ܒܘܚܪܢܐ ܕܢܘܪܡܠܝܘܬܐ

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)؟

ܩܕܡ ܒܘܚܪܢܐ ܕܟܣܐܡ ܢܘܪܡܠܝܘܬܐ (normality) – ܒܘܚܪܢܐ t، ANOVA، ܪܝܓܪܫܢ، ܐܣܘܪܐ ܕܚܕ̈ܕܐ ܕ-Pearson – ܘܒܝܚܝܕܝܘܬܐ ܐܡܬܝ ܕܕܘܡܝܐ ܙܥܘܪܐ ܝܠܗ. Field (2024، ܦܣܩܐ 6.9) ܟܡܦܫܩ ܡܢܐ ܡܛܠ ܟܒܚܪܚ ܡܫܬܚܠܦܢܐ ܓܢܣܗ، ܐܦܢ ܕܣܝܡܐ ܝܠܗ ܥܠ ܛܥܝ̈ܘܬܐ ܕܡܘܕܝܠ: ܐܢ ܡܫܬܚܠܦܢܐ ܕܦܐܪܐ ܦܠܝܓܐ ܝܠܗ ܢܘܪܡܠܐܝܬ، ܐܦ ܛܥܝ̈ܘܬܐ ܣܢܝܩ̈ܐ ܝܢܐ ܕܗܘܝܢ ܗܟܢܐ، ܘܡܛܠ ܗܕܐ ܒܘܚܪܢܐ ܕܦܘܠܓܐ ܕܡܫܬܚܠܦܢܐ ܝܠܗ "ܦܣܥܬܐ ܩܕܡܝܬܐ ܡܘܬܪܢܝܬܐ" – ܘܐܢ ܦܐܪܐ ܓܠܝܐܝܬ ܠܐ ܝܠܗ ܢܘܪܡܠܝܐ (ܠܡܬܠܐ ܥܩܝܡܘܬܐ ܚܝܘܒܬܐ ܝܩܘܪܬܐ)، ܒܠܟܝ ܡܘܕܝܠ ܣܪܛܢܝܐ (linear) ܠܐ ܝܠܗ ܡܘܕܝܠ ܬܪܝܨܐ ܡܢ ܫܘܪܝܐ. Pallant (2020، ܨܚܚܐ 6) ܟܪܗܛܐ ܐܗܐ ܒܘܚܪܢܐ ܒܐܘܪܚܐ ܕ-Explore ܥܠ ܟܠ ܡܫܬܚܠܦܢܐ ܬܠܝܐ ܩܕܡ ܒܘܚܪ̈ܢܐ ܕܓܘ ܡܢܘ̈ܬܐ ܪܒܝܥܝܬܐ ܘܚܡܝܫܝܬܐ ܕܟܬܒܐ ܕܝܠܗ̇، ܘܓܘ ܒܘܚܪ̈ܢܐ ܕܟܦܚܡܝ ܓܘ̈ܕܐ – ܩܐ ܟܠ ܓܘܕܐ ܒܦܪܝܫܘܬܐ (Factor List). ܡܛܠ ܗܕܐ ܦܐܬܐ ܟܡܩܪܒ ܦܘܠܓܐ ܠܓܘ̈ܕܐ.

ܡܘܕܝ ܦܐܬܐ ܠܐ ܟܒܚܪ: ܫܪ̈ܛܐ (assumptions) ܐܚܪ̈ܢܐ – ܣܪܛܢܝܘܬܐ، ܫܘܚܠܦܐ ܫܘܐ، ܠܐ ܬܠܝܘܬܐ – ܕܚܫܝܚ̈ܐ ܝܢܐ ܝܬܝܪ ܡܢ ܢܘܪܡܠܝܘܬܐ (ܦܐܬܐ ܛܝ̈ܡܐ ܢܘܟܪ̈ܝܐ ܘܫܪ̈ܛܐ، ܦܣܩܐ 3)؛ ܘܫܪ̈ܟܐ (residuals) ܕܡܘܕܝܠ ܕܪܝܓܪܫܢ (ܐܢܝ ܓܘ ܦܐܬܐ ܕܪܝܓܪܫܢ ܝܢܐ). ܦܣܘܩܐ ܕ-Likert ܝܚܝܕܝܐ ܝܠܗ ܡܫܬܚܠܦܢܐ ܕܛܟܣܐ (ordinal variable) ܠܦܘܬ ܥܝܕܐ ܕܣܐܝܛ (ܡܫܬܚܠܦ̈ܢܐ ܘܕܪ̈ܓܐ ܕܡܫܘܚܬܐ) – ܫܘܐܠܐ ܕܢܘܪܡܠܝܘܬܐ ܠܐ ܝܠܗ ܫܘܐܠܐ ܬܪܝܨܐ ܩܐܠܗ، ܘܦܐܬܐ ܟܡܙܗܪ ܐܡܬܝ ܕܟܓܒܝܬܘܢ ܠܗ؛ ܡܢܝܢܐ ܕܣܒܠܬܐ ܕܦܣܘ̈ܩܐ ܣܓܝ̈ܐܐ (ܐܠܦܐ ܕ-Cronbach ܘܡܢܝܢܐ ܕܣܒܠܬܐ) – ܐܝܢ.

ܣܘܟܠܐ: ܨܘܪ̈ܬܐ ܩܕܡ ܡܢܝ̈ܢܐ، ܡܢܝ̈ܢܐ ܩܕܡ ܒܘܚܪ̈ܢܐ

ܛܟܣܐ ܕ-Field (2024، ܦܣ̈ܩܐ 6.9.4-6.9.5 ܘܩܘܦܣܐ 6.7) ܝܠܗ ܐܦ ܛܟܣܐ ܕܡܦܩܢܐ ܗܪܟܐ. ܩܕܡܝܬ ܐܣܟܝܡܐ – ܗܝܣܛܘܓܪܡ ܘܨܘܪܬܐ Q-Q: ܬܪܘܝܗܝ ܟܡܚܘܝܢ ܠܥܝܢܐ ܐܢ ܦܘܠܓܐ ܫܘܐ ܝܠܗ ܠܬܪܝܢ ܓܢ̈ܒܐ، ܐܢ ܐܝܬ ܕܘܢܒܐ ܐܪܝܟܐ ܠܚܕ ܓܢܒܐ، ܘܐܢ ܐܝܬ ܛܝ̈ܡܐ ܝܚܝ̈ܕܝܐ ܪܚܝܩ̈ܐ ܡܢ ܐܚܪ̈ܢܐ. ܒܬܪ ܗܕܐ ܡܢܝ̈ܢܐ – ܥܩܝܡܘܬܐ (skewness) ܘܓܒܢܘܬܐ (kurtosis): ܓܘ ܦܘܠܓܐ ܢܘܪܡܠܝܐ ܬܪܘܝܗܝ ܨܦܪܐ ܝܢܐ؛ ܥܩܝܡܘܬܐ ܚܝܘܒܬܐ – ܟܢܫܐ ܓܘ ܛܝ̈ܡܐ ܢܚܝ̈ܬܐ ܘܕܘܢܒܐ ܠܝܡܝܢܐ، ܣܠܝܒܬܐ – ܟܢܫܐ ܓܘ ܛܝ̈ܡܐ ܪ̈ܡܐ؛ ܓܒܢܘܬܐ ܚܝܘܒܬܐ – ܕܘܢ̈ܒܐ ܝܩܘܪ̈ܐ، ܣܠܝܒܬܐ – ܕܘܢ̈ܒܐ ܩܠܝ̈ܠܐ؛ "ܟܡܐ ܕܛܝܡܐ ܪܚܝܩܐ ܝܬܝܪ ܝܠܗ ܡܢ ܨܦܪܐ، ܣܛܝܘܬܐ ܥܣܩܬܐ ܝܬܝܪ ܝܠܗ̇" (ܦܣܩܐ 6.9.5). ܓܘ Pallant (2020، ܨܚܚܐ 6) ܗܝ ܡܫܘܚܬܐ، ܥܡ ܬܘܣܦܬܐ: ܓܘ ܕܘ̈ܡܝܐ ܪܒ̈ܐ ܒܡܫܘܚܬܐ ܥܩܝܡܘܬܐ "ܠܐ ܒܕ ܥܒܕܐ ܦܘܪܫܢܐ ܥܝܩܪܝܐ ܓܘ ܦܘܫܩܐ"، ܘܓܒܢܘܬܐ ܡܨܝܐ ܕܡܙܥܪܐ ܫܘܥܪܐ ܕܫܘܚܠܦܐ (variance) ܐܠܐ ܐܦ ܐܗܐ ܣܘܟܢܐ ܟܙܥܪ ܡܢ 200 ܡܫܬܘܬܦ̈ܢܐ ܘܠܥܠ (Tabachnick ܘ-Fidell, 2013، ܐܝܟ ܕܡܬܡܠܠܝ ܓܘ Pallant). ܘܒܣ ܓܘ ܚܪܬܐ ܒܘܚܪ̈ܢܐ – ܘܥܡ ܙܘܗܪܐ (ܦܣܩܐ ܒܘܚܪ̈ܢܐ ܕܢܘܪܡܠܝܘܬܐ).

