ܒܘܚܪܢܐ t ܠܕܘ̈ܡܝܐ ܠܐ ܬܠܝ̈ܐ (independent-samples t-test)

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 ܕܒܥܝܚ ܕܝܕܥܚ ܐܢ ܡܨܥܝܬܐ (mean) ܕܡܫܬܚܠܦܢܐ ܟܡܝܝܐ (quantitative variable) ܦܪܝܫܬܐ ܝܠܗ ܒܝܢܝ ܬܪܝܢ ܓܘ̈ܕܐ ܦܪ̈ܝܫܐ ܕܡܫܬܘܬܦ̈ܢܐ (participants) – ܓܘܕܐ ܕܢܣܝܘܢܐ ܩܘܒܠ ܓܘܕܐ ܕܦܘܚܡܐ (control group)، ܓܒܪ̈ܐ ܩܘܒܠ ܢܫ̈ܐ، ܙܒܘ̈ܢܐ ܩܘܒܠ ܠܐ-ܙܒܘ̈ܢܐ. Pallant (2020، ܨܚܚܐ 17) ܟܡܚܕܕܐ ܛܘܦܣܐ: ܚܕ ܡܫܬܚܠܦܢܐ ܠܐ ܬܠܝܐ (independent variable) ܕܓܢ̈ܣܐ ܥܡ ܬܪܝܢ ܓܘ̈ܕܐ ܚܬܝܬܐܝܬ، ܘܚܕ ܡܫܬܚܠܦܢܐ ܬܠܝܐ (dependent variable) ܟܡܝܝܐ؛ ܟܠ ܡܫܬܘܬܦܢܐ ܕܝܠܗ ܝܠܗ ܕܚܕܐ ܓܘܕܐ ܒܣ. Field (2024، ܦܣܩܐ 10.5) ܟܦܪܫ ܒܝܢܝ ܬܪܝܢ "ܨܪ̈ܪܐ" ܕܗܝ ܣܛܐܛܝܣܛܝܩܐ: ܒܘܚܪܢܐ t ܠܠܐ ܬܠܝ̈ܐ – ܐܝܡܢ ܕܚܙ̈ܝܬܐ (observations) ܟܐܬܝܐ ܡܢ ܐܝܬܘܬ̈ܐ ܦܪ̈ܝܫܐ؛ ܘܒܘܚܪܢܐ t ܠܙܘܓܢ̈ܝܐ – ܐܝܡܢ ܕܗܢܝ ܡܫܬܘܬܦ̈ܢܐ (ܝܢ ܙܘܓ̈ܐ ܦܐܝ̈ܐ) ܟܡܫܬܚܝ ܬܪܝܢ ܓܗ̈ܐ. Field ܟܡܘܣܦ ܕܒܘܚܪܢܐ t ܠܠܐ ܬܠܝ̈ܐ ܝܠܗ ܚܕ ܓܕܫܐ ܝܚܝܕܝܐ ܕܡܘܕܝܠ ܣܪܛܢܝܐ (linear model): ܪܝܓܪܫܢ (regression) ܥܡ ܡܢܒܝܢܐ (predictor) ܕܬܪܝܢ ܛܝ̈ܡܐ، ܕܓܘܗ ܡܢܝܢܐ ܡܫܘܬܦܐ (coefficient) b ܝܠܗ ܦܘܪܫܢܐ ܒܝܢܝ ܬܪܬܝܢ ܡܨܥܝ̈ܬܐ (ܦܣܩܐ 10.4) – ܗܘ t، ܗܘ p.

ܩܐ ܒܝܫ ܡܢ ܬܪܝܢ ܓܘ̈ܕܐ – ܦܘܫܩܐ ܕܫܘܚܠܦܐ ܕܚܕ ܐܘܪܚܐ (one-way ANOVA)، ܠܐ ܣܕܪܐ ܕܒܘܚܪ̈ܢܐ t (ܦܣܩܐ "ܫܪ̈ܛܐ ܘܙܘܗܪ̈ܐ")؛ ܩܐ ܗܢܝ ܡܫܬܘܬܦ̈ܢܐ (participants) ܒܬܪܝܢ ܡܚܘ̈ܝܢܐ – ܒܘܚܪܢܐ t ܠܙܘܓܢ̈ܝܐ؛ ܐܝܡܢ ܕܡܫܬܚܠܦܢܐ ܬܠܝܐ (dependent variable) ܝܠܗ ܕܛܟܣܐ ܝܢ ܟܡܥܒܪ ܥܠ ܫܪ̈ܛܐ (assumptions) ܣܓܝ – Mann-Whitney (Pallant, 2020, Chapter 16)، ܕܠܐ ܝܠܗ ܓܘ ܐܗܐ ܦܐܬܐ. ܡܢܝܢܐ ܕܣܒܠܬܐ ܕܦܣܘ̈ܩܐ ܣܓܝ̈ܐܐ (multi-item scale score؛ ܡܨܥܝܬܐ ܕܦܣܘ̈ܩܐ، ܦܐܬܐ ܐܠܦܐ ܕ-Cronbach ܘܡܢܝܢܐ ܕܣܒܠܬܐ) ܡܬܛܦܠܐ ܝܠܗ ܐܝܟ ܡܫܬܚܠܦܢܐ ܕܪܘ̈ܚܩܐ ܫܘ̈ܝܐ (interval variable) ܠܦܘܬ ܥܝܕܐ ܕܣܐܝܛ (site convention؛ ܦܐܬܐ ܡܫܬܚܠܦ̈ܢܐ ܘܕܪ̈ܓܐ ܕܡܫܘܚܬܐ)، ܘܡܛܠ ܗܕܐ ܦܐܝܐ ܝܠܗ ܐܝܟ ܡܫܬܚܠܦܢܐ ܬܠܝܐ؛ ܦܣܘܩܐ ܕ-Likert (Likert item) ܝܚܝܕܝܐ – ܠܐ.

ܚܘܫܒܐ: ܐܬܐ (signal) ܡܦܠܓܐ ܥܠ ܫܓܘܫܝܐ (noise)

