ܒܘܚܪܢܐ t ܠܕܘܡܝܐ ܝܚܝܕܝܐ

ܛܥܢܐ ܕܝܗܝ̈ܒܬܐ (loading the data)

ܟܡܕܒܩܚ ܥܡܘ̈ܕܐ ܬܪܝܨܐܝܬ ܡܢ ܓܠܝܘܢܐ (worksheet)، ܥܡ ܣܕܪܐ ܕܪ̈ܫܐ (header row) – ܟܪܫܡܚ ܓܘ ܐܩܣܠ، ܟܢܣܚܚ، ܘܟܡܕܒܩܚ ܠܐܟܐ:

ܓܘܒܝܐ ܕܡܫܬܚܠܦ̈ܢܐ ܘܛܝܡܐ ܕܒܘܚܪܢܐ

ܐܝܡܢ ܡܦܠܚܝܚ (When to use)؟

ܐܡܢ ܕܐܝܬ ܕܘܡܝܐ ܚܕ، ܡܨܥܝܬܐ ܚܕܐ، ܘܫܘܐܠܐ ܚܕ: ܐܢ ܐܗܐ ܡܨܥܝܬܐ ܦܪܝܫܬܐ ܝܠܗ̇ ܡܢ ܛܝܡܐ ܡܚܬܡܐ. Gravetter ܘ-Wallnau (2017، ܨܚܚܐ 9) ܟܡܚܘܝ ܬܪܬܝܢ ܐܝܟܢܝ̈ܘܬܐ. ܩܕܡܝܬܐ – ܟܢܫܐ ܟܠܢܝܐ ܝܕܝܥܐ ܩܕܡ ܐܣܝܘܬܐ: ܡܨܥܝܬܐ ܕܟܢܫܐ ܟܠܢܝܐ (population) ܩܕܡ ܐܣܝܘܬܐ ܝܕܝܥܬܐ ܝܠܗ̇ (ܡܬܠܐ 30)، ܕܘܡܝܐ (sample) ܩܒܠܠܗ ܐܣܝܘܬܐ، ܘܫܘܐܠܐ ܝܠܗ ܐܢ ܡܨܥܝܬܐ ܒܬܪ ܐܣܝܘܬܐ ܗܠ ܗܫܐ 30 ܝܠܗ̇ (ܦܐ̈ܬܐ 274-275، ܨܘܪܬܐ 9.3). ܬܪܝܢܝܬܐ، ܘܕܡܬܚܙܝܐ ܝܬܝܪ ܓܘ ܝܕ̈ܥܬܐ ܕܟܢܫܐ – ܛܝܡܐ ܕܡܦܩܐ ܝܠܗ ܡܢ ܗܘܢܐ، ܕܠܐ ܚܕ ܝܕܥܬܐ ܩܕܡܝܬܐ ܥܠ ܟܢܫܐ ܟܠܢܝܐ: ܫܘܐ̈ܠܐ ܕܛܟܣܐ ܥܠ ܣܒܠܬܐ (scale) 1-7، ܕܓܘܗ̇ 4 ܝܠܗ "ܡܨܥܝܐ"، ܘܫܘܐܠܐ ܕܒܘܨܝܐ ܝܠܗ ܐܢ ܠܡܦܢܝ̈ܢܐ ܐܝܬ ܪܥܝܢܐ ܟܠܗ – H₀: μ = 4 (ܦܐ̈ܬܐ 275-276؛ ܒܘܨܝܐ ܕܓܘܚܟܐ ܕ-McGee ܘ-Shevlin، 2009، ܕܓܘ ܫܘܪܝܐ ܕܨܚܚܐ: ܬܚܘܝܬܐ ܥܡ ܪܓܫܐ ܕܓܘܚܟܐ ܩܒܠܠܗ̇ M = 4.53، ܪܡܐ ܪܫܝܡܐܝܬ ܡܢ 4)؛ ܝܢ ܝܠܘ̈ܕܐ ܕܚܙܝܠܗܘܢ ܒܬܪܝܢ ܦܪ̈ܨܘܦܐ ܓܘ 20 ܪ̈ܦܦܐ – ܐܢ ܠܝܬ ܓܘܒܝܐ، ܡܨܥܝܬܐ ܩܐ ܦܪܨܘܦܐ ܫܦܝܪܐ ܝܠܗ̇ 10 ܪ̈ܦܦܐ، H₀: μ = 10 (ܡܬܠܐ 9.2). "ܟܠ ܡܐ ܕܓܪܓ ܩܐ ܚܘܫܒܢܐ ܕ-t ܝܠܗ ܗܘܦܘܬܣܝܣ ܕܣܦܝܩܘܬܐ ܘܕܘܡܝܐ ܡܢ ܟܢܫܐ ܟܠܢܝܐ ܠܐ ܝܕܝܥܐ" (ܦܐܬܐ 275).

ܐܗܐ ܒܘܚܪܢܐ ܫܬܐܣܐ ܝܠܗ ܕܫܪܒܬܐ ܕ-t: ܬܪܝܢ ܒܘܚܪ̈ܢܐ ܐܚܪ̈ܢܐ ܓܘ ܣܐܝܛ – ܠܕܘ̈ܡܝܐ ܠܐ ܬܠܝ̈ܐ (ܬܪܬܝܢ ܓܘ̈ܕܐ ܦܪ̈ܝܫܐ) ܘܠܕܘ̈ܡܝܐ ܙܘܓܢ̈ܝܐ (ܗܢܝ ܡܫܬܘܬܦ̈ܢܐ ܬܪܝܢ ܙܒ̈ܢܐ) – ܟܦܚܡܝ ܬܪܬܝܢ ܡܨܥܝ̈ܬܐ ܚܕܐ ܥܡ ܚܕܐ؛ ܠܐܟܐ ܟܦܚܡܚ ܡܨܥܝܬܐ ܚܕܐ ܥܡ ܛܝܡܐ ܩܝܡܐ. ܡܢܝܢܐ ܕܣܒܠܬܐ ܕܦܣܘ̈ܩܐ ܣܓܝ̈ܐܐ (multi-item scale؛ ܦܐܬܐ ܐܠܦܐ ܕ-Cronbach ܘܡܢܝܢܐ ܕܣܒܠܬܐ) ܟܡܬܚܫܒ ܐܝܟ ܡܫܬܚܠܦܢܐ ܕܪܘ̈ܚܩܐ ܫܘ̈ܝܐ (interval variable) ܠܦܘܬ ܥܝܕܐ ܕܣܐܝܛ (ܡܫܬܚܠܦ̈ܢܐ ܘܕܪ̈ܓܐ ܕܡܫܘܚܬܐ)، ܘܡܛܠ ܗܕܐ ܡܨܝܚ ܕܒܚܪܚ ܠܗ ܩܘܒܠ ܡܨܥܬܐ ܕܣܒܠܬܐ؛ ܦܣܘܩܐ ܕ-Likert ܝܚܝܕܝܐ – ܠܐ (ܣܓܝܐܘ̈ܬܐ ܘܛܝܡܐ ܡܨܥܝܐ، ܓܘ ܦܐܬܐ ܕܣܓܝܐܘ̈ܬܐ).