ܠܒܣܬܪܐ ܕܟܠ ܐܗܐ ܩܝܡܐ ܢܡܘܣܐ ܕܬܚܘܡܐ ܡܨܥܝܐ (central limit theorem) (Field, 2024, Sections 6.2.7 and 6.8.3): ܡܐ ܕܒܘܚܪ̈ܢܐ ܣܢܝܩܝ ܠܗ ܝܠܗ ܦܘܠܓܐ ܕܓܘܒܝܐ ܕܕܘܡܝܐ (sampling distribution) ܢܘܪܡܠܝܐ ܕܡܨܥܝܬܐ (ܝܢ ܕܡܢܝܢܐ ܡܫܘܬܦܐ)، ܘܗܘ ܟܡܩܪܒ ܠܢܘܪܡܠܝܐ ܟܡܐ ܕܕܘܡܝܐ ܟܪܒܐ – ܕܠܐ ܐܣܘܪܐ ܥܡ ܐܣܟܝܡܐ ܕܝܗܝ̈ܒܬܐ. ܛܝܡܐ ܡܩܒܠܐ ܝܠܗ 30، ܐܠܐ ܓܘ ܦܘܠܓܐ ܥܡ ܕܘܢ̈ܒܐ ܝܩܘܪ̈ܐ ܡܨܝܐ ܕܣܢܝܩܝ 100 ܘܐܦ ܒܢܘܬ (ܩܘܦܣܐ 6.4). ܐܗܐ ܝܠܗ ܥܠܬܐ ܕܩܘܦܣܐ ܕ"ܩܪܝܢܐ ܕܦܐܪܐ" ܟܫܪܐ ܒܪܒܘܬܐ ܕܕܘܡܝܐ (sample size): ܓܘ ܕܘܡܝܐ ܙܥܘܪܐ ܢܘܪܡܠܝܘܬܐ ܫܪܝܪܐܝܬ ܚܫܝܚܬܐ ܝܠܗ̇، ܘܓܘ ܕܘܡܝܐ ܪܒܐ ܩܪܝܒܐ ܠܐ ܟܡܫܢܝܐ ܡܕܡ – ܘܒܘܚܪ̈ܢܐ ܕܢܘܪܡܠܝܘܬܐ ܟܐܡܪܝ ܚܬܝܬܐܝܬ ܗܦܟܐ.

ܩܪܝܢܐ ܕܡܦܩܢܐ (How to read the output)

ܠܘܚܐ 1 – ܬܚܘܝܬܐ ܕܦܘܠܓܐ. ܐܗܐ ܝܠܗ ܠܘܚܐ Descriptives ܕ-Explore، ܥܡ ܬܠܬܐ ܦܘܚܡ̈ܐ ܕܫܘܐ ܠܡܥܒܕ ܓܘܗ. ܡܨܥܝܬܐ ܩܘܒܠ ܛܝܡܐ ܡܨܥܝܐ: ܓܘ ܦܘܠܓܐ ܫܘܐ ܠܬܪܝܢ ܓܢ̈ܒܐ ܐܢܝ ܩܪܝܒ̈ܐ ܝܢܐ؛ ܥܩܝܡܘܬܐ ܚܝܘܒܬܐ ܟܓܪܫܐ ܡܨܥܝܬܐ ܠܥܠ ܘܠܐ ܛܝܡܐ ܡܨܥܝܐ، ܘܡܛܠ ܗܕܐ "ܐܢ ܡܨܥܝܬܐ ܪܒܬܐ ܝܠܗ̇ ܡܢ ܛܝܡܐ ܡܨܥܝܐ، ܡܣܬܟܠܢܐ ܝܠܗ ܕܐܝܬ ܥܩܝܡܘܬܐ ܚܝܘܒܬܐ" (Field, 2024, Section 6.9.5) – ܘܗܦܟܐ. ܡܨܥܝܬܐ ܩܘܒܠ ܡܨܥܝܬܐ ܓܙܝܙܬܐ 5%: SPSS ܟܡܫܩܠ 5% ܡܢ ܛܝ̈ܡܐ ܪ̈ܡܐ ܘ-5% ܡܢ ܢܚ̈ܝܬܐ ܘܟܚܫܒ ܡܨܥܝܬܐ ܚܕܬܐ؛ "ܐܢ ܬܪܬܝܢ ܡܨܥܝ̈ܬܐ ܦܪ̈ܝܫܬܐ ܝܢܐ ܣܓܝ، ܒܠܟܝ ܣܢܝܩ ܒܕ ܗܘܐ ܠܘܟܘܢ ܕܒܨܝܬܘܢ ܐܢܝ ܢܘܩ̈ܙܐ ܕܝܗܝ̈ܒܬܐ" – ܛܝ̈ܡܐ ܕܣܦܪܐ ܟܡܥܒܕܝ (Pallant, 2020، ܨܚܚܐ 6؛ ܓܘ ܡܬܠܐ ܕܝܠܗ̇ 26.73 ܩܘܒܠ 26.64 – ܕܡ̈ܝܐ ܣܓܝ، ܘܓܕ̈ܫܐ ܟܦܝܫܝ). ܥܩܝܡܘܬܐ ܘܓܒܢܘܬܐ ܩܘܒܠ ܛܥܝ̈ܘܬܐ ܬܩܝܢ̈ܬܐ ܕܝܠܗܝܢ: ܦܘܠܓܐ ܟܝܗܒ z (Field, 2024, Equation 6.34) – ܠܥܠ ܡܢ 1.96 ܪܫܝܡܐ ܓܘ .05، ܠܥܠ ܡܢ 2.58 ܓܘ .01، ܠܥܠ ܡܢ 3.29 ܓܘ .001 (ܩܘܦܣܐ 6.7). ܠܘܚܐ ܟܡܚܘܐ ܐܗܐ ܒܟܘ̈ܟܒܐ، ܐܠܐ ܚܙܝܡܘܢ ܡܬܠܐ ܕ-Field ܓܢܣܗ: ܓܘ ܝܗܝ̈ܒܬܐ ܕܕܟܝܘܬܐ (hygiene) ܕܝܘܡܐ 1 (N = 810) ܥܩܝܡܘܬܐ ܗܘܐ 0.004- – ܦܘܠܓܐ ܫܘܐ ܓܡܝܪܐܝܬ – ܘܗܠ ܐܕܝܘܡ ܓܒܢܘܬܐ ܢܦܩܠܗ̇ "ܪܫܝܡܬܐ" (z = −2.38)، ܘ"ܡܛܠ ܕܘܡܝܐ ܪܒܐ ܣܢܝܩ ܝܠܗ ܕܫܩܠܚ ܐܢܝ ܡܫܟܚ̈ܢܘܬܐ ܥܡ ܡܠܚܐ ܘܕܡܬܒܝܐܚ ܒܢܡܘܣܐ ܕܬܚܘܡܐ ܡܨܥܝܐ". ܓܘ ܕܘܡܝܐ ܪܒܐ ܟܘ̈ܟܒܐ ܩܪܝܒܐ ܟܠ ܐܡܬܝ ܟܡܬܚܙܝ؛ ܛܝܡܐ ܓܢܣܗ – ܠܐ z – ܝܠܗ ܡܐ ܕܟܩܪܚ.