Field (2024، ܦܣܩܐ 10.5.1): ܬܪܝܢ ܕܘ̈ܡܝܐ (samples) ܟܝܗܒܝ ܬܪܬܝܢ ܡܨܥܝ̈ܬܐ، ܘܐܢܝ ܦܪ̈ܝܫܐ ܝܢܐ ܡܢ ܚܕ̈ܕܐ ܩܠܝܠ ܝܢ ܣܓܝ. ܐܢ ܬܪܘܝܗܝ ܐܬܝ̈ܐ ܝܢܐ ܡܢ ܗܘ ܟܢܫܐ ܟܠܢܝܐ (population)، ܦܘܪܫܢܐ ܒܝܢܝ ܬܪܘܝܗܝ ܟܐܬܐ ܡܢ ܙܘܥܐ ܕܕܘܡܝܐ ܒܣ، ܘܗܘ ܡܫܝܚܐ ܝܠܗ ܒܛܥܝܘܬܐ ܬܩܝܢܬܐ (standard error) ܕܦܘܪܫܢܐ؛ t ܝܠܗ ܦܘܪܫܢܐ ܚܙܝܐ (observed) ܡܦܠܓܐ ܥܠ ܐܕܐ ܛܥܝܘܬܐ ܬܩܝܢܬܐ – "ܐܬܐ ܡܦܠܓܐ ܥܠ ܫܓܘܫܝܐ". ܟܡܐ ܕܦܘܪܫܢܐ ܪܒܐ ܝܠܗ ܩܘܒܠ ܛܥܝܘܬܐ ܬܩܝܢܬܐ، ܥܣܩ ܝܠܗ ܒܝܫ ܕܡܗܝܡܢܚ ܕܗܘ ܡܢ ܓܕܫܐ ܝܠܗ. ܛܝܡܐ p ܝܠܗ ܡܣܬܒܪܢܘܬܐ (probability) ܕܫܩܠܬܐ ܕ-t ܐܝܟ ܐܗܐ ܝܢ ܪܚܝܩܐ ܒܝܫ ܡܢܗ ܐܢ ܦܘܪܫܢܐ ܫܪܝܪܐ ܓܘ ܟܢܫܐ ܟܠܢܝܐ ܝܠܗ ܣܦܪ.

ܛܥܝܘܬܐ ܬܩܝܢܬܐ (standard error) ܕܦܘܪܫܢܐ ܟܡܬܒܢܝܐ ܡܢ ܫܘܚܠ̈ܦܐ (variances) ܕܬܪܝܢ ܓܘ̈ܕܐ. ܐܝܡܢ ܕܓܘ̈ܕܐ ܦܪ̈ܝܫܐ ܝܢܐ ܒܪܒܘܬܐ ܕܝܗܝ، ܟܡܦܠܚܚ ܒܫܘܚܠܦܐ ܡܫܘܬܦܐ (pooled variance): ܡܨܥܝܬܐ ܡܬܩܠܬܐ ܕܬܪܝܢ ܫܘܚܠ̈ܦܐ، ܐܝܡܢ ܕܡܬܩܠܐ ܕܟܠ ܓܘܕܐ ܝܠܗ ܕܪ̈ܓܐ ܕܚܐܪܘܬܐ (degrees of freedom) ܕܝܠܗ (n − 1)، ܩܐ ܕܕܘܡܝܐ ܪܒܐ ܟܫܥܪ ܟܢܫܐ ܟܠܢܝܐ ܛܒܐ ܒܝܫ (Field, 2024, Section 10.5.3, Equation 10.15; Gravetter & Wallnau, 2017, pp. 305-307). ܕܪ̈ܓܐ ܕܚܐܪܘܬܐ ܕܒܘܚܪܢܐ: df = n₁ + n₂ − 2. ܐܗܐ ܝܠܗ ܣܕܪܐ "ܫܘܚܠ̈ܦܐ ܫܘ̈ܝܐ" ܓܘ ܠܘܚܐ (table). ܣܕܪܐ ܬܪܝܢܐ، Welch، ܠܐ ܟܡܚܕ ܫܘܚܠ̈ܦܐ ܐܠܐ ܟܡܦܠܚ ܒܟܠ ܚܕ ܒܦܪܝܫܘܬܐ، ܘܟܡܬܪܨ ܕܪ̈ܓܐ ܕܚܐܪܘܬܐ ܠܬܚܬ (ܘܡܛܠ ܗܕܐ ܓܘ ܣܓܝ ܓܗ̈ܐ ܠܐ ܝܢܐ ܡܢܝ̈ܢܐ ܓܡܝܪ̈ܐ – 21.54 ܓܘ ܡܬܠܐ ܕ-Field، ܦܣܩܐ 10.8.3)؛ ܐܝܡܢ ܕܫܘܚܠ̈ܦܐ ܘܪ̈ܒܘܬܐ ܫܘ̈ܝܐ ܝܢܐ، ܬܪܝܢ ܣܕܪ̈ܐ ܐܝܟ ܚܕ ܝܢܐ.

ܩܪܝܢܐ ܕܡܦܩܢܐ (How to read the output)

ܠܘܚܐ 1 – ܣܛܐܛܝܣܛܝܩܐ ܕܓܘ̈ܕܐ. Pallant (2020، ܨܚܚܐ 17) ܟܫܪܝܐ ܠܐܟܐ: ܕܒܚܪܚ ܕ-N ܕܟܠ ܓܘܕܐ ܦܐܝܐ ܝܠܗ – ܓܘܕܐ ܣܦܝܩܐ ܝܢ ܙܥܘܪܐ ܣܓܝ ܡܢ ܕܡܣܟܝܚ ܒܐܟܡܐ ܕܥܝܕܐ ܟܡܚܘܝܐ ܪܡܙܐ ܠܐ ܬܪܝܨܐ (0 ܘ-1 ܒܕܘܟܬ 1 ܘ-2) ܝܢ ܛܝ̈ܡܐ ܚܣܝ̈ܪܐ (missing values) ܣܓܝ̈ܐܐ. ܥܡ ܡܨܥܝܬܐ (mean) ܘܣܛܝܘܬܐ ܬܩܝܢܬܐ (standard deviation) – ܛܥܝܘܬܐ ܬܩܝܢܬܐ (standard error) ܕܡܨܥܝܬܐ، ܕܡܢܗ ܟܡܬܒܢܝ ܬܚܘ̈ܡܐ ܕܬܘܟܠܢܐ (confidence intervals) ܕܓܘ ܨܘܪܬܐ.

ܠܘܚܐ 2 – ܒܘܚܪܢܐ، ܒܬܪܝܢ ܣܕܪ̈ܐ. ܐܗܐ ܝܠܗ ܠܘܚܐ Independent Samples Test ܕ-SPSS. ܣܕܪܐ ܩܕܡܝܐ ܟܣܐܡ ܫܘܝܘܬܐ ܕܫܘܚܠ̈ܦܐ، ܬܪܝܢܐ ܠܐ (Welch)، ܘܓܘ ܣܕܪܐ ܩܕܡܝܐ ܛܒܝܥܐ ܝܠܗ ܐܦ ܒܘܚܪܢܐ ܕ-Levene (Levene's test) ܩܐ ܫܘܝܘܬܐ ܕܫܘܚܠ̈ܦܐ. ܐܝܢܐ ܣܕܪܐ ܟܩܪܚ؟ ܠܐܟܐ ܡܒܘ̈ܥܐ ܦܠܝܓ̈ܐ ܝܢܐ، ܘܦܐܬܐ ܟܡܚܘܝܐ ܬܪܝܢ ܪܥܝܢ̈ܐ:

ܒܥܒܕܐ ܬܪܝܢ ܣܕܪ̈ܐ ܟܝܗܒܝ ܟܡܥܛ ܟܠ ܐܡܢ ܗܝ ܚܬܡܬܐ، ܘܩܘܛܝܐ ܕ"ܩܪܝܢܐ ܕܦܐܪܐ" (Interpreting the result) ܓܘ ܡܦܩܢܐ (output) ܟܐܡܪܐ ܐܢ ܐܢܝ ܫܠܡܝ. ܐܝܡܢ ܕܠܐ ܫܠܡܝ – ܒܐܟܡܐ ܕܥܝܕܐ ܓܘ̈ܕܐ ܒܪܒܘܬܐ ܦܪܝܫܬܐ ܣܓܝ ܥܡ ܫܘܚܠ̈ܦܐ (variances) ܦܪ̈ܝܫܐ ܣܓܝ – Gravetter ܘ-Wallnau (2017، ܦܐܬܐ 313-314) ܟܡܦܫܩܝ ܩܡܘܕܝ ܠܐ ܟܡܨܝܚ ܕܬܟܠܚ ܥܠ ܣܕܪܐ ܕܫܘܚܠܦܐ ܡܫܘܬܦܐ (pooled variance): ܐܢ ܬܪܝܢ ܫܘܚܠ̈ܦܐ ܟܫܥܪܝ ܡܕܡ̈ܐ ܦܪ̈ܝܫܐ، ܡܨܥܝܬܐ ܕܝܗܝ ܠܝܬܠܗ ܣܘܟܠܐ، ܘ-t ܪܚܝܩܐ ܡܨܐ ܕܐܬܐ ܡܢܗ ܘܠܐ ܡܢ ܦܘܪܫܢܐ ܕܡܨܥܝ̈ܬܐ؛ ܓܘ ܐܗܐ ܗܘܝܐ ܣܕܪܐ ܕ-Welch ܝܠܗ ܬܘܢܝܐ ܚܣܝܢܐ، ܕܠܐ ܚܫܒܢܐ ܕܢܡܘܣܐ ܕܓܒܠܘܟܘܢ.

t، df ܘ-p. p ܕܬܪܝܢ ܕܘܢ̈ܒܐ (two-tailed، Sig. 2-tailed): ܐܢ ܙܥܘܪܐ ܝܠܗ ܡܢ .05 – ܦܘܪܫܢܐ ܪܫܝܡܐ ܝܠܗ ܣܛܐܛܝܣܛܝܩܐܝܬ (statistically significant)؛ ܐܢ ܪܒܐ – ܠܐ ܐܫܟܚ ܦܘܪܫܢܐ ܪܫܝܡܐ (Pallant, 2020, Chapter 17). ܐܬܐ ܕ-t ܬܠܝܐ ܝܠܗ ܒܣ ܒܐܝܢܐ ܓܘܕܐ ܓܒܝܐ ܝܠܗ ܐܝܟ "ܓܘܕܐ ܐ": ܦܘܪܫܢܐ ܚܫܝܒܐ ܝܠܗ ܐ ܒܨܝܪ ܒ (Field, 2024, Section 10.8.3, Note 5). ܬܚܘܡܐ ܕܬܘܟܠܢܐ (confidence interval) ܩܐ ܦܘܪܫܢܐ. ܦܬܝܘܬܐ (range) ܕܓܘܗ، ܒܕܪܓܐ ܕܬܘܟܠܢܐ 95%، ܐܝܬ ܦܘܪܫܢܐ ܕܡܨܥܝ̈ܬܐ ܓܘ ܟܢܫܐ ܟܠܢܝܐ (population) (Gravetter & Wallnau, 2017, pp. 319-320). ܐܝܡܢ ܕܐܝܬ ܓܘܗ ܣܦܪ، ܒܘܚܪܢܐ ܠܐ ܝܠܗ ܪܫܝܡܐ – ܘܗܕܟܐ ܐܦ ܗܦܟܐ؛ Gravetter ܘ-Wallnau (ܦܐܬܐ 320) ܟܡܚܘܝܝ ܕܐܗܐ ܝܠܗ ܗܝ ܦܣܩܬܐ ܒܬܪܬܝܢ ܠܫܢ̈ܐ. ܬܚܘܡܐ ܕܬܘܟܠܢܐ ܦܬܝܐ ܝܠܗ ܒܝܫ ܟܡܐ ܕܕܘܡܝܐ (sample) ܙܥܘܪܐ ܝܠܗ، ܘܡܛܠ ܗܕܐ ܗܘ ܬܚܘܝܬܐ ܝܠܗ ܕܠܐ ܘܕܐܝܘܬܐ (uncertainty) ܘܠܐ ܡܚܘܝܢܐ ܕܟܝܐ ܕܪܒܘܬܐ ܕܡܥܒܕܢܘܬܐ (effect size).

ܪܒܘܬܐ ܕܡܥܒܕܢܘܬܐ (effect size)

ܪܫܝܡܘܬܐ (significance) ܠܐ ܝܠܗ ܪܒܘܬܐ: ܓܘ ܕܘܡܝܐ (sample) ܪܒܐ ܐܝܟ ܕܣܦܩ ܐܦ ܦܘܪܫܢܐ ܙܥܘܪܐ ܛܒܐ ܟܦܠܛ ܪܫܝܡܐ، ܘܓܘ ܕܘܡܝܐ ܙܥܘܪܐ ܐܦ ܦܘܪܫܢܐ ܪܒܐ ܠܐ (Field، 2024، ܦܣܩܐ 3.7.3 – ܬܪܝܢ ܡܬܠ̈ܐ ܓܘ ܨܘܪ̈ܬܐ 2.21 ܘ-2.22). ܡܛܠ ܗܕܐ ܠܘܚܐ (table) ܟܛܒܥ ܬܪܝܢ ܡܚܘ̈ܝܢܐ (measures) ܕܠܐ ܬܠܝ̈ܐ ܝܢܐ ܒܪܒܘܬܐ ܕܕܘܡܝܐ:

d ܕ-Cohen (Cohen's d) – ܦܘܪܫܢܐ ܒܝܢܝ ܡܨܥܝ̈ܬܐ (means) ܒܡܫܘ̈ܚܬܐ ܕܣܛܝܘܬܐ ܬܩܝܢܬܐ (standard deviation): "ܐܢ ܐܢܫܐ ܙܡܪ ܒܕܘܟܬ ܕܡܡܠܠ، ܙܒܢܐ ܕܫܡܘܥܐ ܟܦܐܫ ܢܚܬ ܒ-0.667 ܣܛܝ̈ܘܬܐ ܬܩܝܢ̈ܝܬܐ" (Field, Section 3.7.3). ܦܐܬܐ ܟܡܦܠܓܐ ܦܘܪܫܢܐ ܥܠ ܫܪܫܐ ܕܫܘܚܠܦܐ ܡܫܘܬܦܐ (pooled variance)، ܐܝܟ Gravetter ܘ-Wallnau (2017، ܦܐܬܐ 317، ܫܘܝܘܬܐ 10.8) ܘܐܝܟ Cohen's d ܓܘ ܡܦܩܢܐ (output) ܕ-SPSS؛ Field (ܦܣܩܐ 3.7.3) ܟܡܥܗܕ ܚܕ ܚܠܦܐ – ܣܛܝܘܬܐ ܬܩܝܢܬܐ ܕܓܘܕܐ ܕܦܘܚܡܐ (control group)، ܐܝܡܢ ܕܐܣܝܘܬܐ ܡܨܝܐ ܕܫܢܝܐ ܐܦ ܒܕܪܐ. ܥܝ̈ܕܐ ܕ-Cohen (1988، ܦܐܬܐ 25-27): 0.2 ܙܥܘܪܐ، 0.5 ܡܨܥܝܐ ("ܚܙܝܐ ܠܥܝܢܐ ܕܠܐ ܡܐܢܐ")، 0.8 ܪܒܐ – ܘܥܡܗܝ ܙܘܗܪܐ ܕ-Cohen ܓܢܒܗ، ܕܟܡܝܬܐ Field: ܬܚܘ̈ܡܐ ܟܡܥܒܪܝ ܚܘܫܒܐ ܕܠܐ ܥܡܠܐ (lazy thinking)، ܘܡܥܒܕܢܘܬܐ (effect) ܡܬܕܝܢܐ ܝܠܗ ܓܘ ܣܝܩܐ ܕܬܚܘܡܐ ܘܕܡܐܢ̈ܐ ܕܡܫܘܚܬܐ. d ܡܬܬܢܐ ܝܠܗ ܒܐܟܡܐ ܕܥܝܕܐ ܐܝܟ ܛܝܡܐ ܕܠܐ ܐܬܐ ܕܒܨܘܪܐ (positive; Gravetter & Wallnau, p. 317).

ܐܝܬܐ ܡܪܒܥܐ (eta squared) (η²، ܓܘ Gravetter ܘ-Wallnau r²) – ܡܢܬܐ ܕܫܘܚܠܦܐ (variance) ܓܘ ܡܫܬܚܠܦܢܐ ܬܠܝܐ (dependent variable) ܕܡܦܫܩܐ ܝܠܗ ܒܗܘܝܐ ܕܓܘ ܓܘܕܐ: t²/(t² + df) (Gravetter & Wallnau, 2017, pp. 317-318, Equation 10.9; Pallant, 2020, Chapter 17). Pallant ܟܡܝܬܝܐ ܬܚܘ̈ܡܐ ܕ-Cohen (1988، ܦܐܬܐ 284-287): .01 ܙܥܘܪܐ، .06 ܡܨܥܝܐ، .14 ܪܒܐ – ܘܟܡܙܗܪܐ ܕܠܐ ܡܚܠܛܚ ܒܝܢܝ ܡܫܘ̈ܚܬܐ: d = 0.5 ܡܨܥܝܐ ܝܠܗ، η² = .06 ܡܨܥܝܐ ܝܠܗ، ܘܐܢܝ ܡܢܝ̈ܢܐ ܦܪ̈ܝܫܐ ܝܢܐ ܩܐ ܗܝ ܡܥܒܕܢܘܬܐ. ܦܐܬܐ ܟܚܫܒܐ η² ܡܢ ܣܕܪܐ ܕܫܘܚܠ̈ܦܐ ܫܘ̈ܝܐ، ܐܝܟ ܓܘ ܡܬܠܐ ܕ-Pallant.

ܫܪ̈ܛܐ ܘܙܘܗܪ̈ܐ (Assumptions and warnings)

ܬܠܬܐ ܫܪ̈ܛܐ (assumptions) (Gravetter & Wallnau, 2017, p. 313): ܚܙ̈ܝܬܐ (observations) ܓܘ ܟܠ ܓܘܕܐ ܠܐ ܬܠܝ̈ܐ ܝܢܐ ܚܕܐ ܒܚܕܐ؛ ܬܪܝܢ ܟܢܫ̈ܐ ܟܠܢܝ̈ܐ (populations) ܐܝܬܠܗܘܢ ܦܘܠܓܐ ܢܘܪܡܠܝܐ (normal distribution)؛ ܘܠܬܪܘܝܗܝ ܐܝܬ ܗܘ ܫܘܚܠܦܐ (variance؛ ܗܘܡܘܓܢܝܘܬܐ). ܠܐ ܬܠܝܘܬܐ ܝܠܗ ܫܪܛܐ ܕܠܝܬܠܗ ܬܘܪܨܐ – ܡܫܬܘܬܦܢܐ (participant) ܕܡܫܝܚܐ ܝܠܗ ܬܪܝܢ ܓܗ̈ܐ، ܙܘܓ̈ܐ، ܝܢ ܬܠܡ̈ܝܕܐ ܡܢ ܗܢܝ ܨܦ̈ܐ ܟܥܒܪܝ ܥܠܗ، ܘܗܝܓܐ ܒܘܚܪܢܐ ܬܪܝܨܐ ܐܚܪܢܐ ܝܠܗ (ܙܘܓܢ̈ܝܐ، ܝܢ ܡܘܕܝܠ ܕܟܚܫܒ ܒܢܝܢܐ). ܢܘܪܡܠܝܘܬܐ (normality) "ܒܨܝܪ ܚܫܝܚܐ ܝܠܗ، ܒܦܪܝܫܘܬܐ ܓܘ ܕܘ̈ܡܝܐ ܪ̈ܒܐ" (Gravetter & Wallnau, p. 313)؛ Field (2024، ܦܣܩܐ 10.6) ܟܡܫܕܪ ܠܨܚܚܐ 6: ܡܐ ܕܣܢܝܩ ܝܠܗ ܦܘܠܓܐ ܢܘܪܡܠܝܐ ܕܓܘܒܝܐ ܕܕܘܡܝܐ (sampling distribution) ܕܦܘܪܫܢܐ، ܘܢܡܘܣܐ ܕܬܚܘܡܐ ܡܨܥܝܐ (central limit theorem) ܟܡܫܪܪ ܠܗ ܓܘ ܕܘܡܝܐ ܦܐܝܐ – ܘܡܛܠ ܗܕܐ ܠܐ ܟܒܚܪܚ ܢܘܪܡܠܝܘܬܐ ܒܒܘܚܪܢܐ ܕܪܫܝܡܘܬܐ (ܩܘܛܝܐ 6.7)، ܐܠܐ ܟܚܙܚ ܗܝܣܛܘܓܪܐܡ، ܥܩܝܡܘܬܐ (skewness) ܘܓܒܢܘܬܐ (kurtosis) ܕܟܠ ܓܘܕܐ (ܦܐܬܐ ܒܘܚܪܢܐ ܕܢܘܪܡܠܝܘܬܐ – ܠܦܘܬ ܓܘܕܐ؛ ܦܐܬܐ ܣܓܝܐܘ̈ܬܐ ܘܣܛܐܛܝܣܛܝܩܐ ܡܚܘܝܢܝܬܐ) ܘܥܠ ܛܝ̈ܡܐ ܢܘܟܪ̈ܝܐ (outliers؛ ܦܐܬܐ ܛܝ̈ܡܐ ܢܘܟܪ̈ܝܐ ܘܫܪ̈ܛܐ).

