ܒܘܚܪܢܐ ܕ-Wilcoxon 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 ܕܬܪܝܢ ܓܘ̈ܕܐ ܕܡܢܝ̈ܢܐ ܐܣܝܪ̈ܐ ܝܢܐ – ܗܢܝ ܡܫܬܘܬܦ̈ܢܐ (participants) ܬܪܝܢ ܙܒ̈ܢܐ، ܝܢ ܙܘܓ̈ܐ ܡܦܐ̈ܝܐ – ܘܒܘܚܪܢܐ t ܠܙܘܓܢ̈ܝܐ ܠܐ ܦܐܝܐ ܝܠܗ. Field (2024، ܦܣܩܐ 7.5) ܟܫܪܐ ܒܡܬܠܐ: ܐܣܝܬܐ ܕܢܦܫܐ (psychologist) ܡܢ ܦܣܩܐ ܕܩܕܡ ܗܫܐ ܒܥܝܐ ܕܒܚܪܐ ܫܘܢܝܐ ܓܘ ܥܩܬܐ ܕܢܦܫܐ (depression) ܓܘ ܟܠ ܡܫܬܘܬܦܢܐ، ܡܢ ܚܕܒܫܒܐ ܠܐܪܒܥܒܫܒܐ، ܓܘ ܟܠ ܚܕ ܡܢ ܬܪܝܢ ܣܡ̈ܐ؛ ܩܐ ܕܦܘܠܓ̈ܐ (distributions) ܠܐ ܗܘܘ ܢܘܪܡܠܝ̈ܐ ܓܘ ܚܕ ܡܢ ܝܘܡ̈ܢܐ ܘܕܘܡܝܐ (sample) ܙܥܘܪܐ ܗܘܐ، "ܦܘܠܓܐ ܕܓܘܒܝܐ ܕܕܘܡܝܐ ܒܕ ܗܘܐ ܠܐ ܢܘܪܡܠܝܐ ܐܦ ܐܝܗܘ"، ܘܡܛܠ ܗܕܐ ܒܘܚܪܢܐ ܠܐ ܦܪܡܝܛܪܝܐ. Pallant (2020، ܨܚܚܐ 16): "ܚܠܦܐ ܠܐ ܦܪܡܝܛܪܝܐ ܕܒܘܚܪܢܐ t ܠܡܫܘ̈ܚܬܐ ܡܬܢ̈ܝܬܐ – ܒܕܘܟܬܐ ܕܦܘܚܡܐ ܕܡܨܥܝ̈ܬܐ، Wilcoxon ܟܫܚܠܦ ܡܢܝ̈ܢܐ ܠܕܪ̈ܓܐ ܕܛܟܣܐ ܘܟܦܚܡ ܠܗܘܢ ܓܘ ܙܒܢܐ 1 ܘܓܘ ܙܒܢܐ 2"؛ ܡܬܠܐ ܕܝܠܗ̇ – ܒܘܚܪܢܐ ܕܙܕܥܬܐ ܡܢ ܣܛܐܛܝܣܛܝܩܐ ܩܕܡ ܦܪܘܓܪܡܐ ܕܡܥܠܬܐ ܘܒܬܪܗ (n = 30). Gravetter ܘ-Wallnau (2017, Appendix E.3) – "ܚܠܦܐ ܕܒܘܚܪܢܐ t ܠܡܫܘ̈ܚܬܐ ܡܬܢ̈ܝܬܐ"، ܥܡ ܗܢܝ ܥܠ̈ܠܬܐ ܕܓܘ ܬܘܣܦܬܐ E.1 ܩܐ ܥܒܪܬܐ ܠܕܪ̈ܓܐ: ܝܗܝ̈ܒܬܐ ܕܛܟܣܐ، ܬܘܒܪܐ ܕܫܪ̈ܛܐ، ܫܘܚܠܦܐ (variance) ܪܡܐ، ܡܢܝܢܐ ܠܐ ܡܬܚܡܐ.

ܓܘ ܐܗܐ ܣܐܝܛ ܕܘܟܬܐ ܛܒܝܥܝܬܐ ܝܠܗ̇ ܩܐ ܬܪܬܝܢ ܐܝܟܢܝ̈ܘܬܐ: ܦܣܘܩܐ ܕܛܟܣܐ ܝܚܝܕܝܐ ܕܡܫܘܚܐ ܝܠܗ ܬܪܝܢ ܙܒ̈ܢܐ (ܠܦܘܬ ܥܝܕܐ ܕܣܐܝܛ – ܡܫܬܚܠܦܢܐ ܕܛܟܣܐ (ordinal variable)، ܡܫܬܚܠܦ̈ܢܐ ܘܕܪ̈ܓܐ ܕܡܫܘܚܬܐ)؛ ܘܡܢܝܢܐ ܕܣܒܠܬܐ ܝܢ ܡܫܬܚܠܦܢܐ ܟܡܝܝܐ ܐܡܢ ܕܦܘܪ̈ܫܢܐ ܠܐ ܟܡܬܚܙܝ ܢܘܪܡܠܝ̈ܐ (ܒܘܚܪܢܐ ܕܢܘܪܡܠܝܘܬܐ ܥܠ ܥܡܘܕܐ ܕܦܘܪ̈ܫܢܐ)، ܐܡܢ ܕܐܝܬ ܛܝ̈ܡܐ ܢܘܟܪ̈ܝܐ (outliers)، ܝܢ ܐܡܢ ܕܕܘܡܝܐ ܙܥܘܪܐ ܝܠܗ. ܠܐ ܚܠܛܝܬܘܢ ܥܡ Mann-Whitney (ܒܘܚܪܢܐ ܕܓܘܡܪܐ ܕܕܪ̈ܓܐ ܕ-Wilcoxon) – ܬܪܬܝܢ ܓܘ̈ܕܐ ܦܪ̈ܝܫܐ؛ Field ܟܙܗܪ ܕܐܝܬ "Wilcoxon ܬܪܝܢܐ ܕܟܒܚܪ ܡܕܡ ܐܚܪܢܐ" (ܦܣܩܐ 7.4). ܐܡܢ ܕܙܘܓ̈ܐ ܣܓܝ̈ܐܐ ܝܢܐ (30 ܘܠܥܠ) ܘܝܗܝ̈ܒܬܐ ܟܡܝ̈ܝܐ ܝܢܐ، ܒܘܚܪܢܐ t ܠܙܘܓܢ̈ܝܐ ܓܘܒܝܐ ܡܩܕܡܐ (default) ܝܠܗ، ܘ-Gravetter ܘ-Wallnau ܟܓܒܝ ܠܗ ܐܡܢ ܕܝܗܝ̈ܒܬܐ ܦܐܝ̈ܐ ܝܢܐ ܠܗ (Appendix E.1).