ܠܘܚܐ 2 – ܒܘܚܪ̈ܢܐ ܕܢܘܪܡܠܝܘܬܐ. ܠܘܚܐ Tests of Normality: ܗܘܦܘܬܣܝܣ ܕܣܦܝܩܘܬܐ (null hypothesis) ܝܠܗ̇ ܕܦܘܠܓܐ ܢܘܪܡܠܝܐ ܝܠܗ، ܘܡܛܠ ܗܕܐ p < .05 ܟܐܡܪ "ܦܪܝܫܐ ܪܫܝܡܐܝܬ ܡܢ ܢܘܪܡܠܝܐ" ܘ-p > .05 – "ܠܐ ܡܫܟܚܐ ܝܠܗ ܦܘܪܫܢܐ" (Field, 2024, Section 6.9.5; Pallant, 2020, Chapter 6). ܕܪ̈ܓܐ ܕܚܐܪܘܬܐ (degrees of freedom) ܫܘ̈ܝܐ ܝܢܐ ܠ-N: ܕܘܡܝܐ ܦܚܝܡܐ ܝܠܗ ܥܡ ܢܘܪܡܠܝܐ ܓܡܝܪܐ، ܠܐ ܠ-N − 1 (Field، ܡܥܝܪܢܘܬܐ 14 ܕܨܚܚܐ 6). Kolmogorov-Smirnov (D) ܟܡܫܚ ܪܘܚܩܐ ܥܠܝܐ ܒܝܢܝ ܦܘܠܓܐ ܟܢܝܫܐ ܕܕܘܡܝܐ ܘܕܢܘܪܡܠܝܐ ܥܡ ܡܨܥܝܬܐ ܘܣܛܝܘܬܐ ܬܩܝܢܬܐ ܕܕܘܡܝܐ؛ ܡܛܠ ܕܡܨܥܝܬܐ ܘܣܛܝܘܬܐ ܬܩܝܢܬܐ ܡܫܘܥܪ̈ܐ ܝܢܐ ܡܢ ܝܗܝ̈ܒܬܐ، p ܪܓܝܠܐ ܕ-Kolmogorov-Smirnov ܠܐ ܝܠܗ ܬܪܝܨܐ، ܘܟܡܦܠܚܚ "ܬܘܪܨܐ ܕ-Lilliefors" – ܐܗܐ ܝܠܗ̇ ܡܥܝܪܢܘܬܐ ܕܠܬܚܬ ܠܘܚܐ ܓܘ SPSS (Gross & Ligges, 2015، ܬܚܘܝܬܐ ܕ-lillie.test). Shapiro-Wilk (W) ܝܠܗ ܡܪܒܥܐ ܕܐܣܘܪܐ ܕܚܕ̈ܕܐ ܒܝܢܝ ܝܗܝ̈ܒܬܐ ܛܟܝܣ̈ܬܐ ܘܛܝ̈ܡܐ ܡܣܟ̈ܝܐ ܡܢ ܢܘܪܡܠܝܐ – 1 ܓܘ ܦܐܝܘܬܐ ܓܡܝܪܬܐ، ܘܙܥܘܪܐ ܡܢܗ ܟܡܐ ܕܣܛܝܘܬܐ ܪܒܬܐ ܝܠܗ̇؛ ܚܫܝܒܐ ܝܠܗ ܥܕܡܐ 5,000 ܚܙ̈ܝܬܐ (R Core Team, 2024، ܬܚܘܝܬܐ ܕ-shapiro.test). ܓܘ SPSS Shapiro-Wilk ܛܒܝܥܐ ܝܠܗ ܓܢܒ Kolmogorov-Smirnov، ܘܓܘ ܗܘ ܠܘܚܐ ܐܦ ܗܪܟܐ. ܐܡܬܝ ܕܬܪܘܝܗܝ ܦܠܝܓ̈ܐ ܝܢܐ – ܡܐ ܕܟܗܘܐ ܠܐ ܩܠܝܠ – ܠܝܬ "ܙܟܝܐ": ܬܪܘܝܗܝ ܪܘܫܡܐ ܝܢܐ ܕܕܥܪܚ ܠܨܘܪ̈ܬܐ.

ܨܘܪܬܐ ܕܗܝܣܛܘܓܪܡ ܥܡ ܣܪܛܐ ܟܦܝܦܐ ܢܘܪܡܠܝܐ (ܡܨܥܝܬܐ ܘܣܛܝܘܬܐ ܬܩܝܢܬܐ ܕܕܘܡܝܐ) – ܟܚܙܝܚ ܫܘܝܘܬܐ ܕܬܪܝܢ ܓܢ̈ܒܐ، ܚܪܝܦܘܬܐ ܝܢ ܦܫܝܛܘܬܐ، ܘܛܝ̈ܡܐ ܝܚܝ̈ܕܝܐ ܪܚܝ̈ܩܐ: ܓܘ ܡܬܠܐ ܕ-Field ܛܝܡܐ 20.02 ܓܘ ܣܒܠܬܐ 0-4 ܐܬܓܠܝܠܗ ܓܘ ܗܝܣܛܘܓܪܡ ܩܕܡ ܟܠ ܒܘܚܪܢܐ، ܘܒܬܪ ܬܘܪܨܐ ܕܝܠܗ ܠ-2.02 ܦܘܠܓܐ ܐܬܚܙܝܠܗ ܢܘܪܡܠܝܐ (ܦܣܩܐ 6.9.3). ܨܘܪܬܐ Q-Q (quantile-quantile; Field, 2024, Section 6.9.4): ܩܐ ܟܠ ܛܝܡܐ ܚܙܝܐ ܚܫܝܒܐ ܝܠܗ ܡܢܝܢܐ ܢܘܪܡܠܝܐ ܕܗܘܐ ܡܣܟܝܐ ܩܐ ܕܪܓܐ ܕܝܠܗ؛ ܐܢ ܝܗܝ̈ܒܬܐ ܢܘܪܡܠܝ̈ܬܐ ܝܢܐ، ܢܘܩ̈ܙܐ ܝܬܝ̈ܒܐ ܝܢܐ ܥܠ ܣܪܛܐ ܡܨܠܝܐ. ܩܫܬܐ (ܢܘܩ̈ܙܐ "ܡܬܚܙܝ̈ܢܐ" ܠܥܠ ܡܢ ܣܪܛܐ ܓܘ ܡܨܥܬܐ) – ܥܩܝܡܘܬܐ؛ ܐܣܟܝܡܐ ܕ-S – ܕܘܢ̈ܒܐ ܝܩܘܪ̈ܐ ܝܢ ܩܠܝ̈ܠܐ (ܨܘܪܬܐ 6.23). ܦܐܬܐ ܟܨܘܪ ܐܝܟ SPSS: ܚܙܝܐ ܥܠ ܣܪܛܐ ܦܫܝܛܐ (horizontal axis) ܘܡܣܟܝܐ ܥܠ ܙܩܝܦܐ؛ ܓܘ R ܣܪ̈ܛܐ ܗܦܝ̈ܟܐ ܝܢܐ، ܘܗܟܢܐ ܐܦ ܛܘܦ̈ܣܐ (Field، ܡܥܝܪܢܘܬܐ 12 ܕܨܚܚܐ 6). ܛܝ̈ܡܐ ܕܡ̈ܝܐ – ܐܝܟ ܓܘ ܣܒܠܬܐ ܕܕܪܓܐ – ܫܘܬܦ̈ܐ ܝܢܐ ܒܢܘܩܙܐ ܚܕ، ܪܒܐ ܝܬܝܪ. ܐܦ Pallant (2020) ܟܩܪܝܐ Q-Q ܗܟܢܐ: "ܣܪܛܐ ܬܪܝܨܐ ܒܡܫܘܚܬܐ ܟܡܚܘܐ ܦܘܠܓܐ ܢܘܪܡܠܝܐ".