ܗܘܡܘܓܢܝܘܬܐ ܕܫܘܚܠ̈ܦܐ (homogeneity of variances). Gravetter ܘ-Wallnau (ܦܐܬܐ 313-314): ܫܪܛܐ ܚܫܝܚܐ ܝܠܗ ܒܦܪܝܫܘܬܐ ܐܝܡܢ ܕܐܝܬ ܦܘܪܫܢܐ ܪܒܐ ܒܪܒܘܬܐ ܕܓܘ̈ܕܐ، ܘܢܡܘܣܐ ܕܨܒܥܐ ܩܕܡ ܟܠ ܒܘܚܪܢܐ – ܐܢ ܚܕ ܫܘܚܠܦܐ ܪܒܐ ܝܠܗ ܬܠܬܐ-ܐܪܒܥܐ ܓܗ̈ܐ ܡܢ ܐܚܪܢܐ، ܐܝܬ ܕܘܟܐ ܩܐ ܙܘܗܪܐ. Field (ܦܣܩܐ 6.9.6) ܟܡܘܣܦ ܕܓܘ ܓܘ̈ܕܐ ܫܘ̈ܝܐ ܒܪܒܘܬܐ ܫܪܛܐ "ܟܡܥܛ ܠܐ ܝܠܗ ܚܫܝܚܐ". ܦܐܬܐ ܟܛܒܥܐ ܒܘܚܪܢܐ ܕ-Levene ܐܝܟ SPSS (ܚܕܪ ܡܨܥܝܬܐ – ܗܕܟܐ ܓܘ ܡܦܩܢܐ ܕܒܘܚܪܢܐ t ܕ-SPSS؛ Explore ܟܛܒܥ ܟܡܐ ܢܘܣ̈ܚܐ ܕܒܘܚܪܢܐ، ܚܕܪ ܡܨܥܝܬܐ ܘܚܕܪ ܛܝܡܐ ܡܨܥܝܐ)، ܘܬܪܝܢ ܣܕܪ̈ܐ؛ ܦܣܩܐ "ܩܪܝܢܐ ܕܡܦܩܢܐ" ܟܡܦܫܩ ܬܪܝܢ ܪܥܝܢ̈ܐ.

ܛܝ̈ܡܐ ܚܣܝ̈ܪܐ (missing values). ܡܫܬܘܬܦܢܐ (participant) ܕܚܣܝܪܐ ܝܠܗ ܛܝܡܐ ܕܝܠܗ ܓܘ ܡܫܬܚܠܦܢܐ ܬܠܝܐ (dependent variable) ܝܢ ܓܘ ܡܫܬܚܠܦܢܐ ܕܓܘ̈ܕܐ ܠܐ ܥܠܝܠܐ ܝܠܗ ܓܘ ܦܘܚܡܐ ܕܗܘ ܡܫܬܚܠܦܢܐ ܬܠܝܐ ܒܣ – ܫܩܠܬܐ ܠܦܘܬ ܦܘܫܩܐ (/MISSING=ANALYSIS ܓܘ ܣܝܢܬܐܟܣ)، ܐܝܟ ܓܘܒܝܐ ܡܩܕܡܐ (default) ܕ-SPSS؛ ܡܛܠ ܗܕܐ N ܡܨܐ ܕܫܢܐ ܡܢ ܡܫܬܚܠܦܢܐ ܬܠܝܐ ܠܐܚܪܢܐ. ܓܘ̈ܕܐ ܕܠܐ ܓܒܝ̈ܐ ܝܢܐ (ܓܘ ܡܫܬܚܠܦܢܐ ܕܓܘ̈ܕܐ ܥܡ ܒܝܫ ܡܢ ܬܪܝܢ ܕܪ̈ܓܐ) ܒܣ ܠܐ ܥܐܠܝ. ܡܘܕܝ ܥܒܕܚ ܥܡ ܚܣܝ̈ܪܐ – ܦܐܬܐ ܛܝ̈ܡܐ ܚܣܝ̈ܪܐ.

ܒܘܚܪ̈ܢܐ ܣܓܝ̈ܐܐ. ܟܡܐ ܡܫܬܚܠܦ̈ܢܐ ܬܠܝ̈ܐ (dependent variables) ܒܚܕ ܕܚܩܐ ܟܡܐ ܒܘܚܪ̈ܢܐ ܝܢܐ، ܘܟܠ ܚܕ ܟܛܥܢ 5% ܣܘܟܢܐ ܕܛܥܝܘܬܐ ܕܙܢܐ I (Type I error)؛ Field (2024، ܦܣܩܐ 10.8.2) ܟܡܥܗܕ ܕܒܘܚܪ̈ܢܐ t ܣܓܝ̈ܐܐ ܟܡܪܒܝ ܡܢܬܐ ܕܛܥܝܘܬܐ، ܘܩܐ ܦܘܚܡܐ ܕܒܝܫ ܡܢ ܬܪܝܢ ܓܘ̈ܕܐ ܟܡܦܠܚܚ ܒ-ANOVA ܘܠܐ ܒܣܕܪܐ ܕܒܘܚܪ̈ܢܐ t. ܐܝܡܢ ܕܟܬܢܚ ܟܡܐ ܒܘܚܪ̈ܢܐ – ܟܬܢܚ ܟܠܗܘܢ، ܐܦ ܐܢܝ ܕܠܐ ܪܫܝܡ̈ܐ ܝܢܐ، ܘܟܚܫܒܚ ܥܠ ܬܘܪܨܐ (ܦܐܬܐ ܕܐܣܘܪ̈ܐ ܕܚܕ̈ܕܐ: Holm / FDR).

ܡܘܕܝ ܠܐ ܟܚܫܒܐ ܐܗܐ ܦܐܬܐ (What this page does not compute). ܬܚܘܡܐ ܕܬܘܟܠܢܐ (confidence interval) ܩܐ d (SPSS 27 ܘܠܥܠ ܟܛܒܥ ܠܗ – Field، ܦܣܩܐ 10.8.5)، ܬܚܘ̈ܡܐ ܕܬܘܟܠܢܐ ܒ-bootstrap ܘܒܘܚܪܢܐ t ܚܣܝܢܐ (robust؛ Yuen – Field, Section 10.8.4)، ܒܘܚܪܢܐ ܕܚܕ ܕܘܢܒܐ (one-tailed؛ Field، ܦܣܩܐ 10.8.3: "ܓܘ ܪܘܒܐ ܕܗܘܝ̈ܐ ܠܐ ܚܫܒܝܬܘܢ ܠܛܝܡܐ ܕܚܕ ܕܘܢܒܐ")، ܘ-Bayes factor. ܒܘܚܪܢܐ t ܠܕܘܡܝܐ ܝܚܝܕܝܐ (one-sample t-test) – ܓܘ ܦܐܬܐ ܕܝܠܗ؛ ܚܠܦܐ ܕܠܐ ܦܪܡܝܛܪ̈ܐ (non-parametric)، Mann-Whitney – ܐܦ ܗܕܟܐ.