ܗܘܢܐ: ܦܘܪܫܢܐ ܡܦܠܓܐ ܥܠ ܛܥܝܘܬܐ ܬܩܝܢܬܐ

ܚܘܫܒܐ ܕ-Gravetter ܘ-Wallnau (2017، ܦܣܩܐ 9.1): ܡܨܥܝܬܐ (mean) ܕܕܘܡܝܐ ܟܡܩܪܒܐ ܠܡܨܥܝܬܐ ܕܟܢܫܐ ܟܠܢܝܐ (population)، ܘܛܥܝܘܬܐ ܬܩܝܢܬܐ (standard error) ܟܐܡܪܐ ܟܡܐ ܦܘܪܫܢܐ ܡܬܩܒܠܐ ܝܠܗ ܕܣܟܝܚ ܒܝܢܬܘܗܝ. ܓܘ z-score ܟܦܠܓܚ ܦܘܪܫܢܐ M − μ ܥܠ ܛܥܝܘܬܐ ܬܩܝܢܬܐ ܫܪܝܪܬܐ، ܕܣܢܩܐ ܝܠܗ̇ ܠܣܛܝܘܬܐ ܬܩܝܢܬܐ (standard deviation) ܕܟܢܫܐ ܟܠܢܝܐ – ܕܩܪܝܒ ܚܕ ܙܒܢܐ ܠܐ ܝܕܝܥܬܐ ܝܠܗ̇؛ "ܟܠܗ̇ ܥܠܬܐ ܕܒܘܚܪܢܐ ܝܠܗ̇ ܕܝܠܦܚ ܥܠ ܟܢܫܐ ܟܠܢܝܐ ܠܐ ܝܕܝܥܐ" (ܦܐܬܐ 269). ܦܘܫܪܐ: ܟܫܥܪܚ ܛܥܝܘܬܐ ܬܩܝܢܬܐ ܡܢ ܕܘܡܝܐ، s_M = s/√n (ܡܥܠܝܬܐ 9.1)، ܘܟܫܩܠܚ t – ܗܘ ܒܢܝܢܐ ܐܝܟ z، ܥܡ ܫܘܥܪܐ ܓܘ ܡܢܝܢܐ ܬܚܬܝܐ: t = (M − μ)/s_M (ܡܥܠܝܬܐ 9.2). ܡܢܝܢܐ ܥܠܝܐ ܟܡܫܘܚ ܦܘܪܫܢܐ ܫܪܝܪܐ ܒܝܢܝ ܝܗܝ̈ܒܬܐ ܘܗܘܦܘܬܣܝܣ؛ ܡܢܝܢܐ ܬܚܬܝܐ – ܟܡܐ ܦܘܪܫܢܐ ܡܬܩܒܠܐ ܝܠܗ ܕܣܟܝܚ ܒܓܕܫܐ؛ ܐܡܢ ܕܡܢܝܢܐ ܥܠܝܐ ܪܒܐ ܝܠܗ ܒܣܓܝ ܡܢ ܡܢܝܢܐ ܬܚܬܝܐ، t ܪܒܐ ܝܠܗ (ܠܥܠ ܡܢ ܨܦܪܐ ܝܢ ܬܚܘܬ ܨܦܪܐ) ܘܝܗܝ̈ܒܬܐ ܠܐ ܫܠܝܡ̈ܐ ܝܢܐ ܥܡ ܗܘܦܘܬܣܝܣ (ܦܐܬܐ 275).

ܩܐ ܕܐܦ ܡܢܝܢܐ ܬܚܬܝܐ ܡܫܥܪܐ ܝܠܗ ܘܟܫܚܠܦ ܡܢ ܕܘܡܝܐ ܠܕܘܡܝܐ، t ܟܫܚܠܦ ܝܬܝܪ ܡܢ z: ܦܘܠܓܐ (distribution) ܕ-t ܫܛܝܚܐ ܘܦܬܝܐ ܝܬܝܪ ܝܠܗ ܡܢ ܢܘܪܡܠܝܐ، ܒܦܪܝܫܘܬܐ ܐܡܢ ܕܕܪ̈ܓܐ ܕܚܐܪܘܬܐ – df = n − 1 (ܡܥܠܝܬܐ 9.3) – ܙܥܘܪ̈ܐ ܝܢܐ، ܘܟܩܪܒ ܠܗ ܐܝܟܡܐ ܕ-n ܟܪܒܐ (ܦܣܩܐ 9.1، ܨܘܪܬܐ 9.1): ܓܘ df = 1 ܛܝܡܐ ܚܪܝܦܐ (critical value) ܕܬܪܝܢ ܕܘܢ̈ܒܐ ܩܐ .05 ܝܠܗ 12.706، ܓܘ df = 8 – 2.306، ܘܓܘ ܠܐ ܬܚܘܡܐ – 1.96 (ܠܘܚܐ 9.1). ܦܐܬܐ ܠܐ ܟܡܦܠܚܐ ܒܠܘܚܐ: ܟܚܫܒܐ p ܚܬܝܬܐ ܡܢ ܦܘܠܓܐ ܕ-t، ܐܝܟ ܕ"ܛܒܥܐ ܕܡܚܫܒܢܐ" ܟܥܒܕ (ܦܐܬܐ 287)، ܘܟܡܘܕܥܐ ܠܗ ܐܝܟ ܡܢܝܢܐ ܘܠܐ ܐܝܟ p < .05.