ܒܘܚܪ̈ܢܐ ܕܢܘܪܡܠܝܘܬܐ – ܡܢܐ ܡܛܠ ܥܡ ܙܘܗܪܐ

Field (2024، ܩܘܦܣܐ 6.7) ܟܟܬܒ ܕܗܘ ܟܡܝܬܐ ܐܢܝ ܒܘܚܪ̈ܢܐ "ܒܝܚܝܕܝܘܬܐ ܡܛܠ ܕܐܢܫ̈ܐ ܟܡܣܟܝ ܕܚܙܝ ܡܕ̈ܡܐ ܐܝܟ ܐܗܐ ܓܘ ܟܬܒ̈ܐ ܕܫܘܪܝܐ، ܘܠܐ ܡܛܠ ܕܪܥܝܢܐ ܛܒܐ ܝܢܐ". ܒܥܬܐ ܬܢܝܢܬܐ ܝܠܗ̇، ܘܬܪܝܢ ܓܢ̈ܒܐ ܕܝܠܗ̇ ܗܦܝ̈ܟܐ ܝܢܐ ܡܢ ܣܢܝܩܘܬܐ: (1) ܓܘ ܕܘܡܝܐ ܪܒܐ ܒܘܚܪ̈ܢܐ ܪܫܝܡ̈ܐ ܝܢܐ ܐܦ ܥܠ ܣܛܝ̈ܘܬܐ ܙܥܘܪ̈ܬܐ ܘܕܠܐ ܚܫܝܚܘܬܐ – ܘܒܝܚܝܕܝܘܬܐ ܬܡܢ، ܡܛܠ ܢܡܘܣܐ ܕܬܚܘܡܐ ܡܨܥܝܐ، ܢܘܪܡܠܝܘܬܐ ܩܪܝܒܐ ܠܐ ܟܡܫܢܝܐ ܡܕܡ؛ ܗܝܕܝܟ ܒܘܚܪܢܐ ܟܡܕܐܓ ܠܢ ܘܟܡܬܪܨ ܡܕܡ ܕܠܐ ܣܢܝܩ ܝܠܗ ܠܬܘܪܨܐ. (2) ܓܘ ܕܘܡܝܐ ܙܥܘܪܐ، ܕܓܘܗ ܣܢܝܩ ܝܠܗ ܕܡܕܐܓܚ، ܠܒܘܚܪܢܐ ܠܝܬ ܚܝܠܐ ܣܛܐܛܝܣܛܝܩܝܐ (statistical power) ܕܡܓܠܐ ܬܒܪܬܐ – ܘܗܘ "ܟܡܠܒܒ ܠܢ ܕܠܐ ܡܕܐܓܚ ܥܠ ܡܕܡ ܕܒܠܟܝ ܣܢܝܩ ܝܠܗ ܕܡܕܐܓܚ ܥܠܗ". ܡܠܟܐ ܕܝܠܗ: ܓܘ ܕܘܡܝܐ ܪܒܐ ܕܠܐ ܡܦܠܚܚ ܒܒܘܚܪ̈ܢܐ ܒܟܠ ("ܫܪܝܪܐܝܬ ܕܠܐ ܡܕܐܓܚ ܒܢܘܬ ܡܢ ܕܣܢܝܩ ܥܠ ܢܘܪܡܠܝܘܬܐ")؛ ܓܘ ܕܘܡܝܐ ܙܥܘܪܐ – ܕܚܙܝܚ ܐܡܬܝ ܕܒܘܚܪܢܐ ܪܫܝܡܐ ܝܠܗ، "ܐܠܐ ܕܩܝܡܚ ܠܩܘܒܠ ܪܓܫܐ ܕܬܘܟܠܢܐ ܕܓܠܐ ܐܡܬܝ ܕܠܐ ܝܠܗ". ܗܝ ܡܕܡ ܓܘ Pallant (2020، ܨܚܚܐ 6): ܓܘ ܡܬܠܐ ܕܝܠܗ̇ (N = 433) Kolmogorov-Smirnov ܢܦܩܠܗ p = .000 ܐܦܢ ܕܗܝܣܛܘܓܪܡ "ܟܡܬܚܙܐ ܢܘܪܡܠܝܐ ܒܡܫܘܚܬܐ" – "ܐܗܐ ܡܬܚܙܐ ܝܠܗ ܣܓܝ ܓܘ ܕܘ̈ܡܝܐ ܪܒ̈ܐ"، ܘ-Tabachnick ܘ-Fidell ܟܡܪܚܩܝ ܕܡܦܠܚܚ ܒܗܝܣܛܘܓܪܡ ܒܕܘܟܬܗ. ܡܬܠܐ ܕ-Field ܕܡܝܐ ܝܠܗ: ܝܘܡܐ 1 (N = 810) ܐܬܚܙܝܠܗ ܢܘܪܡܠܝܐ ܓܡܝܪܐܝܬ ܘ-Kolmogorov-Smirnov ܝܗܒܠܗ p = .097 – "ܩܪܝܒܐ ܒܬܡܝܗܘܬܐ ܠܪܫܝܡܐ"، ܒܣ ܡܛܠ ܪܒܘܬܐ ܕܕܘܡܝܐ (ܦܣܩܐ 6.9.5).

