ܒܘܚܪܢܐ ܕܟܝ ܡܪܒܥܐ ܠܠܐ ܬܠܝܘܬܐ

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 ܒܟܝ ܡܪܒܥܐ ܠܠܐ ܬܠܝܘܬܐ؟

ܐܝܡܢ ܕܬܪܝܢ ܡܫܬܚܠܦ̈ܢܐ (variables) ܕܓܢ̈ܣܐ (categorical) ܝܢܐ ܘܒܥܝܚ ܕܝܕܥܚ ܐܢ ܦܘܠܓܐ (distribution) ܕܚܕ ܬܠܝܐ ܝܠܗ ܒܐܚܪܢܐ: ܐܢ ܡܢܬܐ ܒܡܐܐ ܕܡܫܬܘܬܦ̈ܢܐ ܓܘ ܥܒܕܐ ܕܟܢܘܫܬܐ ܦܪܝܫܐ ܝܠܗ ܒܝܢܝ ܥܬܝܩ̈ܐ ܘܚܕ̈ܬܐ؟ ܐܢ ܓܘܒܝܐ ܕܐܘܪܚܐ ܕܝܘܠܦܢܐ ܐܣܝܪܐ ܝܠܗ ܥܡ ܫܪܫܐ؟ ܥܡ ܡܫܬܚܠܦܢܐ ܕܓܢ̈ܣܐ ܠܝܬ ܡܨܥܝܬܐ (mean) – "ܡܨܥܝܬܐ ܕܡܫܬܚܠܦܢܐ ܕܓܢ̈ܣܐ ܠܝܬ ܠܗ̇ ܣܘܟܠܐ" (Field, 2024, Section 19.3) – ܘܡܛܠ ܗܕܐ ܟܦܫܩܚ ܣܓܝܐܘ̈ܬܐ (frequencies): ܟܡܐ ܡܫܬܘܬܦ̈ܢܐ ܢܦܠܘ ܓܘ ܟܠ ܚܠܛܐ ܕܓܢ̈ܣܐ (categories). Pallant (2020، ܨܚܚܐ 16) ܟܡܬܢܝܐ ܗܘ ܫܘܐܠܐ ܒܬܠܬܐ ܐܘܪ̈ܚܬܐ: ܐܢ ܐܝܬ ܐܣܘܪܐ ܒܝܢܝ ܓܢܣܐ (gender) ܘܬܢܢܐ؟ ܐܢ ܓܒܪ̈ܐ ܡܨܠܝ̈ܢܐ ܝܢܐ ܝܬܝܪ ܠܬܢܢܐ؟ ܐܢ ܡܢܬܐ ܒܡܐܐ ܕܬܢܢ̈ܐ ܚܕܐ ܝܠܗ̇ ܓܘ ܬܪܝܢ ܓܢ̈ܣܐ؟ – ܐܗܐ ܗܘ ܒܘܚܪܢܐ ܝܠܗ. ܐܢ ܚܕ ܡܢ ܡܫܬܚܠܦ̈ܢܐ ܡܬܡܫܚܢܐ (continuous) ܝܠܗ، ܐܗܐ ܠܐ ܝܠܗ ܒܘܚܪܢܐ: ܩܐ ܦܘܚܡܐ ܕܡܨܥܝ̈ܬܐ ܒܝܢܝ ܓܘ̈ܕܐ – ܒܘܚܪܢܐ t ܝܢ ANOVA؛ ܩܐ ܡܢܒܝܢܘܬܐ (prediction) ܕܡܫܬܚܠܦܢܐ ܕܓܢ̈ܣܐ ܡܢ ܡܢܒ̈ܝܢܐ (predictors) ܡܬܡܫ̈ܚܢܐ – ܪܝܓܪܫܢ ܠܘܓܝܣܛܝܩܝܐ (logistic regression؛ Field, Section 19.2). ܠܘܚܐ ܥܠ ܬܠܬܐ ܡܫܬܚܠܦ̈ܢܐ ܕܓܢ̈ܣܐ ܘܠܥܠ – ܦܘܫܩܐ ܠܘܓ-ܣܪܛܢܝܐ (log-linear analysis؛ Field, Section 19.4)، ܕܠܐ ܝܠܗ ܓܘ ܣܐܝܛ.

ܕܟܝ ܒܘܚܪܢܐ ܟܦܠܚ

ܡܘܕܝܠ (model) ܝܠܗ "ܠܝܬ ܐܣܘܪܐ". ܐܢ ܠܝܬ ܐܣܘܪܐ، ܣܓܝܐܘܬܐ ܡܣܟܝܬܐ (expected frequency) ܓܘ ܟܠ ܩܠܝܬܐ (cell) ܟܐܬܝܐ ܒܣ ܡܢ ܣܦܪ̈ܐ ܕܠܘܚܐ: E = (ܓܘܡܪܐ ܕܣܕܪܐ × ܓܘܡܪܐ ܕܥܡܘܕܐ) / N (Field, 2024, Equation 19.3). ܒܘܚܪܢܐ ܟܟܢܫ ܦܘܪܫܢܐ ܒܝܢܝ ܚܙܝܐ ܘܡܣܟܝܐ ܓܘ ܟܠ ܩܠ̈ܝܬܐ، ܡܬܩܢܐ ܠܦܘܬ ܡܣܟܝܐ – χ² = Σ (O − E)²/E (Equation 19.2; Gravetter & Wallnau, 2017, Section 17.3) – ܘܣܛܐܛܝܣܛܝܩ ܐܝܬ ܠܗ ܒܩܘܪܒܐ ܦܘܠܓܐ (distribution) ܕܟܝ ܡܪܒܥܐ ܥܡ df = (r − 1)(c − 1) ܕܪ̈ܓܐ ܕܚܐܪܘܬܐ (degrees of freedom): ܡܢܝܢܐ ܕܩܠ̈ܝܬܐ ܕܡܨܚ "ܕܓܒܚ ܒܚܐܪܘܬܐ" ܒܬܪ ܕܓܘܡܪ̈ܐ ܕܣܕܪ̈ܐ ܘܥܡܘ̈ܕܐ ܝܗܝܒ̈ܐ ܝܢܐ (Gravetter & Wallnau, Equation 17.5). ܡܬܠܐ ܕ-Field (ܠܘܚܐ 19.1): 200 ܫܘܢܪ̈ܐ ܝܠܝܦ̈ܐ ܝܢܐ ܕܪܩܕܝ ܒܚܠܦ ܡܐܟܘܠܬܐ ܝܢ ܚܘܒܐ؛ 28 ܡܢ 38 ܕܩܒܝܠܗܘܢ ܡܐܟܘܠܬܐ ܪܩܕܠܗܘܢ، ܩܘܒܠ 48 ܡܢ 162 ܕܩܒܝܠܗܘܢ ܚܘܒܐ – χ²(1) = 25.36, p < .001. ܡܨܚ ܕܡܕܒܩܚ ܐܗܐ ܠܘܚܐ ܓܘ ܦܐܬܐ ܓܘ ܨܘܪܬܐ ܕ"ܠܘܚܐ ܕܣܓܝܐܘ̈ܬܐ ܡܛܘܝܒܐ" ܘܫܩܠܚ ܟܠ ܡܢܝ̈ܢܐ ܕܐܝܬ ܓܘ ܨܚܚܐ.