ܗܘܢܐ: ܕܪ̈ܓܐ ܕܦܘܪ̈ܫܢܐ ܥܡ ܐܬܐ

ܒܘܚܪܢܐ "ܣܡܝܟܐ ܝܠܗ ܥܠ ܛܟܣܐ ܕܦܘܪ̈ܫܢܐ ܒܝܢܝ ܡܢܝ̈ܢܐ ܓܘ ܬܪܝܢ ܫܪ̈ܛܐ" (Field, 2024, Section 7.5.1). ܕܪ̈ܓܐ: ܟܚܫܒܚ ܩܐ ܟܠ ܡܫܬܘܬܦܢܐ ܦܘܪܫܢܐ (ܓܘ Field – "ܡܢܝܢܐ ܕܚܕܒܫܒܐ ܡܒܨܪܐ ܝܠܗ ܡܢ ܡܢܝܢܐ ܕܐܪܒܥܒܫܒܐ"، ܗܢܘ ܬܪܝܢܝܬܐ ܒܨܝܪ ܩܕܡܝܬܐ؛ ܗܕܟܐ ܐܦ ܠܐܟܐ)؛ ܦܘܪܫܢܐ ܨܦܪܐ – ܡܫܬܘܬܦܢܐ ܟܦܠܛ ܡܢ ܛܟܣܐ؛ ܟܟܬܒܚ ܐܬܐ ܘܟܡܛܟܣܚ ܦܘܪ̈ܫܢܐ ܠܦܘܬ ܛܝܡܐ ܫܪܝܪܐ (absolute value) ܕܝܠܗܘܢ، ܡܢ ܙܥܘܪܐ ܠܪܒܐ، ܥܡ ܡܨܥܝܬܐ ܕܕܪ̈ܓܐ ܩܐ ܛܝ̈ܡܐ ܫܘ̈ܝܐ – ܐܝܟ ܓܘ Mann-Whitney؛ ܘܒܬܪܗ ܟܟܢܫܚ ܕܪ̈ܓܐ ܕܦܘܪ̈ܫܢܐ ܠܥܠ ܡܢ ܨܦܪܐ ܠ-T⁺ ܘܕܬܚܘܬ ܨܦܪܐ ܠ-T⁻. ܓܘ ܡܬܠܐ ܕ-Field (ܠܘܚܐ 7.2): ecstasy – ܬܪܝܢ ܡܫܬܘܬܦ̈ܢܐ ܕܠܐ ܫܘܢܝܐ، T⁺ = 36, T⁻ = 0؛ ܚܡܪܐ – T⁺ = 8, T⁻ = 47. Gravetter ܘ-Wallnau (Appendix E.3) ܟܡܚܘܝ ܥܠ ܬܡܢܝܐ ܡܫܬܘܬܦ̈ܢܐ: ܦܘܪ̈ܫܢܐ ܡܛܟ̈ܣܐ ܝܢܐ "ܠܦܘܬ ܪܒܘܬܐ ܕܝܠܗܘܢ، ܕܠܐ ܐܣܘܪܐ ܥܡ ܐܘܪܚܐ"، ܕܪ̈ܓܐ ܠܥܠ ܡܢ ܨܦܪܐ ܟܡܛܝ ܠ-3 ܘܕܬܚܘܬ ܨܦܪܐ ܠ-33.

