘܠܝܬ ܐܣܘܪܐ ܒܝܢܝ ܣܕܪ̈ܐ – ܗܘ ܡܫܬܘܬܦܢܐ ܕܡܫܝܚܐ ܝܠܗ ܬܪܝܢ ܓܗ̈ܐ، ܝܢ ܬܠܡ̈ܝܕܐ ܡܢ ܗܝ ܨܦܐ، ܟܥܒܪܝ ܥܠ ܐܗܐ ܫܪܛܐ (assumption). ܡܢܝܢܐ ܡܫܘܬܦܐ (coefficient) ܕܐܣܘܪܐ ܕܚܕ̈ܕܐ ܟܬܢܐ ܬܪܝܢ ܡܕܡ̈ܐ ܒܚܕ ܓܗܐ – ܦܢܝܬܐ ܕܐܣܘܪܐ (ܕܙܘܕܐ ܝܢ ܕܒܨܘܪܐ) ܘܚܝܠܐ ܕܝܠܗ. ܚܫܝܚܐ ܝܠܗ ܕܥܗܕܚ: ܐܣܘܪܐ ܕܚܕ̈ܕܐ ܠܐ ܝܠܗ ܥܠܬܢܘܬܐ (causality). ܐܦ ܐܣܘܪܐ ܚܝܠܢܐ ܣܓܝ ܗܠ ܐܕܝܘܡ ܠܐ ܟܐܡܪ ܕܚܕ ܡܫܬܚܠܦܢܐ ܥܠܬܐ ܝܠܗ ܩܐ ܐܚܪܢܐ: ܡܨܝܐ ܝܠܗ ܕܡܫܬܚܠܦܢܐ ܬܠܝܬܝܐ، ܕܠܐ ܡܫܝܚܐ ܝܠܗ ܐܦ ܚܕ ܓܗܐ، ܟܥܒܕ ܐܣܘܪܐ ܒܝܢܝ ܬܪܘܝܗܝ؛ ܡܨܝܐ ܝܠܗ ܕܦܢܝܬܐ ܕܡܥܒܕܢܘܬܐ ܗܦܝܟܬܐ ܝܠܗ ܡܢ ܡܐ ܕܚܫܒܠܢ؛ ܘܡܨܝ ܕܗܘܝ ܬܘܪ̈ܓܡܐ ܐܚܪ̈ܢܐ. ܥܠ ܒܘܚܪܢܐ ܕܚܫܕܐ ܕܡܫܬܚܠܦܢܐ ܬܠܝܬܝܐ ܚܙܝܡܘܢ ܐܣܘܪܐ ܕܚܕ̈ܕܐ ܡܢܬܢܝܐ (partial correlation) ܒܬܚܬܝܬܐ ܕܦܐܬܐ.

Pearson ܝܢ Spearman؟

ܘܐܢ ܚܕ ܡܢ ܡܫܬܚܠܦ̈ܢܐ ܕܬܪܝܢ ܛܝ̈ܡܐ (dichotomous) ܝܠܗ؟ ܐܝܡܢ ܕܚܕ ܡܫܬܚܠܦܢܐ ܕܬܪܝܢ ܛܝ̈ܡܐ ܝܠܗ (ܬܪܝܢ ܛܝ̈ܡܐ ܒܣ، ܡܬܠܐ ܝܠܦ/ܠܐ ܝܠܦ) ܘܐܚܪܢܐ ܟܡܝܝܐ (ܡܬܠܐ ܐܓܪܐ)، ܟܡܦܠܚܚ ܒܐܣܘܪܐ ܕܚܕ̈ܕܐ point-biserial (Point-biserial): ܟܪܡܙܚ ܡܫܬܚܠܦܢܐ ܕܬܪܝܢ ܛܝ̈ܡܐ ܐܝܟ 0 ܘ-1، ܘܚܘܫܒܢܐ ܓܢܒܗ ܐܝܟ ܚܘܫܒܢܐ ܕܐܣܘܪܐ ܕܚܕ̈ܕܐ ܕ-Pearson ܝܠܗ (Gravetter & Wallnau, 2017, pp. 516-517; Field, 2024, Section 8.4.5; Cohen et al., 2003, Section 2.3.3, pp. 29-30) – ܘܡܛܠ ܗܕܐ ܒܥܒܕܐ ܟܡܨܝܚ ܕܚܫܒܚ ܠܗ ܐܦ ܒܡܚܫܒܢܐ (calculator) ܕܓܘ ܐܗܐ ܦܐܬܐ، ܒܝܕ ܪܡܙܢܘܬܐ ܐܝܟ ܐܗܐ.

ܐܠܐ ܠܐ ܥܒܕܚ ܦܠܓܘܬܐ ܠܬܪܝܢ ܕܠܐ ܟܝܢܐ (artificial dichotomy). ܐܘܪܚܐ ܗܦܝܟܬܐ ܠܐ ܝܠܗ ܛܒܬܐ: ܠܐ ܦܠܓܚ ܡܫܬܚܠܦܢܐ ܡܬܡܫܚܢܐ (continuous variable) ܠܬܪܝܢ "ܓܘ̈ܕܐ" (ܡܬܠܐ ܦܠܓܘܬܐ ܓܘ ܛܝܡܐ ܡܨܥܝܐ – median split) ܩܐ "ܕܦܫܛܚ" ܦܘܫܩܐ (analysis). ܦܠܓܘܬܐ ܟܡܘܒܕܐ ܡܘܕܥܢܘܬܐ: ܓܘ ܡܫܬܚܠܦ̈ܢܐ ܕܐܝܬܠܗܘܢ ܦܘܠܓܐ ܢܘܪܡܠܝܐ (normal distribution)، ܐܣܘܪܐ ܕܚܕ̈ܕܐ ܕܒܕ ܐܬܐ ܒܬܪ ܦܠܓܘܬܐ ܓܘ ܡܨܥܝܬܐ (mean) ܒܕ ܗܘܐ ܒܣ ܩܪܝܒ ܠ-80% ܡܢ ܐܣܘܪܐ ܫܪܫܝܐ – ܚܘܣܪܢܐ ܕܩܪܝܒ ܠܚܕ ܡܢ ܚܡܫܐ، ܕܫܘܐ ܝܠܗ ܠܫܒܩܬܐ ܕܩܪܝܒ ܠ-38% ܡܢ ܕܘܡܝܐ (sample)؛ ܘܟܡܐ ܕܢܘܩܙܐ ܕܦܣܩܐ ܟܪܚܩܐ ܡܢ ܡܨܥܝܬܐ (ܡܬܠܐ "ܪܡܐ/ܢܡܘܟܐ" ܠܦܘܬ ܚܕ ܬܚܘܡܐ) ܚܘܣܪܢܐ ܟܪܒܐ – ܒܦܣܩܐ ܓܘ ܚܕܐ ܣܛܝܘܬܐ ܬܩܝܢܬܐ (standard deviation) ܟܦܝܫܝ ܒܣ ܩܪܝܒ ܠܬܪܝܢ ܡܢ ܬܠܬܐ ܡܢ ܐܣܘܪܐ ܕܚܕ̈ܕܐ (Cohen, 1983). ܐܦ ܚܝܠܐ ܣܛܐܛܝܣܛܝܩܝܐ (statistical power) ܟܚܣܪ: ܡܣܬܒܪܢܘܬܐ ܕܓܠܝܐ ܕܐܣܘܪܐ ܕܐܝܬ ܒܫܪܝܪܘܬܐ ܟܢܚܬܐ – ܓܘ ܡܬܠܐ ܕ-MacCallum ܘܚܒܪ̈ܘܗܝ، ܩܐ ρ = .40 ܘ-N = 50، ܚܝܠܐ ܟܢܚܬ ܡܢ .84 ܠ-.63 ܒܬܪ ܦܠܓܘܬܐ ܕܚܕ ܡܫܬܚܠܦܢܐ ܓܘ ܡܨܥܝܬܐ (MacCallum et al., 2002, pp. 26-27). ܐܣܘܪܐ ܕܚܕ̈ܕܐ point-biserial ܥܒܝܕܐ ܝܠܗ ܩܐ ܡܫܬܚܠܦܢܐ ܕܬܪܝܢ ܛܝ̈ܡܐ ܡܢ ܟܝܢܗ – ܠܐ ܩܐ ܡܫܬܚܠܦܢܐ ܡܬܡܫܚܢܐ ܕܦܠܝܓܐ ܝܠܗ.

ܩܪܝܢܐ ܕܦܐܪܐ (Interpreting the result)

ܡܢܝܢܐ ܡܫܘܬܦܐ (coefficient) ܕܐܣܘܪܐ ܕܚܕ̈ܕܐ r – ܘܓܘ ܐܣܘܪܐ ܕ-Spearman: r_s – ܟܙܐܠ ܒܝܢܝ -1 ܘ-+1، ܘܐܝܬ ܓܘܗ ܬܪܝܢ ܡܢܘ̈ܬܐ ܕܟܠ ܚܕ ܡܢܝܗܝ ܟܡܫܬܥܐ ܬܫܥܝܬܐ ܐܚܪܬܐ. ܐܬܐ – ܕܙܘܕܐ ܝܢ ܕܒܨܘܪܐ – ܟܐܡܪ ܡܘܕܝ ܝܠܗ ܦܢܝܬܐ ܕܐܣܘܪܐ. ܪܒܘܬܐ، ܕܠܐ ܚܫܒܢܐ ܕܐܬܐ (|r|)، ܟܐܡܪܐ ܥܕܡܐ ܟܡܐ ܐܣܘܪܐ ܚܝܠܢܐ ܝܠܗ: ܟܡܐ ܕܩܪܝܒܐ ܝܠܗ ܒܝܫ ܠ-1 ܐܣܘܪܐ – ܣܪܛܢܝܐ ܓܘ Pearson، ܡܘܢܘܛܘܢܝܐ ܓܘ Spearman – ܚܝܠܢܐ ܝܠܗ ܒܝܫ، ܘܟܡܐ ܕܩܪܝܒܐ ܝܠܗ ܒܝܫ ܠ-0 – ܟܪܝܗܐ ܒܝܫ.

ܐܣܘܪܐ ܕܚܕ̈ܕܐ ܕ-Pearson ܓܡܝܪܐ (r = ±1) ܣܘܟܠܗ ܝܠܗ ܕܟܠ ܢܘܩ̈ܙܐ ܝܬܒ̈ܐ ܝܢܐ ܚܬܝܬܐܝܬ ܥܠ ܚܕ ܣܪܛܐ ܬܪܝܨܐ – ܕܣܠܩ ܝܢ ܕܢܚܬ. ܐܣܘܪܐ ܕܚܕ̈ܕܐ ܕ-Spearman ܓܡܝܪܐ (r_s = ±1) ܒܥܐ ܒܨܝܪ ܡܢ ܗܕܐ: ܒܣ ܝܠܗ ܕܟܠ ܣܠܩܐ ܓܘ ܚܕ ܡܫܬܚܠܦܢܐ ܐܬܝܐ ܟܠ ܐܡܢ ܥܡ ܣܠܩܐ (ܝܢ ܟܠ ܐܡܢ ܥܡ ܢܚܬܐ) ܓܘ ܡܫܬܚܠܦܢܐ ܐܚܪܢܐ – ܐܦ ܐܢ ܢܘܩ̈ܙܐ ܠܐ ܝܬܒ̈ܐ ܝܢܐ ܥܠ ܣܪܛܐ ܬܪܝܨܐ.

ܘܡܘܕܝ ܟܐܡܪ r = 0؟ ܒܣ ܕܠܝܬ ܐܣܘܪܐ ܣܪܛܢܝܐ (linear). ܐܣܘܪܐ ܕܚܕ̈ܕܐ ܢܡܘܟܐ ܝܢ ܣܦܪ ܠܐ ܟܡܚܘܐ ܕܠܝܬ ܡܕܡ ܐܣܘܪܐ ܒܝܢܝ ܡܫܬܚܠܦ̈ܢܐ (variables): ܗܠ ܐܕܝܘܡ ܡܨܝܐ ܝܠܗ ܕܐܝܬ ܒܝܢܝ ܬܪܘܝܗܝ ܐܣܘܪܐ ܚܝܠܢܐ ܕܠܐ ܝܠܗ ܣܪܛܢܝܐ – ܡܬܠܐ ܒܨܘܪܬܐ ܕ-U – ܕܡܢܝܢܐ ܡܫܘܬܦܐ ܕ-Pearson ܒܣ ܠܐ ܟܚܙܐ. ܡܛܠ ܗܕܐ ܛܒܐ ܝܠܗ ܟܠ ܐܡܢ ܕܚܙܚ ܐܦ ܨܘܪܬܐ ܕܒܕܪܐ (scatter plot) ܕܓܘ ܡܦܩܢܐ (output).

ܗܘ r – ܨܘܪ̈ܬܐ ܦܪ̈ܝܫܐ ܓܡܝܪܐܝܬ. ܡܚܘܝܢܘܬܐ ܝܕܝܥܬܐ ܡܢ ܟܠ ܩܐ ܚܫܝܚܘܬܐ ܕܨܘܪܬܐ ܕܒܕܪܐ (scatter plot) ܝܠܗ "ܐܪܒܥܝܘܬܐ ܕ-Anscombe": ܐܪܒܥܐ ܣܕܪ̈ܐ ܕܝܗܝ̈ܒܬܐ ܕܠܟܠܗܘܢ ܐܝܬ ܗܢܝ ܡܨܥܝ̈ܬܐ (means)، ܗܢܝ ܣܛܝ̈ܘܬܐ ܬܩܝܢ̈ܝܬܐ ܘܗܘ ܐܣܘܪܐ ܕܚܕ̈ܕܐ (correlation) – r = .816 – ܐܠܐ ܓܘ ܨܘܪܬܐ ܕܒܕܪܐ ܐܢܝ ܟܡܬܚܙܝ ܦܪ̈ܝܫܐ ܓܡܝܪܐܝܬ ܡܢ ܚܕ̈ܕܐ: ܓܘ ܩܕܡܝܐ – ܐܣܘܪܐ ܣܪܛܢܝܐ ܥܡܝܐ؛ ܓܘ ܬܪܝܢܐ – ܣܪܛܐ ܟܦܝܦܐ ܕܠܐ ܝܠܗ ܣܪܛܢܝܐ؛ ܓܘ ܬܠܝܬܝܐ – ܣܪܛܐ ܓܡܝܪܐ ܕܚܕ ܢܘܩܙܐ ܢܘܟܪܝܐ (outlier) "ܟܓܪܫ" ܡܢܗ ܡܢܝܢܐ ܡܫܘܬܦܐ؛ ܘܓܘ ܪܒܝܥܝܐ – ܐܣܘܪܐ ܕܟܠܗ ܡܣܡܟ ܝܠܗ ܥܠ ܚܕܐ ܚܙܝܬܐ (observation) ܪܚܝܩܬܐ ܝܚܝܕܝܬܐ (Anscombe, 1973). ܚܬܡܬܐ: ܐܦ ܚܕ ܓܗܐ ܠܐ ܟܣܦܩܚ ܒܡܢܝܢܐ ܡܫܘܬܦܐ ܒܠܚܘܕܘܗܝ – ܟܠ ܐܡܢ ܟܚܙܚ ܐܦ ܥܠ ܝܗܝ̈ܒܬܐ ܓܢܒܗܝ. ܘܐܗܐ ܚܙܝܐ ܠܐ ܣܢܝܩ ܝܠܗ ܕܡܘܚܪܚ ܠܗ ܥܕܡܐ ܠ-SPSS: ܓܘ ܦܐܬܐ ܨܘܪܬܐ ܕܒܕܪܐ ܘܣܪܛܐ ܕܪܝܓܪܫܢ ܕܓܘ ܣܐܝܛ ܟܡܨܝܬܘܢ ܕܛܥܢܝܬܘܢ ܗܘ ܦܐܝܠ ܕܝܗܝ̈ܒܬܐ، ܕܓܒܝܬܘܢ ܙܘܓܐ ܕܡܫܬܚܠܦ̈ܢܐ ܘܕܫܩܠܝܬܘܢ ܡܚܕܐ ܨܘܪܬܐ ܕܒܕܪܐ ܕܝܗܝ – ܥܡ ܣܪܛܐ ܕܪܝܓܪܫܢ (regression line)، ܡܢܝ̈ܢܐ ܡܫܘܬܦ̈ܐ ܕܐܣܘܪܐ ܕܚܕ̈ܕܐ ܘ-R².

ܚܝܠܐ ܕܐܣܘܪܐ. ܠܝܬ ܬܚܘܡܐ ܓܢܝܐ (universal) ܩܐ ܦܘܠܓܐ ܕܐܣܘܪ̈ܐ ܕܚܕ̈ܕܐ ܠܟܪ̈ܝܗܐ، ܡܨܥ̈ܝܐ ܝܢ ܚܝܠܢ̈ܐ. ܩܐ ܬܚܘܝܬܐ ܕܐܘܪܚܐ ܥܝܕܐ ܝܠܗ ܕܡܦܠܚܚ ܒܥܝ̈ܕܐ ܕ-Cohen (Cohen, 1988, pp. 79-81): |r| < .10 – ܙܥܘܪܐ ܛܒܐ (negligible)؛ .10-.30 – ܟܪܝܗܐ؛ .30-.50 – ܡܨܥܝܐ؛ .50 ܘܠܥܠ – ܚܝܠܢܐ. ܐܗܐ ܝܠܗ ܐܦ ܣܒܠܬܐ ܕܒܗ ܟܡܦܠܚܝ ܡܐܡܪ̈ܐ ܕܬܘܢܝܐ (report sentences) ܐܘܛܘܡܐܛܝܩ̈ܝܐ ܕܓܘ ܐܗܐ ܦܐܬܐ. ܐܝܬ ܡܕܒܪ̈ܢܐ ܕܟܡܩܪܒܝ ܦܘܠܓܐ ܩܠܝܠ ܦܪܝܫܐ، ܘ-Cohen ܓܢܒܗ ܟܡܫܪܪ ܕܐܢܝ ܥܝ̈ܕܐ ܝܢܐ ܩܐ ܡܦܠܚܢܘܬܐ ܒܣ ܐܝܡܢ ܕܠܝܬ ܡܫܘ̈ܚܬܐ ܦܐܝ̈ܐ ܒܝܫ ܩܐ ܬܚܘܡܐ. ܡܛܠ ܗܕܐ ܚܝܠܐ ܕܐܣܘܪܐ ܕܚܕ̈ܕܐ ܓܪܓ ܡܬܬܪܓܡ ܠܦܘܬ ܣܝܩܐ ܕܒܘܨܝܐ، ܟܝܢܐ ܕܡܫܬܚܠܦ̈ܢܐ ܘܡܫܟܚ̈ܢܘܬܐ ܩܕܡܝ̈ܐ ܓܘ ܬܚܘܡܐ – ܘܠܐ ܠܦܘܬ ܬܚܘ̈ܡܐ ܡܛܝܒ̈ܐ ܡܢ ܩܕܡ (Cohen, 1988, p. 79; Field, 2024, Section 8.2.2; Pallant, 2020, Chapter 11).