ܩܪܝܢܐ ܕܡܦܩܢܐ (How to read the output)

ܠܘܚܐ 1 – ܣܛܐܛܝܣܛܝܩܐ ܕܕܘܡܝܐ. N ܕܛܝ̈ܡܐ ܬܪܝ̈ܨܐ، ܡܨܥܝܬܐ، ܣܛܝܘܬܐ ܬܩܝܢܬܐ (ܕܕܘܡܝܐ، n − 1) ܘܛܥܝܘܬܐ ܬܩܝܢܬܐ ܕܡܨܥܝܬܐ. ܐܗܐ ܝܠܗ ܠܘܚܐ One-Sample Statistics ܕ-SPSS. ܩܕܡܝܐ ܟܒܚܪܚ ܕ-N ܡܬܩܒܠܐ ܝܠܗ ܒܗܘܢܐ – ܣܓܝ ܚܣܝ̈ܪܐ ܝܢ ܛܝܡܐ ܕܡ̈ܠܐ ܓܘ ܥܡܘܕܐ ܟܡܙܥܪܝ ܠܗ، ܘܦܐܬܐ ܟܡܘܕܥܐ ܥܠ ܐܗܐ ܓܘ ܛܥܢܐ.

ܠܘܚܐ 2 – ܒܘܚܪܢܐ. ܠܘܚܐ One-Sample Test ܕ-SPSS: ܛܝܡܐ ܕܒܘܚܪܢܐ، t، df، p ܕܬܪܝܢ ܕܘܢ̈ܒܐ، ܦܘܪܫܢܐ M − μ₀ (Mean Difference) ܘܬܚܘܡܐ ܕܬܘܟܠܢܐ ܕ-95% ܩܐ ܦܘܪܫܢܐ. ܐܬܐ ܕ-t ܘܕܦܘܪܫܢܐ ܟܐܡܪܐ ܠܐܝܢܐ ܐܘܪܚܐ ܕܘܡܝܐ ܟܣܛܐ ܡܢ ܛܝܡܐ ܕܒܘܚܪܢܐ: ܠܥܠ ܡܢ ܨܦܪܐ – ܡܨܥܝܬܐ ܪܡܬܐ ܝܠܗ̇ ܡܢܗ. p ܙܥܘܪܐ ܡܢ .05 – ܡܨܥܝܬܐ ܦܪܝܫܬܐ ܝܠܗ̇ ܪܫܝܡܐܝܬ ܡܢ ܛܝܡܐ ܕܒܘܚܪܢܐ؛ ܐܢ ܠܐ – ܠܐ ܡܫܟܚܐ ܝܠܗ ܦܘܪܫܢܐ ܪܫܝܡܐ (Gravetter & Wallnau, 2017، ܦܐܬܐ 277: "ܦܘܣܩܢܐ ܣܛܐܛܝܣܛܝܩܝܐ"). ܬܚܘܡܐ ܕܬܘܟܠܢܐ. ܠܘܚܐ ܟܛܒܥ ܬܚܘܡܐ ܩܐ ܦܘܪܫܢܐ، ܐܝܟ SPSS؛ ܓܘ ܡܥܝܪܢܘܬܐ ܕܠܘܚܐ ܘܓܘ ܨܘܪܬܐ ܟܡܬܚܙܐ ܗܘ ܬܚܘܡܐ ܩܐ ܡܨܥܝܬܐ – μ = M ± t·s_M (ܡܥܠܝܬܐ 9.6؛ ܡܬܠܐ 9.5) – ܕܐܝܗܘ ܝܠܗ ܦܫܝܛܐܝܬ ܬܚܘܡܐ ܩܐ ܦܘܪܫܢܐ ܘܝܬܝܪ ܛܝܡܐ ܕܒܘܚܪܢܐ. ܐܡܢ ܕܬܚܘܡܐ ܕܦܘܪܫܢܐ ܟܥܒܥܒ ܨܦܪܐ (ܗܢܘ ܬܚܘܡܐ ܕܡܨܥܝܬܐ ܟܥܒܥܒ ܛܝܡܐ ܕܒܘܚܪܢܐ)، ܒܘܚܪܢܐ ܠܐ ܪܫܝܡܐ ܝܠܗ، ܘܒܗܦܟܐ. ܬܚܘܡܐ ܥܝܩܐ ܝܬܝܪ ܝܠܗ ܐܝܟܡܐ ܕܕܘܡܝܐ ܪܒܐ ܝܠܗ ܘܐܝܟܡܐ ܕܕܪܓܐ ܕܬܘܟܠܢܐ ܢܚܝܬܐ ܝܠܗ (ܦܐܬܐ 286)؛ ܘܡܛܠ ܗܕܐ، Gravetter ܘ-Wallnau ܟܙܗܪܝ، ܐܝܗܘ ܬܚܘܝܬܐ ܝܠܗ ܕܡܥܒܕܢܘܬܐ ܐܠܐ ܠܐ ܚܠܦܐ ܕ-d ܝܢ ܕ-r² (ܦܐܬܐ 286).

ܪܒܘܬܐ ܕܡܥܒܕܢܘܬܐ (effect size)

"ܡܨܝܐ ܕܡܥܒܕܢܘܬܐ ܕܐܣܝܘܬܐ ܙܥܘܪܬܐ ܒܣܓܝ ܗܘܝܐ 'ܪܫܝܡܬܐ ܣܛܐܛܝܣܛܝܩܐܝܬ'، ܒܦܪܝܫܘܬܐ ܐܡܢ ܕܕܘܡܝܐ ܪܒܐ ܝܠܗ ܒܣܓܝ"، ܘܡܛܠ ܗܕܐ ܟܡܘܕܥܚ ܥܡ ܒܘܚܪܢܐ ܐܦ ܡܚܘܝܢܐ (measure) ܕܪܒܘܬܐ ܕܡܥܒܕܢܘܬܐ (effect size؛ Gravetter & Wallnau, 2017, p. 279). ܬܪܝܢ ܐܝܬ ܓܘ ܡܦܩܢܐ، ܘܬܪܘܝܗܘܢ ܩܪܝܒ ܠܐ ܬܠܝ̈ܐ ܝܢܐ ܒܪܒܘܬܐ ܕܕܘܡܝܐ (ܦܐܬܐ 284):

