ܒܘܚܪܢܐ ܕ-Mann-Whitney

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)

ܐܝܡܢ ܡܦܠܚܝܚ (When to use)؟

ܐܝܡܢ ܕܐܝܬ ܬܪܬܝܢ ܓܘ̈ܕܐ ܕܡܫܬܘܬܦ̈ܢܐ (participants) ܦܪ̈ܝܫܐ ܘܚܕ ܡܫܬܚܠܦܢܐ (variable) ܠܦܘܚܡܐ ܒܝܢܝܗܝ – ܘܒܘܚܪܢܐ t ܠܐ ܝܠܗ ܓܘ ܕܘܟܬܗ. Gravetter ܘ-Wallnau (2017, Appendix E.1) ܟܡܢܝ ܣܒ̈ܒܐ ܠܫܚܠܦܐ ܡܢ ܡܢ̈ܝܢܐ ܠܕܪ̈ܓܐ ܕܛܟܣܐ (ranks): ܝܗܝ̈ܒܬܐ ܡܢ ܫܘܪܝܐ ܡܫܝ̈ܚܐ ܝܢܐ ܓܘ ܣܒܠܬܐ ܕܛܟܣܐ (ordinal scale)؛ ܡܢ̈ܝܢܐ ܟܥܒܪܝ ܥܠ ܫܪ̈ܛܐ (assumptions) ܕ-t ܘ-ANOVA (ܢܘܪܡܠܝܘܬܐ، ܫܘܝܘܬܐ ܕܫܘܚܠ̈ܦܐ)؛ ܫܘܚܠܦܐ (variance) ܪܡܐ ܣܓܝ، ܕܕܪ̈ܓܐ ܟ"ܫܐܦܝ" ܠܗ؛ ܝܢ ܡܢܝܢܐ ܕܠܐ ܚܕܝܕܐ – ܡܫܬܘܬܦܢܐ ܕܠܐ ܡܫܘܠܡܠܗ ܥܒܕܐ ܟܫܩܠ ܒܣ ܕܪܓܐ ܪܡܐ ܡܢ ܟܠܗ. Field (2024، ܦܣܩܐ 7.2) ܟܡܘܣܦ ܚܠܬܐ ܕܣܓܝ ܡܬܚܙܝܐ: ܕܘܡܝܐ (sample) ܙܥܘܪܐ، ܕܓܘܗ ܠܐ ܡܨܝܐ ܕܡܬܬܟܠܚ ܥܠ ܢܡܘܣܐ ܕܬܚܘܡܐ ܡܨܥܝܐ (central limit theorem) ܘܠܐ ܡܨܝܐ ܕܬܪܨܚ ܝܗܝ̈ܒܬܐ – ܘܟܡܥܗܕ ܕܐܘܪ̈ܚܬܐ ܚܣܝ̈ܢܬܐ (robust methods؛ ܦܐܬܐ ܛܝ̈ܡܐ ܢܘܟܪ̈ܝܐ ܘܫܪ̈ܛܐ) ܡܢ ܩܕܡ ܝܪܬܠܗܘܢ ܒܘܚܪ̈ܢܐ ܠܐ ܦܪܡܝܛܪ̈ܝܐ، ܐܠܐ SPSS ܟܡܩܪܒ ܩܠܝܠ ܡܢܝܗܝ، ܘܐܗܢܐ ܒܘܚܪ̈ܢܐ ܝܢܐ "ܡܥܠܬܐ ܪܟܝܟܬܐ" ܠܒܘܚܪܢܐ ܕܗܘܦܘܬܣ̈ܝܣ. Pallant (2020، ܨܚܚܐ 16) ܟܡܚܘܝܐ ܠܗ ܐܝܟ ܚܠܦܐ ܠܐ ܦܪܡܝܛܪܝܐ ܕܒܘܚܪܢܐ t ܠܕܘ̈ܡܝܐ ܠܐ ܬܠܝ̈ܐ: "ܐܝܢ ܓܒܪ̈ܐ ܘܢܫ̈ܐ ܦܪ̈ܝܫܐ ܝܢܐ ܓܘ ܕܪܓܐ ܕܐܝܩܪܐ ܕܢܦܫܐ (self-esteem)؟".

ܓܘ ܐܗܐ ܣܐܝܛ ܕܘܟܬܐ ܛܒܝܥܝܬܐ ܝܠܗ̇ ܩܐ ܬܪܬܝܢ ܚܠ̈ܝܬܐ: ܦܣܘܩܐ (item) ܝܚܝܕܝܐ ܕܕܪܓܐ (Likert 1-5)، ܕܠܦܘܬ ܥܝܕܐ ܕܣܐܝܛ (site convention) ܡܫܬܚܠܦܢܐ ܕܛܟܣܐ (ordinal variable) ܝܠܗ ܘܠܝܬܠܗ ܡܨܥܝܬܐ (ܡܫܬܚܠܦ̈ܢܐ ܘܕܪ̈ܓܐ ܕܡܫܘܚܬܐ) – ܦܘܚܡܐ ܒܝܢܝ ܬܪܬܝܢ ܓܘ̈ܕܐ ܥܒܝܕܐ ܝܠܗ ܐܟܐ، ܝܢ ܓܘ ܣܓܝܐܘ̈ܬܐ ܘܒܟܝ ܡܪܒܥܐ (chi-square)؛ ܘܡܢܝܢܐ ܕܣܒܠܬܐ ܝܢ ܡܫܬܚܠܦܢܐ ܟܡܝܝܐ ܓܘ ܕܘܡܝܐ ܙܥܘܪܐ ܝܢ ܥܡ ܛܝ̈ܡܐ ܢܘܟܪ̈ܝܐ، ܐܝܡܢ ܕܒܘܚܪܢܐ ܕܢܘܪܡܠܝܘܬܐ (ܒܘܚܪܢܐ ܕܢܘܪܡܠܝܘܬܐ، ܠܦܘܬ ܓܘܕܐ) ܝܢ boxplot ܟܡܚܘܝܝ ܦܘܠܓܐ (distribution) ܕܠܐ ܦܐܐ ܠ-t. ܐܝܡܢ ܕܬܪܬܝܢ ܓܘ̈ܕܐ ܪ̈ܒܐ ܝܢܐ (30 ܘܠܥܠ) ܘܝܗܝ̈ܒܬܐ ܟܡܝ̈ܝܐ ܝܢܐ، ܒܘܚܪܢܐ t ܝܠܗ ܓܘܒܝܐ ܡܩܕܡܐ (default) – Gravetter ܘ-Wallnau: "ܐܢ ܝܗܝ̈ܒܬܐ ܦܐܝ̈ܐ ܝܢܐ ܠ-ANOVA ܝܢ ܠܚܕ ܡܢ ܒܘܚܪ̈ܢܐ t، ܒܘܚܪܢܐ ܬܩܝܢܐ ܓܒܝܐ ܝܠܗ ܡܢ ܚܠܦܐ ܕܝܗܝ̈ܒܬܐ ܕܛܟܣܐ" (Appendix E.1) – ܘ-Mann-Whitney ܟܡܚܝܠ ܠܗ ܝܢ ܟܚܠܦ ܠܗ ܠܦܘܬ ܚܘܫܒܐ؛ ܩܘܦܣܐ ܕ"ܩܪܝܢܐ ܕܦܐܪܐ" ܟܐܡܪܐ ܓܘ ܐܝܢܐ ܚܠܬܐ ܝܬܘܢ. ܬܠܬܐ ܓܘ̈ܕܐ ܝܢ ܒܝܫ – ܒܘܚܪܢܐ ܕ-Kruskal-Wallis، ܦܘܬܝܐ ܕܐܗܐ ܒܘܚܪܢܐ (Gravetter & Wallnau, Appendix E.4).