ܪܫܝܡܘܬܐ (significance) ܠܐ ܝܠܗ ܚܝܠܐ. ܕܘܡܝܐ (sample) ܪܒܐ ܠܐ ܟܥܒܕ ܐܣܘܪܐ ܓܢܒܗ ܚܝܠܢܐ ܒܝܫ – ܒܣ ܟܥܒܕ ܡܫܘܚܬܐ ܕܝܠܗ ܚܬܝܬܬܐ ܒܝܫ. ܦܐܪܐ: ܓܘ ܕܘܡܝܐ ܪܒܐ ܐܦ ܐܣܘܪܐ ܙܥܘܪܐ ܛܒܐ ܡܨܐ ܕܦܠܛ ܪܫܝܡܐ، ܘܓܘ ܕܘܡܝܐ ܙܥܘܪܐ ܐܣܘܪܐ ܫܪܝܪܐ ܡܨܐ ܕܠܐ ܡܬܓܠܐ. ܡܛܠ ܗܕܐ ܟܬܢܚ ܟܠ ܐܡܢ ܐܦ r، ܐܦ p ܘܐܦ N، ܘܠܐ ܟܣܦܩܚ ܒܚܕ ܡܢܝܗܝ ܒܣ.

ܬܚܘܡܐ ܕܬܘܟܠܢܐ (confidence interval). r ܕܓܘ ܕܘܡܝܐ ܝܠܗ ܫܘܥܪܐ (estimate)؛ ܬܚܘܡܐ ܕܬܘܟܠܢܐ ܕ-95% ܟܐܡܪ ܒܐܝܢܐ ܦܬܝܘܬܐ (range) ܡܣܬܒܪܐ ܝܠܗ ܕܐܝܬ ܐܣܘܪܐ ܕܚܕ̈ܕܐ ܓܘ ܟܢܫܐ ܟܠܢܝܐ (population) – ܘܗܕܟܐ ܟܡܫܠܡ ܡܐ ܕ-p ܒܠܚܘܕܘܗܝ ܠܐ ܟܐܡܪ. ܠܘܚܐ ܕܬܚܘܝܬܐ ܓܡܝܪܬܐ ܘܡܐܡܪ̈ܐ ܕܬܘܢܝܐ ܕܓܘ ܦܐܬܐ ܟܡܚܘܝܝ ܠܗ ܩܐ ܟܠ ܐܣܘܪܐ ܕ-Pearson، ܒܚܘܫܒܢܐ ܕܥܠ ܫܘܢܝܐ ܕ-Fisher (Fisher transformation؛ ܫܘܝܘܬܐ ܘܡܬܠܐ – ܓܘ ܦܣܩܐ ܫܘܝ̈ܘܬܐ؛ Field، 2024، ܦܣܩܐ 8.2.4). ܬܪܝܢ ܡܕܡ̈ܐ ܩܐ ܩܪܝܢܐ ܓܘܗ: ܐܢ ܐܝܬ ܓܘܗ ܣܦܪ (ܐܢ ܐܝܬ – ܝܗܝ̈ܒܬܐ ܠܐ ܟܡܣܠܩܝ ܡܨܝܘܬܐ ܕܠܝܬ ܐܣܘܪܐ، ܘܐܗܐ ܫܘܐ ܝܠܗ ܠ-p ܠܐ ܪܫܝܡܐ)، ܘܟܡܐ ܦܬܝܐ ܝܠܗ – ܬܚܘܡܐ ܐܝܟ [.02, .53] (ܡܬܠܐ r = .30 ܥܡ n = 50) ܟܡܚܘܐ ܕܐܣܘܪܐ ܫܥܝܪܐ ܝܠܗ ܒܠܐ ܚܬܝܬܘܬܐ ܪܒܬܐ، ܐܦ ܐܢ ܪܫܝܡܐ ܝܠܗ. ܬܚܘܡܐ ܠܐ ܝܠܗ ܫܘܐ ܒܬܪܝܢ ܓܢܒ̈ܐ ܕ-r – ܘܐܗܐ ܬܪܝܨܐ ܝܠܗ. Field (2024، ܦܣܩܐ 8.8) ܟܡܩܪܒ ܕܬܢܚ ܬܚܘܡܐ ܕܬܘܟܠܢܐ ܥܡ ܐܣܘܪܐ ܕܚܕ̈ܕܐ – ܘܗܕܟܐ ܟܥܒܕܝ ܡܐܡܪ̈ܐ ܕܬܘܢܝܐ ܕܓܘ ܦܐܬܐ.

ܩܡܘܕܝ ܐܣܘܪܐ ܕܚܕ̈ܕܐ ܢܡܘܟܐ ܝܠܗ ܡܢ ܕܡܣܟܝܚ؟ ܬܪܝܢ ܥܠ̈ܠܬܐ "ܛܟܢܝܩ̈ܝܐ" ܟܡܙܥܪܝ ܐܣܘܪ̈ܐ ܕܚܕ̈ܕܐ ܒܐܘܪܚܐ ܛܟܝܣܬܐ. ܦܬܝܘܬܐ ܟܪܝܬܐ (restriction of range): ܐܝܡܢ ܕܕܘܡܝܐ (sample) ܟܟܣܐ ܒܣ ܡܢܬܐ ܡܢ ܦܬܝܘܬܐ (range) ܕܛܝ̈ܡܐ – ܡܬܠܐ ܒܘܚܪܢܐ ܕܐܣܘܪܐ ܒܝܢܝ ܡܢܝܢܐ ܕܓܘܒܝܐ ܘܨܠܚܘܬܐ ܓܘ ܥܒܕܐ ܒܣ ܓܘ ܐܢܝ ܕܩܒܝܠ̈ܐ ܝܢܐ – ܐܣܘܪܐ ܚܙܝܐ (observed) ܟܦܠܛ ܢܡܘܟܐ ܡܢ ܐܣܘܪܐ ܓܘ ܟܢܫܐ ܟܠܢܝܐ (population) ܓܡܝܪܐ؛ Cohen ܐܦ ܟܡܙܗܪ ܕܠܘ̈ܚܐ ܕܪܒܘܬܐ ܕܕܘܡܝܐ ܕܝܠܗ ܠܐ ܝܢܐ ܬܪ̈ܝܨܐ ܓܘ ܗܘܝܐ ܕܦܬܝܘܬܐ ܟܪܝܬܐ (Cohen, 1988, p. 100). ܡܙܥܪܢܘܬܐ ܡܛܠ ܫܪܝܪܘܬܐ (reliability) (attenuation): ܐܝܡܢ ܕܡܐܢ̈ܐ ܕܡܫܘܚܬܐ ܠܐ ܝܢܐ ܚܬܝ̈ܬܐ، ܥܠ ܡܢܝ̈ܢܐ ܟܡܬܘܣܦ ܫܓܘܫܝܐ ܓܕܫܢܝܐ – ܘܐܗܐ ܫܓܘܫܝܐ ܟܡܙܥܪ ܐܣܘܪܐ ܚܙܝܐ (Cohen, 1988, p. 79). ܢܡܘܣܐ ܩܪܝܒܐܝܬ: ܐܣܘܪܐ ܕܟܡܬܚܙܐ ܓܘ ܕܘܡܝܐ ܫܘܐ ܝܠܗ ܠܐܣܘܪܐ ܫܪܝܪܐ ܟܦܝܠܐ ܒ-√(r_xx·r_yy) – ܫܪܫܐ ܕܡܟܦܠܬܐ ܕܫܪܝܪ̈ܘܬܐ ܕܬܪܝܢ ܡܐܢ̈ܐ. ܡܬܠܐ: ܐܣܘܪܐ ܫܪܝܪܐ ܕ-.50 ܒܝܢܝ ܬܪܝܢ ܡܚܘ̈ܝܢܐ ܕܫܪܝܪܘܬܐ ܕܟܠ ܚܕ ܡܢܝܗܝ .70 ܝܠܗ، ܒܕ ܡܬܚܙܐ ܓܘ ܕܘܡܝܐ ܒܣ ܩܪܝܒ ܠ-.35. ܡܛܠ ܗܕܐ، ܐܝܡܢ ܕܟܦܚܡܚ ܐܣܘܪܐ ܥܡ ܡܫܟܚ̈ܢܘܬܐ ܩܕܡܝ̈ܐ، ܛܒܐ ܝܠܗ ܕܚܙܚ ܐܦ ܠܦܬܝܘܬܐ ܕܕܘܡܝܐ ܘܐܦ ܠܫܪܝܪܘܬܐ ܕܡܐܢ̈ܐ. ܩܐ ܡܡܠܠܐ ܛܟܝܣܐ ܥܠ ܥܠ̈ܠܬܐ ܕܟܡܥܒܕܝ ܥܠ ܪܒܘܬܐ ܕ-r – ܥܡ ܫܘܝ̈ܘܬܐ ܕܬܘܪܨܐ ܩܐ ܬܪܘܝܗܝ ܓܕ̈ܫܐ – ܚܙܝܡܘܢ Cohen et al.‏ (2003، ܦܣܩܐ 2.10).

ܦܘܚܡ̈ܐ ܣܓܝ̈ܐܐ. ܐܝܡܢ ܕܟܒܚܪܚ ܐܣܘܪ̈ܐ ܕܚܕ̈ܕܐ ܣܓܝ̈ܐܐ ܒܚܕ ܓܗܐ، ܡܣܬܒܪܢܘܬܐ (probability) ܕܠܐ ܒܨܝܪ ܡܢ ܚܕ ܡܢܝܗܝ ܦܠܛ ܪܫܝܡܐ ܡܢ ܓܕܫܐ ܟܪܒܐ: ܓܘ ܚܡܫܐ ܡܫܬܚܠܦ̈ܢܐ (variables) ܐܝܬ ܡܢ ܩܕܡ ܥܣܪܐ ܒܘܚܪ̈ܢܐ. ܓܘ ܒܘܨܝܐ ܡܫܪܪܢܐ (confirmatory) ܛܒܐ ܝܠܗ ܕܚܕܕܚ ܗܘܦܘܬܣ̈ܝܣ (hypotheses) ܡܢ ܩܕܡ، ܝܢ ܕܚܫܒܚ ܥܠ ܬܘܪܨܐ ܕܛܝ̈ܡܐ ܕܪܫܝܡܘܬܐ ܡܛܠ ܦܘܚܡ̈ܐ ܣܓܝ̈ܐܐ (ܡܬܠܐ ܬܘܪܨܐ ܕ-Holm ܝܢ FDR).

ܐܣܘܪܐ ܕܚܕ̈ܕܐ ܠܐ ܝܠܗ ܡܢܘ̈ܬܐ ܒܡܐܐ (percentages). ܐܣܘܪܐ ܕ-r = .50 ܠܐ ܟܡܚܘܐ "ܐܣܘܪܐ ܕ-50%". ܩܐ ܕܡܚܘܚ ܡܢܬܐ ܕܫܘܚܠܦܐ ܡܫܘܬܦܐ (shared variance) ܕܬܪܝܢ ܡܫܬܚܠܦ̈ܢܐ، ܟܡܪܒܥܚ ܡܢܝܢܐ ܡܫܘܬܦܐ ܕ-Pearson: ܓܘ ܐܗܐ ܗܘܝܐ r² = .25، ܗܢܘ 25% ܫܘܚܠܦܐ ܡܫܘܬܦܐ. ܬܘܪܓܡܐ ܕܫܘܚܠܦܐ ܡܫܘܬܦܐ ܬܪܝܨܐ ܝܠܗ ܩܐ ܐܣܘܪܐ ܕ-Pearson – ܠܐ ܟܡܦܠܚܚ ܠܗ ܐܘܛܘܡܐܛܝܩܐܝܬ ܥܠ ܡܪܒܥܐ ܕܡܢܝܢܐ ܡܫܘܬܦܐ ܕ-Spearman.

ܛܥܝ̈ܘܬܐ ܕܡܬܚܙܝܢ ܣܓܝ (Common mistakes)

ܬܘܢܝܐ ܕܛܝܡܐ p ܕܠܐ ܬܘܢܝܐ ܕܚܝܠܐ ܕܐܣܘܪܐ (r) – ܪܫܝܡܘܬܐ (significance) ܒܠܚܘܕܘܗܝ ܠܐ ܟܐܡܪܐ ܥܕܡܐ ܟܡܐ ܐܣܘܪܐ ܚܝܠܢܐ ܝܠܗ. ܬܘܪܓܡܐ ܕܦܐܪܐ "ܠܐ ܪܫܝܡܐ" ܐܝܟ ܚܘܝܐ ܕ"ܠܝܬ ܐܣܘܪܐ" – ܒܠܟܝ ܕܘܡܝܐ (sample) ܙܥܘܪܐ ܝܠܗ ܒܝܫ ܩܐ ܓܠܝܐ ܕܐܣܘܪܐ ܕܐܝܬ. ܫܘܠܡܐ ܕܥܠܬܢܘܬܐ (causality) ܡܢ ܐܣܘܪܐ ܕܚܕ̈ܕܐ. ܚܘܝܐ ܕ-r ܐܝܟ ܡܢܘ̈ܬܐ ܒܡܐܐ. ܪܗܛܐ ܕܐܣܘܪܐ ܕ-Pearson ܥܠ ܦܣܘܩܐ ܕ-Likert ܝܚܝܕܝܐ ܕܠܐ ܚܘܫܒܐ ܕ-Spearman – ܩܐ ܦܣܘܩܐ ܝܚܝܕܝܐ Spearman ܦܐܝܐ ܝܠܗ ܒܝܫ ܓܘ ܪܘܒܐ ܕܗܘܝ̈ܐ، ܐܦܢ ܐܗܐ ܥܝܕܐ ܡܩܒܠܐ ܝܠܗ ܘܠܐ ܢܡܘܣܐ ܡܚܬܡܐ: Jamieson (2004) ܒܓܢܒܐ ܚܝܨܐ، Norman (2010) ܒܓܢܒܐ ܡܪܘܚܐ – ܘܗܘ ܐܦ ܚܘܝܠܗ ܥܠ ܝܗܝ̈ܒܬܐ ܫܪܝܪ̈ܬܐ ܕ-Likert (64 ܙܘܓ̈ܐ ܕܐܣܘܪ̈ܐ ܕܚܕ̈ܕܐ) ܕ-Pearson ܘ-Spearman ܟܝܗܒܝ ܟܡܥܛ ܗܢܝ ܦܐܪ̈ܐ، ܐܦ ܓܘ ܦܘ̈ܠܓܐ ܥܩܝܡ̈ܐ ܣܓܝ (ܐܣܘܪܐ ܕ-.99 ܒܝܢܝ ܬܪܝܢ ܙܢ̈ܐ ܕܡܢܝ̈ܢܐ ܡܫܘܬܦ̈ܐ). ܘܢܫܝܐ ܕܬܘܢܝܐ ܕܪܒܘܬܐ ܕܕܘܡܝܐ (N) ܕܥܠܗ ܡܣܡܟ ܝܠܗ ܟܠ ܐܣܘܪܐ.