ܐܝܢܐ T. Field (ܘ-SPSS ܓܘ ܪܫܝܡܬܐ ܚܕܬܐ) ܟܩܪܝ T ܠܓܘܡܪܐ ܕܕܪ̈ܓܐ ܠܥܠ ܡܢ ܨܦܪܐ – 36 ܘ-8؛ Gravetter ܘ-Wallnau (ܘܠܘܚܐ B10 ܕܝܠܗܘܢ) – ܠܙܥܘܪܐ ܡܢ ܬܪܘܝܗܝ – 3. ܦܐܬܐ ܟܛܒܥܐ ܬܪܘܝܗܝ. ܪܫܝܡܘܬܐ (significance). ܓܘ ܕܘܡܝܐ ܙܥܘܪܐ – ܦܘܠܓܐ ܚܬܝܬܐ: ܠܘܚܐ B10 ܕ-Gravetter ܘ-Wallnau (ܩܐ n = 8، T ≤ 3 ܪܫܝܡܐ ܝܠܗ ܓܘ .05 – ܘܡܛܠ ܗܕܐ 3 ܡܣܠܝܐ ܝܠܗ)، ܘ-Exact Sig. ܓܘ SPSS؛ Field (ܩܘܛܝܐ 7.2): ܬܚܘܬ 50 – ܚܬܝܬܐ. ܓܘ ܕܘܡܝܐ ܪܒܐ – ܩܘܪܒܐ ܢܘܪܡܠܝܐ: ܛܝܡܐ ܡܣܟܝܐ (expected value) n(n + 1)/4 ܘܛܥܝܘܬܐ ܬܩܝܢܬܐ (standard error) √(n(n + 1)(2n + 1)/24)، ܕ"ܦܘܢܩܣܝ̈ܘܢܐ ܝܢܐ ܕܪܒܘܬܐ ܕܕܘܡܝܐ، n" – ܡܢܝܢܐ ܕܦܘܪ̈ܫܢܐ ܕܠܐ ܝܢܐ ܨܦܪܐ: ܓܘ Field 8 ܘ-10 (ܡܥܠܝ̈ܬܐ 7.14-7.19: 18 ܘ-7.14، 27.5 ܘ-9.81)، ܘ-z ܝܠܗ ܪܘܚܩܐ ܕ-T ܡܢ ܛܝܡܐ ܡܣܟܝܐ ܕܝܠܗ ܒܚܕܝܘ̈ܬܐ ܕܛܥܝܘܬܐ ܬܩܝܢܬܐ (7.20-7.22: 2.53 ܘ-−1.99؛ Gravetter & Wallnau: "ܐܡܢ ܕܕܘܡܝܐ ܪܒܐ ܝܠܗ ܡܢ 20 ܩܘܪܒܐ ܚܬܝܬܐ ܝܠܗ ܒܣܓܝ"، ܘܓܘ ܡܬܠܐ ܕܝܠܗܘܢ z = −2.10). SPSS ܟܬܪܨ ܛܥܝܘܬܐ ܬܩܝܢܬܐ ܩܐ ܛܝ̈ܡܐ ܫܘ̈ܝܐ (ties) – ܘܐܦ ܦܐܬܐ (7.12 ܘ-9.80 ܓܘ Field، ܒܕܘܟܬܐ ܕ-7.14 ܘ-9.81)؛ Gravetter ܘ-Wallnau ܠܐ ܟܬܪܨܝ.

ܩܪܝܢܐ ܕܡܦܩܢܐ (How to read the output)

ܠܘܚܐ 1 – ܛܝ̈ܡܐ ܡܨܥܝ̈ܐ (medians). ܛܝܡܐ ܡܨܥܝܐ، ܪ̈ܘܒܥܐ (quartiles) ܘܦܬܝܘܬܐ (range) ܕܟܠ ܡܫܘܚܬܐ ܘܕܦܘܪ̈ܫܢܐ – ܡܐ ܕܟܡܘܕܥܚ ܒܕܘܟܬܐ ܕܡܨܥܝ̈ܬܐ (Field, 2024، ܦܣܩܐ 7.5.7؛ Pallant, 2020، ܨܚܚܐ 16، ܬܡܢ ܟܦܠܛܝ ܐܢܝ ܒܕܪܓܐ ܦܪܝܫܐ ܓܘ Frequencies). ܠܘܚܐ 2 – ܕܪ̈ܓܐ ܕܛܟܣܐ. ܠܘܚܐ Ranks ܕ-SPSS: ܟܡܐ ܦܘܪ̈ܫܢܐ ܬܚܘܬ ܨܦܪܐ، ܟܡܐ ܠܥܠ ܡܢ ܨܦܪܐ، ܟܡܐ ܨܦܪܐ، ܘܡܨܥܝܬܐ ܕܕܪ̈ܓܐ (mean rank) ܘܓܘܡܪܐ ܕܕܪ̈ܓܐ ܕܟܠ ܐܬܐ. ܠܐܟܐ ܟܩܪܚ ܐܘܪܚܐ: "ܡܢܝܢܐ ܪܒܐ ܝܬܝܪ ܕܦܘܪ̈ܫܢܐ ܓܘ ܐܘܪܚܐ ܡܚܬܡܬܐ ܟܐܡܪ ܠܘܟܘܢ ܐܘܪܚܐ ܕܦܐܪܐ" (Field، Sam's Tips) – ܓܘ Field، ܩܐ ecstasy 8 ܠܥܠ ܡܢ ܨܦܪܐ ܘ-0 ܬܚܘܬ ܨܦܪܐ (ܥܩܬܐ ܕܢܦܫܐ ܣܠܩܠܗ̇)، ܩܐ ܚܡܪܐ 1 ܩܘܒܠ 9 (ܢܚܬܠܗ̇). ܠܘܚܐ 3 – ܒܘܚܪܢܐ. n (ܦܘܪ̈ܫܢܐ ܕܠܐ ܝܢܐ ܨܦܪܐ)، T، ܛܥܝܘܬܐ ܬܩܝܢܬܐ، z – ܥܡ ܐܬܐ: ܠܥܠ ܡܢ ܨܦܪܐ ܐܡܢ ܕܡܫܘܚܬܐ ܬܪܝܢܝܬܐ ܪܡܬܐ ܝܠܗ̇ (ܓܘ ܡܦܩܢܐ ܥܬܝܩܐ ܕ-SPSS، z ܚܫܝܒܐ ܝܠܗ ܡܢ ܓܘܡܪܐ ܙܥܘܪܐ ܘܟܠ ܙܒܢܐ ܬܚܘܬ ܨܦܪܐ ܝܠܗ؛ ܓܘ ܪܫܝܡܬܐ ܚܕܬܐ ܐܝܬܠܗ ܐܬܐ، ܐܝܟ ܠܐܟܐ) – p ܩܪܝܒܝܐ (asymptotic) ܘp ܚܬܝܬܐ (2·P(T ≤ T_ܙܥܘܪܐ) ܡܢ ܦܘܠܓܐ ܕܠܐ ܛܝ̈ܡܐ ܫܘ̈ܝܐ؛ ܥܝܕܐ ܕܣܐܝܛ: ܚܫܝܒܐ ܝܠܗ ܗܠ 50 ܦܘܪ̈ܫܢܐ)، ܘܬܪܝܢ ܡܚܘ̈ܝܢܐ ܕܡܥܒܕܢܘܬܐ. ܓܘ ܡܬܠܐ ܕ-Field: ecstasy T = 36, SE = 7.12, z = 2.53, p = .012؛ ܚܡܪܐ T = 8, SE = 9.80, z = −1.99, p = .047 – "ܡܥܒܕܢܘܬܐ ܗܦܝܟܬܐ ܕܬܪܝܢ ܣܡ̈ܐ" (ܦܣܩܐ 7.5.5)، ܘܗܢܝ ܛܝ̈ܡܐ ܡܢ ܒܘܚܪ̈ܢܐ ܕܦܐܬܐ ܝܢܐ. ܨܘܪܬܐ ܕܦܘܪ̈ܫܢܐ – ܐܝܟ ܗܝܣܛܘܓܪܡ ܓܘ ܡܦܩܢܐ ܕ-SPSS، ܠܥܠ ܡܢ ܨܦܪܐ ܒܙܪܩܐ ܘܬܚܘܬ ܨܦܪܐ ܒܣܡܩܐ: "ܦܘܚܡܐ ܒܝܢܝ ܥܡܘ̈ܕܐ ܡܚܘܝܢܐ ܥܓܠܐ ܝܠܗ" ܠܐܘܪܚܐ (ܦܣܩܐ 7.5.4).