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

ܡܥܝܪܢܘܬܐ ܥܠ ܢܘܣ̈ܚܐ (versions). ܐܘܪܚܐ ܩܝܡܐ ܝܠܗ ܓܘ ܟܠ ܢܘܣ̈ܚܐ؛ ܚܕ ܦܘܪܫܢܐ ܕܒܕ ܦܓܥܝܬܘܢ ܒܗ ܓܘ ܐܗܐ ܦܐܬܐ: ܡܢ ܢܘܣܚܐ 27 ܟܘܬܐ ܕܕܝܐܠܘܓ ܐܝܬ ܓܘܗ ܩܘܛܝܐ ܕܪܘܫܡܐ Estimate effect sizes ܘܟܛܒܥ ܠܘܚܐ Independent Samples Effect Sizes ܥܡ Cohen's d ܘܬܚܘܡܐ ܕܬܘܟܠܢܐ (confidence interval؛ Field، 2024، ܦܣ̈ܩܐ 10.8.2 ܘ-10.8.5 – ܠܦܘܬ ܢܘܣܚܐ 29)، ܐܠܐ Pallant (2020، ܠܦܘܬ ܢܘܣܚܐ 26) ܟܟܬܒܐ ܕ-SPSS "ܠܐ ܟܝܗܒ ܪܒܘܬܐ ܕܡܥܒܕܢܘܬܐ (effect size) ܩܐ ܒܘܚܪ̈ܢܐ t" ܘܟܚܫܒܐ ܐܝܬܐ ܡܪܒܥܐ (eta squared) ܒܐܝܕܐ. ܓܘ ܢܘܣ̈ܚܐ ܥܬܝ̈ܩܐ – ܫܩܘܠܘܢ ܣܕܪܐ /ES DISPLAY(TRUE) ܡܢ ܣܝܢܬܐܟܣ (syntax) ܕܦܐܬܐ ܟܡܦܩܐ.

ܐܘܪܚܐ (Pallant, 2020, Chapter 17; Field, 2024, Section 10.8.2): Analyze › Compare Means › Independent-Samples T Test… – ܡܫܬܚܠܦܢܐ ܬܠܝܐ (dependent variable؛ ܝܢ ܟܡܐ) ܠܩܘܛܝܐ Test Variable(s)، ܡܫܬܚܠܦܢܐ ܕܓܘ̈ܕܐ (grouping variable) ܠ-Grouping Variable، ܘܒ-button Define Groups… ܟܟܬܒܚ ܬܪܝܢ ܪ̈ܡܙܐ ܕܓܘ̈ܕܐ (1 ܘ-2 ܓܘ ܦܐܝܠ ܕܡܬܠܐ (sample data file)؛ ܐܢ ܠܐ ܟܥܗܕܚ – ܕܚܩܐ ܝܡܝܢܐ ܥܠ ܫܡܐ ܕܡܫܬܚܠܦܢܐ ܘ-Variable Information). Field ܟܡܥܗܕ ܓܘܒܝܐ Cut point – ܦܠܓܘܬܐ ܠܬܪܝܢ ܓܘ̈ܕܐ ܠܦܘܬ ܛܝܡܐ ܕܦܣܩܐ – ܘܟܡܙܗܪ ܡܢ ܦܠܓܘܬܐ ܠܦܘܬ ܛܝܡܐ ܡܨܥܝܐ (median؛ ܩܘܛܝܐ 10.1). Options… – ܕܪܓܐ ܕܬܚܘܡܐ ܕܬܘܟܠܢܐ (95%) ܘܛܘܦܠܐ ܒܚܣܝ̈ܪܐ؛ Bootstrap… – ܬܚܘ̈ܡܐ ܕܬܘܟܠܢܐ ܕܠܐ ܟܣܐܡܝ ܢܘܪܡܠܝܘܬܐ (BCa). ܣܝܢܬܐܟܣ:

T-TEST GROUPS=קבוצה(1 2)
  /MISSING=ANALYSIS
  /VARIABLES=עמדות_ציון גיל
  /ES DISPLAY(TRUE)
  /CRITERIA=CI(.95).

ܩܪܝܢܐ ܕܡܦܩܢܐ (output). Group Statistics = ܠܘܚܐ 1 (N, Mean, Std. Deviation, Std. Error Mean)؛ Independent Samples Test = ܠܘܚܐ 2 – Levene's Test (F, Sig.) ܓܘ ܣܕܪܐ ܩܕܡܝܐ، ܘܒܬܪ ܓܘ ܬܪܝܢ ܣܕܪ̈ܐ t, df, Sig. (2-tailed) (ܓܘ SPSS 27 ܘܠܥܠ ܐܦ One-Sided p – ܠܐ ܚܫܒܝܬܘܢ ܠܗ)، Mean Difference, Std. Error Difference, 95% Confidence Interval of the Difference؛ Independent Samples Effect Sizes – ܣܕܪܐ ܕ-Cohen's d، ܥܡܘܕܐ ܕ-Point Estimate، ܝܠܗ d ܕܓܘ ܡܥܝܪܢܘܬܐ ܕܠܘܚܐ (SPSS ܟܛܒܥ ܐܦ Hedges' correction ܘ-Glass's delta، ܕܠܐ ܝܢܐ ܓܘ ܦܐܬܐ). Button ܕ"ܡܚܬܬܐ ܕܣܝܢܬܐܟܣ SPSS" ܓܘ ܡܦܩܢܐ ܟܡܦܩ ܛܥܢܐ، ܟܬܒܐ ܕܪ̈ܡܙܐ (ܐܢ ܗܘܐ ܡܦܫܩܢܐ) ܘܦܘܩܕܢܐ ܕ-T-TEST ܥܠ ܡܫܬܚܠܦ̈ܢܐ ܘܪ̈ܡܙܐ ܕܓܒܝ̈ܐ ܝܢܐ.

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

ܓܘ R ܒܣܝܣܝܐ t.test() ܟܪܗܛܐ ܒܓܘܒܝܐ ܡܩܕܡܐ (default) Welch؛ var.equal = TRUE ܟܝܗܒ ܣܕܪܐ ܕܫܘܚܠ̈ܦܐ ܫܘ̈ܝܐ. ܒܘܚܪܢܐ ܕ-Levene ܚܕܪ ܡܨܥܝܬܐ – leveneTest(center = mean) ܡܢ ܨܪܪܐ car (ܓܘܒܝܐ ܡܩܕܡܐ ܕܝܠܗ ܝܠܗ ܛܝܡܐ ܡܨܥܝܐ (median)، ܘܐܗܐ ܠܐ ܝܠܗ ܡܐ ܕ-SPSS ܟܛܒܥ ܓܘ ܒܘܚܪܢܐ t). d ܘ-η² ܚܫܝܒ̈ܐ ܝܢܐ ܒܐܝܕܐ ܡܢ ܫܘܝ̈ܘܬܐ ܕܓܘ ܡܕܒܪܢܐ (guide). 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 (ܓܘ Windows: R 4.2 ܘܠܥܠ، ܝܢ Sys.setlocale('LC_ALL', 'Hebrew')).