ܘܬܘܟܠܢܐ ܥܠ ܫܩܠܬܐ ܙܘܓܢܝܬܐ (pairwise deletion) ܕܠܐ ܚܘܫܒܐ. ܡܚܫܒܢܐ (calculator)، SPSS ܘ-R (ܥܡ pairwise.complete.obs) ܟܚܫܒܝ ܟܠ ܐܣܘܪܐ ܥܠ ܡܫܬܘܬܦ̈ܢܐ (participants) ܕܐܝܬܠܗܘܢ ܛܝܡܐ ܬܪܝܨܐ (valid value) ܓܘ ܬܪܝܢ ܡܫܬܚܠܦ̈ܢܐ ܕܗܘ ܙܘܓܐ – ܘܐܗܐ ܝܠܗ ܣܒܒܐ ܕܓܘ ܠܘܚܐ ܕܡܬܠܐ N ܟܙܐܠ ܒܝܢܝ 447 ܘ-483. ܐܗܐ ܦܫܝܩܘܬܐ ܠܐ ܝܠܗ ܡܓܢ. Gelman & Hill (2007، ܦܐܬܐ 531-532) ܟܩܪܝ ܠܐܘܪܚܐ "ܦܘܫܩܐ ܕܓܕ̈ܫܐ ܡܛܝ̈ܐ" (available-case analysis) ܘܟܡܚܘܝܝ ܬܪܬܝܢ ܥܩ̈ܬܐ. ܩܕܡܝܬܐ: ܟܠ ܐܣܘܪܐ ܓܘ ܡܐܛܪܝܟܣ ܚܫܝܒܐ ܝܠܗ ܥܠ ܓܘܕܐ ܙܥܘܪܐ ܐܚܪܢܐ ܕܡܫܬܘܬܦ̈ܢܐ، ܘܡܛܠ ܗܕܐ ܐܣܘܪ̈ܐ "ܠܐ ܝܢܐ ܡܚܬܡܐܝܬ ܫܠܝܡ̈ܐ ܥܡ ܚܕ̈ܕܐ" – ܐܢܝ ܟܡܬܚܘܝ، ܒܥܒܕܐ، ܕܘ̈ܡܝܐ ܦܪ̈ܝܫܐ ܩܠܝܠ. ܬܪܬܝܢ، ܕܐܦ ܥܠ ܫܩܠܬܐ ܕܣܕܪܐ ܟܠܗ (listwise deletion) ܝܠܗ: ܐܢ ܐܝܢܐ ܕܠܐ ܦܢܐ ܦܪܝܫܐ ܝܠܗ ܒܐܘܪܚܐ ܛܟܝܣܬܐ ܡܢ ܐܝܢܐ ܕܦܢܐ، ܫܘܥܪܐ (estimate) ܡܣܛܝܐ ܝܠܗ. ܡܬܠܐ ܕܝܠܗܘܢ ܡܢ ܒܘܨܝܐ ܕܫܘܐ̈ܠܐ (survey) ܓܘ New York: 90% ܡܢ ܡܦܢܝ̈ܢܐ (respondents) ܐܘܟ̈ܡܐ ܬܢܝܠܗܘܢ ܐܓܪܐ ܕܝܗܝ ܩܘܒܠ 81% ܡܢ ܚܘܪ̈ܐ، ܘܡܛܠ ܗܕܐ ܟܢܘܫܝܐ ܕܐܓܪܐ ܟܡܚܘܐ ܟܢܫܐ ܟܠܢܝܐ (population) ܐܚܪܢܐ ܡܢ ܕܟܢܘܫܝܐ ܕܝܘܠܦܢܐ ܟܡܚܘܐ. ܚܬܡܬܐ ܥܒܕܢܝܬܐ ܠܐ ܝܠܗ ܕܫܒܩܚ ܫܩܠܬܐ ܙܘܓܢܝܬܐ – ܐܝܡܢ ܕܚܣܝܪܐ ܙܥܘܪܐ ܘܓܕܫܢܝܐ ܝܠܗ ܗܝ ܦܐܝܬܐ ܝܠܗ، ܘܒܐܟܡܐ ܕܥܝܕܐ ܛܒܬܐ ܝܠܗ ܡܢ ܡܫܕܝܐ ܕܡܫܬܘܬܦ̈ܢܐ ܫܠܡ̈ܐ – ܐܠܐ ܬܠܬܐ ܥܝ̈ܕܐ: ܬܘܢܝܐ ܕܦܬܝܘܬܐ (range) ܕ-N (ܐܝܟ ܕܠܘܚܐ ܟܥܒܕ)؛ ܒܘܚܪܢܐ، ܐܝܡܢ ܕܦܘܪܫܢܐ ܒܝܢܝ ܙܘܓ̈ܐ ܪܒܐ ܝܠܗ، ܡܢܘ ܚܣܝܪܐ ܝܠܗ ܘܓܘ ܐܝܢܐ ܡܫܬܚܠܦܢܐ؛ ܘܥܘܗܕܢܐ ܕܐܝܡܢ ܕܚܣܝܪܐ ܠܐ ܝܠܗ ܓܕܫܢܝܐ، ܫܪܝܐ ܝܠܗ ܡܫܠܡܢܘܬܐ ܕܝܗܝ̈ܒܬܐ ܡܣܡܟܬܐ ܥܠ ܡܘܕܝܠ (imputation؛ ܬܡܐ، ܦܣ̈ܩܐ 25.3-25.6؛ ܚܙܝܡܘܢ ܦܐܬܐ ܛܘܦܠܐ ܒܛܝ̈ܡܐ ܚܣܝ̈ܪܐ)، ܠܐ ܓܘܒܝܐ ܒܝܢܝ ܬܪܬܝܢ ܐܘܪ̈ܚܬܐ ܕܫܩܠܬܐ.

ܐܣܘܪܐ ܕܚܕ̈ܕܐ ܡܢܬܢܝܐ (partial correlation) – ܒܛܠܐ ܕܡܥܒܕܢܘܬܐ ܕܡܫܬܚܠܦܢܐ ܬܠܝܬܝܐ

ܒܓܗ̈ܐ ܐܣܘܪܐ ܕܚܕ̈ܕܐ ܒܝܢܝ ܬܪܝܢ ܡܫܬܚܠܦ̈ܢܐ (variables) ܠܐ ܟܡܚܘܐ ܐܣܘܪܐ ܬܪܝܨܐ ܒܝܢܝ ܬܪܘܝܗܝ، ܐܠܐ "ܡܬܥܒܕܐ ܝܠܗ" ܒܐܝܕܐ ܕܡܫܬܚܠܦܢܐ ܬܠܝܬܝܐ ܕܐܣܝܪܐ ܝܠܗ ܥܡ ܬܪܘܝܗܝ – ܓܕܫܐ ܕܟܡܬܩܪܐ ܐܣܘܪܐ ܕܚܕ̈ܕܐ ܕܓܠܐ (spurious correlation). ܐܣܘܪܐ ܕܚܕ̈ܕܐ ܡܢܬܢܝܐ (Partial correlation) ܟܒܚܪ ܚܫܕܐ ܐܝܟ ܐܗܐ: ܟܚܫܒ ܐܣܘܪܐ ܒܝܢܝ x ܘ-y ܥܡ ܒܛܠܐ ܣܛܐܛܝܣܛܝܩܝܐ ܕܡܫܬܚܠܦܢܐ ܬܠܝܬܝܐ z (Gravetter & Wallnau, 2017, p. 502; Field, 2024, Section 8.5.2; Cohen et al., 2003, Section 3.3.3, p. 74).

ܡܬܠܐ ܝܕܝܥܐ: ܓܘ ܕܘܡܝܐ (sample) ܕܡܕ̈ܝܢܬܐ، ܡܢܝܢܐ ܕܒ̈ܬܐ ܕܨܠܘܬܐ ܓܘ ܡܕܝܢܬܐ ܐܣܝܪܐ ܝܠܗ ܒܚܝܠܐ ܥܡ ܡܢܝܢܐ ܕܥܘܠ̈ܐ ܝܩܝܪ̈ܐ ܓܘܗ – r = .92. ܬܘܪܓܡܐ ܠܐ ܝܠܗ ܕܒ̈ܬܐ ܕܨܠܘܬܐ ܟܝܠܕܝ ܥܘܠܐ: ܬܪܝܢ ܡܫܬܚܠܦ̈ܢܐ ܐܣܝܪ̈ܐ ܝܢܐ ܥܡ ܡܫܬܚܠܦܢܐ ܬܠܝܬܝܐ – ܪܒܘܬܐ ܕܟܢܫܐ ܟܠܢܝܐ (population؛ r = .96 ܥܡ ܡܢܝܢܐ ܕܒ̈ܬܐ ܕܨܠܘܬܐ ܘ-r = .96 ܥܡ ܡܢܝܢܐ ܕܥܘܠ̈ܐ). ܓܘ ܡܕܝܢܬܐ ܪܒܬܐ ܐܝܬ ܣܓܝ ܡܢ ܬܪܘܝܗܝ، ܓܘ ܡܕܝܢܬܐ ܙܥܘܪܬܐ – ܩܠܝܠ ܡܢ ܬܪܘܝܗܝ. ܒܬܪ ܒܛܠܐ ܕܪܒܘܬܐ ܕܟܢܫܐ ܟܠܢܝܐ ܐܣܘܪܐ ܡܢܬܢܝܐ ܟܢܦܠ ܠܣܦܪ – ܐܣܘܪܐ ܕܓܠܐ ܩܠܐܣܝܩܝܐ (Gravetter & Wallnau، 2017، ܦܐܬܐ 497، 503؛ ܝܗܝ̈ܒܬܐ ܓܘ ܐܗܐ ܡܬܠܐ ܡܒܕܝ̈ܬܐ ܝܢܐ ܩܐ ܡܚܘܝܢܘܬܐ، ܐܝܟ ܕܟܬܝܒܐ ܝܠܗ ܓܘ ܟܬܒܐ). ܚܙܝܡܘܢ ܕܠܐܟܐ r_xy ≈ r_xz·r_yz – ܘܐܗܐ ܝܠܗ ܚܬܝܬܐܝܬ ܫܪܛܐ ܛܘܦܣܢܝܐ (formal) ܩܐ ܐܣܘܪܐ ܕܓܠܐ: x ܐܣܝܪܐ ܝܠܗ ܥܡ y ܒܣ ܒܝܕ z (Cohen et al., 2003, Section 3.4.4, p. 78). ܐܠܐ ܒܛܠܐ ܠܐ ܟܠ ܐܡܢ "ܟܫܪܐ" ܐܣܘܪܐ: ܓܘ ܡܬܠܐ ܕ-Pallant (2020، ܨܚܚܐ 12) ܐܣܘܪܐ ܒܝܢܝ ܪܓܫܬܐ ܕܫܘܠܛܢܐ ܘܥܨܪܐ ܕܡܬܪܓܫ ܝܠܗ r = −.58، ܘܒܬܪ ܒܛܠܐ ܕܨܒܝܢܐ ܟܢܫܝܐ (social desirability) ܟܦܐܫ ܟܡܥܛ ܗܘ ܓܢܒܗ (ܐܣܘܪܐ ܡܢܬܢܝܐ r = −.55). ܐܝܡܢ ܕܐܣܘܪܐ ܡܢܬܢܝܐ ܩܪܝܒܐ ܝܠܗ ܠܐܣܘܪܐ ܫܪܫܝܐ، ܐܗܐ ܝܠܗ ܒܥܝܢܗ ܣܗܕܘܬܐ ܕܐܣܘܪܐ ܟܩܐܡ ܒܚܝܠܗ ܘܠܐ ܝܠܗ ܦܐܪܐ ܕܡܫܬܚܠܦܢܐ ܬܠܝܬܝܐ ܕܒܚܝܪܐ ܝܠܗ. ܐܣܘܪܐ ܡܢܬܢܝܐ ܟܡܬܚܫܒ ܡܢ ܬܠܬܐ ܐܣܘܪ̈ܐ ܙܘܓܢ̈ܝܐ:

ܘܓܘ ܡܬܠܐ ܕܒ̈ܬܐ ܕܨܠܘܬܐ ܘܥܘܠ̈ܐ (ܒܡܢܝ̈ܢܐ ܚܬܝ̈ܬܐ ܕܓܘ ܟܬܒܐ):

ܐܚܐ ܩܪܝܒܐ: ܐܣܘܪܐ ܕܚܕ̈ܕܐ ܦܠܓܐ-ܡܢܬܢܝܐ. ܓܘ ܐܣܘܪܐ ܡܢܬܢܝܐ ܡܫܬܚܠܦܢܐ ܬܠܝܬܝܐ ܒܛܝܠܐ ܝܠܗ ܡܢ ܬܪܘܝܗܝ ܡܫܬܚܠܦ̈ܢܐ. ܓܘ ܐܣܘܪܐ ܦܠܓܐ-ܡܢܬܢܝܐ (semi-partial؛ ܓܘ SPSS ܟܡܬܩܪܐ Part) ܟܡܒܛܠܚ z ܡܢ ܚܕ ܡܫܬܚܠܦܢܐ ܒܣ. ܦܘܪܫܢܐ ܓܘ ܬܘܪܓܡܐ: ܡܪܒܥܐ ܕܐܣܘܪܐ ܦܠܓܐ-ܡܢܬܢܝܐ ܟܝܗܒ ܡܢܬܐ ܝܚܝܕܝܬܐ ܕ-x ܓܘ ܬܘܪܓܡܐ ܕ-y، ܐܝܟ ܦܠܓܐ ܡܢ ܟܠ ܫܘܚܠܦܐ (variance) ܕ-y. ܓܘ ܡܪܒܥܐ ܕܐܣܘܪܐ ܡܢܬܢܝܐ، ܒܪܡ، ܦܠܓܐ ܚܫܝܒܐ ܝܠܗ ܒܣ ܡܢ ܫܘܚܠܦܐ ܕܦܝܫܐ ܝܠܗ ܒܬܪ ܒܛܠܐ ܕ-z (Field, 2024, Section 8.5). ܡܚܘܝܢܐ (measure) ܚܫܝܚܐ ܝܠܗ ܒܦܪܝܫܘܬܐ ܓܘ ܪܝܓܪܫܢ (regression) ܣܓܝܐܢܝܐ، ܕܓܘܗ ܟܡܚܘܐ ܡܢܬܐ ܝܚܝܕܝܬܐ ܕܟܠ ܡܢܒܝܢܐ (predictor). ܫܘܝܘܬܐ ܐܝܟ ܕܐܣܘܪܐ ܡܢܬܢܝܐ ܝܠܗ – ܒܣ ܕܓܘ ܡܦܠܓܢܐ ܦܝܫܐ ܚܕ ܫܪܫܐ ܒܣ:

ܡܨܝܐ ܝܠܗ ܐܦ ܕܒܛܠܚ ܬܪܝܢ ܡܫܬܚܠܦ̈ܢܐ ܒܚܕ ܙܒܢܐ – ܐܣܘܪܐ ܡܢܬܢܝܐ ܕܛܟܣܐ ܬܪܝܢܐ (second-order؛ Field, 2024, Section 8.5.3). ܚܙܝܡܘܢ (Note): ܐܣܘܪܐ ܡܢܬܢܝܐ ܢܡܘܟܐ ܠܐ "ܟܡܒܛܠ" ܐܣܘܪܐ ܚܙܝܐ – ܟܡܚܘܐ ܕܡܢܬܐ ܪܒܬܐ ܡܢܗ ܡܬܘܪܓܡܐ ܝܠܗ ܒܝܕ ܡܫܬܚܠܦܢܐ ܬܠܝܬܝܐ؛ ܘܓܘܒܝܐ ܕܡܫܬܚܠܦܢܐ ܩܐ ܒܛܠܐ ܚܘܫܒܐ ܬܐܘܪܝܐ ܝܠܗ، ܠܐ ܣܛܐܛܝܣܛܝܩܝܐ. ܩܐ ܡܦܬܚܢܘܬܐ ܓܡܝܪܬܐ ܕܐܣܘܪܐ ܡܢܬܢܝܐ ܘܦܠܓܐ-ܡܢܬܢܝܐ ܓܘ ܣܝܩܐ ܕܡܫܬܚܠܦ̈ܢܐ ܣܓܝ̈ܐܐ ܚܙܝܡܘܢ Cohen et al.‏ (2003، ܦܣ̈ܩܐ 3.3.2-3.3.3، ܦܐ̈ܬܐ 72-75).

ܬܠܬ ܕܘܟ̈ܝܬܐ ܦܪ̈ܝܫܬܐ ܩܐ ܡܫܬܚܠܦܢܐ ܬܠܝܬܝܐ. ܐܣܘܪܐ ܕܚܕ̈ܕܐ ܡܢܬܢܝܐ (partial correlation) ܟܡܬܛܦܠ ܒܡܫܬܚܠܦܢܐ ܬܠܝܬܝܐ ܓܘ ܚܕܐ ܕܘܟܝܬܐ – ܡܚܠܛܢܐ (confounder)، ܕܟܥܒܕ ܐܣܘܪܐ ܕܓܠܐ ܐܝܟ ܪܒܘܬܐ ܕܟܢܫܐ ܟܠܢܝܐ ܓܘ ܡܬܠܐ ܕܒ̈ܬܐ ܕܨܠܘܬܐ ܘܥܘܠ̈ܐ (Cohen et al., 2003, Section 3.4.4). ܐܠܐ ܡܫܬܚܠܦܢܐ ܬܠܝܬܝܐ ܡܨܐ ܕܗܘܐ ܐܦ ܡܪܟܟܢܐ (moderator): ܚܝܠܐ ܕܐܣܘܪܐ ܒܝܢܝ x ܘ-y ܝܢ ܦܢܝܬܐ ܕܝܠܗ ܟܫܢܝ ܠܦܘܬ ܛܝ̈ܡܐ ܕ-z – ܚܙܝܐ ܩܕܡܝܐ ܩܐ ܗܕܐ ܟܝܗܒ ܦܘܚܡܐ ܕܐܣܘܪܐ ܒܝܢܝ ܓܘ̈ܕܐ (ܚܙܝܡܘܢ "ܦܘܚܡܐ ܒܝܢܝ ܬܪܝܢ ܐܣܘܪ̈ܐ" ܓܘ ܦܣܩܐ ܫܘܝ̈ܘܬܐ)، ܘܒܘܚܪܢܐ ܓܡܝܪܐ ܟܡܬܥܒܕ ܒܥܒܕܐ ܕܚܕ̈ܕܐ (interaction) ܓܘ ܪܝܓܪܫܢ (regression؛ ܡܦܬܚܢܘܬܐ ܩܠܐܣܝܩܝܬܐ: Cohen et al.‏، 2003، ܨܚܚܐ 7)؛ ܝܢ ܡܨܥܝܐ (mediator): z ܝܠܗ ܡܟܢܘܬܐ ܕܒܝܕܗ x ܐܣܝܪܐ ܝܠܗ ܥܡ y (x → z → y)، ܘܗܝܓܐ ܒܦܘܫܩܐ ܕܡܨܥܝܘܬܐ (mediation analysis) ܟܦܠܓܚ ܐܣܘܪܐ ܓܡܝܪܐ ܠܡܥܒܕܢܘܬܐ ܬܪܝܨܬܐ ܘܠܐ ܬܪܝܨܬܐ (ܡܦܬܚܢܘܬܐ: Cohen et al.‏، 2003، ܨܚܚܐ 12؛ Field، 2024، ܦܣ̈ܩܐ 11.3-11.4). ܚܫܝܚܐ ܝܠܗ ܠܡܝܕܥ: ܐܣܘܪܐ ܡܢܬܢܝܐ ܠܐ ܡܨܐ ܕܦܪܫ ܒܝܢܝ ܡܚܠܛܢܐ ܘܡܨܥܝܐ – ܚܘܫܒܢܐ ܐܝܟ ܚܕ ܝܠܗ ܓܘ ܬܪܝܢ ܗܘܝ̈ܐ، ܘܦܘܪܫܢܐ ܒܝܢܝ ܬܪܘܝܗܝ ܡܕܡ ܕܬܐܘܪܝܐ ܘܕܬܘܩܢܐ ܕܒܘܨܝܐ ܝܠܗ. ܡܪܟܟܢܘܬܐ ܘܡܨܥܝܘܬܐ (moderation and mediation) ܕܝܠܗ ܝܢܐ ܕܥܠܡܐ ܕܪܝܓܪܫܢ – ܚܙܝܡܘܢ ܦܐܬܐ ܡܪܟܟܢܘܬܐ ܘܡܨܥܝܘܬܐ (ܥܒܕܐ ܕܚܕ̈ܕܐ، ܡܨܠܝܢܘ̈ܬܐ ܦܫܝܛ̈ܬܐ، ܡܥܒܕܢܘܬܐ ܠܐ ܬܪܝܨܬܐ ܥܡ bootstrap)، ܦܐܬܐ ܪܝܓܪܫܢ ܣܪܛܢܝܐ ܣܓܝܐܢܝܐ، ܘܩܐ ܡܨܥܝܘܬܐ ܓܘ ܡܘܕܝܠ ܕܫܒ̈ܝܠܐ – ܦܐܬܐ ܦܘܫܩܐ ܕܫܒ̈ܝܠܐ ܘܡܨܥܝܘܬܐ، ܕܟܦܠܓ ܐܣܘܪܐ ܠܡܥܒܕܢܘܬܐ ܬܪܝܨܬܐ ܘܠܐ ܬܪܝܨܬܐ ܥܡ ܬܚܘ̈ܡܐ ܕܬܘܟܠܢܐ.