ܚܘܫܒܐ: ܕܪ̈ܓܐ ܕܛܟܣܐ ܒܕܘܟܬܐ ܕܡܢ̈ܝܢܐ

ܚܘܫܒܐ، ܐܝܟ ܕ-Field (2024، ܦܣܩܐ 7.4.1) ܟܡܬܢܐ ܠܗ، "ܫܦܝܪܐ ܣܓܝ" (elegant): ܟܡܛܟܣܚ ܟܠ ܡܢ̈ܝܢܐ ܕܬܪܬܝܢ ܓܘ̈ܕܐ ܐܟܚܕܐ، ܡܢ ܢܚܝܬܐ (ܕܪܓܐ 1) ܠܪܡܐ، ܕܠܐ ܚܙܝܐ ܕܓܘܕܐ. ܐܢ ܠܝܬ ܦܘܪܫܢܐ ܒܝܢܝ ܓܘ̈ܕܐ، ܕܪ̈ܓܐ ܪ̈ܡܐ ܘܢܚܝ̈ܬܐ ܒܕ ܡܬܒܕܪܝ ܒܝܢܝܗܝ ܩܪܝܒ ܫܘܝܐܝܬ، ܘܓܘܡܪ̈ܐ ܕܕܪ̈ܓܐ ܒܕ ܗܘܝ ܕܡ̈ܝܐ؛ ܐܢ ܚܕ ܓܘܕܐ ܪܡܐ ܝܠܗ ܒܝܫ، ܕܪ̈ܓܐ ܪ̈ܡܐ ܒܕ ܡܬܟܢܫܝ ܓܘܗ ܘܓܘܡܪܐ ܕܕܪ̈ܓܐ ܕܝܠܗ ܒܕ ܗܘܐ ܪܒܐ ܒܝܫ. ܛܝ̈ܡܐ ܫܘ̈ܝܐ (ties) ܟܫܩܠܝ ܡܨܥܝܬܐ ܕܕܪ̈ܓܐ ܕܗܘܘ ܫܩܠܝ – ܬܪܝܢ ܡܢ̈ܝܢܐ ܕ-6 ܕܗܘܘ ܕܪ̈ܓܐ 3 ܘ-4 ܟܫܩܠܝ 3.5، ܬܠܬܐ ܡܢ̈ܝܢܐ ܕ-35 ܓܘ ܕܘܟ̈ܝܬܐ 16-18 ܟܫܩܠܝ 17 (Field; Gravetter & Wallnau, 2017, Appendix E.1: "3 4 4 7 9 9 9 12 ← 1 2.5 2.5 4 6 6 6 8"). ܡܢ ܐܟܐ ܬܪܝܢ ܣܛܐܛܝܣܛܝ̈ܩܐ ܫܘ̈ܝܐ: W_s ܕ-Wilcoxon – ܓܘܡܪܐ ܕܕܪ̈ܓܐ ܓܘ ܓܘܕܐ ܙܥܘܪܐ (ܘܐܝܡܢ ܕܓܘ̈ܕܐ ܫܘ̈ܝܐ ܝܢܐ – ܓܘܡܪܐ ܙܥܘܪܐ) – ܘ-U ܕ-Mann-Whitney، ܕܚܫܝܒܐ ܝܠܗ ܡܢܗ: U = n₁n₂ + n₁(n₁ + 1)/2 − R₁ (ܡܬܢܝܬܐ 7.8). Gravetter ܘ-Wallnau (Appendix E.2) ܟܝܗܒܝ ܠ-U ܦܘܫܩܐ ܬܪܝܨܐ: "ܐܝܟ ܕܬܪܬܝܢ ܓܘ̈ܕܐ ܝܢܐ ܬܪܝܢ ܓܘ̈ܕܐ ܕܡܬܟܬܫܝ ܚܕ ܥܡ ܚܕ" – ܟܠ ܡܫܬܘܬܦܢܐ ܓܘ ܓܘܕܐ ܐ ܟܫܩܠ ܢܘܩܙܐ ܩܐ ܟܠ ܡܫܬܘܬܦܢܐ ܓܘ ܓܘܕܐ ܒ ܕܡܛܟܣܐ ܝܠܗ ܠܬܚܬ ܡܢܗ؛ U_A ܝܠܗ ܓܘܡܪܐ ܕܢܘܩ̈ܙܐ ܕ-ܐ، U_B ܕ-ܒ، U_A + U_B = n_An_B، ܘܣܛܐܛܝܣܛܝܩܐ ܕܡܬܬܢܐ ܝܠܗ ܗܘ ܕܙܥܘܪܐ ܝܠܗ ܒܝܢܝܗܝ. ܓܘ ܡܬܠܐ ܕܝܠܗܘܢ (E.1)، ܬܪܬܝܢ ܓܘ̈ܕܐ ܕܫܬܐ: U_A = 30, U_B = 6، ܘܡܛܠ ܗܕܐ U = 6.