ܐܪܒܥܐ ܣܕܪ̈ܐ ܓܘ ܠܘܚܐ ܕܒܘܚܪ̈ܢܐ – ܘܡܐ ܟܡܬܢܚ

ܟܝ ܡܪܒܥܐ ܕ-Pearson ܝܠܗ ܒܘܚܪܢܐ؛ ܣܕܪ̈ܐ ܐܚܪ̈ܢܐ ܟܦܢܝ ܠܫܘܐܠܐ ܡܘܕܝ ܟܗܘܐ ܐܝܡܢ ܕܕܘܡܝܐ (sample) ܙܥܘܪܐ ܝܠܗ. ܒܘܚܪܢܐ ܚܬܝܬܐ ܕ-Fisher (Field, Section 19.3.3) ܠܐ ܝܠܗ ܒܘܚܪܢܐ ܐܚܪܢܐ ܐܠܐ ܚܘܫܒܢܐ ܚܬܝܬܐ ܕܡܣܬܒܪܢܘܬܐ (probability) ܒܕܘܟܬܐ ܕܩܘܪܒܐ ܠܦܘܠܓܐ ܕܟܝ ܡܪܒܥܐ – ܩܘܪܒܐ ܛܒܐ ܝܠܗ ܐܝܡܢ ܕܣܓܝܐܘ̈ܬܐ ܡܣܟ̈ܝܬܐ (expected frequencies) ܪ̈ܒܐ ܝܢܐ ܡܢ 5، ܘܟܡܬܬܙܝܥ ܐܝܡܢ ܕܙܥܘܪ̈ܐ ܝܢܐ؛ ܡܛܠ ܗܕܐ Fisher ܥܒܝܕܐ ܝܠܗ ܩܐ ܠܘܚܐ 2×2 ܥܡ ܕܘܡܝܐ ܙܥܘܪܐ، ܘ-SPSS ܟܛܒܥ ܠܗ ܒܠܚܘܕܗ ܩܐ ܟܠ ܠܘܚܐ 2×2. ܦܘܚܡܐ ܕܡܬܚܙܝܢܘܬܐ (likelihood ratio؛ G²; Section 19.3.4) ܡܣܡܟܐ ܝܠܗ ܥܠ ܡܬܚܙܝܢܘܬܐ ܥܠܝܬܐ (maximum likelihood)، ܐܝܬ ܠܗ ܦܘܠܓܐ ܐܝܟ Pearson، ܘܓܘ ܕܘܡܝܐ ܪܒܐ ܩܪܝܒ ܚܕ ܝܠܗ ܥܡܗ؛ Field ܟܓܒܐ ܠܗ ܓܘ ܕܘ̈ܡܝܐ ܙܥܘܪ̈ܐ. ܬܘܪܨܐ ܕܡܬܡܫܚܢܘܬܐ ܕ-Yates (continuity correction؛ ܦܣܩܐ 19.3.5) ܟܡܒܨܪ 0.5 ܡܢ ܟܠ ܣܛܝܘܬܐ ܫܪܝܪܬܐ ܩܕܡ ܡܪܒܥܐ، ܡܛܠ ܕܓܘ ܠܘܚܐ 2×2 Pearson ܟܡܨܠܐ ܠ-p ܙܥܘܪܐ ܝܬܝܪ ܡܢ ܕܣܢܝܩ – ܘܗܪܟܐ ܬܪܝܢ ܟܬ̈ܒܐ ܦܪ̈ܝܫܐ ܝܢܐ: Field ܟܟܬܒ ܕܐܝܬ "ܣܗܕ̈ܘܬܐ ܠܐ ܩܠܝܠ̈ܐ" ܕܬܘܪܨܐ ܟܬܪܨ ܝܬܝܪ ܡܢ ܕܣܢܝܩ ܘܟܥܒܕ ܛܝ̈ܡܐ ܕ-χ² ܙܥܘܪ̈ܐ ܝܬܝܪ (Howell, 2012, as cited in Field)، ܘܟܟܢܫ "ܛܒܐ ܝܠܗ ܕܝܕܥܚ ܠܗ، ܘܒܠܟܝ ܛܒܐ ܝܬܝܪ ܝܠܗ ܕܠܐ ܚܙܚ ܠܗ"؛ Pallant (2020، ܨܚܚܐ 16) ܟܦܩܕܐ ܕܡܬܢܚ ܓܘ ܠܘܚܐ 2×2 ܣܕܪܐ ܕ-Continuity Correction، ܘܟܡܚܘܝܐ ܐܗܐ ܓܘ ܡܐܡܪܐ ܕܬܘܢܝܐ (report sentence) ܕܝܠܗ̇. ܦܐܬܐ ܟܡܚܘܐ ܬܪܘܬܝܗܝ، ܘܟܪܫܡ ܩܐ ܬܘܢܝܐ ܠܦܘܬ ܢܡܘܣܐ ܕܣܐܝܛ (site rule): Pearson؛ ܘܓܘ ܠܘܚܐ 2×2 ܕܟܬܒܪ ܫܪܛܐ ܕܣܓܝܐܘ̈ܬܐ ܡܣܟ̈ܝܬܐ – Fisher. ܐܢܝ ܕܡܕܒܪܢܐ (supervisor) ܕܝܠܗܘܢ ܟܒܥܐ Yates – ܡܢܝ̈ܢܐ ܓܘ ܠܘܚܐ 3، ܘܬܘܢܝܐ ܒܢܘܣܚܐ ܕ-Pallant (ܦܣܩܐ ܕܬܘܢܝܐ ܕܠܬܚܬ).