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

ܡܚܫܒܢܐ (calculator) ܕܓܘ ܐܗܐ ܦܐܬܐ ܫܘܐ ܝܠܗ ܠܬܘܩ̈ܢܐ ܡܬܚܙܝ̈ܢܐ ܣܓܝ ܕܐܘܪܚܐ Bivariate Correlations ܓܘ SPSS. ܩܐ ܡܕܒܪ̈ܢܐ (guides) ܡܦܪܫ̈ܐ ܚܙܝܡܘܢ Pallant (2020، ܨܚ̈ܚܐ 11-12) ܘ-Field (2024، ܨܚܚܐ 8).

ܡܥܝܪܢܘܬܐ ܥܠ ܢܘܣ̈ܚܐ (versions). ܨܘܪ̈ܬܐ ܕܡܘܢܝܛܪ (screenshots) ܓܘ ܐܗܐ ܦܣܩܐ ܥܒܝ̈ܕܐ ܝܢܐ ܓܘ SPSS ܢܘܣܚܐ 21. ܐܘܪ̈ܚܬܐ ܓܢܒܗܝ ܩܝ̈ܡܐ ܝܢܐ ܓܘ ܟܠ ܢܘܣ̈ܚܐ، ܐܠܐ ܕܘܟܐ ܕܡܕܡ̈ܐ ܓܘ ܪܫܝܡܬܐ (Menu) ܘܫܡ̈ܗܐ ܕܓܘܒ̈ܝܐ ܡܨܝ ܕܫܢܝ ܩܠܝܠ – ܘܐܢ ܡܘܢܝܛܪ ܕܝܘܟܘܢ ܟܡܬܚܙܐ ܩܠܝܠ ܐܚܪܢܐ، ܐܗܐ ܒܠܟܝ ܝܠܗ ܣܒܒܐ. ܡܬܠܐ ܡܬܚܙܝܢܐ ܐܝܬ ܠܬܚܬ ܓܘ ܦܐܬܐ: button ܕ-Confidence Interval ܡܘܣܦܐ ܝܠܗ ܠܟܘܬܐ ܕ-Bivariate Correlations ܒܣ ܓܘ ܢܘܣܚܐ 27، ܘܓܘ ܢܘܣ̈ܚܐ ܩܕܡܝ̈ܐ ܠܐ ܒܕ ܡܫܟܚܝܬܘܢ ܠܗ ܬܡܐ. Field (2024) ܟܬܝܒܐ ܝܠܗ ܠܦܘܬ ܢܘܣܚܐ 29، ܘܗܘ ܓܢܒܗ ܟܡܢܝܚ ܠܢ ܥܠ ܐܗܐ: ܒܝܢܝ ܡܦܩܬܐ ܠܡܦܩܬܐ ܟܦܠܛܝ ܢܘܣ̈ܚܐ ܚܕ̈ܬܐ، ܘܐܘܪ̈ܚܬܐ ܕܟܬܒܐ ܟܡܬܚܘܐ ܟܡܥܛ ܠܐ ܟܡܬܥܒܕܝ ܡܢ ܗܕܐ.

ܓܘ ܪܫܝܡܬܐ (Menu) ܟܓܒܚ Analyze › Correlate › Bivariate…:

ܓܘ ܟܘܬܐ ܕܕܝܐܠܘܓ ܕܟܦܬܚܐ (Bivariate Correlations) ܟܡܬܚܙܝܐ ܓܘ ܚܕ ܓܢܒܐ ܪܫܝܡܬܐ ܕܡܫܬܚܠܦ̈ܢܐ (variables) ܕܐܝܬ ܓܘ ܦܐܝܠ، ܘܠܩܘܛܝܐ Variables ܟܡܥܒܪܚ ܡܫܬܚܠܦ̈ܢܐ ܕܒܥܝܚ ܕܒܚܪܚ ܐܣܘܪܐ ܒܝܢܝ ܬܪܘܝܗܝ (ܬܪܝܢ ܝܢ ܒܝܫ). ܬܚܘܬ Correlation Coefficients، ܡܢܝܢܐ ܡܫܘܬܦܐ ܕ-Pearson (Pearson) ܪܫܝܡܐ ܝܠܗ ܒܐܬܐ ܕܫܘܪܪܐ (check mark) ܒܓܘܒܝܐ ܡܩܕܡܐ (default) – ܕܚܩܐ ܙܘܕܐ ܟܡܒܛܠ ܠܗ – ܐܠܐ ܡܢܝܢܐ ܡܫܘܬܦܐ ܕ-Spearman (Spearman)، ܕܠܐ ܝܠܗ ܪܫܝܡܐ ܒܓܘܒܝܐ ܡܩܕܡܐ، ܟܪܫܡܚ ܓܘ ܗܘ ܩܘܛܝܐ ܓܢܒܗ؛ ܟܡܨܝܚ ܐܦ ܕܪܫܡܚ ܬܪܘܝܗܝ ܐܟܚܕܐ، ܐܝܟ ܓܘܒܝܐ "ܬܪܘܝܗܝ" ܕܓܘ ܐܗܐ ܦܐܬܐ. (Kendall's tau-b ܝܠܗ ܡܢܝܢܐ ܡܫܘܬܦܐ ܐܚܪܢܐ ܕܕܪ̈ܓܐ ܕܛܟܣܐ ܕܟܡܬܚܙܐ ܬܡܐ، ܕܦܐܬܐ ܠܐ ܟܚܫܒܐ.)

ܓܘܒ̈ܝܐ ܡܩܕܡ̈ܐ (defaults) ܕ-SPSS ܐܝܟ ܕܦܐܬܐ ܝܢܐ – ܪܫܝܡܘܬܐ (significance) ܕܬܪܝܢ ܕܘܢ̈ܒܐ (Two-tailed)، ܪܫܡܐ ܕܐܣܘܪ̈ܐ ܪܫܝܡ̈ܐ ܒܟܘ̈ܟܒܐ (Flag significant correlations) ܘܫܩܠܬܐ ܙܘܓܢܝܬܐ (pairwise deletion) ܕܛܝ̈ܡܐ ܚܣܝ̈ܪܐ (Options › Exclude cases pairwise) – ܘܡܛܠ ܗܕܐ ܓܘ ܪܘܒܐ ܕܗܘܝ̈ܐ ܦܐܪ̈ܐ ܓܪܓ ܕܗܘܝ ܐܝܟ ܚܕ ܥܕܡܐ ܠܦܘܪ̈ܫܢܐ ܕܩܘܪܒܐ (rounding). (ܦܐܬܐ ܟܚܫܒܐ ܟܠ ܐܡܢ ܪܫܝܡܘܬܐ ܕܬܪܝܢ ܕܘܢ̈ܒܐ، ܘܠܐ ܐܝܬ ܓܘܗ ܓܘܒ̈ܝܐ ܐܚܪ̈ܢܐ ܕܐܘܪܚܐ ܐܝܟ ܒܘܚܪܢܐ ܕܚܕ ܕܘܢܒܐ.) ܦܘܪܫܢܐ ܙܥܘܪܐ ܚܕ ܓܘ ܪܫܡܐ: SPSS ܟܪܫܡ ܒܣ p < .05 ܘ-p < .01، ܐܠܐ ܠܐܟܐ ܪܫܝܡܐ ܝܠܗ ܐܦ *** ܩܐ p < .001، ܐܝܟ ܥܝܕܐ ܓܘ ܠܘ̈ܚܐ ܕ-APA (American Psychological Association [APA], 2020, Section 7.14).

ܕܚܩܐ ܥܠ Paste ܓܘ ܟܘܬܐ ܕܕܝܐܠܘܓ ܟܢܛܪ ܥܒܕܐ ܐܝܟ ܣܝܢܬܐܟܣ (syntax) – ܡܦܝܕܢܐ ܩܐ ܟܬܒܢܘܬܐ ܕܦܘܫܩܐ ܘܩܐ ܥܒܕܐ ܡܢ ܪܝܫ ܕܝܠܗ:

CORRELATIONS
  /VARIABLES=מנהיגות יעילות מוכנות שייכות אמון
  /PRINT=TWOTAIL NOSIG
  /MISSING=PAIRWISE.

ܘܬܚܘܡܐ ܕܬܘܟܠܢܐ (confidence interval)؟ ܣܝܢܬܐܟܣ ܕܠܥܠ ܠܐ ܟܛܒܥ ܠܗ. ܓܘ SPSS 27 ܘܠܥܠ ܟܕܚܩܚ ܓܘ ܟܘܬܐ ܕ-Bivariate Correlations ܥܠ Confidence interval… ܘܟܪܫܡܚ Estimate confidence interval of bivariate correlation parameter – ܘܠܡܦܩܢܐ ܟܡܬܘܣܦ ܠܘܚܐ ܬܪܝܢܐ ܥܡ ܬܚܘ̈ܡܐ ܬܚܬܝܐ ܘܥܠܝܐ ܕܟܠ ܐܣܘܪܐ (Field, 2024, Sections 8.4.1-8.4.2). ܩܐ Pearson ܚܘܫܒܢܐ ܝܠܗ ܫܘܢܝܐ ܕ-Fisher (Fisher transformation) – ܗܘ ܬܚܘܡܐ ܕܟܡܚܘܐ ܠܘܚܐ ܕܬܚܘܝܬܐ ܓܡܝܪܬܐ ܓܘ ܐܗܐ ܦܐܬܐ. ܓܘ ܢܘܣ̈ܚܐ ܩܕܡܝ̈ܐ ܒܝܫ button ܠܝܬ، ܘܬܚܘܡܐ ܟܚܫܒܚ ܒܫܘܝܘܬܐ ܕܓܘ ܦܣܩܐ ܫܘܝ̈ܘܬܐ – ܝܢ ܠܐܟܐ ܓܘ ܦܐܬܐ.

ܘܗܠ ܩܕܡ ܡܢܝ̈ܢܐ ܡܫܘܬܦ̈ܐ – ܚܙܝܐ ܥܠ ܟܠ ܙܘܓ̈ܐ ܒܚܕ ܓܗܐ. ܡܠܟܐ ܕܨܘܪܬܐ ܕܒܕܪܐ ܟܡܨܝܚ ܕܡܦܠܚܚ ܠܗ ܥܠ ܟܠ ܙܘܓ̈ܐ ܕܡܫܬܚܠܦ̈ܢܐ ܒܚܕ ܓܗܐ، ܒܝܕ ܡܐܛܪܝܟܣ ܕܨܘܪ̈ܬܐ ܕܒܕܪܐ (scatterplot matrix): ܓܘ ܪܫܝܡܬܐ (Menu) Graphs › Legacy Dialogs › Scatter/Dot… › Matrix Scatter › Define، ܟܡܥܒܪܚ ܡܫܬܚܠܦ̈ܢܐ ܠܪܫܝܡܬܐ ܕ-Matrix Variables ܘܟܩܒܠܚ. ܗܝ ܡܐܛܪܝܟܣ ܟܡܨܝܚ ܕܒܢܚ ܐܦ ܓܘ Chart Builder ܚܕܬܐ، ܕܓܘܗ ܟܥܒܕܚ ܐܦ ܨܘܪܬܐ ܕܒܕܪܐ ܝܚܝܕܝܬܐ ܥܡ ܣܪܛܐ ܕܦܐܝܘܬܐ ܝܢ ܨܘܪܬܐ ܕܒܕܪܐ ܟܢܝܫܬܐ ܠܦܘܬ ܓܘ̈ܕܐ (Field, 2024, Section 5.8). ܐܦ ܠܐܟܐ Paste ܟܢܛܪ ܣܝܢܬܐܟܣ (syntax):

ܩܐ ܨܘܪܬܐ ܕܒܕܪܐ ܝܚܝܕܝܬܐ، ܡܦܪܫܬܐ ܒܝܫ – ܥܡ ܣܪܛܐ ܕܪܝܓܪܫܢ (regression line)، R² ܘܡܐܡܪ̈ܐ ܕܬܘܢܝܐ ܡܛܝܒ̈ܐ – ܚܙܝܡܘܢ ܦܐܬܐ ܕܨܘܪܬܐ ܕܒܕܪܐ، ܘܓܘܗ ܐܦ ܡܕܒܪܢܐ (guide) ܕ-SPSS ܓܡܝܪܐ ܥܡ ܨܘܪ̈ܬܐ ܩܐ ܐܘܪܚܐ.

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

ܬܠܬܐ ܢܘܩ̈ܙܐ ܓܘ ܩܪܝܢܐ ܕܡܐܛܪܝܟܣ. ܩܕܡܝܐ، ܟܠ ܩܠ̈ܝܬܐ ܟܡܚܘܝ̈ܐ ܥܢܢܐ ܕܣܠܩ – ܐܝܟ ܥܣܪܐ ܐܣܘܪ̈ܐ ܕܚܕ̈ܕܐ ܕܙܘܕܐ ܘܚܝܠܢ̈ܐ ܕܓܘ ܠܘܚܐ ܕܡܦܩܢܐ، ܘܕܠܐ ܐܬܘ̈ܬܐ ܕܐܣܘܪܐ ܟܦܝܦܐ ܝܢ ܕܛܝ̈ܡܐ ܢܘܟܪ̈ܝܐ (outliers) ܕܟܡܥܒܕܝ؛ ܐܗܐ ܝܠܗ ܚܬܝܬܐܝܬ ܒܘܚܪܢܐ ܕܐܪܒܥܝܘܬܐ ܕ-Anscombe ܟܡܠܦܐ (ܚܙܝܡܘܢ ܠܥܠ). ܬܪܝܢܐ، ܢܘܩ̈ܙܐ ܟܡܬܟܢܫܝ ܥܠ "ܡܨܝܕܬܐ" ܛܟܝܣܬܐ – ܐܗܐ ܡܣܟܝܐ ܝܠܗ ܐܝܡܢ ܕܡܫܬܚܠܦ̈ܢܐ ܡܨܥܝ̈ܬܐ ܝܢܐ ܕܦܣܘ̈ܩܐ (items) ܕܣܒܠܬܐ ܦܪ̈ܝܫܐ (discrete)، ܘܠܐ ܝܠܗ ܥܩܬܐ. ܘܬܠܝܬܝܐ، ܚܙܝܡܘܢ ܕܦܘܩܕܢܐ GRAPH ܟܡܦܠܚ ܒܓܘܒܝܐ ܡܩܕܡܐ (default) ܒܫܩܠܬܐ ܕܣܕܪܐ ܟܠܗ (listwise deletion؛ /MISSING=LISTWISE) – ܠܐ ܐܝܟ ܫܩܠܬܐ ܙܘܓܢܝܬܐ ܕܠܘܚܐ ܕܐܣܘܪ̈ܐ ܕܚܕ̈ܕܐ – ܘܡܛܠ ܗܕܐ ܡܢܝܢܐ ܕܢܘܩ̈ܙܐ ܓܘ ܟܠ ܩܠܝܬܐ ܡܨܐ ܕܗܘܐ ܩܠܝܠ ܙܥܘܪܐ ܡܢ N ܕܗܘ ܙܘܓܐ ܓܘ ܠܘܚܐ.