ܪܒܘܬܐ ܕܡܥܒܕܢܘܬܐ – ܬܪܬܝܢ ܡܫܘ̈ܚܬܐ، "ܐܦ ܐܗܐ ܘܐܦ ܐܗܐ"

r_rb ܕ-Field (2024، ܦܣܩܐ 7.5.6): ܐܣܘܪܐ ܕܚܕ̈ܕܐ rank-biserial ܠܡܫܘ̈ܚܬܐ ܡܬܢ̈ܝܬܐ، ܒܡܥܠܝܬܐ ܦܫܝܛܬܐ ܕ-Kerby: r_rb = (T⁺ − T⁻)/(T⁺ + T⁻) (ܡܥܠܝܬܐ 7.23) – "ܦܘܪܫܢܐ ܒܝܢܝ ܕܪ̈ܓܐ ܠܥܠ ܡܢ ܨܦܪܐ ܘܬܚܘܬ ܨܦܪܐ ܐܝܟ ܡܢܬܐ ܡܢ ܟܠ ܕܪ̈ܓܐ؛ ܐܗܐ ܚܬܝܬܐܝܬ ܡܥܒܕܢܘܬܐ ܝܠܗ̇ ܐܝܟ ܡܢܬܐ". ecstasy: (36 − 0)/36 = 1 – 100% ܡܢ ܕܪ̈ܓܐ ܓܘ ܐܘܪܚܐ "ܐܪܒܥܒܫܒܐ ܪܡܐ ܡܢ ܚܕܒܫܒܐ"؛ ܚܡܪܐ: (8 − 47)/55 = −.71 – 71% ܓܘ ܐܘܪܚܐ ܗܦܝܟܬܐ. ܐܬܐ ܟܐܡܪܐ ܐܘܪܚܐ. r ܕ-Pallant (2020، ܨܚܚܐ 16): r = z/√N – "ܟܛܥܝܚ ܡܢ ܐܬܐ"، ܘ-N ܝܠܗ "ܡܢܝܢܐ ܕܚܙ̈ܝܬܐ ܥܠ ܬܪܝܢ ܢܘܩ̈ܙܐ ܕܙܒܢܐ، ܠܐ ܡܢܝܢܐ ܕܡܫܬܘܬܦ̈ܢܐ": ܓܘ ܡܬܠܐ ܕܝܠܗ̇ z = 4.18, N = 60 (30 ܡܫܬܘܬܦ̈ܢܐ × 2)، r = .54، "ܡܥܒܕܢܘܬܐ ܪܒܬܐ" ܓܘ ܥܝܕ̈ܐ ܕ-Cohen (1988، ܦܐ̈ܬܐ 79-83: .1/.3/.5). ܦܐܬܐ ܟܥܒܕܐ ܐܝܟܘܬܗ̇ (N = 2 × ܙܘܓ̈ܐ) ܘܟܐܡܪܐ ܐܗܐ ܓܘ ܡܥܝܪܢܘܬܐ ܕܠܘܚܐ؛ ܐܢܐ ܕܟܚܫܒ ܥܡ ܡܢܝܢܐ ܕܡܫܬܘܬܦ̈ܢܐ ܒܕ ܫܩܠ ܛܝܡܐ ܪܒܐ √2 ܚܕ̈ܐ. ܬܪܝܢ ܡܚܘ̈ܝܢܐ ܠܐ ܫܘ̈ܝܐ ܝܢܐ ܘܠܐ ܡܨܝ ܕܡܫܬܚܠܦܝ ܚܕ ܠܚܕ؛ ܟܡܘܕܥܚ ܠܟܡܝܘܬܐ ܚܕ، ܘܟܐܡܪܚ ܐܝܢܐ.