ܪܫܝܡܘܬܐ. ܓܘ ܬܪܝܢ ܡܒܘ̈ܥܐ ܐܝܬ ܬܪܬܝܢ ܐܘܪ̈ܚܬܐ. ܓܘ ܕܘܡܝܐ (sample) ܙܥܘܪܐ – ܦܘܠܓܐ ܚܬܝܬܐ (exact distribution): ܠܘܚܐ B9 ܕ-Gravetter ܘ-Wallnau ܟܝܗܒ ܛܝܡܐ ܚܪܝܦܐ (critical value؛ ܩܐ 6 ܩܘܒܠ 6، U ≤ 5 ܪܫܝܡܐ ܝܠܗ ܓܘ .05؛ U = 6 ܠܐ)، ܘ-SPSS ܟܛܒܥ Exact Sig.؛ Field (ܩܘܦܣܐ 7.2): ܓܘ ܕܘܡܝܐ ܙܥܘܪܐ – "ܒܫܪܝܪܘܬܐ ܟܠ ܡܕܡ ܕܠܬܚܬ ܡܢ 50" – ܟܡܦܠܚܚ ܒ-p ܚܬܝܬܐ. ܓܘ ܕܘܡܝܐ ܪܒܐ – ܩܘܪܒܐ ܢܘܪܡܠܝܐ (normal approximation): ܛܝܡܐ ܡܣܟܝܐ (expected value) ܘܛܥܝܘܬܐ ܬܩܝܢܬܐ (standard error) ܕܣܛܐܛܝܣܛܝܩܐ ܢܦܝܩ̈ܐ ܝܢܐ ܒܣ ܡܢ ܪܒܘܬܐ ܕܓܘ̈ܕܐ – W̄_s = n₁(n₁ + n₂ + 1)/2، SE = √(n₁n₂(n₁ + n₂ + 1)/12) (Field، ܡܬܢܝ̈ܬܐ 7.1-7.2؛ ܩܐ 10 ܩܘܒܠ 10: 105 ܘ-13.23) – ܘ-z ܝܠܗ ܪܘܚܩܐ ܕܣܛܐܛܝܣܛܝܩܐ ܡܢ ܛܝܡܐ ܡܣܟܝܐ ܕܝܠܗ ܒܡܫܘ̈ܚܬܐ ܕܛܥܝܘܬܐ ܬܩܝܢܬܐ (ܡܬܢܝܬܐ 7.5؛ Gravetter & Wallnau، ܬܘܣܦܬܐ E.2، ܥܡ U: z = (U − n_An_B/2)/√(n_An_B(n_A + n_B + 1)/12)؛ ܓܘ ܡܬܠܐ E.1 – −1.92، ܠܐ ܓܘ ܦܢܝܬܐ ܚܪܝܦܬܐ ܕ-±1.96، "ܗܝ ܚܬܡܬܐ ܐܝܟ ܡܢ ܠܘܚܐ"). SPSS ܟܬܪܨ ܛܥܝܘܬܐ ܬܩܝܢܬܐ ܩܐ ܛܝ̈ܡܐ ܫܘ̈ܝܐ (ties) – ܘܐܦ ܦܐܬܐ؛ Gravetter ܘ-Wallnau ܘ-PSPP ܠܐ ܟܬܪܨܝ، ܘܦܘܪܫܢܐ ܓܘ z ܓܘ ܣܓܝܐܐ ܕܥܕ̈ܢܐ ܝܠܗ ܓܘ ܡܢܝܢܐ (digit) ܬܠܝܬܝܐ.

ܩܪܝܢܐ ܕܡܦܩܢܐ (How to read the output)

ܠܘܚܐ 1 – ܕܪ̈ܓܐ ܕܛܟܣܐ ܘܛܝ̈ܡܐ ܡܨܥ̈ܝܐ. ܐܗܐ ܝܠܗ ܠܘܚܐ Ranks ܕ-SPSS (N, Mean Rank, Sum of Ranks) ܥܡ ܬܘܣܦܬܐ ܕܛܝܡܐ ܡܨܥܝܐ (median)، ܪ̈ܘܒܥܐ (quartiles) ܘܦܬܝܘܬܐ (range) ܕܟܠ ܓܘܕܐ. ܡܕܡ ܩܕܡܝܐ ܕܟܩܪܝܚ: ܡܨܥܝܬܐ ܕܕܪ̈ܓܐ (mean rank) – "ܓܘܕܐ ܥܡ ܡܨܥܝܬܐ ܕܕܪ̈ܓܐ ܢܚܝܬܐ ܝܠܗ ܓܘܕܐ ܕܓܘܗ ܐܝܬ ܝܬܝܪ ܡܢ̈ܝܢܐ ܢܚܝ̈ܬܐ" (Field, 2024, Section 7.4.4)؛ ܓܘ ܡܬܠܐ ܕܣܡ̈ܐ ܕ-Field، ܓܘ ܚܕܒܫܒܐ ܡܨܥܝ̈ܬܐ ܕܕܪ̈ܓܐ ܗܘܘ 11.95 ܘ-9.05 – ܕܡ̈ܝܐ – ܘܓܘ ܐܪܒܥܒܫܒܐ 15.10 ܩܘܒܠ 5.90. ܛܝܡܐ ܡܨܥܝܐ ܝܠܗ ܡܐ ܕܟܬܢܚ ܒܕܘܟܬܐ ܕܡܨܥܝܬܐ: "ܣܛܐܛܝܣܛܝܩܐ ܦܐܝܐ ܒܝܫ ܩܐ ܒܘܚܪ̈ܢܐ ܠܐ ܦܪܡܝܛܪ̈ܝܐ" (Field، ܦܣܩܐ 7.4.6؛ Pallant, 2020، ܨܚܚܐ 16 – ܬܡܢ ܟܡܦܩܝ ܠܗ ܒܦܣܥܐ ܦܪܝܫܐ ܓܘ Means). ܚܙܝܡܘܢ ܕܛܝ̈ܡܐ ܡܨܥ̈ܝܐ ܫܘ̈ܝܐ ܠܐ ܟܐܡܪܝ ܕܠܝܬ ܦܘܪܫܢܐ: ܒܘܚܪܢܐ ܟܦܚܡ ܟܠܗ ܦܘܠܓܐ (distribution) ܒܐܝܕܐ ܕܕܪ̈ܓܐ، ܠܐ ܛܝ̈ܡܐ ܡܨܥ̈ܝܐ – ܘܡܛܠ ܗܕܐ ܡܨܐ ܕܗܘܐ ܒܘܚܪܢܐ ܪܫܝܡܐ ܥܡ ܛܝ̈ܡܐ ܡܨܥ̈ܝܐ ܫܘ̈ܝܐ، ܝܬܝܪ ܓܘ ܦܣܘܩܐ (item) ܕܕܪܓܐ.