ܚܝܠܐ ܕܐܣܘܪܐ: φ، V ܕ-Cramér ܘܦܘܚܡܐ ܕܣܟܘ̈ܝܐ

ܪܫܝܡܘܬܐ (significance) ܟܐܡܪܐ ܕܐܝܬ ܐܣܘܪܐ؛ ܠܐ ܟܐܡܪܐ ܟܡܐ ܚܝܠܬܢܐ ܝܠܗ، ܘܓܘ ܕܘܡܝܐ (sample) ܪܒܐ ܐܦ ܦܘܪܫܢܐ ܙܥܘܪܐ ܒܡܢܘ̈ܬܐ ܒܡܐܐ ܟܦܠܛ ܪܫܝܡܐ (Field, 2024, Section 19.5.3). ܬܠܬܐ ܡܚܘ̈ܝܢܐ ܟܬܪܨܝ χ² ܩܐ ܪܒܘܬܐ ܕܕܘܡܝܐ ܘܩܐ ܡܫܘܚ̈ܬܐ ܕܠܘܚܐ ܩܐ ܕܫܩܠܚ ܡܢܝܢܐ ܒܝܢܝ 0 ܘ-1 (Field, Section 19.3.6): φ – √(χ²/N)، ܚܬܝܬܐ ܩܐ ܠܘܚܐ 2×2 ܘܓܘܗ ܫܘܝܐ ܝܠܗ ܠܐܣܘܪܐ ܕܚܕ̈ܕܐ ܕ-Pearson ܒܝܢܝ ܬܪܝܢ ܡܫܬܚܠܦ̈ܢܐ ܕܬܪܝܢ ܛܝ̈ܡܐ (dichotomous) (ܘܡܛܠ ܗܕܐ ܐܝܬ ܠܗ ܪܘܫܡܐ؛ Gravetter & Wallnau, 2017، ܫܘܝܘܬܐ 17.8)؛ ܡܢܝܢܐ ܡܫܘܬܦܐ ܕܡܓܥܬܐ (contingency coefficient) ܕ-Pearson، ܕܩܠܝܠ ܓܗ̈ܐ ܟܡܛܐ ܠ-1؛ ܘ-V ܕ-Cramér – √(χ²/(N·df*)) ܐܝܡܢ ܕ-df* = min(r − 1, c − 1) (Gravetter & Wallnau, Equation 17.9) – ܕܡܨܐ ܕܡܛܐ ܠ-1 ܐܦ ܓܘ ܠܘܚܐ ܪܒܐ، ܘܡܛܠ ܗܕܐ "ܡܘܬܪܢܐ ܒܝܬܝܪ" ܝܠܗ (Field). ܓܘ ܠܘܚܐ 2×2 φ ܘ-V ܚܕ ܝܢܐ. ܬܚܘ̈ܡܐ: ܩܐ ܦܘܫܩܐ ܕ-φ ܟܡܦܠܚܚ ܒܬܚܘ̈ܡܐ ܕܐܣܘܪܐ ܕܚܕ̈ܕܐ (correlation) – .10 ܙܥܘܪܐ، .30 ܡܨܥܝܐ، .50 ܪܒܐ (Cohen، 1988، ܐܝܟ ܕܡܬܝܬܐ ܝܠܗ ܓܘ Pallant، 2020، ܘܓܘ Gravetter & Wallnau، 2017)؛ ܩܐ V ܓܘ ܠܘܚܐ ܪܒܐ ܝܬܝܪ ܬܚܘ̈ܡܐ ܢܡܘ̈ܟܐ ܝܬܝܪ ܝܢܐ، ܠܦܘܬ df* (Gravetter & Wallnau, Table 17.10): ܩܐ df* = 2 – .07 / .21 / .35؛ ܩܐ df* = 3 – .06 / .17 / .29. ܦܐܬܐ ܟܡܬܪܓܡ ܠܦܘܬ ܐܗܐ ܠܘܚܐ. ܐܣܘܪܐ ܒܝܢܝ ܬܪܘܬܝܗܝ: Cohen ܟܣܝܡ w ܐܝܟ V·√df* ܥܡ ܬܚܘ̈ܡܐ .10 / .30 / .50 – ܗܢܝ ܬܚܘ̈ܡܐ ܚܬܝܬܐܝܬ، ܒܣܒܠܬܐ (scale) ܐܚܪܬܐ.

ܦܘܚܡܐ ܕܣܟܘ̈ܝܐ (odds ratio؛ OR) ܝܠܗ، ܠܦܘܬ ܪܥܝܢܐ ܕ-Field (ܦܣܩܐ 19.8.4)، ܡܚܘܝܢܐ ܕܡܥܒܕܢܘܬܐ (effect) ܕܡܬܚܙܐ ܣܓܝ ܘܡܘܬܪܢܐ ܝܬܝܪ ܩܐ ܠܘܚܐ 2×2 – "ܚܠܦܐ ܕܓܢ̈ܣܐ ܕܦܘܚܡܐ ܡܟܘܢܐ". ܣܟܘ̈ܝܐ (odds) ܐܢܝ ܝܢܐ ܡܢܝܢܐ ܕܓܗ̈ܐ ܕܐܝܢ ܦܠܝܓܐ ܥܠ ܡܢܝܢܐ ܕܓܗ̈ܐ ܕܠܐ: ܣܟܘ̈ܝܐ ܕܪܩܕܐ ܒܬܪ ܡܐܟܘܠܬܐ 28/10 = 2.8، ܒܬܪ ܚܘܒܐ 48/114 = .42، ܘܦܘܚܡܐ ܒܝܢܬܗܘܢ 6.65 – "ܐܢ ܫܘܢܪܐ ܝܠܝܦܐ ܝܠܗ ܒܡܐܟܘܠܬܐ، ܣܟܘ̈ܝܐ ܕܪܩܕ ܪ̈ܡܐ ܝܢܐ 6.65 ܐܥܦ̈ܐ ܡܢ ܐܢ ܝܠܝܦܐ ܗܘܐ ܒܚܘܒܐ" (ܫܘܝ̈ܘܬܐ 19.40-19.42). ܦܐܬܐ ܟܡܘܣܦ ܬܚܘܡܐ ܕܬܘܟܠܢܐ (confidence interval) ܕ-95% ܥܠ ܣܒܠܬܐ ܕ-log (ܐܝܟ Risk Estimate ܓܘ SPSS): ܬܚܘܡܐ ܕܠܐ ܐܝܬ ܓܘܗ 1 – ܐܣܘܪܐ ܪܫܝܡܐ ܣܛܐܛܝܣܛܝܩܐܝܬ (statistically significant) ܝܠܗ. ܚܙܝܡܘܢ ܠܓܢܒܐ: ܣܟܘ̈ܝܐ ܩܐ ܓܢܣܐ ܩܕܡܝܐ ܕܥܡܘ̈ܕܐ، ܓܘ ܣܕܪܐ ܩܕܡܝܐ ܩܘܒܠ ܬܪܝܢܐ – ܛܟܣܐ ܕܓܢ̈ܣܐ ܓܘ ܠܘܚܐ ܟܦܣܩ ܐܢ ܒܕ ܫܩܠܝܬܘܢ 6.65 ܝܢ 1/6.65 = .15، ܘܬܪܘܬܝܗܝ ܚܕܐ ܡܫܟܚܢܘܬܐ ܝܢܐ.