d ܕ-Cohen (ܫܘܥܪܐ). ܦܘܪܫܢܐ ܒܝܢܝ ܡܨܥܝܬܐ (mean) ܕܕܘܡܝܐ ܘܛܝܡܐ ܕܒܘܚܪܢܐ ܒܚܕܝܘ̈ܬܐ ܕܣܛܝܘܬܐ ܬܩܝܢܬܐ (standard deviation) ܕܕܘܡܝܐ: d = (M − μ)/s (ܡܥܠܝܬܐ 9.4). ܓܘ ܡܬܠܐ ܕܝܠܘ̈ܕܐ: (13 − 10)/3 = 1.00 – ܡܥܒܕܢܘܬܐ ܫܘܝܐ ܝܠܗ̇ ܠܣܛܝܘܬܐ ܬܩܝܢܬܐ ܚܕܐ (ܡܬܠܐ 9.3، ܨܘܪܬܐ 9.5). Gravetter ܘ-Wallnau ܟܡܥܝܪܝ ܕܐܡܢ ܕܟܣܝܡܝ ܛܝ̈ܡܐ ܕܕܘܡܝܐ ܒܕܘܟܬܐ ܕܦܪܡܝ̈ܛܪܐ، ܣܓܝ ܒܨܘ̈ܝܐ ܟܓܒܝ ܕܩܪܝ ܠܐܗܐ "d ܫܘܥܪܐ" (ܦܐܬܐ 280)؛ ܐܗܐ ܝܠܗ ܐܦ Cohen's d ܕܓܘ ܡܦܩܢܐ ܕ-SPSS 27 ܘܠܥܠ ܩܐ ܕܘܡܝܐ ܝܚܝܕܝܐ. ܥܝܕ̈ܐ ܕ-Cohen (1988، ܦܐ̈ܬܐ 25-27): 0.2 ܙܥܘܪܐ، 0.5 ܡܨܥܝܐ، 0.8 ܪܒܐ – ܥܡ ܙܘܗܪܐ ܕܝܠܗ ܕܬܚܘ̈ܡܐ ܩܐ ܡܕܒܪܢܘܬܐ ܝܢܐ، ܘܡܥܒܕܢܘܬܐ ܟܡܬܕܝܢܐ ܓܘ ܣܘܟܠܐ ܕܦܢܝܬܐ ܕܝܕܥܬܐ.

r² – ܡܢܬܐ ܒܡܐܐ ܕܫܘܚܠܦܐ ܡܦܫܩܐ (explained variance). ܟܡܐ ܡܢ ܫܘܚܠܦܐ (variance) ܓܘ ܡܢܝ̈ܢܐ "ܡܦܫܩܐ ܝܠܗ" ܒܙܘܥܐ ܡܢ ܛܝܡܐ ܕܒܘܚܪܢܐ: ܓܘ ܡܬܠܐ، ܫܘܚܠܦܐ ܚܕܪ 10 ܝܠܗ SS = 153، ܘܒܬܪ ܫܩܠܬܐ ܕܡܥܒܕܢܘܬܐ (3 ܢܘܩ̈ܙܐ ܡܢ ܟܠ ܡܢܝܢܐ) – 72؛ ܦܘܪܫܢܐ، 81 ܡܢ 153، ܝܠܗ 52.94% (ܠܘܚܐ 9.2). ܡܥܠܝܬܐ ܡܢ ܒܘܚܪܢܐ ܒܓܢܒܗ: r² = t²/(t² + df) (ܡܥܠܝܬܐ 9.5) – ܓܘ ܣܘܟܠܐ ܕ-t ܒܥܕ̈ܢܐ ܟܩܪܝ ܠܐܗܐ ܐܦ ω². ܬܚܘ̈ܡܐ ܕ-Cohen ܩܐ r² (ܠܘܚܐ 9.3): .01 ܙܥܘܪܐ، .09 ܡܨܥܝܐ، .25 ܪܒܐ – ܚܙܝܡܘܢ ܕܗܢܝ ܬܚܘ̈ܡܐ ܕ-r ܡܪܒܥܐ ܝܢܐ (.1/.3/.5)، ܘܐܢܝ ܦܪ̈ܝܫܐ ܝܢܐ ܡܢ ܬܚܘ̈ܡܐ ܕܦܐܬܐ ܕܒܘܚܪܢܐ t ܠܕܘ̈ܡܝܐ ܠܐ ܬܠܝ̈ܐ ܟܡܝܬܝܐ ܩܐ η² ܡܢ Pallant (.01/.06/.14)؛ ܐܗܐ ܦܐܬܐ ܟܐܙܠܐ ܒܬܪ ܡܒܘܥܐ ܕܝܠܗ̇، Gravetter ܘ-Wallnau. ܣܛܝܘܬܐ ܬܩܝܢܬܐ ܪܒܬܐ ܟܡܙܥܪܐ ܐܦ t ܘܐܦ ܬܪܝܢ ܡܚܘ̈ܝܢܐ ܕܡܥܒܕܢܘܬܐ؛ ܪܒܘܬܐ ܕܕܘܡܝܐ ܟܡܙܥܪܐ ܒܣ p (ܦܐ̈ܬܐ 278، 284).