ܠܘܚܐ 2 – ܒܘܚܪܢܐ. ܠܘܚܐ Test Statistics ܕܪܫܝܡܬܐ ܥܬܝܩܬܐ ܓܘ SPSS: Mann-Whitney U، Wilcoxon W، Z، Asymp. Sig. (2-tailed) ܘ-Exact Sig.. U ܘ-W ܝܢܐ ܬܚܘܝܬܐ – ܪܒܘܬܐ ܕܝܠܗܘܢ ܬܠܝܬܐ ܝܠܗ̇ ܒܪܒܘܬܐ ܕܓܘ̈ܕܐ، ܘܠܐ ܟܡܫܘܚܝ ܡܥܒܕܢܘܬܐ (effect)؛ z ܟܠ ܐܡܢ ܣܠܝܒܐ ܝܠܗ، ܡܛܠ ܕ-U ܝܠܗ ܗܘ ܕܙܥܘܪܐ ܡܢ ܬܪܘܝܗܝ، ܘܡܛܠ ܗܕܐ ܠܐ ܟܐܡܪ ܡܕܡ ܥܠ ܐܘܪܚܐ – ܐܘܪܚܐ ܡܬܩܪܝܐ ܝܠܗ ܡܢ ܠܘܚܐ 1. ܦܐܬܐ ܟܛܒܥܐ ܬܪܝܢ ܛܝ̈ܡܐ ܕ-p: ܩܪܝܒܝܐ (asymptotic؛ ܡܢ ܩܘܪܒܐ ܢܘܪܡܠܝܐ، ܥܡ ܬܘܪܨܐ ܕܛܝ̈ܡܐ ܫܘ̈ܝܐ) ܘܚܬܝܬܐ (2·P(U ≤ U_ܚܙܝܐ) ܡܢ ܦܘܠܓܐ ܚܬܝܬܐ ܕ-U ܕܠܐ ܛܝ̈ܡܐ ܫܘ̈ܝܐ – ܡܐ ܕ-SPSS ܟܛܒܥ ܐܝܟ Exact Sig. [2*(1-tailed Sig.)]؛ ܥܝܕܐ ܕܣܐܝܛ (site convention): ܚܫܝܒܐ ܝܠܗ ܐܝܡܢ ܕܬܪܬܝܢ ܓܘ̈ܕܐ ܗܕܟܡܐ 50 ܡܫܬܘܬܦ̈ܢܐ ܝܢܐ). ܢܡܘܣܐ ܕ-Field (ܩܘܦܣܐ 7.2): ܕܘܡܝܐ (sample) ܙܥܘܪܐ – ܚܬܝܬܐ؛ ܪܒܐ – ܩܪܝܒܝܐ ܣܦܩ ܝܠܗ. ܓܘ ܡܬܠܐ ܕܝܠܗ، ܓܘ ܚܕܒܫܒܐ U = 35.5، p = .280 (ܠܐ ܪܫܝܡܐ: "ecstasy ܠܐ ܟܥܒܕ ܥܩܬܐ ܕܢܦܫܐ ܒܝܫ ܡܢ ܐܠܟܘܗܠ ܠܝܘܡܐ ܕܒܬܪܗ")، ܘܓܘ ܐܪܒܥܒܫܒܐ U = 4، p < .001 – "ܟܟܬܒܚ p < .001 ܡܛܠ ܕ-p ܚܙܝܐ ܙܥܘܪܐ ܣܓܝ ܝܠܗ"؛ ܐܗܢܐ ܛܝ̈ܡܐ ܝܢܐ ܡܢ ܒܘܚܪ̈ܢܐ ܕܦܐܬܐ. ܬܪܝܢ ܥܡܘ̈ܕܐ ܐܚܪ̈ܝܐ – ܡܚܘ̈ܝܢܐ ܕܡܥܒܕܢܘܬܐ.

boxplot (box plot) ܟܡܚܘܝܐ ܡܐ ܕܒܘܚܪܢܐ ܟܒܚܪ: ܐܝܟܐ ܝܬܝ̈ܒܐ ܝܢܐ ܦܘܠ̈ܓܐ ܚܕ ܠܘܬ ܚܕ – ܛܝܡܐ ܡܨܥܝܐ (median؛ ܣܪܛܐ ܥܒܝܐ)، ܪ̈ܘܒܥܐ (ܩܘܦܣܐ)، whiskers ܘܛܝ̈ܡܐ ܢܘܟܪ̈ܝܐ (outliers؛ Pallant, 2020, Chapter 6). Field (ܦܣܩܐ 7.4.6): "ܬܢܘܢ ܛܝ̈ܡܐ ܡܨܥ̈ܝܐ ܘܦܬܝ̈ܘܬܐ ܕܝܠܗܘܢ، ܝܢ ܨܘܪܘܢ boxplot".

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

SPSS ܠܐ ܟܛܒܥ ܡܚܘܝܢܐ ܕܡܥܒܕܢܘܬܐ ܩܐ ܒܘܚܪܢܐ، ܘܬܪܝܢ ܡܒܘ̈ܥܐ ܟܡܩܪܒܝ ܬܪܝܢ ܦܪ̈ܝܫܐ. r ܕ-Pallant (2020، ܨܚܚܐ 16): r = |z|/√N، ܐܝܡܢ ܕ-N ܝܠܗ ܡܢܝܢܐ ܕܟܠ ܡܫܬܘܬܦ̈ܢܐ (participants) – "ܛܝܡܐ ܩܪܝܒܐ ܕ-r" – ܥܡ ܥܝ̈ܕܐ ܕ-Cohen (1988، ܦܐܬܐ 79-83): .1 ܙܥܘܪܐ، .3 ܡܨܥܝܐ، .5 ܪܒܐ؛ ܓܘ ܡܬܠܐ ܕܝܠܗ̇ z = −1.23, N = 436، r = .06، "ܙܥܘܪܐ ܣܓܝ". r_rb ܕ-Field (2024، ܦܣܩܐ 7.4.5): ܐܣܘܪܐ ܕܚܕ̈ܕܐ (correlation) ܕܕܪ̈ܓܐ-ܬܪܝܢ ܣܕܪ̈ܐ (rank-biserial; Cureton, as cited in Field)، ܒܡܬܢܝܬܐ ܕ-Wendt: r_rb = 1 − 2U/(n₁n₂) (ܡܬܢܝܬܐ 7.11)، ܥܡ ܦܘܫܩܐ ܡܬܦܗܡܢܐ ܕ-Kerby: ܓܘ ܡܬܠܐ، r_rb = .29 ܓܘ ܚܕܒܫܒܐ – "ܩܪܝܒ ܠ-29% ܡܢ ܝܗܝ̈ܒܬܐ ܡܛܟܣ̈ܬܐ ܟܣܡܟܝ ܠܚܘܫܒܐ ܕܥܩܬܐ ܕܢܦܫܐ ܪܡܬܐ ܝܠܗ̇ ܒܝܫ ܒܬܪ ecstasy" – ܘ-.92 ܓܘ ܐܪܒܥܒܫܒܐ، "ܣܡܟܐ ܚܝܠܢܐ ܣܓܝ". ܦܐܬܐ ܟܚܫܒܐ ܠܗ ܡܢ U₁ ܕܓܘܕܐ ܩܕܡܝܐ ܕܓܒܝܬܘܢ، ܗܕܟܐ ܕܐܬܐ ܟܐܡܪܐ ܐܘܪܚܐ: ܥܠ ܡܢ ܣܦܪ (positive) – ܓܘܕܐ ܐ ܪܡܐ ܝܠܗ؛ ܘܟܡܚܘܝܐ ܡܢܬܐ ܒܡܐܐ ܕܙܘ̈ܓܐ ܕܟܣܡܟܝ. ܬܪܝܢ ܡܚܘ̈ܝܢܐ ܠܐ ܝܢܐ ܚܕ ܘܠܐ ܡܨܝ ܕܡܬܚܠܦܝ ܚܕ ܠܚܕ (r ܬܠܝܐ ܝܠܗ ܐܦ ܒ-N ܒܐܝܕܐ ܕ-z)؛ ܟܬܢܚ ܚܕ ܠܐ ܒܨܝܪ، ܘܟܐܡܪܚ ܐܝܢܐ.