ܩܪܝܢܐ ܕܡܦܩܢܐ (How to read the output)

ܠܘܚܐ 1 – ܡܢܘ̈ܬܐ ܒܡܐܐ. Field (2024، ܦܣܩܐ 19.8) ܟܩܪܐ ܠܘܚܐ ܕܨܠܝܒܘܬܐ (crosstabulation) ܕܫܘܢܪ̈ܐ ܒܓܘ ܡܢܘ̈ܬܐ ܒܡܐܐ ܓܘ ܟܠ ܙܢܐ ܕܝܘܠܦܢܐ: ܡܢ ܝܠܝܦ̈ܐ ܒܡܐܟܘܠܬܐ 73.7% ܪܩܕܠܗܘܢ، ܡܢ ܝܠܝܦ̈ܐ ܒܚܘܒܐ 29.6% – "ܐܝܡܢ ܕܡܐܟܘܠܬܐ ܗܘܐ ܦܘܪܥܢܐ ܣܓܝܐܐ ܡܢ ܫܘܢܪ̈ܐ ܪܩܕܠܗܘܢ، ܐܝܡܢ ܕܚܘܒܐ ܗܘܐ ܦܘܪܥܢܐ ܣܓܝܐܐ ܡܢܝܗܝ ܠܐ ܨܒܝܠܗܘܢ". Pallant (2020، ܨܚܚܐ 16) ܟܥܒܕܐ ܐܗܐ ܥܡ "% within sex": 17.9% ܡܢ ܓܒܪ̈ܐ ܬܢܢ̈ܐ ܝܢܐ ܩܘܒܠ 20.6% ܡܢ ܢܫ̈ܐ، ܘܟܡܥܗܕܐ ܕܒܚܪܚ ܕܬܪܝܢ ܡܢܘ̈ܬܐ ܒܡܐܐ ܓܘ ܟܠ ܣܕܪܐ ܟܡܛܝ ܠ-100. ܐܗܐ ܝܠܗ ܩܪܝܢܐ ܪܝܫܝܐ ܕܦܐܪܐ (outcome)؛ ܒܘܚܪܢܐ ܒܣ ܟܐܡܪ ܐܢ ܦܘܪܫܢܐ ܒܝܢܝ ܣܕܪ̈ܐ ܪܒܐ ܝܠܗ ܡܢ ܡܐ ܕܓܕܫܐ ܡܨܐ ܕܡܦܫܩ.

ܠܘܚܐ 2 – ܡܣܟܝܐ ܘܫܪ̈ܟܐ. ܩܕܡ ܟܒܚܪܚ ܣܓܝܐܘܬܐ ܡܣܟܝܬܐ ܙܥܘܪܬܐ (ܫܪܛܐ – ܓܘ ܦܣܩܐ ܕܫܪ̈ܛܐ). ܒܬܪ ܗܕܐ، ܓܘ ܠܘܚܐ ܪܒܐ ܡܢ 2×2، ܫܪ̈ܟܐ (residuals) ܟܐܡܪܝ ܐܝܢܝ ܩܠ̈ܝܬܐ (cells) ܟܡܙܝܥܝ ܠܐܣܘܪܐ: ܫܪܟܐ ܡܬܩܢܐ (O − E)/√E ܡܢܝܢܐ z ܝܠܗ (Field, Section 19.8.1) – ܠܒܪ ܡܢ ±1.96 ܩܠܝܬܐ ܟܦܪܫܐ ܡܢ ܡܣܟܝܐ ܪܫܝܡܐܝܬ ܒ-.05، ±2.58 ܒ-.01، ±3.29 ܒ-.001، ܘܪܘܫܡܐ ܟܐܡܪ ܐܢ ܝܬܝܪ ܝܢ ܒܨܝܪ ܡܢ ܡܣܟܝܐ ܝܠܗ؛ ܓܘ ܩܛ̈ܘܬܐ ܬܪܬܝܢ ܩܠ̈ܝܬܐ ܕܐܟܘܠܬܐ ܪܫܝܡ̈ܐ ܝܢܐ (3.6 ܘ-−2.8) ܘܬܪܬܝܢ ܩܠ̈ܝܬܐ ܕܚܘܒܐ ܠܐ (−1.7 ܘ-1.4): "ܐܣܘܪܐ ܒܝܢܝ ܙܢܐ ܕܦܘܪܥܢܐ ܘܪܩܕܐ ܡܙܝܥܐ ܝܠܗ ܒܪܫܐ ܒܐܝܕܐ ܕܐܟܘܠܬܐ". Pallant ܟܡܦܠܚܐ ܒܫܪܟܐ ܡܬܩܢܐ-ܡܬܘܪܨܐ (Adjusted Residual)، ܕܟܬܪܨ ܐܦ ܠܪܒܘܬܐ ܕܣܕܪܐ ܘܕܥܡܘܕܐ: ܠܥܠ ܡܢ 2 – ܝܬܝܪ ܡܢ ܡܣܟܝܐ، ܠܬܚܬ ܡܢ −2 – ܒܨܝܪ، "ܐܝܟ ܒܘܚܪܢܐ ܕܒܬܪ ܗܕܐ (post hoc)". ܐܗܐ ܦܐܬܐ ܟܡܚܘܐ ܠܬܪܘܝܗܝ، ܘܟܪܫܡ ܒܨܒܥܐ ܙܪܕܐ ܩܠ̈ܝܬܐ ܕܡܬܘܪܨܐ ܕܝܗܘܢ ܠܒܪ ܡܢ ±1.96 ܝܠܗ.

ܠܘܚܐ 3 – ܒܘܚܪ̈ܢܐ. ܟܩܪܚ Pearson (ܝܢ ܣܕܪܐ ܪܫܝܡܐ)؛ ܓܘ ܠܘܚܐ 2×2 ܚܙܝܡܘܢ (Note) ܕܛܝܡܐ ܚܬܝܬܐ ܕ-Fisher ܛܒܝܥܐ ܝܠܗ ܓܘ ܥܡܘܕܐ ܕ-p ܕܠܐ ܛܝܡܐ ܕ-χ². ܠܘܚܐ 4 – ܚܝܠܐ ܕܐܣܘܪܐ. V (ܝܢ φ) ܥܡ ܡܠܬܐ ܠܦܘܬ ܬܚܘ̈ܡܐ، ܘܓܘ ܠܘܚܐ 2×2 ܦܘܚܡܐ ܕܣܟܘ̈ܝܐ (odds ratio) ܥܡ ܬܚܘܡܐ ܕܬܘܟܠܢܐ (confidence interval). ܨܘܪܬܐ ܟܡܚܘܝܐ ܠܘܚܐ 1 ܩܕܡ ܥܝ̈ܢܐ: ܐܢ ܥܡܘ̈ܕܐ ܓܘ ܟܠ ܓܘܕܐ ܒܚܕ ܦܘܚܡܐ ܝܢܐ – ܠܝܬ ܐܣܘܪܐ.