ܫܪ̈ܛܐ ܘܙܘܗܪ̈ܐ (Assumptions and warnings)

ܫܪ̈ܛܐ (assumptions؛ Pallant, 2020, Chapter 16): ܓܘܒܝܐ ܕܕܘܡܝܐ ܓܕܫܢܝܐ؛ ܘܚܙ̈ܝܬܐ (observations) ܠܐ ܬܠܝ̈ܬܐ – ܥܡ ܦܠܛܬܐ ܕܡܫܘ̈ܚܬܐ ܡܬܢ̈ܝܬܐ: "ܗܢܝ ܡܫܬܘܬܦ̈ܢܐ ܡܒܘܚܪ̈ܐ ܝܢܐ ܬܘܒ ܓܘ ܙܒ̈ܢܐ ܝܢ ܫܪ̈ܛܐ ܦܪ̈ܝܫܐ" – ܐܗܐ ܚܬܝܬܐܝܬ ܐܗܐ ܒܘܚܪܢܐ ܝܠܗ. Field (ܡܥܝܪܢܘܬܐ 2 ܕܨܚܚܐ 7): ܐܦ ܒܘܚܪ̈ܢܐ ܠܐ ܦܪܡܝܛܪ̈ܝܐ ܟܡܣܡܝ ܦܘܠܓܐ ܡܬܡܫܚܢܐ (continuous) – ܘܡܛܠ ܗܕܐ ܓܘ ܝܗܝ̈ܒܬܐ ܕܛܟܣܐ ܥܡ ܣܓܝ ܦܘܪ̈ܫܢܐ ܫܘ̈ܝܐ ܬܘܪܨܐ ܩܐ ܛܝ̈ܡܐ ܫܘ̈ܝܐ ܐܝܬܠܗ ܐܪܙܐ. ܦܘܪ̈ܫܢܐ ܨܦܪܐ. Field ܘ-SPSS ܟܡܦܠܛܝ ܠܗܘܢ، ܘ-n ܟܙܥܪ؛ Gravetter ܘ-Wallnau (Appendix E.3) ܟܡܥܝܪܝ ܕܡܦܠܛܐ "ܟܛܥܐ ܡܢ ܕܦܘܪܫܢܐ ܨܦܪܐ ܣܗܕܘܬܐ ܝܠܗ̇ ܩܐ ܗܘܦܘܬܣܝܣ ܕܣܦܝܩܘܬܐ"، ܟܡܩܪܒܝ ܕܦܠܓܚ ܠܗܘܢ ܫܘܝܐܝܬ ܒܝܢܝ ܐܢܝ ܕܠܥܠ ܡܢ ܨܦܪܐ ܘܐܢܝ ܕܬܚܘܬ ܨܦܪܐ (ܘܐܢ ܡܢܝܢܐ ܠܐ ܙܘܓܐ ܝܠܗ – ܟܫܩܠܚ ܚܕ)، ܘܟܒܥܝ ܕܡܘܕܥܚ ܐܝܟܢܐ ܥܒܝ̈ܕܐ ܝܢܐ ܥܡܗܘܢ. ܦܐܬܐ ܟܐܙܠܐ ܒܬܪ SPSS ܘܟܡܘܕܥܐ ܡܢܝܢܐ ܕܝܠܗܘܢ؛ ܓܘ ܦܣܘܩܐ ܕܛܟܣܐ ܕܓܘܗ ܣܓܝ ܡܢ ܡܫܬܘܬܦ̈ܢܐ ܠܐ ܙܝܥܠܗܘܢ – ܐܗܐ ܝܠܗ̇ ܡܫܟܚܢܘܬܐ. ܚܝܠܐ. ܕܪ̈ܓܐ ܟܡܘܒܕܝ ܪܒܘܬܐ ܕܦܘܪ̈ܫܢܐ (Field, Box 7.1)؛ ܒܘܚܪܢܐ ܕܐܬܐ (sign test)، ܕܟܛܥܐ ܐܦ ܡܢ ܕܪ̈ܓܐ، "ܠܝܬܠܗ ܚܝܠܐ ܐܠܐ ܐܢ ܕܘܡܝܐ ܙܥܘܪܐ ܝܠܗ ܒܣܓܝ" (ܡܥܝܪܢܘܬܐ 7.2). ܥܡ ܒܨܝܪ ܡܢ ܫܬܐ ܦܘܪ̈ܫܢܐ ܒܘܚܪܢܐ ܠܐ ܡܨܐ ܕܦܠܛ ܪܫܝܡܐ ܓܘ .05.

ܛܝ̈ܡܐ ܚܣܝ̈ܪܐ (missing values). ܡܫܬܘܬܦܢܐ ܥܠܝܠܐ ܝܠܗ ܐܡܢ ܕܐܝܬܠܗ ܬܪܬܝܢ ܡܫܘ̈ܚܬܐ (/MISSING ANALYSIS). ܡܘܕܝ ܠܐ ܟܚܫܒܐ ܐܗܐ ܦܐܬܐ. p ܚܬܝܬܐ ܠܥܠ ܡܢ 50 ܦܘܪ̈ܫܢܐ، Monte Carlo، ܒܘܚܪܢܐ ܕܐܬܐ، McNemar (ܩܐ ܬܪܬܝܢ ܡܫܘ̈ܚܬܐ ܕܬܪܝܢ ܛܝ̈ܡܐ) ܘ-Marginal Homogeneity (ܡܥܝܪܢܘܬܐ 7.2 ܕ-Field)، ܬܚܘܡܐ ܕܬܘܟܠܢܐ ܕ-Hodges-Lehmann (ܕ-R)، ܒܘܚܪܢܐ ܠܦܘܬ ܓܘܕܐ (ܓܘ SPSS – Split File، ܦܣܩܐ 7.5.2؛ ܠܐܟܐ ܟܡܪܗܛܚ ܟܠ ܓܘܕܐ ܓܘ ܦܐܝܠ ܦܪܝܫܐ)، bootstrap.