ܫܪ̈ܛܐ ܘܙܘܗܪ̈ܐ (Assumptions and warnings)

ܬܪܝܢ ܫܪ̈ܛܐ ܟܠܢܝ̈ܐ (assumptions؛ Pallant, 2020, Chapter 16): ܓܘܒܝܐ ܓܕܫܢܝܐ ܕܕܘܡܝܐ (random sampling)، ܘܚܙ̈ܝܬܐ (observations) ܠܐ ܬܠܝ̈ܐ – "ܟܠ ܡܫܬܘܬܦܢܐ ܡܬܡܢܐ ܝܠܗ ܚܕ ܓܗܐ، ܠܐ ܡܨܐ ܕܡܬܚܙܐ ܓܘ ܒܝܫ ܡܢ ܚܕ ܓܘܕܐ، ܘܝܗܝ̈ܒܬܐ ܕܚܕ ܡܫܬܘܬܦܢܐ ܠܐ ܟܡܥܒܕܝ ܥܠ ܕܐܚܪܢܐ"؛ ܡܫܘ̈ܚܬܐ ܡܬܢ̈ܝܬܐ (repeated measures) ܕܗܢܝ ܡܫܬܘܬܦ̈ܢܐ – ܩܐ ܒܘܚܪܢܐ ܕ-Wilcoxon ܠܕܘ̈ܡܝܐ ܙܘܓܢ̈ܝܐ، ܠܐ ܩܐ ܐܟܐ. Field (2024، ܡܥܝܪܢܘܬܐ 2 ܕܨܚܚܐ 7) ܟܡܥܗܕ ܕܐܦ ܐܗܢܐ ܒܘܚܪ̈ܢܐ ܠܐ ܝܢܐ "ܕܠܐ ܦܘܠܓܐ" (distribution-free): ܟܣܒܪܝ ܦܘܠܓܐ ܡܬܡܫܚܢܐ (continuous) – ܘܡܛܠ ܗܕܐ ܓܘ ܝܗܝ̈ܒܬܐ ܕܕܪܓܐ ܥܡ ܣܓܝ ܛܝ̈ܡܐ ܫܘ̈ܝܐ، ܬܘܪܨܐ ܕܛܝ̈ܡܐ ܫܘ̈ܝܐ ܓܘ z ܚܫܝܚܐ ܝܠܗ. ܚܝܠܐ ܣܛܐܛܝܣܛܝܩܝܐ (statistical power). Field (ܩܘܦܣܐ 7.1): ܕܪ̈ܓܐ ܟܡܘܒܕܝ ܝܕܥܬܐ ܥܠ ܪܒܘܬܐ ܕܦܘܪ̈ܫܢܐ، ܘܡܛܠ ܗܕܐ ܐܝܡܢ ܕܫܪ̈ܛܐ ܕܒܘܚܪܢܐ ܦܪܡܝܛܪܝܐ ܩܝ̈ܡܐ ܝܢܐ، ܐܗܘ ܚܝܠܢܐ ܝܠܗ ܒܝܫ؛ ܐܠܐ ܐܝܡܢ ܕܦܘܠܓܐ ܕܓܘܒܝܐ ܕܕܘܡܝܐ (sampling distribution) ܠܐ ܝܠܗ ܢܘܪܡܠܝܐ، ܡܢܬܐ ܕܛܥܝܘܬܐ ܕܙܢܐ I (Type I error) ܕܒܘܚܪܢܐ ܦܪܡܝܛܪܝܐ ܠܐ ܝܠܗ̇ ܝܕܝܥܬܐ – ܘܒܬܪ ܐܡܪܬܐ "ܠܒܘܚܪ̈ܢܐ ܠܐ ܦܪܡܝܛܪ̈ܝܐ ܐܝܬ ܚܝܠܐ ܒܨܝܪ" ܒܣ ܠܐ ܝܠܗ̇ ܡܚܕܕܬܐ. ܓܘ̈ܕܐ ܙܥܘܪ̈ܐ ܣܓܝ. ܥܡ ܒܨܝܪ ܡܢ ܚܡܫܐ ܡܫܬܘܬܦ̈ܢܐ ܓܘ ܓܘܕܐ ܒܘܚܪܢܐ ܩܪܝܒ ܠܐ ܡܨܐ ܕܢܦܩ ܪܫܝܡܐ (ܦܘܠܓܐ ܚܬܝܬܐ ܥܒܝܐ ܝܠܗ)؛ ܦܐܬܐ ܟܡܙܗܪܐ.