ܫܪ̈ܛܐ ܘܙܘܗܪ̈ܐ (Assumptions and warnings)

ܬܪܝܢ ܫܪ̈ܛܐ (assumptions؛ Gravetter & Wallnau, 2017, pp. 277-278): ܚܙ̈ܝܬܐ (observations) ܠܐ ܬܠܝ̈ܬܐ ܝܢܐ ܚܕܐ ܒܚܕܐ – ܓܕܫܐ ܚܕ ܠܐ ܟܡܥܒܕ ܥܠ ܡܣܬܒܪܢܘܬܐ ܕܐܚܪܢܐ (ܡܫܬܘܬܦܢܐ ܕܡܫܘܚܐ ܝܠܗ ܬܪܝܢ ܙܒ̈ܢܐ، ܙܘܓ̈ܐ، ܨܦ̈ܐ – ܟܬܒܪܝ ܐܗܐ)؛ ܘܟܢܫܐ ܟܠܢܝܐ (population) ܦܠܝܓܐ ܝܠܗ ܢܘܪܡܠܐܝܬ – ܫܪܛܐ ܕܓܪܓ ܝܠܗ ܩܐ ܡܬܡܛܝܩܐ، ܐܠܐ "ܠܬܘܒܪܐ ܕܝܠܗ ܐܝܬ ܡܥܒܕܢܘܬܐ ܥܒܕܢܝܬܐ ܙܥܘܪܬܐ، ܒܦܪܝܫܘܬܐ ܐܡܢ ܕܕܘܡܝܐ ܪܒܐ ܝܠܗ ܒܦܘܚܡܐ"؛ ܓܘ ܕܘܡܝܐ ܙܥܘܪܐ ܒܣܓܝ ܐܝܬܠܗ ܐܪܙܐ، ܘ"ܐܢ ܐܝܬ ܥܠܬܐ ܕܚܫܕܚ ܕܦܘܠܓܐ ܠܐ ܝܠܗ ܢܘܪܡܠܝܐ – ܦܠܘܚܘܢ ܒܕܘܡܝܐ ܪܒܐ، ܩܐ ܫܠܝܘܬܐ ܝܬܝܪܬܐ". Field (2024) ܟܡܦܫܩ ܩܐ ܡܘܕܝ: ܡܐ ܕܓܪܓ ܝܠܗ ܦܘܠܓܐ ܕܓܘܒܝܐ ܕܕܘܡܝܐ (sampling distribution) ܢܘܪܡܠܝܐ ܕܡܨܥܝܬܐ، ܘܢܡܘܣܐ ܕܬܚܘܡܐ ܡܨܥܝܐ (central limit theorem) ܟܡܫܪܪ ܠܗ ܐܡܢ ܕܕܘܡܝܐ ܪܒܐ ܝܠܗ ܣܦܝܩܐܝܬ (ܦܣ̈ܩܐ 6.2.7 ܘ-6.8.3) – ܛܝܡܐ ܡܩܒܠܐ ܝܠܗ 30، ܐܠܐ ܓܘ ܦܘܠܓܐ ܥܡ ܕܘܢ̈ܒܐ ܝܩܘܪ̈ܐ ܡܨܝܐ ܕܓܪܓܝ 100 ܘܐܦ ܝܬܝܪ (ܩܘܛܝܐ 6.4)؛ ܓܘ ܕܘܡܝܐ ܙܥܘܪܐ ܟܚܙܚ ܒܗܝܣܛܘܓܪܡ (ܣܓܝܐܘ̈ܬܐ ܘܣܛܐܛܝܣܛܝܩܐ ܡܚܘܝܢܝܬܐ) ܘܒܛܝ̈ܡܐ ܢܘܟܪ̈ܝܐ (ܛܝ̈ܡܐ ܢܘܟܪ̈ܝܐ ܘܫܪ̈ܛܐ)، ܘܓܘ ܕܘܡܝܐ ܪܒܐ ܠܐ ܟܦܣܩܚ ܠܦܘܬ ܒܘܚܪܢܐ ܕܢܘܪܡܠܝܘܬܐ (ܩܘܛܝܐ 6.7). ܩܘܛܝܐ ܕ"ܩܪܝܢܐ ܕܦܐܪܐ" ܟܡܥܗܕܐ ܐܗܐ ܐܡܢ ܕ-n ܙܥܘܪܐ ܝܠܗ ܡܢ 30.

ܛܝܡܐ ܕܒܘܚܪܢܐ ܦܘܣܩܢܐ ܝܠܗ، ܠܐ ܡܫܟܚܢܘܬܐ. ܦܣܝܩܐ ܝܠܗ ܩܕܡ ܦܘܫܩܐ ܡܢ ܗܘܢܐ ܝܢ ܝܕܥܬܐ ܕܠܒܪ – ܡܨܥܬܐ ܕܣܒܠܬܐ، ܡܨܥܝܬܐ ܦܪܣܝܬܐ، ܢܘܪܡܐ – ܘܡܘܕܥܐ ܝܠܗ ܥܡ ܥܠܬܐ ܕܝܠܗ. ܓܘܒܝܐ ܕܝܠܗ ܒܬܪ ܕܚܙܚ ܡܨܥܝܬܐ، ܝܢ ܢܣܝܘܢܐ ܕܟܡܐ ܛܝ̈ܡܐ ܗܠ ܕܦܠܛ ܪܫܝܡܐ، ܟܚܪܒ ܣܘܟܠܐ ܕ-p (ܚܙܝܡܘܢ ܐܝܬܝܩܐ ܕܒܘܨܝܐ، ܦܣܩܐ 7).

ܒܘܚܪܢܐ ܕܚܕ ܕܘܢܒܐ. Gravetter ܘ-Wallnau (ܦܣܩܐ 9.4) ܟܡܚܘܝ ܐܝܟܢܐ ܟܡܪܗܛܚ ܒܘܚܪܢܐ ܕܐܘܪܚܐ – ܛܝܡܐ ܚܪܝܦܐ (critical value) ܫܩܝܠܐ ܝܠܗ ܡܢ ܕܘܢܒܐ ܚܕ، ܘܟܡܘܕܥܚ "ܕܚܕ ܕܘܢܒܐ" ܓܠܝܐܝܬ – ܘܟܡܚܘܝ ܕܕܬܪܝܢ ܕܘܢ̈ܒܐ ܡܬܚܙܐ ܝܬܝܪ ܝܠܗ، ܘܕܐܘܪܚܐ ܦܐܝܐ ܝܠܗ ܐܡܢ ܕܐܝܬ ܥܠܬܐ ܡܢ ܩܕܡ. ܦܐܬܐ ܟܚܫܒܐ p ܕܬܪܝܢ ܕܘܢ̈ܒܐ ܒܠܚܘܕ؛ ܐܢܐ ܕܬܘܩܢܠܗ ܡܢ ܩܕܡ ܒܘܚܪܢܐ ܕܚܕ ܕܘܢܒܐ، ܘܦܘܪܫܢܐ ܓܘ ܐܘܪܚܐ ܡܣܟܝܬܐ ܝܠܗ، ܟܦܠܓ p ܥܠ ܬܪܝܢ – ܘܟܡܘܕܥ ܐܗܐ.