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

ܐܘܪܚܐ ܚܕܬܐ (Pallant, 2020, Chapter 16; Field, 2024, Section 7.5.3): Analyze › Nonparametric Tests › Related Samples… – ܓܘ Objective: Customize analysis؛ ܓܘ Fields: ܬܪܬܝܢ ܡܫܘ̈ܚܬܐ ܠ-Test Fields؛ ܓܘ Settings: Customize tests ܘ-Wilcoxon matched-pair signed-rank (2 samples). ܡܦܩܢܐ: Hypothesis Test Summary، ܘܒܕܚܝܬܐ ܥܦܝܦܬܐ – Related-Samples Wilcoxon Signed Rank Test Summary ܥܡ ܗܝܣܛܘܓܪܡ ܨܒܝܥܐ: Total N، Test Statistic (= T⁺)، Standard Error، Standardized Test Statistic (z، ܥܡ ܐܬܐ) ܘ-Asymptotic Sig.؛ Field (ܦܣܩܐ 7.5.2) ܟܡܚܘܐ ܐܝܟܢܐ ܕܒܚܪܚ ܠܦܘܬ ܓܘܕܐ ܥܡ Data › Split File. ܛܝ̈ܡܐ ܡܨܥܝ̈ܐ – Pallant ܟܦܠܛܐ ܠܗܘܢ ܓܘ Frequencies ܥܡ Quartiles.

ܐܘܪܚܐ ܥܬܝܩܬܐ، ܕܦܐܬܐ ܟܒܢܝܐ ܐܝܟ ܣܝܢܬܐܟܣ: Analyze › Nonparametric Tests › Legacy Dialogs › 2 Related Samples… – ܙܘܓܐ ܠ-Test Pairs، Wilcoxon ܪܫܝܡܐ:

NPAR TESTS
  /WILCOXON=עמדות_ציון WITH עמדות_ציון_2 (PAIRED)
  /MISSING ANALYSIS.

FREQUENCIES VARIABLES=עמדות_ציון עמדות_ציון_2
  /FORMAT=NOTABLE
  /NTILES=4
  /ORDER=ANALYSIS.

ܩܪܝܢܐ ܕܡܦܩܢܐ (output). Ranks = ܠܘܚܐ 2 – Negative Ranks (ܬܪܝܢܝܬܐ ܒܨܝܪܬܐ ܝܠܗ̇ ܡܢ ܩܕܡܝܬܐ)، Positive Ranks، Ties، ܥܡ N, Mean Rank, Sum of Ranks؛ Test Statistics – Z (ܡܢ ܓܘܡܪܐ ܙܥܘܪܐ، ܟܠ ܐܡܢ ܬܚܘܬ ܨܦܪܐ؛ ܡܥܝܪܢܘܬܐ ܕܬܚܬܝܬܐ ܟܐܡܪܐ "based on negative/positive ranks") ܘ-Asymp. Sig. (2-tailed)؛ Frequencies – ܛܝ̈ܡܐ ܡܨܥܝ̈ܐ (medians). ܣܝܢܬܐܟܣ (syntax) ܡܒܘܚܪܐ ܝܠܗ ܩܘܒܠ PSPP (ܢܘܣܚܐ ܚܐܪܐ): ܡܢܝ̈ܢܐ، ܡܨܥܝ̈ܬܐ ܕܕܪ̈ܓܐ، ܓܘܡܪ̈ܐ ܘ-z ܫܘ̈ܝܐ ܝܢܐ – ܐܠܐ PSPP ܟܪܫܡ ܦܘܪܫܢܐ ܒܗܦܘܟܐ (ܩܕܡܝܬܐ ܒܨܝܪ ܬܪܝܢܝܬܐ)، ܗܕܟܐ ܕ"ܬܚܘܬ ܨܦܪܐ" ܘ"ܠܥܠ ܡܢ ܨܦܪܐ" ܟܡܫܚܠܦܝ ܕܘܟܬܐ.

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

ܓܘ R ܒܣܝܣܝܐ wilcox.test(x2, x1, paired = TRUE) – ܡܢܝܢܐ ܣܛܐܛܝܣܛܝܩܝܐ V ܕ-R ܝܠܗ T⁺ (ܓܘܡܪܐ ܕܕܪ̈ܓܐ ܠܥܠ ܡܢ ܨܦܪܐ ܕ-x2 − x1)؛ ܓܘܒܝܐ ܡܩܕܡܐ (default) ܟܡܘܣܦ ܬܘܪܨܐ ܕܡܬܡܫܚܢܘܬܐ (continuity correction) – correct = FALSE ܟܝܗܒ p ܕ-SPSS ܘܕܦܐܬܐ؛ exact = TRUE ܚܫܝܒܐ ܝܠܗ ܒܣ ܕܠܐ ܛܝ̈ܡܐ ܫܘ̈ܝܐ (ties) ܘܕܠܐ ܨܦܪ̈ܐ. ܣܩܪܝܦܬ (script) ܪܗܛܐ ܝܠܗ ܐܝܟ ܕܐܝܬܘܗܝ ܥܠ ܦܐܝܠ ܕܡܬܠܐ (sample data file) ܘܝܗܒܠܗ ܛܝ̈ܡܐ ܕܠܘ̈ܚܐ (ܓܘ ܡܥܝܪ̈ܢܘܬܐ). ܢܡܘܣܐ ܕܣܐܝܛ (site rule) ܩܐ ܣܘܪܝܬ ܒ-R: ܦܐܝܠ UTF-8، ܟܠ ܣܕܪܐ ܕܡܥܝܪܢܘܬܐ ܟܫܪܐ ܒܡܠܬܐ ܕܣܘܪܝܬ، ܘܐܬܪܐ (locale) UTF-8 ܩܐ ܫܡ̈ܗܐ ܥܒܪ̈ܝܐ.