ܛܝ̈ܡܐ ܚܣܝ̈ܪܐ. ܡܫܬܘܬܦܢܐ ܥܠܝܠܐ ܝܠܗ ܐܝܡܢ ܕܐܝܬܠܗ ܛܝܡܐ ܬܪܝܨܐ ܓܘ ܡܫܬܚܠܦܢܐ ܬܠܝܐ (dependent variable) ܘܓܘ ܡܫܬܚܠܦܢܐ ܕܓܘ̈ܕܐ – ܫܩܠܬܐ ܠܦܘܬ ܦܘܫܩܐ (/MISSING ANALYSIS). ܒܘܚܪ̈ܢܐ ܣܓܝ̈ܐܐ. ܟܡܐ ܡܫܬܚܠܦ̈ܢܐ ܒܚܕ ܕܚܩܐ ܟܡܐ ܒܘܚܪ̈ܢܐ ܝܢܐ، ܟܠ ܚܕ ܥܡ 5% ܣܘܟܢܐ ܕܛܥܝܘܬܐ ܕܙܢܐ I. ܡܘܕܝ ܠܐ ܟܚܫܒܐ ܐܗܐ ܦܐܬܐ. p ܚܬܝܬܐ ܩܐ ܓܘ̈ܕܐ ܪ̈ܒܐ ܡܢ 50، Monte Carlo (ܩܘܦܣܐ 7.2)، Kolmogorov-Smirnov ܩܐ ܬܪܬܝܢ ܓܘ̈ܕܐ، Moses ܘ-Wald-Wolfowitz (Tip 7.1 ܕ-Field)، ܒܘܚܪܢܐ ܕܚܕ ܕܘܢܒܐ (one-tailed) ܐܝܟ ܡܦܩܢܐ، ܬܚܘܡܐ ܕܬܘܟܠܢܐ (confidence interval) ܩܐ ܦܘܪܫܢܐ ܕܛܝ̈ܡܐ ܡܨܥ̈ܝܐ (Hodges-Lehmann ܕ-R) ܘ-bootstrap.

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

ܬܪܬܝܢ ܪ̈ܫܝܡܬܐ، ܬܪܝܢ ܡܦܩ̈ܢܐ. ܐܘܪܚܐ ܚܕܬܐ (Pallant, 2020, Chapter 16; Field, 2024, Sections 7.3 and 7.4.3): Analyze › Nonparametric Tests › Independent Samples… – ܓܘ tab Objective ܟܓܒܚ Customize analysis (Field: "ܠܐ ܛܒܐ ܝܠܗ ܕܫܒܩܚ ܠܡܚܫܒܢܐ ܕܚܫܒ ܒܕܘܟܬܘܟܘܢ")؛ ܓܘ Fields – ܡܫܬܚܠܦܢܐ ܕܓܢ̈ܣܐ (categorical variable) ܠ-Groups ܘܬܠܝܐ ܠ-Test Fields؛ ܓܘ Settings – Customize tests ܘ-Mann-Whitney U (2 samples)؛ ܩܕܡ ܗܕܐ، Pallant: ܓܘ Edit › Options › Output ܓܒܝܐ Pivot tables and charts. ܡܦܩܢܐ (output): Hypothesis Test Summary (ܒܣ ܦܣܩܐ ܕܕܝܢܐ)، ܘܕܚܩܐ ܬܢܝܢܐ ܟܦܬܚ Independent-Samples Mann-Whitney U Test Summary ܥܡ ܨܘܪܬܐ ܕܕܪ̈ܓܐ – Total N، Mann-Whitney U، Wilcoxon W، Standard Error، Standardized Test Statistic (z) ܘ-Asymptotic Sig.، ܘܓܘ ܢܘ̈ܣܚܐ ܥܡ ܡܘܕܘܠ ܕܒܘܚܪ̈ܢܐ ܚܬܝ̈ܬܐ ܐܦ Exact Sig.. ܚܙܝܡܘܢ: ܓܘ ܪܫܝܡܬܐ ܚܕܬܐ U ܘ-W ܚܫܝܒ̈ܐ ܝܢܐ ܡܢ ܓܘܕܐ ܬܪܝܢܐ (ܪܡܙܐ ܪܡܐ) ܘܠܐ ܝܢܐ ܡܢ ܡܬܘܡ ܙܥܘܪ̈ܐ – ܓܘ ܡܬܠܐ ܕ-Pallant U = 21594 ܐܝܡܢ ܕ-n = 184 × 252، ܘܣܛܐܛܝܣܛܝܩܐ ܡܬܩܢܐ ܬܚܬ ܣܦܪ ܝܢ ܥܠ ܣܦܪ ܠܦܘܬ ܐܘܪܚܐ؛ p ܗܘ ܝܠܗ. ܛܝ̈ܡܐ ܡܨܥ̈ܝܐ (medians) ܠܝܬ ܓܘ ܡܦܩܢܐ – Pallant ܟܡܦܩܐ ܠܗܘܢ ܓܘ Analyze › Compare Means › Means ܥܡ Median ܓܘ Cell Statistics.

ܐܘܪܚܐ ܥܬܝܩܬܐ، ܕܦܐܬܐ ܟܒܢܐ ܐܝܟ ܣܝܢܬܐܟܣ (syntax؛ ܡܛܠ ܕܟܫܒܩܐ ܠܓܘܒܝܐ ܕܬܪܬܝܢ ܡܢ ܟܡܐ ܓܘ̈ܕܐ ܘܟܛܒܥܐ U ܘ-W ܐܝܟ ܓܘ ܠܘܚܐ 2): Analyze › Nonparametric Tests › Legacy Dialogs › 2 Independent Samples… – ܡܫܬܚܠܦܢܐ ܠ-Test Variable List، ܡܫܬܚܠܦܢܐ ܕܓܘ̈ܕܐ ܠ-Grouping Variable ܥܡ Define Groups، ܘ-Mann-Whitney U ܪܫܝܡܐ:

NPAR TESTS
  /M-W=עמדות_ציון BY קבוצה(1 2)
  /MISSING ANALYSIS.

MEANS TABLES=עמדות_ציון BY קבוצה
  /CELLS=COUNT MEDIAN.

ܩܪܝܢܐ ܕܡܦܩܢܐ. Ranks = ܠܘܚܐ 1 (N, Mean Rank, Sum of Ranks)؛ Test Statistics = ܠܘܚܐ 2 – Mann-Whitney U, Wilcoxon W, Z, Asymp. Sig. (2-tailed)، ܘܩܐ ܓܘ̈ܕܐ ܙܥܘܪ̈ܐ ܐܦ Exact Sig. [2*(1-tailed Sig.)]؛ MEANS – ܛܝ̈ܡܐ ܡܨܥ̈ܝܐ. ܣܝܢܬܐܟܣ (syntax) ܒܚܝܪܐ ܝܠܗ ܩܘܒܠ PSPP (ܡܦܠܚܢܘܬܐ ܚܐܪܬܐ): U، W ܘܓܘܡܪ̈ܐ ܕܕܪ̈ܓܐ ܫܘ̈ܝܐ ܝܢܐ؛ z ܕ-PSPP ܕܠܐ ܬܘܪܨܐ ܕܛܝ̈ܡܐ ܫܘ̈ܝܐ.