ܫܪ̈ܛܐ ܘܙܘܗܪ̈ܐ (Assumptions and warnings)

ܠܐ ܬܠܝܘܬܐ ܕܚܙ̈ܝܬܐ (observations). ܒܘܚܪܢܐ ܠܐ ܟܡܣܡܟ ܥܠ ܫܪ̈ܛܐ (assumptions) ܕܡܘܕܝܠ ܣܪܛܢܝܐ (ܢܘܪܡܠܝܘܬܐ ܘܕܐܟܘܬܗ – ܡܫܬܚܠܦܢܐ ܕܓܢ̈ܣܐ (categorical variable) ܠܐ ܡܨܐ ܕܗܘܐ ܦܠܝܓܐ ܢܘܪܡܠܐܝܬ)، ܐܝܢܐ ܐܝܬ ܠܗ ܬܪܝܢ ܕܝܠܗ (Field, 2024, Section 19.5). ܩܕܡܝܐ: ܟܠ ܡܫܬܘܬܦܢܐ (participant)، ܦܣܘܩܐ ܝܢ ܡܕܡ ܟܝܗܒ ܠܚܕܐ ܩܠܝܬܐ ܒܣ (Section 19.5.1; Gravetter & Wallnau, 2017, Section 17.4). ܡܛܠ ܗܕܐ ܠܐ ܟܡܨܝܚ ܕܡܪܗܛܚ ܟܝ ܡܪܒܥܐ (chi-square) ܥܠ ܡܫܘ̈ܚܬܐ ܡܬܢ̈ܝܬܐ (repeated measures) – ܗܢ ܐܢܫ̈ܐ ܩܕܡ ܘܒܬܪ – ܘܠܐ ܥܠ ܡܫܬܘܬܦܢܐ ܕܪܫܝܡܐ ܝܠܗ ܓܘ ܟܡܐ ܓܢ̈ܣܐ. ܩܐ ܡܫܘ̈ܚܬܐ ܡܬܢ̈ܝܬܐ ܓܘ ܬܪܝܢ ܡܫܬܚܠܦ̈ܢܐ ܕܬܪܝܢ ܛܝ̈ܡܐ – ܒܘܚܪܢܐ ܕ-McNemar (Pallant, 2020, Chapter 16)؛ ܩܐ ܬܘܩ̈ܢܐ ܕܒܘܨܝܐ ܡܪܟܒ̈ܐ ܝܬܝܪ Field ܟܡܫܕܪ ܠܡܘܕܝ̈ܠܐ ܡܚܠܛ̈ܐ ܓܢܣ̈ܝܐ (generalized mixed models).

ܣܓܝܐܘ̈ܬܐ ܡܣܟ̈ܝܬܐ (expected frequencies). ܓܘ ܠܘܚܐ 2×2 ܚܕܐ ܩܠܝܬܐ ܠܐ ܘܠܐ ܕܗܘܝܐ ܠܬܚܬ ܡܢ 5؛ ܓܘ ܠܘܚܐ ܪܒܐ ܝܬܝܪ – ܟܠ ܩܠ̈ܝܬܐ ܠܥܠ ܡܢ 1 ܘܠܐ ܝܬܝܪ ܡܢ 20% ܠܬܚܬ ܡܢ 5 (Field, Section 19.5.2). Pallant ܟܡܘܣܦܐ ܕܐܝܬ ܟܬܘ̈ܒܐ ܕܟܡܦܝܣܝ ܓܘ ܠܘܚܐ 2×2 ܥܠ 10 ܠܟܡܝܘܬܐ. ܥܒܪܬܐ ܥܠ ܫܪܛܐ "ܟܡܚܠܫܐ ܠܚܝܠܐ ܕܒܘܚܪܢܐ ܒܐܘܪܚܐ ܕܪܡܛܝܬ – ܗܕܟܐ ܕܒܠܟܝ ܠܐ ܫܘܝܐ ܠܥܡܠܐ" (Field). ܣܡ̈ܡܢܐ: ܓܘ ܠܘܚܐ 2×2 – ܒܘܚܪܢܐ ܚܬܝܬܐ ܕ-Fisher؛ ܓܘ ܠܘܚܐ ܪܒܐ – ܚܘܝܕܐ ܕܓܢ̈ܣܐ (categories؛ ܒܣ ܐܡܬܝ ܕܐܝܬ ܠܗ ܣܘܟܠܐ ܒܓܘ ܡܐ ܕܐܝܬ: ܒܗܪܐ، ܩܝܛܐ ܘ"ܬܫܪܝܢ/ܣܬܘܐ")، ܝܢ ܝܗܝ̈ܒܬܐ ܝܬܝܪ. ܡܘܣܦܐ ܕܡܢܝܢܐ ܩܝܡܐ ܠܟܠ ܩܠ̈ܝܬܐ ܠܐ ܟܫܪܐ ܡܢܕܝ. ܚܙܝܡܘܢ: ܫܪܛܐ ܥܠ ܣܓܝܐܘܬܐ ܡܣܟܝܬܐ ܝܠܗ، ܠܐ ܚܙܝܬܐ – ܩܠܝܬܐ ܚܙܝܬܐ ܣܦܝܩܬܐ ܠܐ ܝܠܗ ܥܘܩܬܐ ܒܓܢܗ.

ܕܘܡܝܐ (sample) ܪܒܐ. "ܦܘܪ̈ܫܢܐ ܙܥܘܪ̈ܐ ܒܚܘܫܒܢܐ ܓܘ ܣܓܝܐܘ̈ܬܐ ܕܩܠ̈ܝܬܐ ܡܨܝ ܕܝܗܒܝ ܐܣܘܪܐ ܪܫܝܡܐ ܐܢ ܕܘܡܝܐ ܪܒܐ ܝܠܗ ܒܣܦܩ" (Field, Section 19.5.3) – ܘܡܛܠ ܗܕܐ ܟܩܪܚ ܡܢܘ̈ܬܐ ܒܡܐܐ ܘܡܚܘܝܢܐ ܕܡܥܒܕܢܘܬܐ، ܠܐ p ܒܣ (ܨܘܪܬܐ 1).

ܡܘܕܝ ܠܐ ܟܚܫܒܐ ܐܗܐ ܦܐܬܐ. ܡܢܝܢܐ ܡܫܘܬܦܐ ܕܡܓܥܬܐ (contingency coefficient) ܘ-λ ܕ-Goodman ܘ-Kruskal (Field، ܡܥܝܪܢܘܬܐ 19.1)؛ ܒܘܚܪܢܐ z ܠܦܘܚܡܐ ܕܡܢܘ̈ܬܐ ܕܥܡܘ̈ܕܐ ܥܡ ܬܘܪܨܐ ܕ-Bonferroni (Compare column proportions – Field، ܦܣܩܐ 19.8: ܐܬܘ̈ܬܐ ܓܢܒ ܣܓܝܐܘ̈ܬܐ ܓܘ ܡܦܩܢܐ (output) ܕ-SPSS)؛ Bayes factor ܩܐ ܠܘܚܐ (ܦܣܩܐ 19.8.3)؛ ܦܘܫܩܐ ܠܘܓ-ܣܪܛܢܝܐ (log-linear) ܩܐ ܬܠܬܐ ܡܫܬܚܠܦ̈ܢܐ ܘܠܥܠ (ܦܣ̈ܩܐ 19.4, 19.9-19.11)؛ ܒܘܚܪܢܐ ܕ-McNemar ܘܒܘܚܪܢܐ ܕܟܝ ܡܪܒܥܐ ܕܦܐܝܘܬܐ (goodness of fit؛ Gravetter & Wallnau, Sections 17.1-17.2). ܬܚܘܡܐ ܕ-Field ܩܐ ܫܪ̈ܟܐ ܡܬܩ̈ܢܐ (±1.96) ܘܬܚܘܡܐ ܕ-Pallant (±2) – ܚܕ ܪܥܝܢܐ ܝܠܗ ܒܥܓܘܠܐ ܦܪܝܫܐ؛ ܐܗܐ ܦܐܬܐ ܟܡܦܠܚܐ ܒ-1.96.