ܘܒܘܚܪܢܐ ܕܢܘܪܡܠܝܘܬܐ (normality) ܒܥܒܕܐ؟ ܐܝܟ ܕܥܗܝܕܐ ܝܠܗ، ܢܘܪܡܠܝܘܬܐ ܐܣܝܪܬܐ ܝܠܗ ܒܦܪܝܫܘܬܐ ܥܡ ܬܪܝܨܘܬܐ (validity) ܕܒܘܚܪܢܐ ܕܪܫܝܡܘܬܐ، ܘܒܦܪܝܫܘܬܐ ܓܘ ܕܘ̈ܡܝܐ ܙܥܘ̈ܪܐ. ܒܘܚܪܢܐ ܟܥܒܕܚ ܒܨܘܪ̈ܬܐ: ܓܘ ܪܫܝܡܬܐ (Menu) Analyze › Descriptive Statistics › Explore ܟܪܫܡܚ Normality plots with tests ܘܟܫܩܠܚ ܨܘܪܬܐ Q-Q – ܐܢ ܢܘܩ̈ܙܐ ܩܪܝܒ̈ܐ ܝܢܐ ܠܣܪܛܐ ܡܨܠܝܢܐ، ܦܘܠܓܐ (distribution) ܩܪܝܒܐ ܝܠܗ ܠܢܘܪܡܠܝܐ – ܥܡ ܡܚܘ̈ܝܢܐ ܕܥܩܝܡܘܬܐ (skewness) ܘܕܓܒܢܘܬܐ (kurtosis) ܕܓܘ ܗܘ ܡܦܩܢܐ (Field, 2024, Sections 6.9.4-6.9.5). ܘܐܝܡܢ ܕܦܝܫܐ ܦܠܓܘܬ ܠܒܐ – ܬܚܘܡܐ ܕܬܘܟܠܢܐ ܒ-bootstrap (ܚܙܝܡܘܢ ܓܘ ܦܣܩܐ ܫܘܝ̈ܘܬܐ) ܟܡܙܥܪ ܣܓܝ ܬܠܝܘܬܐ ܥܠ ܫܪܛܐ ܕܢܘܪܡܠܝܘܬܐ؛ ܐܦ ܗܘ، ܡܢ ܟܝܢܐ، ܡܣܡܟ ܝܠܗ ܥܠ ܚܙ̈ܝܬܐ ܚܐܪ̈ܬܐ ܘܥܠ ܕܘܡܝܐ ܕܟܡܚܘܐ ܟܢܫܐ ܟܠܢܝܐ (population).

ܩܪܝܢܐ ܕܡܦܩܢܐ (How to read the output)

ܗܕܟܐ ܟܡܬܚܙܐ ܠܘܚܐ ܕܡܦܩܢܐ (output) ܕ-SPSS (Correlations) ܩܐ ܚܡܫܐ ܡܫܬܚܠܦ̈ܢܐ ܕܚܣܝܢܘܬܐ (resilience) – ܡܕܒܪܢܘܬܐ، ܡܦܝܕܢܘܬܐ، ܡܛܝܒܘܬܐ، ܕܝܠܢܝܘܬܐ ܘܬܘܟܠܢܐ. ܠܘܚܐ ܕܡܦܩܢܐ ܡܐܛܪܝܟܣ ܫܘܝܬܐ ܝܠܗ (symmetric): ܡܫܬܚܠܦ̈ܢܐ ܟܡܬܦܠܚܝ ܐܝܟ ܪ̈ܫܐ ܐܦ ܓܘ ܣܕܪ̈ܐ ܘܐܦ ܓܘ ܥܡܘ̈ܕܐ، ܘܟܠ ܙܘܓܐ ܟܫܩܠ ܬܪܬܝܢ ܩܠ̈ܝܬܐ ܐܝܟ ܚܕ̈ܕܐ – ܚܕܐ ܠܥܠ ܡܢ ܣܪܛܐ ܡܨܠܝܢܐ ܘܚܕܐ ܠܬܚܬ ܡܢܗ. ܓܘ ܟܠ ܩܠܝܬܐ ܬܠܬܐ ܣܕܪ̈ܐ:

ܣܕܪܐ ܩܕܡܝܐ ܓܘ ܟܠ ܩܠܝܬܐ – ܡܢܝܢܐ ܡܫܘܬܦܐ ܕܐܣܘܪܐ (Pearson Correlation). ܓܘ ܣܕܪܐ ܕܪܫܝܡܐ ܝܠܗ ܒܓܐܪܐ (arrow)، ܡܬܠܐ، ܐܣܘܪܐ ܒܝܢܝ ܡܛܝܒܘܬܐ ܘܡܕܒܪܢܘܬܐ ܝܠܗ .722 – ܐܣܘܪܐ ܕܙܘܕܐ: ܕܪ̈ܓܐ ܪ̈ܡܐ ܕܡܛܝܒܘܬܐ ܒܐܟܡܐ ܕܥܝܕܐ ܟܐܙܠܝ ܐܟܚܕܐ ܥܡ ܕܪ̈ܓܐ ܪ̈ܡܐ ܕܡܕܒܪܢܘܬܐ، ܘܠܦܘܬ ܥܝ̈ܕܐ ܕ-Cohen ܐܗܐ ܐܣܘܪܐ ܚܝܠܢܐ ܝܠܗ. ܐܢ ܐܬܐ ܗܘܐ ܕܒܨܘܪܐ، ܣܘܟܠܐ ܗܘܐ ܗܦܝܟܐ – ܟܡܐ ܕܛܝܡܐ ܕܚܕ ܣܠܩ، ܛܝܡܐ ܕܐܚܪܢܐ ܢܚܬ. ܥܠ ܣܪܛܐ ܡܨܠܝܢܐ ܟܠ ܐܡܢ ܒܕ ܡܬܚܙܐ 1: ܟܠ ܡܫܬܚܠܦܢܐ ܐܣܝܪܐ ܝܠܗ ܓܡܝܪܐܝܬ ܥܡ ܓܢܒܗ. ܐܗܐ ܠܐ ܝܠܗ ܡܫܟܚܢܘܬܐ – ܒܣ ܟܫܒܩܚ ܣܪܛܐ ܡܨܠܝܢܐ.

ܣܕܪܐ ܬܪܝܢܐ – ܪܫܝܡܘܬܐ (Sig. (2-tailed)). SPSS ܟܡܚܘܐ ܛܝܡܐ p ܒܬܠܬܐ ܡܢܝ̈ܢܐ ܒܬܪ ܢܘܩܙܐ، ܘܡܛܠ ܗܕܐ .000 ܠܐ ܝܠܗ ܣܦܪ ܐܠܐ p < .001 – ܘܗܕܟܐ ܐܦ ܟܬܢܚ (ܠܐ ܚܕ ܓܗܐ p = 0؛ APA، 2020، ܦܣܩܐ 6.36). ܟܘ̈ܟܒܐ ܕܓܢܒ ܡܢܝ̈ܢܐ ܡܫܘܬܦ̈ܐ، ܕܡܦܫܩ̈ܐ ܝܢܐ ܓܘ ܡܥܝܪܢܘܬܐ ܕܬܚܬ ܠܘܚܐ، ܟܪܫܡܝ ܐܣܘܪܐ ܪܫܝܡܐ؛ ܓܘ ܐܗܐ ܠܘܚܐ ܟܠ ܐܣܘܪ̈ܐ ܪܫܝܡ̈ܐ ܝܢܐ.

ܣܕܪܐ ܬܠܝܬܝܐ – ܪܒܘܬܐ ܕܕܘܡܝܐ (N). ܡܢܝܢܐ ܕܡܫܬܘܬܦ̈ܢܐ (participants) ܕܥܠ ܝܗܝ̈ܒܬܐ ܕܝܗܝ ܚܫܝܒܐ ܝܠܗ ܗܘ ܐܣܘܪܐ. ܚܙܝܡܘܢ ܕ-N ܟܫܢܐ ܡܢ ܙܘܓܐ ܠܙܘܓܐ (ܡܬܠܐ 455 ܓܘ ܙܘܓܐ ܡܕܒܪܢܘܬܐ-ܡܦܝܕܢܘܬܐ ܩܘܒܠ 447 ܓܘ ܙܘܓܐ ܡܕܒܪܢܘܬܐ-ܡܛܝܒܘܬܐ): ܐܗܐ ܝܠܗ ܫܩܠܬܐ ܙܘܓܢܝܬܐ (pairwise deletion) – ܟܠ ܐܣܘܪܐ ܚܫܝܒܐ ܝܠܗ ܥܠ ܡܫܬܘܬܦ̈ܢܐ ܕܐܝܬܠܗܘܢ ܛܝܡܐ ܬܪܝܨܐ ܓܘ ܬܪܝܢ ܡܫܬܚܠܦ̈ܢܐ ܕܗܘ ܙܘܓܐ، ܠܦܘܬ /MISSING=PAIRWISE ܕܓܘ ܣܝܢܬܐܟܣ.

ܡܘܕܝ ܚܫܝܚܐ ܝܠܗ ܠܡܝܕܥ ܥܠ ܫܩܠܬܐ ܙܘܓܢܝܬܐ. ܝܘܬܪܢܐ – ܟܠ ܐܣܘܪܐ ܟܡܦܠܚ ܒܐܟܡܐ ܕܡܨܝܐ ܝܠܗ ܡܢ ܝܗܝ̈ܒܬܐ ܕܐܝܬ. ܐܓܪܐ – ܟܠ ܐܣܘܪܐ ܚܫܝܒܐ ܝܠܗ ܥܠ ܕܘܡܝܐ ܙܥܘܪܐ ܦܪܝܫܐ ܩܠܝܠ، ܘܡܛܠ ܗܕܐ ܦܘܚܡܐ ܒܝܢܝ ܡܢܝ̈ܢܐ ܡܫܘܬܦ̈ܐ ܓܘ ܡܐܛܪܝܟܣ ܠܐ ܝܠܗ ܡܣܡܟܐ ܚܬܝܬܐܝܬ ܥܠ ܗܢܝ ܡܫܬܘܬܦ̈ܢܐ؛ ܐܝܡܢ ܕܚܣܝ̈ܪܐ ܣܓܝ̈ܐܐ ܝܢܐ، ܡܐܛܪܝܟܣ ܐܝܟ ܐܗܐ ܐܦ ܡܨܝܐ ܕܦܠܛܐ ܠܐ ܫܠܝܡܬܐ ܩܐ ܦܘܫܩ̈ܐ ܕܒܬܪ ܕܡܣܡܟܝ ܥܠܗ (ܐܝܟ ܪܝܓܪܫܢ (regression) ܣܓܝܐܢܝܐ ܝܢ SEM). ܡܛܠ ܗܕܐ ܟܬܢܚ N ܩܐ ܟܠ ܐܣܘܪܐ (ܐܝܟ ܓܘ ܡܥܝܪܢܘܬܐ ܕܠܘܚܐ ܕܟܡܚܘܐ ܐܗܐ ܦܐܬܐ)، ܘܐܝܡܢ ܕܐܝܬ ܝܗܝ̈ܒܬܐ ܚܣܝ̈ܪܬܐ ܣܓܝ̈ܐܐ ܟܚܫܒܚ ܥܠ ܫܩܠܬܐ ܕܣܕܪܐ ܟܠܗ (listwise deletion؛ Options › Exclude cases listwise ܓܘ ܟܘܬܐ ܕ-Bivariate) ܝܢ ܛܘܦܠܐ ܝܚܝܕܝܐ ܒܝܗܝ̈ܒܬܐ ܚܣܝ̈ܪܬܐ.

ܬܪܝܢ ܡܕܡ̈ܐ ܟܚܬܡܝ ܩܪܝܢܐ: ܪܒܘܬܐ ܕܡܢܝܢܐ ܡܫܘܬܦܐ (coefficient)، ܕܡܢܗ ܟܡܬܩܪܐ ܚܝܠܐ، ܘܐܬܐ ܕܝܠܗ، ܕܡܢܗ ܟܡܬܩܪܝܐ ܦܢܝܬܐ. ܓܘ ܐܗܐ ܠܘܚܐ ܟܠ ܥܣܪܐ ܐܣܘܪ̈ܐ ܕܙܘܕܐ، ܚܝܠܢ̈ܐ (.622-.738) ܘܪܫܝܡ̈ܐ ܝܢܐ. ܠܘܚܐ ܕܡܦܩܢܐ ܕܐܣܘܪܐ ܕ-Spearman ܒܢܝܐ ܝܠܗ ܚܬܝܬܐܝܬ ܒܗܘ ܒܢܝܢܐ. ܐܗܐ ܦܐܬܐ ܟܡܚܘܐ ܗܝ ܡܘܕܥܢܘܬܐ ܒܨܘܪܬܐ ܕ-APA ܩܛܝܢܬܐ ܒܝܫ: ܡܐܛܪܝܟܣ ܕܡܬܠܬܐ ܬܚܬܝܐ ܕܓܘܗ ܟܘ̈ܟܒܐ ܟܪܫܡܝ ܪܫܝܡܘܬܐ (significance)، ܘ-N ܡܬܬܢܐ ܝܠܗ ܓܘ ܡܥܝܪܢܘܬܐ ܕܠܘܚܐ.

ܬܘܢܝܐ ܕܡܫܟܚ̈ܢܘܬܐ (reporting the results)

ܦܣܩܬܐ ܒܝܢܝ ܡ̈ܠܐ ܘܠܘܚܐ ܡܕܡ ܕܟܡܝܘܬܐ ܝܠܗ: ܚܕ ܙܘܓܐ ܟܫܠܡ ܒܚܕ ܡܐܡܪܐ؛ ܥܣܪܐ ܙܘܓ̈ܐ، ܐܝܟ ܠܐܟܐ، ܠܐ ܟܡܬܩܪܝ ܒܚܕ ܣܕܪܐ – ܘܡܛܠ ܗܕܐ ܟܡܚܠܛܚ ܬܪܝܢ ܕܪ̈ܓܐ: ܠܘܚܐ ܩܛܝܢܐ ܕܟܡܟܢܫ ܟܠ ܐܣܘܪ̈ܐ ܕܚܕ̈ܕܐ، ܘܡ̈ܠܐ ܕܟܡܚܘܝ̈ܐ ܨܘܪܬܐ ܕܟܦܠܛܐ ܡܢ ܠܘܚܐ – ܕܠܐ ܬܢܝܐ ܕܟܠ ܡܢܝܢܐ ܕܟܡܬܚܙܐ ܓܘܗ ܡܢ ܩܕܡ. ܗܕܟܐ ܒܕ ܡܬܚܙܐ ܬܘܢܝܐ ܩܐ ܡܦܩܢܐ ܕܩܪܝܠܢ ܗܫܐ.

ܠܘܚܐ. ܡܐܛܪܝܟܣ ܕ-SPSS ܠܐ ܟܢܣܚܚ ܠܥܒܕܐ ܐܝܟ ܕܐܝܬܝܗ: ܗܝ ܟܡܚܘܝܐ ܟܠ ܐܣܘܪܐ ܬܪܝܢ ܓܗ̈ܐ، ܘܓܘ ܬܘܢܝܐ ܕܒܘܨܝܐ ܠܝܬ ܣܢܝܩܘܬܐ ܕܬܢܚ ܐܦ ܚܕ ܐܣܘܪܐ ܒܝܫ ܡܢ ܚܕ ܓܗܐ. ܠܘܚܐ ܕܐܣܘܪ̈ܐ ܛܒܐ ܝܠܗ ܕܗܘܐ ܩܛܝܢܐ ܘܕܐܝܬ ܓܘܗ ܡܘܕܥܢܘܬܐ ܣܢܝܩܬܐ ܒܣ: ܡܬܠܬܐ ܬܚܬܝܐ، ܛܝ̈ܡܐ ܕܠܐ ܣܦܪ ܩܕܡܝܐ ܘܒܬܪܝܢ ܡܢܝ̈ܢܐ ܒܬܪ ܢܘܩܙܐ – ܗܕܟܐ ܟܒܥܐ ܨܘܪܬܐ ܕ-APA (APA, 2020, Section 6.36) – ܘܕܠܐ ܛܝ̈ܡܐ ܕ-p ܚܬܝ̈ܬܐ – ܪܫܝܡܘܬܐ ܟܪܫܡܚ ܒܟܘ̈ܟܒܐ، ܕܡܦܫܩܢܐ ܕܝܗܝ ܟܬܝܒܐ ܝܠܗ ܬܚܬ ܠܘܚܐ (ܦܣܩܐ 7.14). ܐܗܐ ܝܠܗ ܚܬܝܬܐܝܬ ܒܢܝܢܐ ܕܠܘܚܐ ܕܐܣܘܪ̈ܐ ܕܡܬܠܐ ܓܘ ܡܕܒܪܢܐ: ܡܫܬܚܠܦ̈ܢܐ ܡܢܝ̈ܢܐ ܝܢܐ ܓܘ ܥܡܘܕܐ ܕܪ̈ܫܐ، ܓܘ ܪ̈ܫܐ ܕܥܡܘ̈ܕܐ ܟܡܬܚܙܝ ܡܢܝ̈ܢܐ ܒܣ، ܘܣܪܛܐ ܡܨܠܝܢܐ – ܕܓܘܗ ܐܣܘܪܐ ܕܡܫܬܚܠܦܢܐ ܥܡ ܓܢܒܗ ܝܠܗ 1 – ܪܫܝܡܐ ܝܠܗ ܒܣܪܛܐ ܦܪܫܢܐ ܐܪܝܟܐ (em dash)، ܘܠܐ ܒܡܢܝܢܐ (ܦܣܩܐ 7.21، ܠܘܚܐ 7.10). ܐܦ ܪܒܘܬܐ ܕܕܘܡܝܐ ܠܐ ܣܢܝܩ ܝܠܗ ܕܟܬܒܚ ܓܘ ܟܠ ܩܠܝܬܐ: ܐܝܡܢ ܕܗܘ N ܟܬܢܐ ܓܢܒܗ ܟܬܢܚ ܠܗ ܚܕ ܓܗܐ، ܬܚܬ ܠܘܚܐ ܝܢ ܬܚܬ ܪܫܐ ܕܝܠܗ، ܘܐܝܡܢ ܕܟܫܢܐ ܡܢ ܙܘܓܐ ܠܙܘܓܐ – ܐܝܟ ܠܐܟܐ، ܡܛܠ ܫܩܠܬܐ ܙܘܓܢܝܬܐ – ܟܬܢܚ ܦܬܝܘܬܐ (range). (ܡܐܛܪܝܟܣ ܕܐܣܘܪ̈ܐ ܕܦܐܬܐ ܟܡܚܘܐ ܓܘ ܡܦܩܢܐ ܟܦܝܫܐ ܒܬܠܬܐ ܡܢܝ̈ܢܐ، ܐܝܟ ܓܘ SPSS ܘܓܘ R، ܩܐ ܕܗܘܐ ܦܫܝܩܐ ܒܘܚܪܢܐ ܘܦܘܚܡܐ ܥܡܗܝ؛ ܓܘ ܠܘܚܐ ܕܟܡܩܪܒܚ ܓܘ ܥܒܕܐ ܟܩܪܒܚ ܠܬܪܝܢ – button ܕ"ܢܣܚܐ ܕܠܘܚܐ ܩܐ ܡܩܪܒܬܐ" ܕܬܚܬ ܡܐܛܪܝܟܣ ܟܥܒܕ ܐܗܐ ܡܢ ܓܢܒܗ.) ܚܙܝܡܘܢ (Note): ܐܣܘܪ̈ܐ ܕܪܫܝܡ̈ܐ ܝܢܐ ܓܘ ܡܦܩܢܐ ** (ܪܫܝܡܐ ܓܘ ܕܪܓܐ .01) ܒܥܒܕܐ p < .001 ܝܢܐ – ܘܡܛܠ ܗܕܐ ܓܘ ܠܘܚܐ ܪܫܝܡ̈ܐ ܝܢܐ ***.