# ܒܘܚܪܢܐ ܕ-Wilcoxon 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_wx_example_heb.xlsx", sheet = "נתונים")
ok <- !is.na(d[["עמדות_ציון"]]) & !is.na(d[["עמדות_ציון_2"]])
x1 <- d[["עמדות_ציון"]][ok]; x2 <- d[["עמדות_ציון_2"]][ok]

# ܛܝ̈ܡܐ ܡܨܥܝ̈ܐ ܘܪ̈ܘܒܥܐ (type = 6 = SPSS) – ܠܘܚܐ 1
median(x1); median(x2)                                  # 3.25, 3.50
quantile(x2 - x1, c(.25, .5, .75), type = 6)            # ܦܘܪ̈ܫܢܐ

# ܦܘܪ̈ܫܢܐ (ܬܪܝܢܝܬܐ ܒܨܝܪ ܩܕܡܝܬܐ)، ܦܠܛܬܐ ܕܨܦܪ̈ܐ، ܕܪ̈ܓܐ ܕ-|ܦܘܪܫܢܐ|، T+ ܘ-T− – ܠܘܚܐ 2
dd <- x2 - x1; nz <- dd[dd != 0]; r <- rank(abs(nz))
Tp <- sum(r[nz > 0]); Tm <- sum(r[nz < 0]); n <- length(nz)
c(zeros = sum(dd == 0), n = n, Tplus = Tp, Tminus = Tm)  # ܨܦܪ̈ܐ 14، n = 99, T+ = 3507, T− = 1443

# ܒܘܚܪܢܐ: V = T+؛ p ܩܪܝܒܝܐ ܕܠܐ ܬܘܪܨܐ ܕܡܬܡܫܚܢܘܬܐ = SPSS (ܥܡ ܬܘܪܨܐ ܩܐ ܛܝ̈ܡܐ ܫܘ̈ܝܐ) – ܠܘܚܐ 3
wt <- wilcox.test(x2, x1, paired = TRUE, exact = FALSE, correct = FALSE)
wt                                                      # V = 3507, p = .0003

# ܐܬܐ ܕ-z (ܠܥܠ ܡܢ ܨܦܪܐ = ܬܪܝܢܝܬܐ ܪܡܬܐ)، r_rb (Field) ܘ-r = |z|/√N ܥܡ N = 2 × ܙܘܓ̈ܐ (Pallant)
z <- sign(Tp - n * (n + 1) / 4) * abs(qnorm(wt$p.value / 2))
c(z = z, r_rb = (Tp - Tm) / (Tp + Tm), r = abs(z) / sqrt(2 * length(dd)))   # 3.62, .417, .240

# ܕܘܡܝܐ ܙܥܘܪܐ ܕܠܐ ܛܝ̈ܡܐ ܫܘ̈ܝܐ ܘܕܠܐ ܨܦܪ̈ܐ – p ܚܬܝܬܐ (ܠܘܚܐ E.1 ܕ-Gravetter ܘ-Wallnau: ܦܘܪ̈ܫܢܐ ܒܢܦܫܝܗܘܢ)
wilcox.test(c(4, -14, 5, -20, -6, -16, -8, -24), exact = TRUE)   # V = 3, p = .039

ܬܘܢܝܐ ܕܡܫܟܚ̈ܢܘܬܐ (reporting the results)

Field (2024، ܦܣܩܐ 7.5.7): "ܟܡܘܕܥܚ ܡܢܝܢܐ ܣܛܐܛܝܣܛܝܩܝܐ (T)، ܪܫܝܡܘܬܐ (significance) ܚܬܝܬܬܐ ܘܡܚܘܝܢܐ (index / measure) ܕܡܥܒܕܢܘܬܐ" – ܥܡ ܛܝ̈ܡܐ ܡܨܥܝ̈ܐ (medians) ܕܬܪܝܢ ܫܪ̈ܛܐ: "ܓܘ ܡܦܠܚܢ̈ܐ ܕ-ecstasy ܕܪ̈ܓܐ ܕܥܩܬܐ ܕܢܦܫܐ ܪ̈ܡܐ ܗܘܘ ܒܐܘܪܚܐ ܪܫܝܡܬܐ ܓܘ ܐܪܒܥܒܫܒܐ (Mdn = 33.50) ܩܘܒܠ ܚܕܒܫܒܐ (Mdn = 17.50)، T = 36, p = .012, r_rb = 1. ܓܘ ܡܦܠܚܢ̈ܐ ܕܥܪܩܐ ܗܦܘܟܐ: ܢܚܝ̈ܬܐ ܒܐܘܪܚܐ ܪܫܝܡܬܐ ܓܘ ܐܪܒܥܒܫܒܐ (Mdn = 7.50) ܩܘܒܠ ܚܕܒܫܒܐ (Mdn = 16.0)، T = 8, p = .047, r_rb = −.71" – ܝܢ ܥܡ z ܒܕܘܟܬܐ ܕ-T. Pallant (2020، ܨܚܚܐ 16): "z = −4.18, n = 30, p < .001، ܥܡ ܡܥܒܕܢܘܬܐ ܪܒܬܐ (r = .54). ܛܝܡܐ ܡܨܥܝܐ ܢܚܬܠܗ ܡܢ 40 ܠ-38". Gravetter ܘ-Wallnau (Appendix E.3) ܟܡܘܣܦܝ ܓܘܡܪ̈ܐ ܕܕܪ̈ܓܐ ܘܡܕܒܪܢܘܬܐ ܕܨܦܪ̈ܐ. ܡܐܡܪ̈ܐ ܕܬܘܢܝܐ (report sentences) ܕܓܘ ܡܦܩܢܐ ܒܢܝ̈ܐ ܝܢܐ ܗܕܟܐ – ܛܝ̈ܡܐ ܡܨܥܝ̈ܐ، n، T, z, p (ܚܬܝܬܐ ܐܡܢ ܕܚܫܝܒܐ ܝܠܗ)، r_rb ܘ-r. ܢܡܘ̈ܣܐ ܕܐܣܟܝܡܐ (American Psychological Association [APA], 2020, Section 6.36): p ܘ-r ܕܠܐ ܨܦܪܐ ܩܕܡ ܢܘܩܙܐ؛ T ܘ-z ܥܡ ܨܦܪܐ.