ܛܝ̈ܡܐ ܚܣܝ̈ܪܐ (missing values). ܩܐ ܟܠ ܡܫܬܚܠܦܢܐ ܡܒܘܚܪܐ ܥܠܝ̈ܠܐ ܝܢܐ ܡܫܬܘܬܦ̈ܢܐ ܕܐܝܬܠܗܘܢ ܛܝܡܐ ܬܪܝܨܐ ܓܘܗ – ܫܩܠܬܐ ܠܦܘܬ ܦܘܫܩܐ (/MISSING=ANALYSIS)، ܐܝܟ ܓܘܒܝܐ ܡܩܕܡܐ (default) ܕ-SPSS؛ N ܡܨܐ ܕܫܚܠܦ ܡܢ ܡܫܬܚܠܦܢܐ ܠܐܚܪܢܐ. ܒܘܚܪ̈ܢܐ ܣܓܝ̈ܐܐ. ܟܡܐ ܡܫܬܚܠܦ̈ܢܐ ܒܕܚܝܬܐ ܚܕܐ ܟܡܐ ܒܘܚܪ̈ܢܐ ܝܢܐ، ܟܠ ܚܕ ܥܡ ܣܘܟܢܐ ܕ-5% ܕܛܥܝܘܬܐ ܕܙܢܐ I؛ ܟܡܘܕܥܚ ܟܠܗܘܢ، ܘܟܚܫܒܚ ܥܠ ܬܘܪܨܐ (ܦܐܬܐ ܕܐܣܘܪ̈ܐ ܕܚܕ̈ܕܐ: Holm / FDR).

ܡܘܕܝ ܠܐ ܟܚܫܒܐ ܐܗܐ ܦܐܬܐ. ܬܚܘܡܐ ܕܬܘܟܠܢܐ ܩܐ d (SPSS 27 ܘܠܥܠ ܟܛܒܥ ܠܗ)، bootstrap، ܒܘܚܪܢܐ ܕܚܕ ܕܘܢܒܐ ܐܝܟ ܡܦܩܢܐ، ܒܘܚܪܢܐ ܕܐܬܐ ܘ-Wilcoxon ܠܕܘܡܝܐ ܝܚܝܕܝܐ (ܚܠ̈ܦܐ ܠܐ ܦܪܡܝܛܪ̈ܝܐ)، ܘ-Bayes factor.

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

ܡܒܘ̈ܥܐ ܕܣܐܝܛ ܟܣܡܟ ܥܠܝܗܝ (Field, 2024؛ Pallant, 2020) ܠܐ ܟܡܚܘܝ ܐܗܐ ܐܘܪܚܐ – ܐܢܝ ܟܥܒܪܝ ܬܪܝܨܐܝܬ ܠܒܘܚܪ̈ܢܐ ܩܐ ܬܪܬܝܢ ܓܘ̈ܕܐ – ܘܡܛܠ ܗܕܐ ܬܚܘܝܬܐ ܕܠܐܟܐ ܕܣܐܝܛ ܝܠܗ̇، ܫܪܝܪܬܐ ܩܘܒܠ PSPP (ܥܒܕܐ ܡܓܢܝܐ ܕ-SPSS): Analyze › Compare Means › One-Sample T Test… – ܡܫܬܚܠܦܢܐ (ܝܢ ܟܡܐ) ܠܩܘܛܝܐ Test Variable(s)، ܛܝܡܐ ܕܒܘܚܪܢܐ ܓܘ ܕܘܟܬܐ Test Value (ܓܘܒܝܐ ܡܩܕܡܐ 0 – ܩܪܝܒ ܚܕ ܙܒܢܐ ܠܐ ܐܝܗܘ ܕܒܥܝܚ)؛ Options… – ܕܪܓܐ ܕܬܚܘܡܐ ܕܬܘܟܠܢܐ ܘܥܒܕܐ ܥܡ ܚܣܝ̈ܪܐ؛ ܓܘ ܢܘܣܚܐ 27 ܘܠܥܠ – ܩܘܛܝܐ Estimate effect sizes. ܣܝܢܬܐܟܣ (syntax) ܕܦܐܬܐ ܟܒܢܝܐ:

T-TEST
  /TESTVAL=3
  /MISSING=ANALYSIS
  /VARIABLES=עמדות_ציון
  /ES DISPLAY(TRUE)
  /CRITERIA=CI(.95).

ܩܪܝܢܐ ܕܡܦܩܢܐ. One-Sample Statistics = ܠܘܚܐ 1 (N, Mean, Std. Deviation, Std. Error Mean)؛ One-Sample Test = ܠܘܚܐ 2 – ܓܘ ܪܫܐ Test Value = 3، ܘܒܬܪܗ t, df, Sig. (2-tailed) (ܓܘ 27 ܘܠܥܠ ܐܦ One-Sided p – ܛܥܘܢ ܡܢܗ)، Mean Difference ܘ-95% Confidence Interval of the Difference – ܬܚܘܡܐ ܩܐ ܦܘܪܫܢܐ، ܠܐ ܩܐ ܡܨܥܝܬܐ؛ One-Sample Effect Sizes – ܣܕܪܐ ܕ-Cohen's d، Point Estimate (SPSS ܟܛܒܥ ܐܦ Hedges' correction، ܕܠܝܬ ܓܘ ܦܐܬܐ). ܛܝܡܐ ܕܒܘܚܪܢܐ ܚܕ ܩܐ ܟܠ ܡܫܬܚܠܦ̈ܢܐ ܓܘ ܦܘܩܕܢܐ؛ ܐܡܢ ܕܓܘ ܦܐܬܐ ܓܒܝ̈ܐ ܝܢܐ ܛܝ̈ܡܐ ܦܪ̈ܝܫܐ ܩܐ ܡܫܬܚܠܦ̈ܢܐ ܦܪ̈ܝܫܐ، ܣܝܢܬܐܟܣ ܐܝܬ ܓܘܗ ܦܘܩܕܢܐ T-TEST ܩܐ ܟܠ ܛܝܡܐ.