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

ܓܘ R ܒܣܝܣܝܐ wilcox.test(x, y) – ܒܫܡܐ "Wilcoxon rank sum test"، ܗܘ ܒܘܚܪܢܐ. ܬܠܬܐ ܦܘܪ̈ܫܢܐ ܡܢ SPSS ܕܛܒܐ ܝܠܗ ܠܡܝܕܥ: ܣܛܐܛܝܣܛܝܩܐ W ܕ-R ܝܠܗ ܡܢܝܢܐ ܕܙܘ̈ܓܐ ܕܓܘܗܘܢ ܓܘܕܐ ܩܕܡܝܐ ܪܡܐ ܝܠܗ (ܠܐ U ܙܥܘܪܐ ܘܠܐ W ܕ-Wilcoxon)؛ ܓܘܒܝܐ ܡܩܕܡܐ (default) ܟܡܘܣܦ ܬܘܪܨܐ ܕܡܬܡܫܚܢܘܬܐ (continuity correction) ܠ-p ܩܪܝܒܝܐ – correct = FALSE ܟܝܗܒ p ܕ-SPSS ܘܕܦܐܬܐ؛ ܘ-p ܚܬܝܬܐ (exact = TRUE) ܚܫܝܒܐ ܝܠܗ ܒܣ ܕܠܐ ܛܝ̈ܡܐ ܫܘ̈ܝܐ. 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-Mann-Whitney – 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_mw_example_heb.xlsx", sheet = "נתונים")
y <- d[["עמדות_ציון"]]; g <- d[["קבוצה"]]
y1 <- y[g == 1 & !is.na(y)]; y2 <- y[g == 2 & !is.na(y)]

# ܛܝܡܐ ܡܨܥܝܐ ܘܪ̈ܘܒܥܐ (type = 6 = SPSS) ܩܐ ܟܠ ܓܘܕܐ – ܠܘܚܐ 1
median(y1); quantile(y1, c(.25, .75), type = 6)      # ܢܣܝܘܢܐ: Mdn 3.375, [2.91, 4.00]
median(y2); quantile(y2, c(.25, .75), type = 6)      # ܦܘܚܡܐ: Mdn 3.125, [2.50, 3.55]

# ܕܪ̈ܓܐ: ܓܘܡܪܐ ܘܡܨܥܝܬܐ ܕܕܪ̈ܓܐ ܩܐ ܟܠ ܓܘܕܐ (ܡܨܥܝܬܐ ܕܕܪ̈ܓܐ ܩܐ ܛܝ̈ܡܐ ܫܘ̈ܝܐ)
r <- rank(c(y1, y2)); R1 <- sum(r[seq_along(y1)]); R2 <- sum(r[-seq_along(y1)])
c(R1, R2, R1 / length(y1), R2 / length(y2))          # 4147, 3113؛ ܡܨܥܝ̈ܬܐ ܕܕܪ̈ܓܐ 69.12, 51.88

# ܒܘܚܪܢܐ: p ܩܪܝܒܝܐ ܕܠܐ ܬܘܪܨܐ ܕܡܬܡܫܚܢܘܬܐ = SPSS؛ W ܕ-R = n1n2 − U1
wt <- wilcox.test(y1, y2, exact = FALSE, correct = FALSE)
wt                                                    # W = 2317, p = .0066
n1 <- length(y1); n2 <- length(y2)
U1 <- n1 * n2 + n1 * (n1 + 1) / 2 - R1; U2 <- n1 * n2 + n2 * (n2 + 1) / 2 - R2
c(U = min(U1, U2), W = min(R1, R2))                  # U = 1283, W = 3113 – ܐܝܟ SPSS

# z (ܣܠܝܒܐ ܐܝܟ ܓܘ SPSS)، r = |z|/√N (Pallant) ܘ-r_rb = 1 − 2U1/(n1n2) (Field)
z <- -abs(qnorm(wt$p.value / 2))
c(z = z, r = abs(z) / sqrt(n1 + n2), r_rb = 1 - 2 * U1 / (n1 * n2))   # −2.72, .248, .287

# ܕܘܡܝܐ ܙܥܘܪܐ ܕܠܐ ܛܝ̈ܡܐ ܫܘ̈ܝܐ – p ܚܬܝܬܐ (ܡܬܠܐ E.1 ܕ-Gravetter ܘ-Wallnau)
wilcox.test(c(27, 2, 9, 48, 6, 15), c(71, 63, 18, 68, 94, 8), exact = TRUE)   # W = 6, p = .065

ܬܘܢܝܐ ܕܡܫܟܚ̈ܢܘܬܐ (reporting the results)

Field (2024، ܦܣܩܐ 7.4.6): ܟܬܢܚ ܣܛܐܛܝܣܛܝܩܐ (U، ܝܢ W_s ܐܢ ܓܒܚ)، z، p ܚܬܝܬܐ (ܠܐ p ≤ .05)، ܡܚܘܝܢܐ ܕܡܥܒܕܢܘܬܐ – ܘܛܝ̈ܡܐ ܡܨܥ̈ܝܐ ܕܬܪܬܝܢ ܓܘ̈ܕܐ: "ܕܪ̈ܓܐ ܕܥܩܬܐ ܕܢܦܫܐ ܕܡܦܠܚ̈ܢܐ ܕ-ecstasy (Mdn = 17.50) ܠܐ ܗܘܘ ܦܪ̈ܝܫܐ ܪܫܝܡܐܝܬ ܡܢ ܡܦܠܚ̈ܢܐ ܕܐܠܟܘܗܠ (Mdn = 16.00) ܠܝܘܡܐ ܕܒܬܪܗ، U = 35.50, z = −1.11, p = .280, r_rb = .29. ܐܠܐ ܗܕܟܡܐ ܐܪܒܥܒܫܒܐ ܡܦܠܚ̈ܢܐ ܕ-ecstasy (Mdn = 33.50) ܗܘܘ ܥܩܝ̈ܐ ܪܫܝܡܐܝܬ ܒܝܫ (Mdn = 7.50)، U = 4.00, z = −3.48, p < .001, r_rb = .92". Pallant (2020، ܨܚܚܐ 16) ܒܗܘ ܛܘܦܣܐ ܥܡ n ܘ-r: "U = 21594, z = −1.23, p = .22, r = .06". Gravetter ܘ-Wallnau (Appendix E.2) ܟܡܘܣܦܝ ܕܠܦܘܬ APA ܛܒܐ ܝܠܗ ܕܥܠܠܚ ܐܦ ܓܘܡܪ̈ܐ ܕܕܪ̈ܓܐ. ܡܐܡܪ̈ܐ ܕܬܘܢܝܐ (report sentences) ܓܘ ܡܦܩܢܐ ܒܢܝ̈ܐ ܝܢܐ ܗܕܟܐ – ܛܝܡܐ ܡܨܥܝܐ ܘ-n ܩܐ ܟܠ ܓܘܕܐ، U, z, p (ܚܬܝܬܐ ܐܝܡܢ ܕܚܫܝܒܐ ܝܠܗ)، r_rb ܘ-r. ܢܡܘ̈ܣܐ ܕܨܘܪܬܐ (American Psychological Association [APA], 2020, Section 6.36): p ܘ-r ܕܠܐ ܣܦܪ ܩܕܡ ܢܘܩܙܐ؛ U, W, z ܥܡ.