# ܒܘܚܪܢܐ t ܠܕܘ̈ܡܝܐ ܠܐ ܬܠܝ̈ܐ – ܦܪܘܦܣܘܪ ܣܛܐܛ. ܐܗܐ ܦܐܝܠ ܢܛܝܪܐ ܝܠܗ ܒ-UTF-8؛ ܟܠ ܣܕܪܐ ܕܡܥܝܪܢܘܬܐ ܟܫܪܐ ܒܡܠܬܐ ܕܣܘܪܝܬ
library(readxl)   # ܩܪܝܢܐ ܕܐܩܣܠ
library(car)      # ܒܘܚܪܢܐ ܕ-Levene: leveneTest

# ܛܥܢܐ: ܛܘܦܣܐ ܬܩܝܢܐ – ܣܕܪܐ = ܡܫܬܘܬܦܢܐ، ܥܡܘܕܐ = ܡܫܬܚܠܦܢܐ؛ ܓܠܝܘܢܐ "נתונים"
d <- read_excel("C:/Rdata/DATA_ttest_example_heb.xlsx", sheet = "נתונים")
g <- factor(d[["קבוצה"]], levels = c(1, 2), labels = c("ניסוי", "ביקורת"))
y <- d[["עמדות_ציון"]]

# ܣܛܐܛܝܣܛܝܩܐ ܕܓܘ̈ܕܐ – ܠܘܚܐ 1
tapply(y, g, function(v) c(n = sum(!is.na(v)), M = mean(v, na.rm = TRUE), SD = sd(v, na.rm = TRUE)))
# ܦܐܪܐ: ניסוי n 60, M 3.474, SD 0.682; ביקורת n 60, M 3.065, SD 0.754

# ܒܘܚܪܢܐ ܕ-Levene ܚܕܪ ܡܨܥܝܬܐ – ܐܝܟ ܓܘ ܡܦܩܢܐ ܕܒܘܚܪܢܐ t ܕ-SPSS
leveneTest(y ~ g, center = mean)                         # F = 0.387, p = .535

# ܣܕܪܐ 1 – ܫܘܚܠ̈ܦܐ ܫܘ̈ܝܐ؛ ܣܕܪܐ 2 – Welch (ܓܘܒܝܐ ܡܩܕܡܐ ܕ-R)
t.test(y ~ g, var.equal = TRUE)    # t = 3.11, df = 118, p = .0023, ܦܘܪܫܢܐ 0.409, ܬܚܘܡܐ ܕܬܘܟܠܢܐ [0.149, 0.669]
t.test(y ~ g)                      # t = 3.11, df = 116.8, p = .0024

# ܪܒܘܬܐ ܕܡܥܒܕܢܘܬܐ: d ܕ-Cohen ܥܠ ܫܘܚܠܦܐ ܡܫܘܬܦܐ، ܘܐܝܬܐ ܡܪܒܥܐ = t²/(t² + df)
a <- y[g == "ניסוי" & !is.na(y)]; b <- y[g == "ביקורת" & !is.na(y)]
sp2 <- ((length(a) - 1) * var(a) + (length(b) - 1) * var(b)) / (length(a) + length(b) - 2)
(mean(a) - mean(b)) / sqrt(sp2)                          # d = 0.568
tt <- t.test(a, b, var.equal = TRUE); unname(tt$statistic^2 / (tt$statistic^2 + tt$parameter))   # ܐܝܬܐ ܡܪܒܥܐ = .076

ܬܘܢܝܐ ܕܡܫܟܚ̈ܢܘܬܐ (reporting the results)

ܟܬܢܚ ܡܫܟܚܢܘܬܐ ܘܒܬܪ ܣܛܐܛܝܣܛܝܩܐ: ܡܨܥܝܬܐ (mean) ܘܣܛܝܘܬܐ ܬܩܝܢܬܐ (standard deviation؛ ܝܢ ܛܥܝܘܬܐ ܬܩܝܢܬܐ) ܕܟܠ ܓܘܕܐ، t ܥܡ ܕܪ̈ܓܐ ܕܚܐܪܘܬܐ (degrees of freedom) ܓܘ ( )، p ܚܬܝܬܐ، ܦܘܪܫܢܐ ܥܡ ܬܚܘܡܐ ܕܬܘܟܠܢܐ (confidence interval)، ܘܪܒܘܬܐ ܕܡܥܒܕܢܘܬܐ (effect size؛ Field, 2024, Section 10.10; Gravetter & Wallnau, 2017, p. 321; American Psychological Association [APA], 2020, Section 6.43). ܡܬܠܐ ܕ-Field (ܦܣܩܐ 10.10.1): "ܒܡܨܥܝܬܐ، ܡܫܬܘܬܦ̈ܢܐ ܕܫܩܠܠܗܘܢ ܓܠܝܡܬܐ ܕܡܛܫܝܢܘܬܐ ܥܒܕܠܗܘܢ ܒܝܫ ܥܒ̈ܕܐ ܕܡܓܚܟܢܘܬܐ (M = 5, SE = 0.48) ܡܢ ܐܢܝ ܕܠܐ (M = 3.75, SE = 0.55). ܦܘܪܫܢܐ، −1.25، 95% CI [−2.70, 0.07]، ܠܐ ܝܠܗ ܗܘܐ ܪܫܝܡܐ، t(21.54) = −1.71, p = .101؛ ܐܦܢ ܗܕܟܐ ܗܘ ܚܘܝܠܗ ܡܥܒܕܢܘܬܐ ܕ-d = 0.70 [−1.52, 0.13]" – ܚܙܝܡܘܢ (Note) ܕܚܬܡܬܐ "ܠܐ ܪܫܝܡܐ" ܘ"ܡܥܒܕܢܘܬܐ ܪܒܬܐ" ܝܬܒ̈ܐ ܝܢܐ ܓܘ ܗܘ ܡܐܡܪܐ، ܘܬܪܘܝܗܝ ܫܪܝܪ̈ܐ ܝܢܐ. Gravetter ܘ-Wallnau (ܦܐܬܐ 321): ܐܝܡܢ ܕ-p ܚܬܝܬܐ ܡܛܝܐ ܝܠܗ ܡܢ ܟܘܡܦܝܘܬܪ ܟܬܢܚ ܠܗ (p = .018، ܠܐ p < .05)، ܘܬܚܘܡܐ ܕܬܘܟܠܢܐ ܟܐܬܐ ܒܬܪ ܒܘܚܪܢܐ ܡܚܕܐ. Pallant (2020، ܨܚܚܐ 17) ܟܬܢܝܐ "ܕܬܪܝܢ ܕܘܢ̈ܒܐ" ܘܐܝܬܐ ܡܪܒܥܐ (eta squared)، ܘܩܐ ܣܕܪܐ ܕܒܘܚܪ̈ܢܐ – ܠܘܚܐ (table) APA ܥܡ n, M, SD ܩܐ ܟܠ ܓܘܕܐ، df, t, p، ܦܘܪܫܢܐ ܥܡ ܬܚܘܡܐ ܕܬܘܟܠܢܐ ܘܪܒܘܬܐ ܕܡܥܒܕܢܘܬܐ.