ܛܥܝ̈ܘܬܐ ܕܡܬܚܙܝܢ ܣܓܝ (Common mistakes)

ܚܘܠܛܐ ܥܡ Mann-Whitney. ܬܪܝܢ ܒܘܚܪ̈ܢܐ ܕ-Wilcoxon: ܓܘܡܪܐ ܕܕܪ̈ܓܐ – ܩܐ ܓܘ̈ܕܐ ܦܪ̈ܝܫܐ؛ ܕܪ̈ܓܐ ܥܡ ܐܬܐ – ܩܐ ܗܢܝ ܡܫܬܘܬܦ̈ܢܐ (participants) (Field, 2024, Section 7.5).

ܩܪܝܢܐ ܕܐܘܪܚܐ ܡܢ ܐܬܐ ܕ-z ܓܘ ܡܦܩܢܐ ܥܬܝܩܐ. ܬܡܢ ܟܠ ܐܡܢ ܬܚܘܬ ܨܦܪܐ ܝܠܗ؛ ܐܘܪܚܐ – ܡܢ ܡܢܝܢܐ ܘܡܢ ܕܪ̈ܓܐ (ܦܣܩܐ 7.5.4).

ܬܘܢܝܐ ܕܡܨܥܝ̈ܬܐ. ܒܘܚܪܢܐ ܥܠ ܕܪ̈ܓܐ ܝܠܗ؛ ܟܡܘܕܥܚ ܛܝ̈ܡܐ ܡܨܥܝ̈ܐ (medians) (Field, Section 7.5.7; Pallant, 2020, Chapter 16).

ܛܥܝܘܬܐ ܕܨܦܪ̈ܐ. ܐܢܝ ܟܦܠܛܝ ܡܢ ܚܘܫܒܢܐ، ܐܠܐ ܠܐ ܡܢ ܬܫܥܝܬܐ: Gravetter ܘ-Wallnau ܟܒܥܝ ܕܡܘܕܥܚ ܟܡܐ ܗܘܘ ܘܕܟܝ ܡܕܒܪ̈ܐ ܗܘܘ (Appendix E.3).

ܚܘܫܒܢܐ ܕ-r ܕ-Pallant ܥܡ ܡܢܝܢܐ ܕܡܫܬܘܬܦ̈ܢܐ. ܓܘܬܗ̇ N ܝܠܗ ܡܢܝܢܐ ܕܚܙ̈ܝܬܐ (observations) – ܥܦܝܦܐ؛ ܛܝܡܐ ܟܦܠܛ ܙܥܘܪܐ √2 ܐܥܦ̈ܐ، ܘܟܐܡܪܚ ܐܝܢܐ N.

ܥܪܩܐ ܠ-Wilcoxon ܟܠ ܐܡܢ ܕܒܘܚܪܢܐ ܕܢܘܪܡܠܝܘܬܐ (normality) ܪܫܝܡܐ ܝܠܗ. ܥܡ 30 ܙܘܓ̈ܐ ܘܠܥܠ ܢܡܘܣܐ ܕܬܚܘܡܐ ܡܨܥܝܐ (central limit theorem) ܟܡܟܣܐ ܠ-t (Field, 2024، ܦܣܩܐ 6.2.7؛ ܒܘܚܪܢܐ ܕܢܘܪܡܠܝܘܬܐ) – ܘ-Wilcoxon ܟܡܘܒܕ ܪܒܘܬܐ ܕܦܘܪ̈ܫܢܐ (ܩܘܦܬܐ 7.1).

ܡܦܠܚܢܘܬܐ ܕܒܘܚܪܢܐ ܕܐܬܐ ܐܡܢ ܕܐܝܬ ܕܪ̈ܓܐ. ܐܗܘ ܠܐ ܟܚܫܒ ܠܪܒܘܬܐ ܕܫܘܢܝܐ – ܚܣܝܪܐ ܝܠܗ ܡܢ ܚܝܠܐ ܣܛܐܛܝܣܛܝܩܝܐ (statistical power) (ܡܠܟܐ 7.2).

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.). Open University Press.

Wilcoxon (1945)، King ܘܚܒܪ̈ܘܗܝ (2011) ܘ-Kerby (2014) – ܐܝܟ ܕܡܬܝ̈ܬܐ ܝܢܐ ܓܘ Field (2024). ܠܦܘܬ ܢܡܘܣܐ ܕܣܐܝܛ (site rule)، ܓܘ ܪܫܝܡܬܐ ܕܡܒܘ̈ܥܐ (reference list) ܟܡܬܚܙܝ ܒܣ ܡܒܘ̈ܥܐ ܕܩܪܝ̈ܐ ܝܢܐ ܓܘ ܫܪܫܐ ܕܝܗܝ؛ Gravetter ܘ-Wallnau (2017, Appendix E, pp. 692-695)، Cohen (1988)، Pallant (2020) ܘ-APA (2020) – ܠܦܘܬ ܦܐܬܐ، ܨܚܚܐ ܘܦܣܩܐ ܕܢܘܣܚܐ ܛܒܝܥܐ؛ Field (2024) ܓܘ ܢܘܣܚܐ ܕܝܓܝܛܠܝܐ ܪܕܝܐ (reflowable) – ܠܦܘܬ ܦܣܩܐ، ܡܥܠܝܬܐ ܘܩܘܦܬܐ (ܠܘܚܐ 7.1 ܕܝܠܗ، ܕܡܢܗ ܢܦܝܩܐ ܝܠܗ ܠܘܚܐ 7.2، ܝܠܗ ܦܐܝܠ ܕܒܘܚܪܢܐ ܕܦܐܬܐ). ܣܝܢܬܐܟܣ – ܡܫܪܪܐ ܩܘܒܠ PSPP؛ R ܪܗܛܐ ܝܠܗ ܓܘ 4.3.3.