ܥܝܕܐ ܕܣܐܝܛ – "ܐܦ ܐܗܐ ܘܐܦ ܐܗܐ". ܒܘܚܪ̈ܢܐ ܛܒܝܥ̈ܐ ܝܢܐ، ܡܛܠ ܕܟܡܬܚܙܝ ܓܘ ܡܦܩܢܐ ܕ-SPSS ܘܓܘ ܡܐܡܪ̈ܐ ܘܣܢܝܩ ܝܠܗ ܕܝܕܥܚ ܕܩܪܚ ܠܗܘܢ؛ ܐܠܐ ܩܘܦܣܐ ܕ"ܩܪܝܢܐ ܕܦܐܪܐ" ܟܝܗܒܐ ܠܗܘܢ ܡܬܩܠܐ ܠܦܘܬ ܪܒܘܬܐ ܕܕܘܡܝܐ – ܓܘ ܕܘܡܝܐ ܕ-200 ܘܠܥܠ ܟܐܡܪܐ ܓܠܝܐܝܬ ܕܠܐ ܚܫܒܚ ܠܗܘܢ، ܒܝܢܝ 30 ܘ-200 ܕܦܣܩܚ ܠܦܘܬ ܐܣܟܝܡܐ، ܘܠܬܚܬ ܡܢ 30 ܕܚܫܒܚ ܠܒܘܚܪܢܐ ܪܫܝܡܐ ܘܕܠܐ ܣܡܟܚ ܥܠ ܠܐ ܪܫܝܡܐ. ܬܘܢܝܐ ܕܒܘܚܪܢܐ ܕܢܘܪܡܠܝܘܬܐ ܒܠܚܘܕ، ܕܠܐ ܥܩܝܡܘܬܐ، ܓܒܢܘܬܐ ܘܨܘܪܬܐ، ܠܐ ܝܠܗ ܬܘܢܝܐ ܕܒܘܚܪܢܐ ܕܢܘܪܡܠܝܘܬܐ.

ܡܘܕܝ ܟܥܒܕܚ ܐܡܬܝ ܕܠܐ ܝܠܗ ܢܘܪܡܠܝܐ

ܩܕܡ ܟܠ ܡܕܡ – ܠܐ ܕܡܕܐܓܚ: ܢܘܪܡܠܝܘܬܐ ܝܠܗ̇ ܣܝܡܐ ܕܚܫܝܚܐ ܒܨܝܪ ܝܠܗ ܡܢ ܫܪ̈ܛܐ ܕܡܘܕܝܠ ܣܪܛܢܝܐ، ܘܝܠܗ ܥܠ ܛܥܝ̈ܘܬܐ (ܦܐܬܐ ܛܝ̈ܡܐ ܢܘܟܪ̈ܝܐ ܘܫܪ̈ܛܐ، ܦܣ̈ܩܐ 3-4؛ Field, 2024، ܦܣܩܐ 6.8). ܛܟܣܐ ܬܡܢ: ܛܝ̈ܡܐ ܢܘܟܪ̈ܝܐ ܘܛܥܝ̈ܘܬܐ ܕܟܬܝܒܬܐ ܩܕܡ ܟܠ ܡܕܡ – ܛܝܡܐ ܕܠܒܪ ܡܢ ܦܬܝܘܬܐ ܕܣܒܠܬܐ ܛܥܝܘܬܐ ܝܠܗ̇ ܘܠܐ "ܠܐ ܢܘܪܡܠܝܘܬܐ"؛ ܛܝܡܐ ܢܘܟܪܝܐ ܫܪܝܪܐ ܟܦܝܫ، ܐܠܐ ܐܢ ܚܘܝܐ ܝܠܗ ܕܠܐ ܝܠܗ ܡܢ ܟܢܫܐ ܟܠܢܝܐ (population). ܒܬܪ ܗܕܐ، ܐܡܬܝ ܕܬܒܪܬܐ ܫܪܝܪܬܐ ܝܠܗ̇ ܘܕܘܡܝܐ ܙܥܘܪܐ ܝܠܗ، ܐܘܪ̈ܚܬܐ ܚܣܝܢ̈ܬܐ (robust) ܘ-bootstrap ܒܕܘܟܬܐ ܕܫܘܢܝܐ (transformation) ܕܦܐܪܐ (ܦܣܩܐ 6 ܬܡܢ). ܘܐܡܬܝ ܕܒܥܝܚ ܒܘܚܪܢܐ ܕܠܐ ܟܣܐܡ ܢܘܪܡܠܝܘܬܐ – ܓܒܝ̈ܬܐ ܠܐ ܦܪܡܝܛܪ̈ܝܬܐ (nonparametric): Mann-Whitney ܒܕܘܟܬܐ ܕ-t ܠܠܐ ܬܠܝ̈ܐ، Wilcoxon ܒܕܘܟܬܐ ܕ-t ܠܙܘܓܢ̈ܝܐ، Kruskal-Wallis ܒܕܘܟܬܐ ܕ-ANOVA ܕܚܕ ܐܘܪܚܐ. Pallant (2020، ܨܚܚܐ 6) ܟܡܘܣܦܐ ܡܥܝܪܢܘܬܐ ܕܟܡܢܝܚܐ: ܣܒ̈ܠܬܐ ܣܓܝ̈ܐܐ ܓܘ ܝܕ̈ܥܬܐ ܕܟܢܫܐ ܥܩܝܡ̈ܬܐ ܝܢܐ "ܠܐ ܡܛܠ ܒܥܬܐ ܓܘ ܣܒܠܬܐ ܐܠܐ ܡܛܠ ܟܝܢܐ ܕܡܕܡ ܕܡܫܘܚܐ ܝܠܗ" – ܣܒܥܘܬܐ ܡܢ ܚܝ̈ܐ ܥܩܝܡܬܐ ܝܠܗ̇ ܣܠܝܒܐܝܬ (ܣܓܝܐܐ ܡܢ ܐܢܫ̈ܐ ܣܒܝܥ̈ܐ ܝܢܐ ܒܡܫܘܚܬܐ)، ܡܚܘ̈ܝܢܐ ܕܙܘܥܬܐ ܘܥܩܬܐ ܕܢܦܫܐ ܓܘ ܟܢܫܐ ܟܠܢܝܐ ܥܩܝܡ̈ܐ ܝܢܐ ܚܝܘܒܐܝܬ؛ ܐܗܐ ܬܚܘܝܬܐ ܝܠܗ̇ ܕܥܠܡܐ، ܘܓܘ ܕܘܡܝܐ ܪܒܐ ܠܐ ܝܠܗ̇ ܒܥܬܐ ܩܐ ܒܘܚܪܢܐ.

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

ܐܘܪܚܐ ܕ-Pallant (2020، ܨܚܚܐ 6، "ܫܘܥܪܐ ܕܢܘܪܡܠܝܘܬܐ"): Analyze › Descriptive Statistics › Explore… – ܡܫܬܚܠܦ̈ܢܐ ܠܩܘܦܣܐ Dependent List؛ ܡܫܬܚܠܦܢܐ ܕܓܘ̈ܕܐ (ܐܢ ܐܝܬ) ܠ-Factor List؛ ܡܫܬܚܠܦܢܐ ܕܡܢܝܢܐ ܡܦܪܫܢܐ ܠ-Label Cases by؛ ܓܘ Display – Both؛ Statistics… – Descriptives ܘ-Outliers؛ Plots… – Histogram (ܘܕܒܛܠܚ Stem-and-leaf) ܘ-Normality plots with tests؛ Options… – Exclude cases pairwise. Field (2024، ܦܣܩܐ 6.9.2) ܟܡܚܝܠ ܠܓܒܝܬܐ ܐܚܪܝܬܐ: ܓܘܒܝܐ ܡܩܕܡܐ (default)، listwise، ܟܫܩܠ ܡܫܬܘܬܦܢܐ ܡܢ ܟܠ ܡܫܬܚܠܦ̈ܢܐ ܐܢ ܚܣܝܪܐ ܠܗ ܛܝܡܐ ܓܘ ܚܕ ܡܢܝܗܘܢ – ܓܘ ܡܬܠܐ ܕܝܠܗ 810 ܡܫܬܘܬܦ̈ܢܐ ܓܘ ܝܘܡܐ 1 ܗܘܘ ܒܕ ܗܘܝ 123. ܣܝܢܬܐܟܣ (syntax) ܕܦܐܬܐ ܟܒܢܐ:

EXAMINE VARIABLES=עמדות_ציון גיל BY קבוצה
  /PLOT HISTOGRAM NPPLOT
  /STATISTICS DESCRIPTIVES
  /CINTERVAL 95
  /MISSING PAIRWISE
  /NOTOTAL.