ܡ̈ܠܐ. ܬܘܢܝܐ ܒܡ̈ܠܐ ܥܠ ܐܣܘܪܐ ܕܚܕ̈ܕܐ ܐܝܬ ܓܘܗ ܬܠܬܐ ܡܢܘ̈ܬܐ: ܐܣܘܪܐ ܓܢܒܗ، ܪܫܝܡܘܬܐ (significance) ܕܝܠܗ ܘܪܒܘܬܐ ܕܕܘܡܝܐ (sample size). ܢܡܘܣܐ ܕܒܬܪܝܗܝ: ܡ̈ܠܐ ܓܪܓ ܕܐܝܬ ܓܘܝܗܝ ܡܘܕܥܢܘܬܐ ܕܡܣܦܩܐ ܩܐ ܕܩܪܘܝܐ ܦܗܡ ܦܘܫܩܐ ܕܥܒܝܕܐ ܝܠܗ ܘܡܨܐ ܕܡܫܪܪ ܠܗ، ܘܐܦ ܪ̈ܒܘܬܐ ܕܡܥܒܕܢܘܬܐ (effect sizes) ܘܬܚܘ̈ܡܐ ܕܬܘܟܠܢܐ ܐܝܡܢ ܕܐܝܬ (APA, 2020, Section 6.43). ܟܟܬܒܚ ܠܗ ܗܕܟܐ ܕܡܫܟܚܢܘܬܐ ܟܡܬܩܪܝܐ ܒܡ̈ܠܐ ܘܣܛܐܛܝܣܛܝܩܐ ܟܐܬܝܐ ܓܘ ( )، ܡܬܠܐ: ܐܫܟܚ ܕܟܡܐ ܕܡܦܝܕܢܘܬܐ ܪܡܬܐ ܝܠܗ ܒܝܫ، ܗܕܟܐ ܐܦ ܬܘܟܠܢܐ ܪܡܐ ܝܠܗ ܒܝܫ (r = .74, 95% CI [.69, .78], p < .001, n = 479). ܬܚܘܡܐ ܕܬܘܟܠܢܐ (confidence interval) ܟܥܐܠ ܓܘ ( ) ܒܬܪ r – ܗܕܟܐ ܟܬܢܐ ܐܦ Field (2024، ܦܣܩܐ 8.8)، ܘܗܕܟܐ ܟܟܬܒܝ ܡܐܡܪ̈ܐ ܕܬܘܢܝܐ ܕܓܘ ܦܐܬܐ. ܪܒܘܬܐ ܕܕܘܡܝܐ ܟܡܨܝܚ ܕܬܢܚ ܐܝܟ n، ܝܢ ܐܝܟ ܕܪ̈ܓܐ ܕܚܐܪܘܬܐ (degrees of freedom) ܓܘ ( ) ܒܬܪ r – r(477) = .74، ܐܝܡܢ ܕ-df = N − 2 – ܘܐܝܡܢ ܕ-N ܐܝܟ ܚܕ ܝܠܗ ܩܐ ܟܠ ܐܣܘܪ̈ܐ، ܟܬܢܚ ܠܗ ܚܕ ܓܗܐ ܒܪܫܐ ܕܨܚܚܐ ܕܡܫܟܚ̈ܢܘܬܐ (results chapter) ܘܟܚܣܟܚ ܬܢܝܬܐ. ܓܘ ܓܘܫܡܐ ܕܡ̈ܠܐ ܟܡܫܕܪܚ ܠܠܘܚܐ، ܟܡܚܘܚ ܕܡܘܬܐ ܓܢܝܬܐ ܘܟܡܢܗܪܚ ܡܫܟܚ̈ܢܘܬܐ ܡܬܚܙܝ̈ܢܐ، ܡܬܠܐ ܐܣܘܪܐ ܚܝܠܢܐ ܡܢ ܟܠ ܘܟܪܝܗܐ ܡܢ ܟܠ:

ܠܘܚܐ ܘܡܐܡܪ̈ܐ ܕܬܘܢܝܐ (report sentences) ܒܐܗܐ ܨܘܪܬܐ ܟܡܦܩ ܡܚܫܒܢܐ (calculator) ܕܓܘ ܐܗܐ ܦܐܬܐ ܡܢ ܓܢܒܗ ܡܢ ܦܐܝܠ ܕܝܗܝ̈ܒܬܐ، ܘܟܡܨܝܬܘܢ ܕܡܚܬܝܬܘܢ ܡܦܩܢܐ ܓܡܝܪܐ ܐܝܟ ܦܐܝܠ Word.

ܘܨܘܪܬܐ. ܐܝܡܢ ܕܨܘܪܬܐ ܕܒܕܪܐ (scatter plot) ܓܢܒܗ ܥܐܠܐ ܠܨܚܚܐ ܕܡܫܟܚ̈ܢܘܬܐ (results chapter) – ܘܠܐ ܒܣ ܡܬܦܠܚܐ ܩܐ ܒܘܚܪܢܐ ܕܫܪ̈ܛܐ ܩܕܡ ܚܘܫܒܢܐ – ܗܝ ܨܘܪܬܐ ܡܢܝܬܐ (figure)، ܘܠܨܘܪܬܐ ܐܝܬ ܒܢܝܢܐ ܕܝܠܗ: ܡܢܝܢܐ، ܪܫܐ ܒܐܬܘ̈ܬܐ ܡܨܠܝ̈ܢܬܐ (italic)، ܫܡ̈ܗܐ ܕܡܫܬܚܠܦ̈ܢܐ ܥܠ ܬܪܝܢ ܣܪ̈ܛܐ، ܘܡܥܝܪܢܘܬܐ ܬܚܘܬܗ. ܡܥܝܪܢܘܬܐ ܦܫܝܩܐ ܝܠܗ ܕܢܫܝܚ، ܐܠܐ ܗܝ ܝܠܗ ܡܢܬܐ ܕܟܥܒܕܐ ܨܘܪܬܐ ܕܩܝܡܐ ܒܓܢܒܗ، ܘ-APA (2020، ܦܣܩܐ 7.28) ܟܡܦܪܫܐ ܡܘܕܝ ܓܪܓ ܕܐܡܪܐ: ܕܡܦܫܩܐ ܡܫܘ̈ܚܬܐ، ܐܬܘ̈ܬܐ ܘܩܨܝܪ̈ܬܐ ܕܠܐ ܡܦܫܩ̈ܐ ܝܢܐ ܓܘ ܡܦܫܩܢܐ (legend)، ܘܕܡܦܫܩܐ ܟܠ ܛܠܠܐ، ܓܘܢܐ ܝܢ ܡܢܬܐ ܐܚܪܬܐ ܕܨܘܒܥܐ ܕܐܝܬܠܗ ܣܘܟܠܐ. ܓܘ ܨܘܪܬܐ ܕܒܕܪܐ ܐܗܐ ܟܡܬܬܪܓܡ ܠܬܪܝܢ ܡܐܡܪ̈ܐ ܩܨܝܪ̈ܐ – ܡܘܕܝ ܟܡܚܘܐ ܟܠ ܢܘܩܙܐ (ܚܕ ܡܫܬܘܬܦܢܐ، ܠܦܘܬ ܛܝ̈ܡܐ ܕܝܠܗ ܓܘ ܬܪܝܢ ܡܫܬܚܠܦ̈ܢܐ) ܘܡܘܕܝ ܝܠܗ ܣܪܛܐ (ܣܪܛܐ ܕܪܝܓܪܫܢ ܣܪܛܢܝܐ). ܘܐܢ ܓܘ ܨܘܪܬܐ ܡܚܘܝ̈ܐ ܝܢܐ ܐܬܘ̈ܬܐ ܕܛܥܝܘܬܐ (error bars) ܝܢ ܐܣܪܐ ܕܬܘܟܠܢܐ (confidence band)، ܓܪܓ ܕܐܡܪܚ ܓܠܝܐܝܬ ܐܢ ܐܢܝ ܟܡܚܘܝ̈ܐ ܣܛܝ̈ܘܬܐ ܬܩܝܢ̈ܝܬܐ، ܛܥܝ̈ܘܬܐ ܬܩܝܢ̈ܝܬܐ، ܬܚܘ̈ܡܐ ܕܬܘܟܠܢܐ ܝܢ ܦܬܝ̈ܘܬܐ – ܘܡܕܒܪܢܐ ܟܡܘܣܦ ܕܛܒܐ ܝܠܗ ܕܐܡܪܚ ܥܡܗܝ ܐܦ ܪܒܘܬܐ ܕܕܘܡܝܐ (ܬܡܐ). ܡܥܝܪܢܘܬܐ ܕܨܘܪܬܐ ܟܬܝܒܬܐ ܝܠܗ ܒܨܘܪܬܐ ܕܡܥܝܪܢܘܬܐ ܕܠܘܚܐ، ܘܒܗܘ ܛܟܣܐ – ܓܢܝܬܐ، ܝܚܝܕܝܬܐ، ܡܣܬܒܪܢܘܬܐ – ܘܟܘ̈ܟܒܐ ܕܪܫܝܡܘܬܐ، ܐܢ ܐܝܬ، ܡܦܫܩ̈ܐ ܝܢܐ ܓܘ ܡܥܝܪܢܘܬܐ ܕܡܣܬܒܪܢܘܬܐ ܚܬܝܬܐܝܬ ܐܝܟ ܬܚܬ ܠܘܚܐ (ܦܣܩܐ 7.14).

ܓܘ ܡܦܩܢܐ (output) ܕܐܗܐ ܦܐܬܐ ܟܠ ܨܘܪܬܐ ܕܒܕܪܐ ܟܐܬܝܐ ܥܡ ܡܥܝܪܢܘܬܐ ܕܨܘܪܬܐ ܐܝܟ ܐܗܐ، ܕܟܡܬܒܢܝܐ ܡܢ ܓܢܒܗ: ܡܘܕܝ ܟܡܚܘܐ ܟܠ ܢܘܩܙܐ ܘܥܠ ܐܝܢܐ ܣܪܛܐ ܟܠ ܡܫܬܚܠܦܢܐ، ܡܘܕܝ ܝܠܗ ܣܪܛܐ (ܘܐܝܡܢ ܕܓܒܝܐ ܝܠܗ Spearman ܒܣ ܠܝܬ ܣܪܛܐ – ܘܡܐܡܪܐ ܟܡܬܫܒܩ)، ܘܪܒܘܬܐ ܕܕܘܡܝܐ ܥܡ ܐܘܪܚܐ ܕܛܘܦܠܐ ܒܚܣܝ̈ܪܐ. ܨܘܪܬܐ ܓܢܒܗ ܟܢܣܚܚ ܡܢ ܡܘܢܝܛܪ (ܗܝ ܠܐ ܝܠܗ ܥܠܝܠܬܐ ܓܘ ܦܐܝܠ ܕ-Word)، ܘܡܥܝܪܢܘܬܐ – ܡܢ ܠܘܚܐ ܕܡܦܩܢܐ.

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

R ܝܠܗ ܐܬܪܐ ܕܥܒܕܐ ܡܓܢ ܒܪܡܙܐ ܦܬܝܚܐ (open source) ܩܐ ܣܛܐܛܝܣܛܝܩܐ، ܘܗܘ ܦܘܫܩܐ ܚܬܝܬܐܝܬ ܟܡܬܥܒܕ ܓܘܗ ܒܟܡܐ ܣܕܪ̈ܐ: cor() ܟܝܗܒܐ ܡܐܛܪܝܟܣ ܕܐܣܘܪ̈ܐ ܕܚܕ̈ܕܐ (correlation matrix)، crossprod(!is.na()) – N ܕܟܠ ܙܘܓܐ، ܘ-cor.test() – ܩܐ ܙܘܓܐ ܝܚܝܕܝܐ – t، p ܘܬܚܘܡܐ ܕܬܘܟܠܢܐ (ܒܫܘܢܝܐ ܕ-Fisher، ܐܝܟ ܦܐܬܐ). ܣܩܪܝܦܬ (script) ܕܠܬܚܬ ܪܗܛܐ ܝܠܗ ܐܝܟ ܕܐܝܬܘܗܝ ܥܠ ܦܐܝܠ ܕܡܬܠܐ (sample data file) ܕܦܐܬܐ (DATA_correlations_example_heb.xlsx، ܬܠܬܐ ܡܫܬܚܠܦ̈ܢܐ ܕܓܒܝ̈ܐ ܝܢܐ ܓܘܗ ܒܓܘܒܝܐ ܡܩܕܡܐ)، ܘܦܐܪ̈ܐ – ܐܝܟ ܠܘ̈ܚܐ 1-2 ܘܡܐܡܪ̈ܐ ܕܬܘܢܝܐ – ܟܬܝܒ̈ܐ ܝܢܐ ܓܘ ܡܥܝܪ̈ܢܘܬܐ. ܢܡܘܣܐ ܕܣܐܝܛ (site rule) ܩܐ ܣܘܪܝܬ ܒ-R: ܦܐܝܠ UTF-8، ܟܠ ܣܕܪܐ ܕܡܥܝܪܢܘܬܐ ܟܫܪܐ ܒܡܠܬܐ ܕܣܘܪܝܬ، ܫܡ̈ܗܐ ܩܨܝܪ̈ܐ ܒܐܢܓܠܝܙܝܐ ܩܐ ܚܘܫܒܢܐ، ܘܐܬܪܐ (locale) UTF-8 ܩܐ ܫܡ̈ܗܐ ܥܒܪ̈ܝܐ (ܓܘ Windows: Sys.setlocale("LC_ALL", "Hebrew") ܝܢ R 4.2 ܘܠܥܠ). ܚܠܦܘܢ ܫܒܝܠܐ (path) ܘܫܡ̈ܗܐ ܕܡܫܬܚܠܦ̈ܢܐ ܒܕܝܘܟܘܢ؛ ܓܘ R ܟܟܬܒܚ ܓܘ ܫܒܝܠܐ ܣܪܛܐ ܡܨܠܝܢܐ ܥܡܝܐ (/).