ܛܥܝ̈ܘܬܐ ܕܡܬܚܙܝܢ ܣܓܝ (Common mistakes)

ܩܪܝܢܐ ܕܐܘܪܚܐ ܡܢ ܐܬܐ ܕ-z. ܓܘ ܡܦܩܢܐ ܥܬܝܩܐ z ܟܠ ܐܡܢ ܣܠܝܒܐ ܝܠܗ؛ ܐܘܪܚܐ – ܡܢ ܡܨܥܝ̈ܬܐ ܕܕܪ̈ܓܐ ܝܢ ܡܢ ܛܝ̈ܡܐ ܡܨܥ̈ܝܐ (Field, 2024, Section 7.4.4).

ܬܘܢܝܐ ܕܡܨܥܝ̈ܬܐ. ܒܘܚܪܢܐ ܥܠ ܕܪ̈ܓܐ ܝܠܗ؛ ܟܬܢܚ ܛܝ̈ܡܐ ܡܨܥ̈ܝܐ (medians؛ Field, Section 7.4.6; Pallant, 2020, Chapter 16).

ܩܪܝܢܐ ܕ"ܠܐ ܪܫܝܡܐ" ܓܘ ܕܘܡܝܐ ܙܥܘܪܐ ܐܝܟ "ܠܝܬ ܦܘܪܫܢܐ". ܥܡ 6 ܩܘܒܠ 6 ܡܫܬܘܬܦ̈ܢܐ، U = 6 ܠܐ ܝܠܗ ܪܫܝܡܐ ܐܦܢ ܕܓܘ̈ܕܐ ܓܠܝܐܝܬ ܦܪ̈ܝܫܐ ܝܢܐ (Gravetter & Wallnau، ܡܬܠܐ E.1) – ܚܝܠܐ ܣܛܐܛܝܣܛܝܩܝܐ (statistical power).

ܦܘܚܡܐ ܕ-U ܕ-R، ܕܪܫܝܡܬܐ ܚܕܬܐ ܘܕܥܬܝܩܬܐ. ܬܠܬܐ ܚܘ̈ܕܕܐ (ܡܢܝܢܐ ܕܙܘ̈ܓܐ؛ ܡܢ ܓܘܕܐ ܬܪܝܢܐ؛ ܙܥܘܪܐ) – ܗܘ p.

ܚܘܫܒܐ ܕܛܝ̈ܡܐ ܡܨܥ̈ܝܐ ܫܘ̈ܝܐ = ܒܘܚܪܢܐ ܠܐ ܪܫܝܡܐ. ܒܘܚܪܢܐ ܟܦܚܡ ܦܘܠ̈ܓܐ (distributions)؛ ܓܘ ܦܣܘܩܐ (item) ܕܕܪܓܐ ܬܪܝܢ ܛܝ̈ܡܐ ܡܨܥ̈ܝܐ "3" ܡܨܝ ܕܛܫܝ ܦܘܪܫܢܐ ܪܫܝܡܐ ܓܘ ܕܪ̈ܓܐ.

ܥܪܩܐ ܠ-Mann-Whitney ܟܠ ܓܗܐ ܕܒܘܚܪܢܐ ܕܢܘܪܡܠܝܘܬܐ ܪܫܝܡܐ ܝܠܗ. ܓܘ ܓܘ̈ܕܐ ܪ̈ܒܐ ܢܡܘܣܐ ܕܬܚܘܡܐ ܡܨܥܝܐ (central limit theorem) ܟܡܟܣܐ t (Field, 2024، ܦܣܩܐ 6.2.7؛ ܦܐܬܐ ܒܘܚܪܢܐ ܕܢܘܪܡܠܝܘܬܐ) – ܘ-Mann-Whitney ܟܡܘܒܕ ܪܒܘܬܐ ܕܦܘܪ̈ܫܢܐ (ܩܘܦܣܐ 7.1).

ܬܘܢܝܐ ܕ-r ܒܠܚܘܕ ܝܢ ܕ-r_rb ܒܠܚܘܕ ܕܠܐ ܐܡܪܬܐ ܐܝܢܐ. ܬܪܬܝܢ ܡܫܘ̈ܚܬܐ ܦܪ̈ܝܫܐ؛ .29 ܓܘ Field ܝܠܗ r_rb، .06 ܓܘ Pallant ܝܠܗ r.

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.

Mann ܘ-Whitney (1947)، Wilcoxon (1945)، Cureton (1956)، Wendt (1972) 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. 687-692)، Cohen (1988)، Pallant (2020) ܘ-APA (2020) – ܠܦܘܬ ܦܐܬܐ، ܨܚܚܐ ܘܦܣܩܐ ܕܡܦܩܬܐ ܛܒܝܥܬܐ؛ Field (2024) ܒܢܘܣܚܐ ܕܝܓܝܛܠܝܐ ܕܪܕܝܐ (reflowable) – ܠܦܘܬ ܦܣܩܐ، ܡܬܢܝܬܐ ܘܩܘܦܣܐ (ܠܘܚܐ 7.1 ܕܝܠܗ ܝܠܗ ܦܐܝܠ ܕܒܘܚܪܢܐ ܕܦܐܬܐ). ܣܝܢܬܐܟܣ – ܒܚܝܪܐ ܝܠܗ ܩܘܒܠ PSPP؛ R ܪܗܛܐ ܝܠܗ ܓܘ 4.3.3.