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

Analyze › Descriptive Statistics › Crosstabs… – ܚܕ ܡܫܬܚܠܦܢܐ (variable) ܠ-Row(s)، ܐܚܪܢܐ ܠ-Column(s) (Pallant, 2020, Chapter 16; Field, 2024, Section 19.7.3). ܓܘ button Statistics…: Chi-square، Phi and Cramer's V، ܘܩܐ ܠܘܚܐ 2×2 ܐܦ Risk (ܦܘܚܡܐ ܕܣܟܘ̈ܝܐ). ܓܘ button Cells…: Observed، Expected (ܩܐ ܒܘܚܪܢܐ ܕܫܪܛܐ)، Row ܒܡܢܘ̈ܬܐ ܒܡܐܐ، ܘܓܘ ܫܪ̈ܟܐ Standardized (Field) ܘ/ܝܢ Adjusted standardized (Pallant). ܒܘܚܪܢܐ ܕ-Fisher ܛܒܝܥܐ ܝܠܗ ܡܢ ܓܢܗ ܩܐ ܠܘܚܐ 2×2؛ ܩܐ ܠܘܚܐ ܪܒܐ ܝܬܝܪ – button Exact…. ܣܝܢܬܐܟܣ (syntax) ܕ-Pallant، ܥܡ ܩܠ̈ܝܬܐ ܘܡܚܘ̈ܝܢܐ ܕܐܗܐ ܦܐܬܐ ܟܡܚܘܐ:

CROSSTABS
  /TABLES=training BY dance
  /FORMAT=AVALUE TABLES
  /STATISTICS=CHISQ PHI RISK
  /CELLS=COUNT ROW EXPECTED SRESID ASRESID
  /COUNT ROUND CELL.

ܠܘܚܐ ܕܣܓܝܐܘ̈ܬܐ ܡܛܝܒܐ (Field, Section 19.7.2): ܟܟܬܒܚ ܣܕܪܐ ܩܐ ܟܠ ܩܠܝܬܐ – ܪܡܙܐ ܕܣܕܪܐ، ܪܡܙܐ ܕܥܡܘܕܐ ܘܣܓܝܐܘܬܐ – ܘܟܬܩܠܚ: Data › Weight Cases… › Weight cases by ܡܫܬܚܠܦܢܐ ܕܣܓܝܐܘܬܐ (WEIGHT BY freq.). ܐܗܐ ܝܠܗ ܡܐ ܕܣܝܢܬܐܟܣ ܕܦܐܬܐ ܟܥܒܕ ܐܡܬܝ ܕܝܗܝ̈ܒܬܐ ܠܘܚܐ ܡܛܝܒܐ ܝܢܐ، ܥܡ ܪܘ̈ܫܡܐ (labels) ܕܛܝ̈ܡܐ. ܩܪܝܢܐ ܕܡܦܩܢܐ: Crosstabulation – Count ܘ-% within = ܠܘܚܐ 1، Expected Count، Std. Residual ܘ-Adjusted Residual = ܠܘܚܐ 2؛ Chi-Square Tests – Pearson Chi-Square، Continuity Correction (Yates)، Likelihood Ratio، Fisher's Exact Test ܓܘ Exact Sig. (2-sided) ܘ-(1-sided) = ܠܘܚܐ 3، ܘܡܥܝܪܢܘܬܐ ܕܬܚܬ "a" – ܟܡܐ ܩܠ̈ܝܬܐ ܠܬܚܬ ܡܢ 5 ܘܡܣܟܝܐ ܙܥܘܪܐ؛ Symmetric Measures – Phi، Cramer's V = ܠܘܚܐ 4؛ Risk Estimate – Odds Ratio ܥܡ ܬܚܘܡܐ ܕܬܘܟܠܢܐ = ܠܘܚܐ 4. Linear-by-Linear Association ܕܓܘ ܡܦܩܢܐ – ܒܘܚܪܢܐ ܩܐ ܡܓܡܐ ܣܪܛܢܝܬܐ ܒܝܢܝ ܬܪܝܢ ܡܫܬܚܠܦ̈ܢܐ ܕܛܟܣܐ (ordinal)، ܠܐ ܝܠܗ ܓܘ ܐܗܐ ܦܐܬܐ.

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

ܟܠ ܡܕܡ ܒ-R ܐܣܝܐ: table ܩܐ ܠܘܚܐ، chisq.test ܥܡ correct = FALSE ܩܐ Pearson (ܓܘܒܝܐ ܡܩܕܡܐ (default) ܕ-R ܬܘܪܨܐ ܕ-Yates ܝܠܗ ܓܘ ܠܘܚܐ 2×2 – ܗܦܘܟܐ ܕ-SPSS)، $expected، $residuals (ܡܬܩ̈ܢܐ) ܘ-$stdres (ܡܬܘܪ̈ܨܐ)، fisher.test. ܣܩܪܝܦܬ (script) ܪܗܛܐ ܝܠܗ ܐܝܟ ܕܐܝܬܘܗܝ ܥܠ ܦܐܝܠ ܕܡܬܠܐ (sample data file) ܘܝܗܒܠܗ ܛܝ̈ܡܐ ܕܠܘܚܐ (ܓܘ ܡܥܝܪ̈ܢܘܬܐ). ܢܡܘܣܐ ܕܣܐܝܛ (site rule) ܩܐ ܣܘܪܝܬ ܒ-R: ܦܐܝܠ ܢܛܝܪܐ ܝܠܗ ܒ-UTF-8، ܟܠ ܣܕܪܐ ܕܡܥܝܪܢܘܬܐ ܟܫܪܐ ܒܡܠܬܐ ܕܣܘܪܝܬ، ܘܫܡ̈ܗܐ ܥܒܪ̈ܝܐ ܣܢܝܩ̈ܐ ܝܢܐ ܠܐܬܪܐ (locale) UTF-8 (ܓܘ Windows: R 4.2 ܘܠܥܠ، ܝܢ Sys.setlocale('LC_ALL', 'Hebrew')).