ܢܡܘ̈ܣܐ ܕܨܘܪܬܐ (APA, 2020, Section 6.36): t ܘܦܘܪܫܢܐ ܕܡܨܥܝ̈ܬܐ ܥܡ ܣܦܪ ܩܕܡ ܢܘܩܙܐ (ܡܨܝ ܕܥܒܪܝ ܥܠ 1)، p ܘ-η² ܕܠܐ (ܠܐ ܡܨܝ)، d ܥܡ ܣܦܪ؛ ܕܪ̈ܓܐ ܕܚܐܪܘܬܐ (degrees of freedom) ܠܐ ܓܡܝܪ̈ܐ ܕ-Welch – ܒܬܪܝܢ ܡܢܝ̈ܢܐ ܒܬܪ ܢܘܩܙܐ (t(21.54)). ܡܐܡܪ̈ܐ ܕܬܘܢܝܐ (report sentences) ܕܓܘ ܡܦܩܢܐ ܒܢܝ̈ܐ ܝܢܐ ܗܕܟܐ، ܒܣܘܪܝܬ ܘܒܐܢܓܠܝܙܝܐ.

ܛܥܝ̈ܘܬܐ ܕܡܬܚܙܝܢ ܣܓܝ (Common mistakes)

ܩܪܝܢܐ ܕܣܕܪܐ ܠܐ ܬܪܝܨܐ – ܝܢ ܕܬܪܘܝܗܝ ܘܓܘܒܝܐ ܕܗܘ ܕܦܫܝܩ. ܟܡܚܕܕܚ ܡܢ ܩܕܡ ܢܡܘܣܐ (Levene، ܝܢ "ܟܠ ܐܡܢ Welch") ܘܟܬܢܚ ܠܦܘܬܗ؛ ܐܝܡܢ ܕܣܕܪ̈ܐ ܠܐ ܫܠܡܝ، ܣܕܪܐ ܕ-Welch ܝܠܗ ܚܣܝܢܐ (Gravetter & Wallnau, 2017, pp. 313-314).

ܬܘܪܓܡܐ ܕ"ܠܐ ܪܫܝܡܐ" ܐܝܟ "ܠܝܬ ܦܘܪܫܢܐ". ܬܚܘܡܐ ܕܬܘܟܠܢܐ (confidence interval) ܕܐܝܬ ܓܘܗ ܣܦܪ ܟܐܡܪ ܕܦܘܪܫܢܐ ܫܪܝܪܐ ܡܨܐ ܕܗܘܐ ܕܒܨܘܪܐ، ܕܙܘܕܐ ܝܢ ܣܦܪ (Field, 2024, Section 10.8.4) – ܠܐ ܕܗܘ ܣܦܪ ܝܠܗ. ܟܬܢܚ d ܘܬܚܘܡܐ.

ܬܘܢܝܐ ܕ-p ܕܠܐ ܡܨܥܝ̈ܬܐ، ܣܛܝ̈ܘܬܐ ܬܩܝܢ̈ܝܬܐ ܘܪܒܘܬܐ ܕܡܥܒܕܢܘܬܐ (effect size). ܩܪܘܝܐ ܣܢܝܩ ܝܠܗ ܕܝܕܥ ܠܐ ܒܣ ܐܢ ܐܝܬ ܦܘܪܫܢܐ ܐܠܐ ܟܡܐ (Field, 2024, Section 3.7.6; Pallant, 2020, Chapter 17).

ܣܕܪܐ ܕܒܘܚܪ̈ܢܐ t ܒܕܘܟܬ ANOVA. ܬܠܬܐ ܓܘ̈ܕܐ ܬܠܬܐ ܒܘܚܪ̈ܢܐ t ܝܢܐ، ܘܟܠ ܒܘܚܪܢܐ ܙܘܕܐ ܟܡܪܒܐ ܛܥܝܘܬܐ ܕܙܢܐ I (Type I error؛ Field, 2024, Section 10.8.2).

ܒܘܚܪܢܐ ܠܠܐ ܬܠܝ̈ܐ ܥܠ ܝܗܝ̈ܒܬܐ ܙܘܓܢ̈ܝܬܐ. ܩܕܡ-ܒܬܪ ܕܗܢܝ ܐܢܫ̈ܐ، ܙܘܓ̈ܐ، ܐܚ̈ܐ – ܟܥܒܪܝ ܥܠ ܠܐ ܬܠܝܘܬܐ؛ ܟܥܒܪܚ ܠܒܘܚܪܢܐ t ܠܙܘܓܢ̈ܝܐ (Field, 2024, Section 10.5).

ܚܠܛܐ ܒܝܢܝ ܡܫܘ̈ܚܬܐ ܕ-d ܘܕܐܝܬܐ ܡܪܒܥܐ (eta squared). 0.5 ܝܠܗ d ܡܨܥܝܐ؛ .06 ܝܠܗ η² ܡܨܥܝܐ (Pallant, 2020, Chapter 17).

ܦܠܓܘܬܐ ܕܡܫܬܚܠܦܢܐ ܡܬܡܫܚܢܐ (continuous variable) ܠܬܪܝܢ ܓܘ̈ܕܐ ܠܦܘܬ ܛܝܡܐ ܡܨܥܝܐ (median) ܩܐ ܕܪܗܛܚ ܒܘܚܪܢܐ t. ܟܡܘܒܕܚ ܚܝܠܐ ܘܡܘܕܥܢܘܬܐ (Field, 2024, Box 10.1)؛ ܟܫܒܩܚ ܡܫܬܚܠܦܢܐ ܡܬܡܫܚܢܐ ܘܟܡܦܠܚܚ ܒܐܣܘܪܐ ܕܚܕ̈ܕܐ (correlation) ܝܢ ܒܪܝܓܪܫܢ (regression).

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.). Routledge.

Student (1908)، Levene (1960)، Yuen (1974) ܘ-Zimmerman (2004) – ܐܝܟ ܕܡܬܝ̈ܬܐ ܝܢܐ ܓܘ Field (2024). 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) ܘ-APA (2020) – ܠܦܘܬ ܦܐܬܐ ܘܦܣܩܐ ܕܡܦܩܬܐ ܛܒܝܥܬܐ.