ܩܪܝܢܐ ܕܡܦܩܢܐ. Descriptives = ܠܘܚܐ 1 (ܥܡ 5% Trimmed Mean، Interquartile Range، Skewness ܘ-Kurtosis ܥܡ Std. Error؛ SPSS ܠܐ ܟܛܒܥ z – ܟܦܠܓܚ ܒܐܝܕܐ، ܝܢ ܟܩܪܚ ܠܗ ܗܪܟܐ)؛ Tests of Normality = ܠܘܚܐ 2 (ܥܡ ܡܥܝܪܢܘܬܐ Lilliefors Significance Correction، ܘ-.200* ܐܡܬܝ ܕ-p ܕ-Kolmogorov-Smirnov ܝܠܗ .200 ܘܠܥܠ – "ܬܚܘܡܐ ܬܚܬܝܐ ܕܪܫܝܡܘܬܐ ܫܪܝܪܬܐ"؛ ܦܐܬܐ ܟܛܒܥ ܛܝܡܐ ܚܫܝܒܐ)؛ Histogram، Normal Q-Q Plot ܘ-Detrended Normal Q-Q Plot (ܣܛܝܘܬܐ ܕܢܘܩ̈ܙܐ ܡܢ ܣܪܛܐ – ܣܢܝܩ̈ܐ ܝܢܐ ܕܒܕܪܝ ܚܕܪ ܨܦܪܐ ܕܠܐ ܟܢܫܐ؛ Pallant) ܘ-Boxplot؛ Extreme Values – ܚܡܫܐ ܛܝ̈ܡܐ ܪ̈ܡܐ ܘܢܚ̈ܝܬܐ ܥܡ ܡܢܝܢܐ ܕܣܕܪܐ (ܗܟܢܐ Field ܐܫܟܚܠܗ 20.02). ܕܠܐ /NOTOTAL SPSS ܟܡܘܣܦ ܐܦ ܣܕܪܐ ܩܐ ܟܠ ܕܘܡܝܐ ܐܡܬܝ ܕܐܝܬ ܡܫܬܚܠܦܢܐ ܕܓܘ̈ܕܐ.

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

ܓܘ R ܫܪܫܝܐ: shapiro.test()، qqnorm() ܘ-qqline()، hist()؛ ܩܐ Kolmogorov-Smirnov ܥܡ ܬܘܪܨܐ ܕ-Lilliefors – lillie.test() ܡܢ ܚܒܝܫܘܬܐ nortest (Gross & Ligges, 2015؛ p ܕ-ks.test() ܫܪܫܝܐ ܠܐ ܝܠܗ ܬܪܝܨܐ ܐܡܬܝ ܕܡܨܥܝܬܐ ܘܣܛܝܘܬܐ ܬܩܝܢܬܐ ܡܫܘܥܪ̈ܐ ܝܢܐ ܡܢ ܝܗܝ̈ܒܬܐ – ܗܟܢܐ ܓܘ ܬܚܘܝܬܐ ܕܚܒܝܫܘܬܐ)، ܘܩܐ ܥܩܝܡܘܬܐ ܘܓܒܢܘܬܐ ܒܢܘ̈ܣܚܐ ܕ-SPSS – skewness() ܘ-kurtosis() ܡܢ ܚܒܝܫܘܬܐ e1071 ܥܡ type = 2. ܚܙܝܡܘܢ: mean(x, trim = 0.05) ܕ-R ܟܓܙܙ ܡܢܝܢܐ ܓܡܝܪܐ ܕܚܙ̈ܝܬܐ ܡܢ ܟܠ ܓܢܒܐ، ܘܡܛܠ ܗܕܐ ܠܐ ܝܠܗ ܕܡܝܐ ܠ-5% Trimmed Mean ܕ-SPSS؛ ܘܦܬܝܘܬܐ ܒܝܢܝ ܪ̈ܘܒܥܐ ܕ-SPSS ܟܢܦܩܐ ܒ-quantile(type = 6). ܣܩܪܝܦܬ ܪܗܛܐ ܝܠܗ ܐܝܟ ܕܐܝܬܘܗܝ ܥܠ ܦܐܝܠ ܕܡܬܠܐ ܘܝܗܒܠܗ ܛܝ̈ܡܐ ܕܠܘ̈ܚܐ (ܓܘ ܡܥܝܪ̈ܢܘܬܐ). ܢܡܘܣܐ ܕܣܐܝܛ ܩܐ ܣܘܪܝܬ ܓܘ R: ܦܐܝܠ UTF-8، ܟܠ ܣܕܪܐ ܕܡܥܝܪܢܘܬܐ ܟܫܪܐ ܒܡܠܬܐ ܕܣܘܪܝܬ، ܘܣܒܝܒܘܬܐ UTF-8 ܩܐ ܫܡ̈ܗܐ ܥܒܪ̈ܝܐ.

# ܒܘܚܪܢܐ ܕܢܘܪܡܠܝܘܬܐ – ܦܪܘܦܣܘܪ ܣܛܐܛ. ܐܗܐ ܦܐܝܠ ܢܛܝܪܐ ܝܠܗ ܒ-UTF-8؛ ܟܠ ܣܕܪܐ ܕܡܥܝܪܢܘܬܐ ܟܫܪܐ ܒܡܠܬܐ ܕܣܘܪܝܬ
library(readxl)   # ܩܪܝܢܐ ܕܐܩܣܠ
library(e1071)    # ܥܩܝܡܘܬܐ ܘܓܒܢܘܬܐ ܒܢܘ̈ܣܚܐ ܕ-SPSS (type = 2)
library(nortest)  # ܒܘܚܪܢܐ ܕ-Lilliefors (Kolmogorov-Smirnov ܥܡ ܬܘܪܨܐ ܕ-Lilliefors)

# ܛܥܢܐ: ܛܘܦܣܐ ܬܩܝܢܐ – ܣܕܪܐ = ܡܫܬܘܬܦܢܐ، ܥܡܘܕܐ = ܡܫܬܚܠܦܢܐ؛ ܓܠܝܘܢܐ "נתונים"
d <- read_excel("C:/Rdata/DATA_normality_example_heb.xlsx", sheet = "נתונים")
y <- d[["עמדות_ציון"]]; y <- y[!is.na(y)]

# ܬܚܘܝܬܐ – ܠܘܚܐ 1: ܡܨܥܝܬܐ، ܛܥܝܘܬܐ ܬܩܝܢܬܐ، ܛܝܡܐ ܡܨܥܝܐ، ܣܛܝܘܬܐ ܬܩܝܢܬܐ، ܬܚܘܡܐ ܕܬܘܟܠܢܐ، ܦܬܝܘܬܐ ܒܝܢܝ ܪ̈ܘܒܥܐ (type = 6 = SPSS)
n <- length(y)
c(n = n, M = mean(y), SE = sd(y) / sqrt(n), Mdn = median(y), SD = sd(y))   # ܛܝ̈ܡܐ: 120, 3.269, 0.068, 3.25, 0.745
mean(y) + c(-1, 1) * qt(0.975, n - 1) * sd(y) / sqrt(n)                   # ܬܚܘܡܐ ܕܬܘܟܠܢܐ 95% [3.135, 3.404]
quantile(y, c(0.25, 0.75), type = 6)                                       # ܪ̈ܘܒܥܐ: 2.75, 3.84 – ܦܬܝܘܬܐ ܒܝܢܝ ܪ̈ܘܒܥܐ 1.09