# ܟܝ ܡܪܒܥܐ ܠܠܐ ܬܠܝܘܬܐ – 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_chi_example_heb.xlsx", sheet = "נתונים")

# ܠܘܚܐ ܕܨܠܝܒܘܬܐ: ܣܕܪ̈ܐ = ܥܬܝܩܘܬܐ، ܥܡܘ̈ܕܐ = ܫܘܬܦܘܬܐ (ܡܫܬܘܬܦ̈ܢܐ ܥܡ ܛܝܡܐ ܚܣܝܪܐ ܓܘ ܚܕ ܡܢܝܗܘܢ ܫܩܝܠ̈ܐ ܝܢܐ)
tab <- table(d$"ותק_בקהילה", d$"השתתפות")
tab
prop.table(tab, 1)                       # ܡܢܘ̈ܬܐ ܒܡܐܐ ܡܢ ܣܕܪܐ

# ܒܘܚܪܢܐ ܕܟܝ ܡܪܒܥܐ ܕ-Pearson ܕܠܐ ܬܘܪܨܐ ܕܡܬܡܫܚܢܘܬܐ (ܐܝܟ Pearson Chi-Square ܓܘ SPSS)
ct <- chisq.test(tab, correct = FALSE)
ct                                       # χ² = 17.79, df = 2, p < .001
ct$expected                              # ܣܓܝܐܘ̈ܬܐ ܡܣܟ̈ܝܬܐ – ܒܘܚܪܢܐ ܕܫܪܛܐ (ܚܕܐ ܩܠܝܬܐ ܠܐ ܠܬܚܬ ܡܢ 5)
ct$residuals                             # ܫܪ̈ܟܐ ܡܬܩ̈ܢܐ (O − E)/√E
ct$stdres                                # ܫܪ̈ܟܐ ܡܬܩ̈ܢܐ-ܡܬܘܪ̈ܨܐ (Adjusted Residual ܓܘ SPSS)

# ܡܚܘܝܢܐ V ܕ-Cramér: √(χ² / (N · min(r − 1, c − 1)))
sqrt(ct$statistic / (sum(tab) * (min(dim(tab)) - 1)))   # V = .242

# ܠܘܚܐ 2×2: ܓܢܣܐ × ܫܘܬܦܘܬܐ – ܬܘܪܨܐ ܕ-Yates، ܒܘܚܪܢܐ ܚܬܝܬܐ ܕ-Fisher ܘܦܘܚܡܐ ܕܣܟܘ̈ܝܐ
tab2 <- table(d$"מגדר", d$"השתתפות")
chisq.test(tab2, correct = FALSE)$statistic     # ܛܝܡܐ ܕ-Pearson = .023
chisq.test(tab2, correct = TRUE)$statistic      # ܬܘܪܨܐ ܕ-Yates = .001
fisher.test(tab2)$p.value                       # ܒܘܚܪܢܐ ܕ-Fisher ܕܬܪܝܢ ܓܢ̈ܒܐ = .907
(tab2[1, 1] * tab2[2, 2]) / (tab2[1, 2] * tab2[2, 1])   # ܦܘܚܡܐ ܕܣܟܘ̈ܝܐ ܡܢ ܕܘܡܝܐ = .965 (fisher.test ܟܛܒܥ ܫܘܥܪܐ ܬܠܝܐ، ܦܪܝܫܐ ܩܠܝܠ)

ܬܘܢܝܐ ܕܡܫܟܚ̈ܢܘܬܐ (reporting the results)

ܟܡܬܢܚ ܠܡܢܝܢܐ ܣܛܐܛܝܣܛܝܩܝܐ ܥܡ ܕܪ̈ܓܐ ܕܚܐܪܘܬܐ (degrees of freedom) ܘ-N ܓܘ ܩܘܠܦ̈ܐ، ܠ-p ܘܠܡܚܘܝܢܐ ܕܡܥܒܕܢܘܬܐ؛ ܠܦܘܬ APA (2020، ܦܣܩܐ 6.36) φ ܘ-V – ܕܠܐ ܟܥܒܪܝ ܥܠ 1 – ܕܠܐ ܨܦܪܐ ܩܕܡܝܐ، ܘ-χ² ܒܓܢܗ ܒܬܪܬܝܢ ܡܢܝ̈ܢܐ. Field (2024، ܦܣܩܐ 19.8.5): "ܐܣܘܪܐ ܪܫܝܡܐ ܡܫܟܚܐ ܝܠܗ ܒܝܢܝ ܙܢܐ ܕܝܘܠܦܢܐ ܘܐܢ ܩܛ̈ܘܬܐ ܪܩܕܠܗܘܢ، χ²(1) = 25.36, p < .001. ܦܘܚܡܐ ܕܣܟܘ̈ܝܐ ܚܘܝܠܗ ܕܣܟܘ̈ܝܐ ܕܪܩܕܐ ܪܡ̈ܐ ܝܢܐ ܗܘܘ 6.65 ܓܗ̈ܐ ܐܢ ܩܛܘ ܝܠܦܐ ܝܠܗ ܗܘܐ ܒܐܟܘܠܬܐ" – ܘܗܘ ܟܡܦܝܣ ܕܡܘܣܦܚ ܐܦ ܠܘܚܐ ܕܨܠܝܒܘܬܐ (crosstabulation). Gravetter ܘ-Wallnau (2017، ܦܣܩܐ 17.4) ܟܡܘܣܦܝ N ܘ-φ: χ²(1, n = 200) = 6.381, p < .05, φ = 0.179، ܘܒܬܪܗ ܡܐܡܪܐ ܥܠ ܐܘܪܚܐ. Pallant (2020، ܨܚܚܐ 16)، ܥܡ Yates: "ܒܘܚܪܢܐ ܕܟܝ ܡܪܒܥܐ ܠܠܐ ܬܠܝܘܬܐ (ܥܡ ܬܘܪܨܐ ܕܡܬܡܫܚܢܘܬܐ ܕ-Yates) ܠܐ ܚܘܝܠܗ ܐܣܘܪܐ ܪܫܝܡܐ ܒܝܢܝ ܓܢܣܐ ܘܬܢܢܐ، χ²(1, n = 436) = .34, p = .56, phi = −.03". ܡܐܡܪ̈ܐ ܕܬܘܢܝܐ (report sentences) ܕܓܘ ܐܗܐ ܦܐܬܐ ܟܐܙܠܝ ܒܐܘܪܚܐ ܕ-Field ܥܡ N ܓܘ ܩܘܠܦ̈ܐ ܐܝܟ Gravetter ܘ-Wallnau؛ ܡܐܡܪܐ ܕܣܘܩܒܠܐ ("ܓܘ X 72% ܗܘܘ…") ܝܠܗ "ܐܘܪܚܐ" ܕܬܪܘܝܗܝ ܟܬܒ̈ܐ ܟܒܥܝ ܒܬܪ ܡܢܝ̈ܢܐ. ܐܡܬܝ ܕܬܢܝܬܘܢ Fisher – ܟܟܬܒܚ "ܒܘܚܪܢܐ ܚܬܝܬܐ ܕ-Fisher، p = …" ܕܠܐ χ².