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

ܓܘ R ܫܬܐܣܝܐ t.test(x, mu = …) ܟܝܗܒ t، df، p ܘܬܚܘܡܐ ܕܬܘܟܠܢܐ (confidence interval) ܩܐ ܡܨܥܝܬܐ (ܘܠܐ ܩܐ ܦܘܪܫܢܐ ܐܝܟ SPSS – ܟܡܒܨܪܚ μ₀ ܩܐ ܦܘܚܡܐ)؛ d ܘ-r² ܚܫܝ̈ܒܐ ܝܢܐ ܒܐܝܕܐ. ܣܩܪܝܦܬ (script) ܪܗܝܛܐ 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، ܘܐܬܪܐ ܕ-UTF-8 ܩܐ ܫܡ̈ܗܐ ܥܒܪ̈ܝܐ.

# ܒܘܚܪܢܐ t ܠܕܘܡܝܐ ܝܚܝܕܝܐ – 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_ttest1_example_heb.xlsx", sheet = "נתונים")
y <- d[["עמדות_ציון"]]; y <- y[!is.na(y)]

# ܣܛܐܛܝܣܛܝܩܐ ܕܕܘܡܝܐ – ܠܘܚܐ 1
c(n = length(y), M = mean(y), SD = sd(y), SE = sd(y) / sqrt(length(y)))   # n 120, M 3.270, SD 0.745, SE 0.068

# ܒܘܚܪܢܐ ܩܘܒܠ ܛܝܡܐ ܕܒܘܚܪܢܐ 3 (ܡܨܥܬܐ ܕܣܒܠܬܐ 1-5) – ܠܘܚܐ 2؛ ܬܚܘܡܐ ܕܬܘܟܠܢܐ ܕ-R ܩܐ ܡܨܥܝܬܐ ܝܠܗ
tt <- t.test(y, mu = 3)
tt                                   # t = 3.96, df = 119, p = .00013، ܬܚܘܡܐ ܕܬܘܟܠܢܐ ܩܐ ܡܨܥܝܬܐ [3.135, 3.404]
tt$conf.int - 3                      # ܬܚܘܡܐ ܕܬܘܟܠܢܐ ܩܐ ܦܘܪܫܢܐ، ܐܝܟ SPSS: [0.135, 0.404]

# ܪܒܘܬܐ ܕܡܥܒܕܢܘܬܐ: d ܕ-Cohen = (M − μ)/s، ܘ-r² = t²/(t² + df)
(mean(y) - 3) / sd(y)                                                     # d = 0.362
unname(tt$statistic^2 / (tt$statistic^2 + tt$parameter))                # r² = .117

ܬܘܢܝܐ ܕܡܫܟܚ̈ܢܘܬܐ (reporting the results)

ܟܡܘܕܥܚ ܬܚܘܝܬܐ ܘܒܬܪܗ̇ ܒܘܚܪܢܐ: ܡܨܥܝܬܐ (mean) ܘܣܛܝܘܬܐ ܬܩܝܢܬܐ (standard deviation)، ܛܝܡܐ ܕܒܘܚܪܢܐ ܘܡܘܢܐ ܟܡܚܘܐ، t ܥܡ ܕܪ̈ܓܐ ܕܚܐܪܘܬܐ ܓܘ ܩܘܫ̈ܬܐ، p ܚܬܝܬܐ، ܪܒܘܬܐ ܕܡܥܒܕܢܘܬܐ (effect size) – ܘܬܚܘܡܐ ܕܬܘܟܠܢܐ ܬܪܝܨܐܝܬ ܒܬܪ ܒܘܚܪܢܐ (Gravetter & Wallnau, 2017, p. 287; American Psychological Association [APA], 2020, Section 6.43). ܡܬܠܐ ܕ-Gravetter ܘ-Wallnau: "ܝܠܘ̈ܕܐ ܚܙܝܠܗܘܢ ܒܦܪܨܘܦܐ ܫܦܝܪܐ M = 13 ܡܢ 20 ܪ̈ܦܦܐ ܒܡܨܥܝܬܐ، SD = 3.00. ܙܒܢܐ ܪܡܐ ܗܘܐ ܪܫܝܡܐܝܬ ܡܢ ܡܐ ܕܡܣܟܝܐ ܗܘܐ ܐܢ ܠܝܬ ܓܘܒܝܐ، t(8) = 3.00, p = .017, r² = 0.5294"، ܘܥܡ ܬܚܘܡܐ ܕܬܘܟܠܢܐ: t(8) = 3.00, p < .05, 80% CI [11.603, 14.397]. ܐܡܢ ܕ-p ܚܬܝܬܐ ܐܝܬܠܗ – ܟܡܘܕܥܚ ܠܗ (p = .017، ܠܐ p < .05)؛ ܘ"p = 0.000" ܓܘ ܛܒܥܐ ܠܐ ܝܠܗ ܨܦܪܐ ܐܠܐ ܥܓܘܠܐ – ܟܟܬܒܚ p < .001 (ܦܐܬܐ 287). ܓܘ ܒܘܚܪܢܐ ܕܚܕ ܕܘܢܒܐ ܟܟܬܒܚ "ܕܚܕ ܕܘܢܒܐ" ܓܠܝܐܝܬ (ܦܐܬܐ 289).

ܢܡܘ̈ܣܐ ܕܐܣܟܝܡܐ (APA, 2020, Section 6.36): t ܘܦܘܪܫܢܐ ܥܡ ܨܦܪܐ ܩܕܡ ܢܘܩܙܐ؛ p ܘ-r² ܕܠܐ (ܠܐ ܡܨܝ ܕܣܠܩܝ ܠܥܠ ܡܢ 1)؛ d ܥܡ ܨܦܪܐ. ܡܐܡܪ̈ܐ ܕܬܘܢܝܐ (report sentences) ܕܓܘ ܡܦܩܢܐ ܒܢܝ̈ܐ ܝܢܐ ܗܕܟܐ، ܒܣܘܪܝܬ ܘܒܐܢܓܠܝܙܝܐ، ܥܡ ܬܚܘܡܐ ܕܬܘܟܠܢܐ ܕ-95% ܩܐ ܡܨܥܝܬܐ.