# ܥܩܝܡܘܬܐ ܘܓܒܢܘܬܐ ܐܝܟ SPSS (type = 2)، ܛܥܝ̈ܘܬܐ ܬܩܝܢ̈ܬܐ ܘ-z
sk <- skewness(y, type = 2); ku <- kurtosis(y, type = 2)                 # ܛܝ̈ܡܐ: −0.060, −0.142
se_sk <- sqrt(6 * n * (n - 1) / ((n - 2) * (n + 1) * (n + 3)))           # ܛܥܝܘܬܐ ܬܩܝܢܬܐ: 0.221
se_ku <- sqrt(4 * (n^2 - 1) * se_sk^2 / ((n - 3) * (n + 5)))              # ܛܥܝܘܬܐ ܬܩܝܢܬܐ: 0.438
c(z_skew = sk / se_sk, z_kurt = ku / se_ku)                                # ܛܝ̈ܡܐ ܕ-z: −0.27, −0.32

# ܒܘܚܪ̈ܢܐ ܕܢܘܪܡܠܝܘܬܐ – ܠܘܚܐ 2
shapiro.test(y)                      # ܦܐܪܐ: W = 0.993, p = .818
lillie.test(y)                       # ܦܐܪܐ: D = 0.045, p = .795

# ܨܘܪ̈ܬܐ: ܗܝܣܛܘܓܪܡ ܥܡ ܣܪܛܐ ܟܦܝܦܐ ܢܘܪܡܠܝܐ، ܘܨܘܪܬܐ Q-Q (ܓܘ R ܡܣܟܝܐ ܥܠ ܣܪܛܐ ܦܫܝܛܐ – ܗܦܝܟܐ ܡܢ SPSS)
hist(y, freq = FALSE); curve(dnorm(x, mean(y), sd(y)), add = TRUE)
qqnorm(y); qqline(y)

# ܠܦܘܬ ܓܘܕܐ: ܗܝ ܡܕܡ ܩܐ ܟܠ ܕܪܓܐ ܕ-"קבוצה"
by(d[["עמדות_ציון"]], d[["קבוצה"]], shapiro.test)   # ܓܘܕܐ 1: W = 0.972, p = .179؛ ܓܘܕܐ 2: W = 0.985, p = .692

ܬܘܢܝܐ ܕܡܫܟܚ̈ܢܘܬܐ (reporting the results)

ܟܡܘܕܥܚ ܡܐ ܕܚܙܐܠܘܟܘܢ، ܠܐ ܒܣ ܡܐ ܕܒܚܝܪܐ ܝܠܗ: ܐܣܟܝܡܐ ܒܡ̈ܠܐ (ܫܘܝܐ ܠܬܪܝܢ ܓܢ̈ܒܐ ܒܩܘܪܒܐ؛ ܥܩܝܡܘܬܐ ܚܝܘܒܬܐ ܡܡܫܚܬܐ)، ܥܩܝܡܘܬܐ ܘܓܒܢܘܬܐ ܥܡ ܛܥܝ̈ܘܬܐ ܬܩܝܢ̈ܬܐ، ܘܐܢ ܟܡܘܕܥܚ ܒܘܚܪܢܐ – ܣܛܐܛܝܣܛܝܩܐ، ܕܪ̈ܓܐ ܕܚܐܪܘܬܐ (= N) ܘ-p ܚܬܝܬܐ. ܡܬܠܐ ܕ-Field (2024، ܦܣܩܐ 6.9.5) ܬܚܘܝܬܐ ܝܠܗ̇: "ܓܘ ܝܘܡܐ 1 ܥܩܝܡܘܬܐ ܫܪܝܪܐܝܬ ܨܦܪܐ ܝܠܗ̇، ܦܘܠܓܐ ܫܘܐ ܠܬܪܝܢ ܓܢ̈ܒܐ؛ ܓܘ ܝܘ̈ܡܐ 2 ܘ-3 ܛܝ̈ܡܐ ܕܥܩܝܡܘܬܐ ܚܕܪ 1، ܥܩܝܡܘܬܐ ܚܝܘܒܬܐ". ܡܐܡܪ̈ܐ ܕܬܘܢܝܐ (report sentences) ܕܓܘ ܡܦܩܢܐ ܒܢܝ̈ܐ ܝܢܐ ܗܟܢܐ، ܒܣܘܪܝܬ ܘܒܐܢܓܠܝܙܝܐ: ܐܣܟܝܡܐ ܕܦܘܠܓܐ (ܠܦܘܬ ܬܚܘ̈ܡܐ ܕܥܝܕܐ ܕܣܐܝܛ ܝܢܐ: ܥܩܝܡܘܬܐ ܥܕܡܐ 0.5 ܓܘ ܛܝܡܐ ܫܪܝܪܐ ܕܝܠܗ̇ – "ܫܘܐ ܠܬܪܝܢ ܓܢ̈ܒܐ ܒܩܘܪܒܐ"، 0.5-1 "ܡܡܫܚܬܐ"، ܠܥܠ ܡܢ 1 "ܪܒܬܐ"؛ ܗܢ ܬܚܘ̈ܡܐ ܩܐ ܓܒܢܘܬܐ)، ܛܝ̈ܡܐ ܥܡ ܛܥܝ̈ܘܬܐ ܬܩܝܢ̈ܬܐ، ܡܨܥܝܬܐ، ܛܝܡܐ ܡܨܥܝܐ ܘܣܛܝܘܬܐ ܬܩܝܢܬܐ، ܘܒܬܪ ܗܕܐ ܬܪܘܝܗܝ ܒܘܚܪ̈ܢܐ. ܐܡܬܝ ܕܕܘܡܝܐ ܪܒܐ ܝܠܗ، ܟܟܬܒܚ ܓܠܝܐܝܬ ܕܦܣܩܐ ܝܠܗ ܠܦܘܬ ܐܣܟܝܡܐ ܘܠܐ ܠܦܘܬ ܒܘܚܪܢܐ، ܘܟܡܚܘܝܚ ܢܡܘܣܐ ܕܬܚܘܡܐ ܡܨܥܝܐ. ܢܡܘ̈ܣܐ ܕܨܘܪܬܐ (American Psychological Association [APA], 2020, Section 6.36): D ܘ-W ܘ-p ܕܠܐ ܨܦܪܐ ܩܕܡ ܢܘܩܙܐ (ܠܐ ܡܨܝܝ ܕܣܠܩܝ ܠܥܠ ܡܢ 1)؛ ܥܩܝܡܘܬܐ ܘܓܒܢܘܬܐ – ܥܡ ܨܦܪܐ.

ܛܥܝ̈ܘܬܐ ܕܡܬܚܙܝܢ ܣܓܝ (Common mistakes)

ܕܦܣܩܚ ܠܦܘܬ p ܕܒܘܚܪܢܐ ܕܢܘܪܡܠܝܘܬܐ ܓܘ ܕܘܡܝܐ ܪܒܐ. ܓܘ N ܕܡܐܐ̈ܐ ܩܪܝܒܐ ܟܠ ܡܕܡ "ܪܫܝܡܐ" ܝܠܗ، ܘܩܪܝܒܐ ܠܐ ܡܕܡ ܟܡܫܢܐ (Field, 2024, Box 6.7; Pallant, 2020, Chapter 6).