ܛܥܝ̈ܘܬܐ ܕܡܬܚܙܝܢ ܣܓܝ (Common mistakes)

ܩܪܝܢܐ ܕܣܓܝܐܘ̈ܬܐ ܒܕܘܟܬܐ ܕܡܢܘ̈ܬܐ ܒܡܐܐ. 48 ܩܛ̈ܘܬܐ ܕܪܩܕܠܗܘܢ ܒܬܪ ܚܘܒܐ ܝܬܝܪ ܝܢܐ ܡܢ 28 ܒܬܪ ܐܟܘܠܬܐ – ܘܥܡ ܕܐܗܐ ܐܟܘܠܬܐ ܟܦܠܚܐ ܛܒ ܝܬܝܪ، ܡܛܠ ܕ-162 ܩܒܠܠܗܘܢ ܚܘܒܐ ܘܒܣ 38 ܐܟܘܠܬܐ. Field (ܦܣܩܐ 19.5.3): ܡܢܘ̈ܬܐ ܒܡܐܐ ܟܡܚܘܝ̈ܐ ܛܘܦܣܐ، ܣܓܝܐܘ̈ܬܐ ܬܠܝ̈ܐ ܝܢܐ ܒܪܒܘܬܐ ܕܓܘ̈ܕܐ.

ܒܘܚܪܢܐ ܕܫܪܛܐ ܥܠ ܣܓܝܐܘܬܐ ܚܙܝܬܐ. ܫܪܛܐ ܥܠ ܣܓܝܐܘܬܐ ܡܣܟܝܬܐ ܝܠܗ. ܩܠܝܬܐ (cell) ܚܙܝܬܐ ܥܡ 2 ܡܫܬܘܬܦ̈ܢܐ (participants) ܡܨܝܐ ܕܗܘܝܐ ܛܒܐ ܓܡܝܪܐܝܬ؛ ܩܠܝܬܐ ܡܣܟܝܬܐ 2.4 – ܠܐ.

ܟܝ ܡܪܒܥܐ (chi-square) ܥܠ ܡܫܘ̈ܚܬܐ ܡܬܢ̈ܝܬܐ (repeated measures). ܗܢ 100 ܐܢܫ̈ܐ ܩܕܡ ܘܒܬܪ 100 ܚܙ̈ܝܬܐ (observations) ܝܢܐ، ܠܐ 200. McNemar (Pallant, Chapter 16).

ܬܘܢܝܐ ܕ-p ܕܠܐ ܡܢܘ̈ܬܐ ܒܡܐܐ ܘܕܠܐ ܡܚܘܝܢܐ ܕܡܥܒܕܢܘܬܐ. ܓܘ ܕܘܡܝܐ (sample) ܕ-2,000 ܐܦ ܦܘܪܫܢܐ ܕܬܠܬܐ ܢܘܩ̈ܙܐ ܕܡܢܬܐ ܒܡܐܐ ܪܫܝܡܐ ܝܠܗ؛ V = .04 ܟܐܡܪ ܠܩܪܘܝܐ ܡܐ ܕ-p ܟܛܫܐ (ܨܘܪܬܐ 1).

ܫܓܘܫܝܐ ܓܘ ܐܘܪܚܐ ܕܦܘܚܡܐ ܕܣܟܘ̈ܝܐ (odds ratio). OR = 6.65 ܘ-OR = .15 ܚܕ ܡܫܟܚܢܘܬܐ ܝܠܗ ܒܐܘܪܚܐ ܗܦܝܟܬܐ؛ ܟܐܡܪܚ ܒܡ̈ܠܐ ܕܡܢܘ ܝܢܐ ܣܟܘ̈ܝܐ ܘܩܐ ܡܘܕܝ، ܐܝܟ ܓܘ ܡܐܡܪܐ ܕܐܗܐ ܦܐܬܐ ܟܥܒܕ.

ܡܦܠܚܢܘܬܐ ܒܝܫܬܐ ܕܐܪܒܥܐ ܣܕܪ̈ܐ. ܓܘܒܝܐ ܒܝܢܝ Pearson، Yates، ܦܘܚܡܐ ܕܡܬܚܙܝܢܘܬܐ (likelihood ratio) ܘ-Fisher ܠܦܘܬ ܐܝܢܐ ܕܟܝܗܒ p ܙܥܘܪܐ ܝܬܝܪ. ܟܦܣܩܚ ܡܢ ܩܕܡ – ܢܡܘܣܐ ܕܣܐܝܛ (site rule)، ܝܢ ܦܘܩܕܢܐ ܕܡܕܒܪܢܐ ܕܒܘܨܝܐ – ܘܟܡܬܢܚ ܗܢ ܣܕܪܐ ܓܘ ܟܠ ܠܘ̈ܚܐ ܕܒܘܨܝܐ.

ܚܘܝܕܐ ܕܓܢ̈ܣܐ (categories) ܒܬܪ ܕܚܙܐ ܦܐܪܐ. ܚܘܝܕܐ ܦܣܝܩܐ ܝܠܗ ܐܡܬܝ ܕܐܝܬ ܠܗ ܣܘܟܠܐ ܒܓܘ ܡܐ ܕܐܝܬ ܘܟܬܝܒܐ ܝܠܗ ܡܢ ܩܕܡ (Field, Section 19.5.2)؛ ܚܘܝܕܐ ܕܓܒܝܐ ܝܠܗ ܡܛܠ ܕܟܥܒܕ ܠܒܘܚܪܢܐ ܪܫܝܡܐ p-hacking ܝܠܗ.

ܡܒܘ̈ܥܐ

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

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

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

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

Pearson (1900)، Fisher (1922)، Yates ܘ-Howell (2012) – ܐܝܟ ܕܡܬܡܠܠܝ ܓܘ Field (2024)؛ Cohen (1988) – ܐܝܟ ܕܡܬܡܠܠ ܓܘ Gravetter ܘ-Wallnau (2017) ܘܓܘ Pallant (2020). ܠܦܘܬ ܢܡܘܣܐ ܕܣܐܝܛ، ܓܘ ܪܫܝܡܬܐ ܕܡܒܘ̈ܥܐ (reference list) ܟܡܬܚܙܝ ܒܣ ܡܒܘ̈ܥܐ ܕܩܪܝ̈ܐ ܝܢܐ ܓܘ ܢܘܣܚܐ ܫܪܫܝܐ. ܡܥܝܪܢܘܬܐ ܠܩܪܘܝܐ ܕܟܦܚܡ ܥܡ ܟܬܒ̈ܐ: Pallant ܟܛܒܥܐ ܩܐ ܬܚܘܡܐ "ܙܥܘܪܐ" ܕ-V ܓܘ ܬܪܝܢ ܓܢ̈ܣܐ .01 – ܛܥܝܘܬܐ ܕܛܒܥܐ ܝܠܗ ܕ-.10 (ܛܝܡܐ ܓܘ Gravetter & Wallnau، ܠܘܚܐ 17.10، ܘܓܘ Cohen)؛ Gravetter ܘ-Wallnau ܟܛܒܥܝ χ² = 6.381 ܩܐ ܡܬܠܐ 17.4 – ܚܘܫܒܢܐ ܚܬܝܬܐ ܟܝܗܒ 6.380 (ܐܢܝ ܥܓܠܠܗܘܢ ܐܪܒܥܐ ܗܕ̈ܡܐ ܩܕܡ ܓܘܡܪܐ).