ܛܥܝ̈ܘܬܐ ܕܡܬܚܙܝܢ ܣܓܝ (Common mistakes)

ܫܒܩܬܐ ܕܛܝܡܐ ܕܒܘܚܪܢܐ 0. ܓܘܒܝܐ ܡܩܕܡܐ (default) ܕ-SPSS ܟܒܚܪ ܐܢ ܡܨܥܝܬܐ ܦܪܝܫܬܐ ܝܠܗ̇ ܡܢ ܨܦܪܐ – ܩܪܝܒ ܟܠ ܙܒܢܐ "ܪܫܝܡܐ" ܘܩܪܝܒ ܟܠ ܙܒܢܐ ܕܠܐ ܣܘܟܠܐ. ܛܝܡܐ ܕܒܘܚܪܢܐ ܗܘܦܘܬܣܝܣ (hypothesis) ܝܠܗ (Gravetter & Wallnau, 2017, pp. 275-276).

ܓܘܒܝܐ ܕܛܝܡܐ ܕܒܘܚܪܢܐ ܒܬܪ ܕܚܙܚ ܡܨܥܝܬܐ. ܗܘܦܘܬܣܝܣ ܟܐܬܝܐ ܩܕܡ ܝܗܝ̈ܒܬܐ؛ ܐܢ ܠܐ p ܠܐ ܟܐܡܪ ܡܕܡ.

ܩܪܝܢܐ ܕܬܚܘܡܐ ܕܬܘܟܠܢܐ ܕ-SPSS ܐܝܟ ܬܚܘܡܐ ܩܐ ܡܨܥܝܬܐ. ܐܝܗܘ ܬܚܘܡܐ ܝܠܗ ܩܐ ܦܘܪܫܢܐ ܡܢ ܛܝܡܐ ܕܒܘܚܪܢܐ؛ ܩܐ ܡܨܥܝܬܐ – ܟܡܘܣܦܚ ܛܝܡܐ ܕܒܘܚܪܢܐ (ܝܢ ܟܩܪܚ ܡܥܝܪܢܘܬܐ ܕܠܘܚܐ ܓܘ ܦܐܬܐ).

ܦܘܫܩܐ ܕ"ܠܐ ܪܫܝܡܐ" ܐܝܟ "ܡܨܥܝܬܐ ܫܘܝܐ ܝܠܗ̇ ܠܛܝܡܐ ܕܒܘܚܪܢܐ". ܬܚܘܡܐ ܕܬܘܟܠܢܐ ܕܟܥܒܥܒ ܛܝܡܐ ܕܒܘܚܪܢܐ ܟܐܡܪ ܕܦܘܪܫܢܐ ܫܪܝܪܐ ܡܨܐ ܕܗܘܐ ܬܚܘܬ ܨܦܪܐ، ܨܦܪܐ ܝܢ ܠܥܠ ܡܢ ܨܦܪܐ – ܠܐ ܕܐܝܗܘ ܨܦܪܐ ܝܠܗ. ܟܡܘܕܥܚ d ܘܬܚܘܡܐ.

ܒܘܚܪܢܐ ܠܕܘܡܝܐ ܝܚܝܕܝܐ ܥܠ ܦܣܘܩܐ ܕ-Likert ܝܚܝܕܝܐ. ܠܦܘܬ ܥܝܕܐ ܕܣܐܝܛ ܦܣܘܩܐ (item) ܝܚܝܕܝܐ ܡܫܬܚܠܦܢܐ ܕܛܟܣܐ (ordinal variable) ܝܠܗ – ܣܓܝܐܘ̈ܬܐ ܘܛܝܡܐ ܡܨܥܝܐ؛ ܡܨܥܝܬܐ ܕܡܢܝܢܐ ܕܣܒܠܬܐ ܕܦܣܘ̈ܩܐ ܣܓܝ̈ܐܐ – ܐܝܢ.

ܚܘܠܛܐ ܒܝܢܝ ܣܒ̈ܠܬܐ ܕ-r² ܘܕ-η². .09 ܝܠܗ r² ܡܨܥܝܐ ܓܘ Gravetter ܘ-Wallnau (ܠܘܚܐ 9.3)؛ .06 ܝܠܗ η² ܡܨܥܝܐ ܓܘ Pallant – ܬܪܬܝܢ ܣܒ̈ܠܬܐ، ܗܘ ܚܘܫܒܐ، ܡܢܝ̈ܢܐ ܦܪ̈ܝܫܐ.

ܦܘܠܓܐ ܕ-p ܥܠ ܬܪܝܢ ܒܬܪ ܕܚܙܐ ܐܘܪܚܐ. ܒܘܚܪܢܐ ܕܚܕ ܕܘܢܒܐ ܬܘܩܢܐ ܝܠܗ ܡܢ ܩܕܡ، ܥܡ ܥܠܬܐ، ܘܡܘܕܥܐ ܝܠܗ ܗܕܟܐ (Gravetter & Wallnau, 2017, Section 9.4).

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.

McGee ܘ-Shevlin (2009) ܘ-Slater ܘܚܒܪ̈ܘܗܝ (1998) – ܐܝܟ ܕܡܬܝ̈ܬܐ ܝܢܐ ܓܘ Gravetter ܘ-Wallnau (2017). ܠܦܘܬ ܢܡܘܣܐ ܕܣܐܝܛ (site rule)، ܓܘ ܪܫܝܡܬܐ ܕܡܒܘ̈ܥܐ (reference list) ܟܡܬܚܙܝ ܒܣ ܡܒܘ̈ܥܐ ܕܩܪܝ̈ܐ ܝܢܐ ܓܘ ܫܪܫܐ ܕܝܗܝ؛ Gravetter ܘ-Wallnau (2017)، Cohen (1988) ܘ-APA (2020) – ܠܦܘܬ ܦܐܬܐ ܘܦܣܩܐ ܕܡܦܩܬܐ ܛܒܝܥܬܐ؛ Field (2024) ܒܢܘܣܚܐ ܕܝܓܝܛܠܝܐ ܕܪܕܝܐ (reflowable) – ܠܦܘܬ ܦܣܩܐ. ܐܘܪܚܐ ܕ-SPSS – ܬܚܘܝܬܐ ܕܣܐܝܛ، ܫܪܝܪܬܐ ܩܘܒܠ PSPP (ܠܐ ܡܬܝܬܐ ܝܠܗ̇ ܡܢ ܡܒܘܥܐ).