ܕܡܬܢܝܚܚ ܡܢ p ܠܐ ܪܫܝܡܐ ܓܘ ܕܘܡܝܐ ܙܥܘܪܐ. ܠܒܘܚܪܢܐ ܠܝܬ ܚܝܠܐ ܣܛܐܛܝܣܛܝܩܝܐ؛ "ܠܐ ܡܫܟܚܐ ܝܠܗ̇ ܣܛܝܘܬܐ" ܠܐ ܝܠܗ "ܠܝܬ ܣܛܝܘܬܐ". ܟܚܙܝܚ ܨܘܪ̈ܬܐ.

ܕܩܪܚ ܟܘ̈ܟܒܐ ܕ-z ܒܕܘܟܬܐ ܕܛܝܡܐ. z ܟܪܒܐ ܥܡ ܕܘܡܝܐ؛ ܥܩܝܡܘܬܐ 0.3 ܥܩܝܡܘܬܐ ܙܥܘܪܬܐ ܝܠܗ̇ ܓܘ N = 50 ܘܐܦ ܓܘ N = 5,000، ܐܦܢ ܕܒܣ ܓܘ ܬܪܝܢܝܐ ܐܝܬ ܟܘ̈ܟܒܐ.

ܕܒܚܪܚ ܟܠ ܕܘܡܝܐ ܐܡܬܝ ܕܒܘܚܪܢܐ ܟܦܚܡ ܓܘ̈ܕܐ. ܣܝܡܐ ܝܠܗ ܥܠ ܦܘܠܓܐ ܓܘ ܟܠ ܓܘܕܐ؛ ܬܪܬܝܢ ܓܘ̈ܕܐ ܢܘܪܡܠܝ̈ܬܐ ܥܡ ܡܨܥܝ̈ܬܐ ܦܪ̈ܝܫܬܐ ܐܟܚܕܐ ܟܡܬܚܙܝ ܕܬܪܝܢ ܓܒ̈ܢܐ (bimodal).

ܕܥܒܕܚ ܫܘܢܝܐ (transformation) ܡܛܠ ܥܩܝܡܘܬܐ. ܩܕܡ ܗܕܐ – ܛܝ̈ܡܐ ܢܘܟܪ̈ܝܐ ܘܛܥܝ̈ܘܬܐ ܕܟܬܝܒܬܐ؛ ܒܬܪ ܗܕܐ – ܐܘܪ̈ܚܬܐ ܚܣܝܢ̈ܬܐ ܘ-bootstrap، ܠܐ ܫܘܢܝܐ ܕܦܐܪܐ (ܦܐܬܐ ܛܝ̈ܡܐ ܢܘܟܪ̈ܝܐ ܘܫܪ̈ܛܐ، ܦܣܩܐ 6).

ܕܒܚܪܚ ܢܘܪܡܠܝܘܬܐ ܕܦܣܘܩܐ ܕ-Likert ܝܚܝܕܝܐ. ܚܡܫܐ ܛܝ̈ܡܐ ܕܡܨܝܐ ܕܗܘܝܢ ܠܐ ܦܠܝܓ̈ܐ ܝܢܐ ܢܘܪܡܠܐܝܬ ܘܠܐ ܣܢܝܩ̈ܐ ܝܢܐ؛ ܦܣܘܩܐ ܝܚܝܕܝܐ ܝܠܗ ܡܫܬܚܠܦܢܐ ܕܛܟܣܐ – ܣܓܝܐܘ̈ܬܐ ܘܛܝܡܐ ܡܨܥܝܐ (ܣܓܝܐܘ̈ܬܐ ܘܣܛܐܛܝܣܛܝܩܐ ܡܚܘܝܢܝܬܐ).

ܕܫܒܩܚ ܓܘܒܝܐ ܡܩܕܡܐ listwise ܓܘ Explore. ܡܫܬܘܬܦܢܐ ܥܡ ܛܝܡܐ ܚܣܝܪܐ ܓܘ ܚܕ ܡܢ ܡܫܬܚܠܦ̈ܢܐ ܟܫܩܝܠ ܡܢ ܟܠܗܘܢ (Field, 2024, Section 6.9.2; Pallant, 2020, Chapter 6) – ܟܓܒܚ pairwise، ܐܝܟ ܦܐܬܐ.

ܕܡܦܠܚܚ ܒ-p ܕ-ks.test ܓܘ R. ܗܘ ܟܣܐܡ ܡܨܥܝܬܐ ܘܣܛܝܘܬܐ ܬܩܝܢܬܐ ܝܕܝܥ̈ܐ؛ ܩܐ ܢܘܪܡܠܝܘܬܐ ܥܡ ܦܪܡܝ̈ܛܪܐ ܡܫܘܥܪ̈ܐ – lillie.test (Gross & Ligges, 2015).

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.

Gross, J., & Ligges, U. (2015). nortest: Tests for normality (R package version 1.0-4) [Computer software]. https://CRAN.R-project.org/package=nortest

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

R Core Team. (2024). R: A language and environment for statistical computing (Version 4.3.3) [Computer software]. R Foundation for Statistical Computing. https://www.R-project.org/

Tabachnick ܘ-Fidell (2013) – ܐܝܟ ܕܡܬܡܠܠܝ ܓܘ Pallant (2020)؛ Royston (1995) – ܐܝܟ ܕܡܬܡܠܠܐ ܓܘ ܬܚܘܝܬܐ ܕ-shapiro.test ܕ-R؛ Dallal ܘ-Wilkinson (1986) ܘ-Stephens (1974) – ܐܝܟ ܕܡܬܡܠܠܝ ܓܘ ܬܚܘܝܬܐ ܕܚܒܝܫܘܬܐ nortest؛ Joel ܘ-Charlot (2022) – ܐܝܟ ܕܡܬܡܠܠܝ ܓܘ Field (2024). ܠܦܘܬ ܢܡܘܣܐ ܕܣܐܝܛ (site rule)، ܓܘ ܪܫܝܡܬܐ ܕܡܒܘ̈ܥܐ (reference list) ܟܡܬܚܙܝ ܒܣ ܡܒܘ̈ܥܐ ܕܩܪܝ̈ܐ ܝܢܐ ܓܘ ܢܘܣܚܐ ܩܕܡܝܐ؛ Pallant (2020) ܘ-APA (2020) – ܠܦܘܬ ܨܚܚܐ ܘܦܣܩܐ ܕܢܘܣܚܐ ܛܒܝܥܐ؛ Field (2024) ܓܘ ܢܘܣܚܐ ܕܝܓܝܛܠܝܐ ܪܕܝܐ (reflowable) – ܠܦܘܬ ܦܣܩܐ، ܩܘܦܣܐ ܘܡܥܝܪܢܘܬܐ؛ ܬܚܘܝܬܐ ܕ-R ܘ-nortest – ܐܝܟ ܕܛܒܝܥܐ ܝܠܗ̇ ܓܘ R 4.3.3. ܐܠܓܘܪܝܬܡ ܕ-Shapiro-Wilk ܘܩܘܪܒܐ ܕ-p ܕ-Lilliefors ܥܒܝܕ̈ܐ ܝܢܐ ܓܘ ܦܐܬܐ ܠܦܘܬ ܥܒܕܐ ܕ-R ܘܫܪܝܪ̈ܐ ܝܢܐ ܩܘܒܠܗ ܘܩܘܒܠ PSPP.