# ܐܣܘܪ̈ܐ ܕܚܕ̈ܕܐ ܕ-Pearson ܘ-Spearman – 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_correlations_example_heb.xlsx", sheet = "נתונים")
d <- d[, c("גיל", "עמדות1", "עמדות_ציון")]              # ܡܫܬܚܠܦ̈ܢܐ ܕܓܒܝ̈ܐ ܝܢܐ ܓܘ ܦܐܬܐ (ܓܘܒܝܐ ܡܩܕܡܐ ܕܦܐܝܠ ܕܡܬܠܐ)
names(d) <- c("age", "att1", "att")                    # ܫܡ̈ܗܐ ܩܨܝܪ̈ܐ ܒܐܢܓܠܝܙܝܐ

# ܠܘܚܐ 1 – ܡܐܛܪܝܟܣ ܕ-Pearson ܒܫܩܠܬܐ ܙܘܓܢܝܬܐ، ܬܠܬܐ ܡܢܝ̈ܢܐ ܐܝܟ SPSS ܘܐܝܟ ܠܘܚܐ ܓܘ ܦܐܬܐ
round(cor(d, use = "pairwise.complete.obs"), 3)   # גיל-עמדות1 .116, גיל-עמדות_ציון .209, עמדות1-עמדות_ציון .684

# ܡܢܝܢܐ ܕܡܫܬܘܬܦ̈ܢܐ ܓܘ ܟܠ ܙܘܓܐ (N ܕܫܩܠܬܐ ܙܘܓܢܝܬܐ – ܡܥܝܪܢܘܬܐ ܕܠܘܚܐ)
crossprod(!is.na(d))                                  # 114, 116, 118 (ܘܓܘ ܣܪܛܐ ܡܨܠܝܢܐ: 116, 118, 120 ܚܙ̈ܝܬܐ ܬܪ̈ܝܨܬܐ ܩܐ ܟܠ ܡܫܬܚܠܦܢܐ)

# ܠܘܚܐ 2 – ܙܘܓܐ ܝܚܝܕܝܐ: r, df, t, p ܘܬܚܘܡܐ ܕܬܘܟܠܢܐ 95% ܒܫܘܢܝܐ ܕ-Fisher (ܐܝܟ ܦܐܬܐ)
cor.test(d$age, d$att)                                # r = .209, t(114) = 2.278, p = .0246, ܬܚܘܡܐ ܕܬܘܟܠܢܐ [.027, .377] – ܐܝܟ ܠܘܚܐ 2 ܘܡܐܡܪܐ ܕܬܘܢܝܐ

# ܐܣܘܪܐ ܕ-Spearman – ܗܝ ܡܐܛܪܝܟܣ ܥܠ ܕܪ̈ܓܐ ܕܛܟܣܐ؛ ܩܐ p ܕܙܘܓܐ ܝܚܝܕܝܐ: cor.test(..., method = "spearman", exact = FALSE)
round(cor(d, use = "pairwise.complete.obs", method = "spearman"), 3)   # .095, .226, .669
cor.test(d$age, d$att, method = "spearman", exact = FALSE)   # rho = .226, p = .0145 (ܩܘܪܒܐ t، ܐܝܟ SPSS ܘܐܝܟ ܦܐܬܐ)

ܬܪܝܢ ܢܘܩ̈ܙܐ ܚܫܝ̈ܚܐ ܓܘ ܪܡܙܐ: ܐܪܓܘܡܢܬ use = "pairwise.complete.obs" ܝܠܗ ܫܩܠܬܐ ܙܘܓܢܝܬܐ (pairwise deletion) – ܕܠܐ ܗܘ، ܐܝܡܢ ܕܐܝܬ ܛܝ̈ܡܐ ܚܣܝ̈ܪܐ R ܒܕ ܡܕܥܪ NA، ܘܥܡ ܫܩܠܬܐ ܕܣܕܪܐ ܟܠܗ ܦܐܪ̈ܐ ܠܐ ܒܕ ܦܐܝܝ ܠ-SPSS؛ ܘ-cor.test ܟܚܫܒܐ ܩܐ ܙܘܓܐ ܝܚܝܕܝܐ ܥܠ ܚܙ̈ܝܬܐ ܓܡܝܪ̈ܬܐ ܕܗܘ ܙܘܓܐ ܒܣ (ܘܡܛܠ ܗܕܐ df = 114 ܓܘ ܡܬܠܐ – 116 ܡܫܬܘܬܦ̈ܢܐ ܥܡ ܛܝܡܐ ܓܘ ܬܪܝܢ ܡܫܬܚܠܦ̈ܢܐ). p-value < 2.2e-16 ܝܠܗ ܪܫܡܐ ܕ-R ܩܐ ܛܝܡܐ ܙܥܘܪܐ ܡܢ ܟܠ ܡܐ ܕܟܡܚܘܐ – ܘܓܘ ܬܘܢܝܐ ܟܟܬܒܚ p < .001. ܓܘ Spearman، ܐܝܡܢ ܕܐܝܬ ܕܪ̈ܓܐ ܫܘ̈ܝܐ، cor.test ܕܠܐ exact = FALSE ܒܕ ܡܙܗܪܐ "Cannot compute exact p-value with ties" – ܐܗܐ ܬܪܝܨܐ ܝܠܗ: ܗܝ ܟܥܒܪܐ ܠܩܘܪܒܐ، ܗܘ ܩܘܪܒܐ ܕܐܦ SPSS ܘܐܦ ܐܗܐ ܦܐܬܐ ܟܡܦܠܚܝ ܒܗ. (ܡܨܝܐ ܝܠܗ ܐܦ: ܨܪܪܐ Hmisc ܥܡ rcorr() ܟܛܒܥ r، n ܘ-p ܩܐ ܟܠ ܙܘܓ̈ܐ ܓܘ ܚܕ ܡܦܩܢܐ ܒܙܢܐ ܕ-SPSS.)

ܬܠܬܐ ܡܐܢ̈ܐ – SPSS، R ܘܡܚܫܒܢܐ (calculator) ܕܓܘ ܐܗܐ ܦܐܬܐ – ܟܚܫܒܝ ܗܢܝ ܡܢܝ̈ܢܐ ܡܫܘܬܦ̈ܐ ܐܝܡܢ ܕܣܝܡ̈ܐ ܝܢܐ ܒܗܘ ܐܘܪܚܐ – ܫܩܠܬܐ ܙܘܓܢܝܬܐ ܘܪܫܝܡܘܬܐ ܕܬܪܝܢ ܕܘܢ̈ܒܐ: ܓܘ SPSS ܘܓܘ ܡܚܫܒܢܐ ܐܢܝ ܝܢܐ ܓܘܒ̈ܝܐ ܡܩܕܡ̈ܐ (defaults)، ܘܓܘ R ܐܗܐ ܟܬܝܒܐ ܝܠܗ ܓܠܝܐܝܬ ܓܘ ܪܡܙܐ ܕܠܥܠ. ܡܛܠ ܗܕܐ ܥܠ ܗܘ ܦܐܝܠ ܕܝܗܝ̈ܒܬܐ ܐܢܝ ܟܡܕܥܪܝ ܗܢܝ ܦܐܪ̈ܐ. ܦܘܚܡܐ ܡܚܠܦܢܐ ܐܝܟ ܐܗܐ ܒܝܢܝ ܬܪܝܢ ܡܐܢ̈ܐ ܝܠܗ ܐܘܪܚܐ ܛܒܬܐ ܩܐ ܫܘܪܪܐ ܕܦܘܫܩܐ ܥܒܝܕܐ ܝܠܗ ܬܪܝܨܐܝܬ.

ܫܘܝ̈ܘܬܐ ܕܒܬܪ ܡܢܝ̈ܢܐ ܡܫܘܬܦ̈ܐ

ܩܐ ܡܦܬܚܢܘܬܐ ܡܦܪܫܬܐ ܕܫܘܝ̈ܘܬܐ ܕܓܘ ܐܗܐ ܦܣܩܐ ܚܙܝܡܘܢ Gravetter & Wallnau (2017، ܨܚܚܐ 15).

ܡܢܝܢܐ ܡܫܘܬܦܐ ܕ-Pearson – ܡܢ ܡܢܝ̈ܢܐ z (z-scores). ܐܘܪܚܐ ܓܠܝܬܐ ܡܢ ܟܠ ܩܐ ܦܗܡܐ ܕ-Pearson ܝܠܗ ܒܝܕ ܡܢܝ̈ܢܐ z: ܟܡܫܚܠܦܚ ܟܠ ܛܝܡܐ ܠܡܢܝܢܐ z – ܟܡܐ ܣܛܝ̈ܘܬܐ ܬܩܝܢ̈ܝܬܐ (standard deviations) ܗܘ ܝܠܗ ܠܥܠ ܝܢ ܠܬܚܬ ܡܢ ܡܨܥܝܬܐ (mean) ܕܡܫܬܚܠܦܢܐ ܕܝܠܗ، z_x = (x − x) / s_x – ܘܒܬܪ ܟܓܡܪܚ ܡܟܦ̈ܠܬܐ ܕܙܘܓ̈ܐ ܕܡܢܝ̈ܢܐ z ܘܟܦܠܓܚ ܥܠ n − 1:

(ܩܡܘܕܝ n − 1؟ ܡܛܠ ܕܐܗܐ ܝܠܗ ܦܠܓܘܬܐ ܕܓܘ ܣܛܝܘܬܐ ܬܩܝܢܬܐ ܕܕܘܡܝܐ s ܕܡܢܗ ܒܢܝ̈ܐ ܝܢܐ ܡܢܝ̈ܢܐ z. ܓܘ ܟܬܒ̈ܐ ܕܟܡܚܕܕܝ ܡܢܝ̈ܢܐ z ܥܡ ܣܛܝܘܬܐ ܬܩܝܢܬܐ ܕܟܢܫܐ ܟܠܢܝܐ (population) ܐܦ ܠܐܟܐ ܟܦܠܓܝ ܥܠ n – ܘܐܢ ܥܝܕܐ ܐܝܟ ܚܕ ܝܠܗ ܓܘ ܡܬܦܠܓܢܐ (numerator) ܘܓܘ ܡܦܠܓܢܐ (denominator)، r ܟܦܠܛ ܐܝܟ ܚܕ.)

ܚܘܫܒܐ: ܐܝܡܢ ܕܚܙܝܬܐ (observation) ܪܡܬܐ ܝܠܗ ܡܢ ܡܨܥܝܬܐ ܓܘ ܬܪܝܢ ܡܫܬܚܠܦ̈ܢܐ، ܬܪܝܢ ܡܢܝ̈ܢܐ z ܕܙܘܕܐ ܝܢܐ ܘܡܟܦܠܬܐ ܕܙܘܕܐ ܝܠܗ؛ ܐܝܡܢ ܕܪܡܬܐ ܝܠܗ ܓܘ ܚܕ ܘܢܡܘܟܬܐ ܓܘ ܐܚܪܢܐ، ܡܟܦܠܬܐ ܕܒܨܘܪܐ ܝܠܗ. ܐܢ ܪܘܒܐ ܕܡܟܦ̈ܠܬܐ ܕܙܘܕܐ ܝܢܐ – r ܟܦܠܛ ܕܙܘܕܐ؛ ܐܢ ܪܘܒܐ ܕܝܗܝ ܕܒܨܘܪܐ – ܕܒܨܘܪܐ؛ ܘܐܝܡܢ ܕܠܝܬ ܕܡܘܬܐ ܩܝܡܬܐ، ܡܟܦ̈ܠܬܐ ܕܙܘܕܐ ܘܕܒܨܘܪܐ ܟܡܒܛܠܝ ܚܕ̈ܕܐ ܘ-r ܟܩܪܒ ܠ-0.

ܫܘܚܠܦܐ ܡܫܘܬܦܐ (Covariance). ܟܡܨܝܚ ܕܡܛܚ ܠܗܘ ܚܘܫܒܐ ܐܦ ܡܢ ܛܝ̈ܡܐ ܫܪ̈ܫܝܐ (raw values): ܩܐ ܟܠ ܚܙܝܬܐ ܟܟܦܠܚ ܣܛܝܘܬܐ ܡܢ ܡܨܥܝܬܐ ܕ-x ܒܣܛܝܘܬܐ ܡܢ ܡܨܥܝܬܐ ܕ-y، ܟܓܡܪܚ ܡܟܦ̈ܠܬܐ ܘܟܦܠܓܚ ܥܠ n − 1 – ܗܘ ܥܝܕܐ ܕܣܛܝܘܬܐ ܬܩܝܢܬܐ ܕܕܘܡܝܐ:

covariance ܟܡܫܚܐ ܥܕܡܐ ܟܡܐ ܬܪܝܢ ܡܫܬܚܠܦ̈ܢܐ "ܟܙܝܥܝ ܐܟܚܕܐ"، ܐܠܐ ܒܛܝ̈ܡܐ ܫܪ̈ܫܝܐ – ܘܡܛܠ ܗܕܐ ܪܒܘܬܐ ܕܝܠܗ ܬܠܝܐ ܝܠܗ ܒܝܚܝܕ̈ܝܐ ܕܡܫܘܚܬܐ (ܡܫܘܚܬܐ ܕܪܘܡܐ ܒ-cm ܒܕܘܟܬ ܡܝܬܪ̈ܐ ܒܕ ܡܪܒܐ ܠܗ 100 ܓܗ̈ܐ). ܩܐ ܕܫܩܠܚ ܡܚܘܝܢܐ ܚܐܪܐ ܡܢ ܝܚܝܕ̈ܝܐ ܟܦܠܓܚ ܥܠ ܣܛܝ̈ܘܬܐ ܬܩܝܢ̈ܝܬܐ ܕܬܪܝܢ ܡܫܬܚܠܦ̈ܢܐ – ܘܦܐܪܐ ܝܠܗ ܚܬܝܬܐܝܬ ܡܢܝܢܐ ܡܫܘܬܦܐ ܕ-Pearson:

ܐܗܐ ܦܠܓܘܬܐ ܟܡܬܩܢܐ ܫܘܚܠܦܐ ܡܫܘܬܦܐ ܠܦܬܝܘܬܐ (range) ܩܝܡܬܐ، ‎-1 ܥܕܡܐ ‎+1. ܚܙܝܡܘܢ (Note) ܠܦܘܪܫܢܐ ܒܝܢܝ ܬܪܝܢ ܫܡ̈ܗܐ ܩܪܝܒ̈ܐ ܕܦܓܥܠܢ ܓܘ ܦܐܬܐ: covariance ܝܠܗ ܫܘܢܝܐ ܡܫܘܬܦܐ ܒܝܚܝܕ̈ܝܐ ܫܪ̈ܫܝܐ، ܐܠܐ r² ܟܡܚܘܐ ܡܢܬܐ ܕܫܘܚܠܦܐ ܡܫܘܬܦܐ – ܡܚܘܝܢܐ ܡܬܩܢܐ (standardized) ܘܕܠܐ ܝܚܝ̈ܕܝܐ. (ܡܥܝܪܢܘܬܐ ܛܟܢܝܩܝܬܐ: ܐܝܬ ܟܬܒ̈ܐ ܕܟܦܠܓܝ ܥܠ n ܘܐܝܬ ܥܠ n − 1؛ r ܟܦܠܛ ܐܝܟ ܚܕ، ܡܛܠ ܕܗܘ ܡܢܝܢܐ ܟܡܬܚܙܐ ܓܘ ܡܬܦܠܓܢܐ ܘܓܘ ܡܦܠܓܢܐ ܘܟܡܒܛܠ.)

ܬܠܬ ܕܝ̈ܠܝܘܬܐ ܕܛܒܐ ܝܠܗ ܠܡܝܕܥ. ܩܕܡܝܐ، r ܠܐ ܟܡܬܥܒܕ ܡܢ ܫܘܢܝܐ ܣܪܛܢܝܐ (linear transformation) ܕܡܫܬܚܠܦ̈ܢܐ – ܡܘܣܦܬܐ ܕܡܢܝܢܐ ܩܝܡܐ ܝܢ ܟܦܠܐ ܒܡܢܝܢܐ ܩܝܡܐ ܕܙܘܕܐ (ܥܒܪܬܐ ܡܢ cm ܠܡܝܬܪ̈ܐ، ܡܢ ܢܘܩ̈ܙܐ ܠܡܢܘ̈ܬܐ ܒܡܐܐ) ܠܐ ܟܡܫܢܝ ܠܗ ܐܦ ܡܕܡ؛ ܟܦܠܐ ܒܡܢܝܢܐ ܩܝܡܐ ܕܒܨܘܪܐ ܟܗܦܟ ܒܣ ܐܬܐ، ܘܚܝܠܐ |r| ܟܦܐܫ ܢܛܝܪܐ. ܬܪܝܢܐ، r ܓܢܒܗ ܠܐ ܟܡܬܪܓܡܚ ܐܝܟ ܣܒܠܬܐ ܕܦܘܚܡܐ (ratio scale): r = .40 ܠܐ ܝܠܗ ܐܣܘܪܐ "ܚܝܠܢܐ ܬܪܝܢ ܓܗ̈ܐ" ܡܢ r = .20؛ ܩܐ ܦܘܚܡܐ ܕܟܡܝܘ̈ܬܐ ܕܫܘܚܠܦܐ ܡܫܘܬܦܐ ܟܦܚܡܚ ܡܪ̈ܒܥܐ (.16 ܩܘܒܠ .04). ܘܬܠܝܬܝܐ، Pearson ܟܫܩܠ ܒܚܘܫܒܢܐ ܛܝ̈ܡܐ ܫܪ̈ܝܪܐ ܕܚܙ̈ܝܬܐ – ܠܐ ܐܝܟ Spearman، ܕܟܚܙܐ ܒܣ ܕܘܟܬܗܝ ܓܘ ܛܟܣܐ.

ܡܢܝܢܐ ܡܫܘܬܦܐ ܕ-Spearman – ܡܢ ܕܪ̈ܓܐ ܕܛܟܣܐ (ranks). Spearman ܚܫܝܒܐ ܝܠܗ ܥܠ ܛܟܣ̈ܐ ܒܣ. ܐܝܡܢ ܕܠܝܬ ܛܟܣ̈ܐ ܫܘ̈ܝܐ، ܟܡܨܝܚ ܕܡܦܠܚܚ ܒܫܘܝܘܬܐ ܩܛܝܢܬܐ ܝܕܝܥܬܐ:

ܐܝܡܢ ܕ-d_i ܝܠܗ ܦܘܪܫܢܐ ܕܕܪ̈ܓܐ ܕܚܙܝܬܐ i ܒܝܢܝ ܬܪܝܢ ܡܫܬܚܠܦ̈ܢܐ، ܘ-n ܡܢܝܢܐ ܕܚܙ̈ܝܬܐ. ܐܢ ܬܪܝܢ ܛܟܣ̈ܐ ܐܝܟ ܚܕ ܝܢܐ ܓܡܝܪܐܝܬ، ܟܠ ܦܘܪ̈ܫܢܐ 0 ܝܢܐ ܘܟܦܠܛ r_s = +1؛ ܐܢ ܛܟܣܐ ܓܘ ܚܕ ܡܢ ܡܫܬܚܠܦ̈ܢܐ ܗܦܝܟܐ ܝܠܗ ܚܬܝܬܐܝܬ ܡܢ ܛܟܣܐ ܓܘ ܐܚܪܢܐ، ܟܦܠܛ r_s = -1. ܠܛܝ̈ܡܐ ܫܪ̈ܫܝܐ ܠܝܬ ܐܦ ܡܕܡ ܡܬܩܠܐ – ܒܣ ܠܕܘܟܐ ܓܘ ܛܟܣܐ.

ܡܬܠܐ ܙܥܘܪܐ: ܚܡܫܐ ܡܩܪ̈ܒܢܐ (candidates) ܛܟܝܣ̈ܐ ܝܢܐ ܓܘ ܡܫܐܠܬܐ (interview) ܒܝܕ ܬܪܝܢ ܡܫܐܠ̈ܢܐ، ܘܒܥܝܚ ܕܝܕܥܚ ܥܕܡܐ ܟܡܐ ܛܟܣ̈ܐ ܟܫܠܡܝ ܥܡ ܚܕ̈ܕܐ:

ܗܢܘ ܫܠܡܘܬܐ ܪܒܬܐ ܒܝܢܝ ܬܪܝܢ ܡܫܐܠ̈ܢܐ. ܡܥܝܪܢܘܬܐ ܚܫܝܚܬܐ ܩܐ ܡܦܠܚܢܘܬܐ ܒܥܒܕܐ: ܐܝܡܢ ܕܐܝܬ ܛܟܣ̈ܐ ܫܘ̈ܝܐ (ties) ܟܝܗܒܚ ܠܚܙ̈ܝܬܐ ܫܘ̈ܝܬܐ ܡܨܥܝܬܐ ܕܕܪ̈ܓܐ ܕܝܗܝ، ܘܗܝܓܐ ܫܘܝܘܬܐ ܩܛܝܢܬܐ ܠܐ ܝܠܗ ܒܝܫ ܚܬܝܬܬܐ. ܐܘܪܚܐ ܓܢܝܬܐ – ܕܬܪܝܨܬܐ ܝܠܗ ܟܠ ܐܡܢ – ܝܠܗ ܚܘܫܒܢܐ ܕܡܢܝܢܐ ܡܫܘܬܦܐ ܕ-Pearson ܥܠ ܕܪ̈ܓܐ. ܗܕܟܐ ܚܬܝܬܐܝܬ ܚܫܝܒܐ ܝܠܗ Spearman ܐܦ ܓܘ ܐܗܐ ܦܐܬܐ ܘܐܦ ܓܘ SPSS، ܘܡܛܠ ܗܕܐ ܐܝܡܢ ܕܠܝܬ ܛܟܣ̈ܐ ܫܘ̈ܝܐ ܬܪܝܢ ܐܘܪ̈ܚܬܐ ܟܡܕܥܪܝ ܚܬܝܬܐܝܬ ܗܘ ܛܝܡܐ.

ܒܘܚܪܢܐ ܕܪܫܝܡܘܬܐ (significance) ܕܐܣܘܪܐ ܕܚܕ̈ܕܐ. ܐܣܘܪܐ ܕܐܫܟܚ ܓܘ ܕܘܡܝܐ (sample) ܗܠ ܐܕܝܘܡ ܣܢܝܩ ܝܠܗ ܠܒܘܚܪܢܐ: ܐܝܬ ܣܗܕ̈ܘܬܐ ܕܡܣܦܩܝ ܕܗܘ ܐܝܬ ܐܦ ܓܘ ܟܢܫܐ ܟܠܢܝܐ (population)؟ ܗܘܦܘܬܣܝܣ ܕܣܦܝܩܘܬܐ (null hypothesis) ܝܠܗ ܕܠܝܬ ܐܣܘܪܐ ܓܘ ܟܢܫܐ ܟܠܢܝܐ (ρ = 0). ܡܢ r ܘܡܢ ܪܒܘܬܐ ܕܕܘܡܝܐ n ܟܚܫܒܚ ܛܝܡܐ t:

ܐܗܐ ܛܝܡܐ ܐܝܬܠܗ ܦܘܠܓܐ t ܥܡ df = n − 2 ܕܪ̈ܓܐ ܕܚܐܪܘܬܐ (degrees of freedom) – ܐܢܝ ܝܢܐ ܕܪ̈ܓܐ ܕܚܐܪܘܬܐ ܕܦܓܥܠܢ ܓܘ ܨܘܪܬܐ ܕܬܘܢܝܐ r(df). ܐܢ ܛܝܡܐ p ܕܟܦܠܛ ܙܥܘܪܐ ܝܠܗ ܡܢ ܕܪܓܐ ܕܪܫܝܡܘܬܐ (ܒܐܟܡܐ ܕܥܝܕܐ 5%)، ܟܡܣܠܩܚ ܗܘܦܘܬܣܝܣ ܕܣܦܝܩܘܬܐ ܘܟܫܠܡܚ ܕܐܝܬ ܐܣܘܪܐ ܓܘ ܟܢܫܐ ܟܠܢܝܐ. ܫܘܝܘܬܐ ܟܬܝܒܬܐ ܝܠܗ ܩܐ Pearson؛ ܛܝܡܐ p ܕ-Spearman ܚܫܝܒܐ ܝܠܗ – ܓܘ ܐܗܐ ܦܐܬܐ ܘܐܦ ܓܘ SPSS – ܒܗܘ ܩܘܪܒܐ t ܓܢܒܗ، ܘܡܢ ܐܟܐ ܙܘܗܪܐ ܕܥܗܝܕܐ ܝܠܗ ܠܥܠ ܥܠ ܕܘ̈ܡܝܐ ܙܥܘ̈ܪܐ. ܗܘܦܘܬܣܝܣ (hypothesis) ܟܡܨܝܚ ܕܟܬܒܚ ܠܗ ܐܝܟ ܕܠܐ ܦܢܝܬܐ (ܕܬܪܝܢ ܕܘܢ̈ܒܐ) ܝܢ ܐܝܟ ܕܦܢܝܬܐ (ܕܚܕ ܕܘܢܒܐ)، ܠܦܘܬ ܗܘܦܘܬܣܝܣ ܕܒܘܨܝܐ. ܦܘܪܫܢܐ ܡܨܐ ܕܦܣܩ: ܓܘ ܡܬܠܐ ܕ-Gravetter & Wallnau (2017، ܦܐܬܐ 507-509)، ܐܣܘܪܐ ܕ-r = .35 ܓܘ ܕܘܡܝܐ ܕ-30 ܡܫܬܘܬܦ̈ܢܐ ܟܝܗܒ t(28) = 1.97 – ܛܝܡܐ ܕܠܐ ܟܥܒܪ ܬܚܘܡܐ ܕܬܪܝܢ ܕܘܢ̈ܒܐ (2.048) ܐܠܐ ܟܥܒܪ ܬܚܘܡܐ ܕܚܕ ܕܘܢܒܐ (1.701). ܗܘ ܐܣܘܪܐ ܓܢܒܗ ܪܫܝܡܐ ܝܠܗ ܓܘ ܒܘܚܪܢܐ ܕܦܢܝܬܐ ܘܠܐ ܝܠܗ ܪܫܝܡܐ ܓܘ ܒܘܚܪܢܐ ܕܠܐ ܦܢܝܬܐ؛ ܡܛܠ ܗܕܐ ܦܢܝܬܐ ܕܗܘܦܘܬܣܝܣ ܟܡܚܕܕܚ ܡܢ ܩܕܡ، ܠܦܘܬ ܬܐܘܪܝܐ، ܘܠܐ ܒܬܪ ܕܚܙܝܚ ܦܐܪܐ. ܫܘܝܘܬܐ، ܬܘܪܓܡܐ ܕܕܪ̈ܓܐ ܕܚܐܪܘܬܐ ܘܒܘܚܪܢܐ t ܡܦܬܚ̈ܐ ܝܢܐ ܐܦ ܓܘ Field (2024، ܦܣܩܐ 8.2.3).

ܬܚܘܡܐ ܕܬܘܟܠܢܐ (confidence interval) ܩܐ ܐܣܘܪܐ ܕ-Pearson. r ܕܐܫܟܚ ܓܘ ܕܘܡܝܐ ܝܠܗ ܫܘܥܪܐ ܕܢܘܩܙܐ (point estimate)، ܘܥܡܗ ܛܒܐ ܝܠܗ ܕܬܢܚ ܐܦ ܬܚܘܡܐ ܕܬܘܟܠܢܐ. ܡܛܠ ܕܦܘܠܓܐ ܕܓܘܒܝܐ ܕܕܘܡܝܐ (sampling distribution) ܕ-r ܠܐ ܝܠܗ ܫܘܐ ܒܬܪܝܢ ܓܢܒ̈ܐ، ܬܚܘܡܐ ܚܫܝܒܐ ܝܠܗ ܒܝܕ ܫܘܢܝܐ ܕ-Fisher (Fisher z): ܟܡܫܚܠܦܚ r ܠܛܝܡܐ z′،

ܕܛܥܝܘܬܐ ܬܩܝܢܬܐ (standard error) ܕܝܠܗ ܝܠܗ 1/√(n − 3). ܟܒܢܚ ܬܚܘܡܐ ܕܬܘܟܠܢܐ ܕ-95% ܚܕܪ z′ (±1.96 ܛܥܝ̈ܘܬܐ ܬܩܝܢ̈ܝܬܐ) ܘܟܡܥܒܪܚ ܬܚܘ̈ܡܐ ܕܝܠܗ ܠܣܒܠܬܐ ܕ-r. ܬܚܘܡܐ ܕܟܦܠܛ ܠܐ ܝܠܗ ܫܘܐ ܒܬܪܝܢ ܓܢܒ̈ܐ ܕ-r – ܘܐܗܐ ܬܪܝܨܐ ܝܠܗ. ܡܬܠܐ: r = .30 ܥܡ n = 50 ܟܝܗܒ ܬܚܘܡܐ ܕܬܘܟܠܢܐ ܡܢ .02 ܥܕܡܐ .53 – ܥܘܗܕܢܐ ܡܬܚܙܝܢܐ ܕܓܘ ܕܘ̈ܡܝܐ ܙܥܘ̈ܪܐ ܐܦ "ܐܣܘܪܐ ܡܨܥܝܐ" ܫܥܝܪܐ ܝܠܗ ܒܠܐ ܚܬܝܬܘܬܐ ܣܓܝ. ܗܕܟܐ ܚܬܝܬܐܝܬ ܚܫܝܒܐ ܝܠܗ ܬܚܘܡܐ ܕܬܘܟܠܢܐ ܕܓܘ ܠܘܚܐ ܕܬܚܘܝܬܐ ܓܡܝܪܬܐ ܘܓܘ ܡܐܡܪ̈ܐ ܕܬܘܢܝܐ ܕܦܐܬܐ (Field، 2024، ܦܣܩܐ 8.2.4، ܫܘܝ̈ܘܬܐ 8.12-8.14؛ ܓܘ ܡܬܠܐ ܕܝܠܗ – r = .87 ܥܡ n = 5 – ܬܚܘܡܐ ܝܠܗ [−.05, .99]: ܓܘ ܕܘܡܝܐ ܙܥܘܪܐ ܛܒܐ ܬܚܘܡܐ ܟܡܥܛ ܕܠܐ ܦܐܝܕܐ ܝܠܗ). ܓܘ SPSS 27 ܘܠܥܠ ܟܡܨܝܚ ܕܒܥܝܚ ܗܢܝ ܬܚܘ̈ܡܐ ܬܪܝܨܐܝܬ ܓܘ ܟܘܬܐ ܕ-Bivariate Correlations (button ܕ-Confidence interval؛ ܚܙܝܡܘܢ ܠܥܠ).

ܬܚܘܡܐ ܕܬܘܟܠܢܐ ܒ-bootstrap. ܐܝܡܢ ܕܐܝܬ ܙܘܥܐ ܡܢ ܥܒܪܬܐ ܥܠ ܫܪܛܐ ܕܢܘܪܡܠܝܘܬܐ، ܟܡܨܝܚ ܕܒܢܚ ܬܚܘܡܐ ܕܬܘܟܠܢܐ ܐܦ ܒ-bootstrap – ܓܘܒܝܐ ܕܕܘܡܝܐ ܡܢ ܪܝܫ (resampling) ܡܢ ܕܘܡܝܐ ܓܢܒܗ، ܕܠܐ ܫܪ̈ܛܐ ܥܠ ܨܘܪܬܐ ܕܦܘܠܓܐ (ܐܠܐ ܥܡ ܫܪܛܐ ܕܚܙ̈ܝܬܐ ܚܐܪ̈ܬܐ ܘܕܘܡܝܐ ܕܟܡܚܘܐ ܟܢܫܐ ܟܠܢܝܐ)؛ ܐܗܐ ܝܠܗ ܐܦ ܐܘܪܚܐ ܡܩܒܠܐ ܩܐ ܬܚܘܡܐ ܕܬܘܟܠܢܐ ܕܐܣܘܪܐ ܕ-Spearman. ܓܘ SPSS: button ܕ-Bootstrap ܓܘ ܟܘܬܐ ܕ-Bivariate، ܘܥܝܕܐ ܝܠܗ ܕܬܢܚ ܢܘܣܚܐ ܕܬܪܝܨ ܝܠܗ ܩܐ ܡܣܛܝܢܘܬܐ (bias-corrected؛ BCa) ܕܬܚܘܡܐ ܕܬܘܟܠܢܐ. ܦܐܪ̈ܐ ܕ-bootstrap ܟܫܢܝ ܩܠܝܠ ܡܢ ܪܗܛܐ ܠܪܗܛܐ، ܡܛܠ ܕܐܘܪܚܐ ܡܣܡܟܬܐ ܝܠܗ ܥܠ ܓܘܒܝܐ ܓܕܫܢܝܐ – ܐܗܐ ܕܝܠܝܘܬܐ ܝܠܗ، ܠܐ ܛܥܝܘܬܐ (Field, 2024, Sections 8.4, 6.10.8).

ܦܘܚܡܐ ܒܝܢܝ ܬܪܝܢ ܐܣܘܪ̈ܐ. ܫܘܢܝܐ ܕ-Fisher ܡܬܦܠܚܐ ܝܠܗ ܐܦ ܠܐܟܐ. ܐܝܡܢ ܕܐܣܘܪ̈ܐ ܐܬܝ̈ܐ ܝܢܐ ܡܢ ܬܪܝܢ ܓܘ̈ܕܐ ܠܐ ܬܠܝ̈ܐ (ܡܬܠܐ: ܐܢ ܐܣܘܪܐ ܒܝܢܝ ܙܘܥܐ ܕܒܘܚܪ̈ܢܐ ܘܡܢܝܢܐ ܦܪܝܫܐ ܝܠܗ ܒܝܢܝ ܓܒܪ̈ܐ ܘܢܫ̈ܐ؟)، ܟܡܫܚܠܦܚ ܟܠ ܐܣܘܪܐ ܠ-z′ ܘܟܒܚܪܚ ܦܘܪܫܢܐ:

z ܕܟܦܠܛ ܟܦܚܡܚ ܠܗ ܥܡ ܦܘܠܓܐ ܢܘܪܡܠܝܐ (normal distribution): ܛܝܡܐ ܡܛܠܩܐ ܠܥܠ ܡܢ 1.96 ܣܘܟܠܗ ܝܠܗ ܦܘܪܫܢܐ ܪܫܝܡܐ ܒܕܪܓܐ ܕ-5% (ܕܬܪܝܢ ܕܘܢ̈ܒܐ). ܐܝܡܢ ܕܐܣܘܪ̈ܐ ܐܬܝ̈ܐ ܝܢܐ ܡܢ ܗܘ ܕܘܡܝܐ (ܡܬܠܐ: ܐܢ x ܐܣܝܪܐ ܝܠܗ ܥܡ y ܒܚܝܠܐ ܒܝܫ ܡܢ ܕ-z ܐܣܝܪܐ ܝܠܗ ܥܡܗ؟) ܦܘܚܡܐ ܟܡܬܥܒܕ ܒܒܘܚܪܢܐ t ܥܡ df = N − 3، ܕܟܡܦܠܚ ܒܬܠܬܐ ܐܣܘܪ̈ܐ ܙܘܓܢ̈ܝܐ؛ ܓܘ SPSS ܠܝܬ ܩܐ ܗܕܐ ܪܫܝܡܬܐ (Menu) ܒܢܝܬܐ (Field, 2024, Section 8.6). ܘܚܙܝܡܘܢ (Note): ܕܚܕ ܐܣܘܪܐ ܦܠܛܠܗ ܪܫܝܡܐ ܘܐܚܪܢܐ ܠܐ – ܠܐ ܝܠܗ ܣܗܕܘܬܐ ܕܐܢܝ ܦܪ̈ܝܫܐ ܝܢܐ ܡܢ ܚܕ̈ܕܐ؛ ܦܘܪܫܢܐ ܓܢܒܗ ܓܪܓ ܡܬܒܚܪ ܬܪܝܨܐܝܬ.

ܡܒܘ̈ܥܐ

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Cohen, J. (1983). The cost of dichotomization. Applied Psychological Measurement, 7(3), 249-253. https://doi.org/10.1177/014662168300700301

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

Cohen, J., Cohen, P., West, S. G., & Aiken, L. S. (2003). Applied multiple regression/correlation analysis for the behavioral sciences (3rd ed.). Lawrence Erlbaum Associates.

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

Gelman, A., & Hill, J. (2007). Data analysis using regression and multilevel/hierarchical models. Cambridge University Press.

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

Jamieson, S. (2004). Likert scales: How to (ab)use them. Medical Education, 38(12), 1217-1218. https://doi.org/10.1111/j.1365-2929.2004.02012.x

MacCallum, R. C., Zhang, S., Preacher, K. J., & Rucker, D. D. (2002). On the practice of dichotomization of quantitative variables. Psychological Methods, 7(1), 19-40. https://doi.org/10.1037/1082-989X.7.1.19

Norman, G. (2010). Likert scales, levels of measurement and the "laws" of statistics. Advances in Health Sciences Education, 15(5), 625-632. https://doi.org/10.1007/s10459-010-9222-y

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

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)، Cohen ܘܐܚܪ̈ܢܐ (2003)، Gelman ܘ-Hill (2007) ܘ-APA (2020) – ܠܦܘܬ ܦܐܬܐ ܘܦܣܩܐ ܕܡܦܩܬܐ ܛܒܝܥܬܐ؛ ܡܐܡܪ̈ܐ (Anscombe, 1973; Cohen, 1983; MacCallum et al., 2002; Jamieson, 2004; Norman, 2010) – ܠܦܘܬ ܢܘܣܚܐ ܫܪܫܝܐ. ܚܘܫܒܢܐ ܓܘ ܦܐܬܐ ܡܫܪܪܐ ܝܠܗ ܥܡ scipy ܘ-R.