ܛܝ̈ܡܐ ܚܣܝ̈ܪܐ: ܩܐ ܡܘܕܝ ܚܣܝ̈ܪܐ ܝܢܐ، ܘܡܐ ܟܥܒܕܚ
ܐܪܒܥܐ ܡܟܝܢܘ̈ܝܬܐ ܕܚܣܝܪܘܬܐ، ܡܐ ܟܠ ܐܘܪܚܐ ܟܫܕܝܐ ܘܡܐ ܟܡܥܩܡܐ – ܫܩܠܬܐ ܕܣܕܪܐ ܟܠܗ (listwise deletion) ܘܫܩܠܬܐ ܙܘܓܢܝܬܐ (pairwise deletion)، ܚܘܠܦܐ ܒܡܨܥܝܬܐ (mean)، ܡܠܝܐ ܩܝܡܐ ܘܓܕܫܢܝܐ، ܡܠܝܐ ܣܓܝܐܐ (multiple imputation) – ܘܕܟܝ ܟܬܢܚ. ܡܢܬܐ ܒ – ܡܛܝܒܘܬܐ ܕܝܗܝ̈ܒܬܐ ܠܦܘܫܩܐ.
ܡܐ ܐܝܬ ܓܘ ܐܗܐ ܦܐܬܐ (On this page)
ܛܝ̈ܡܐ ܚܣܝ̈ܪܐ (missing values) ܐܝܬ ܡܩܪܒܘܬ ܓܘ ܟܠ ܦܘܫܩܐ (analysis) ܪܨܝܢܐ (Gelman & Hill, 2007, p. 529): ܐܝܢܐ ܕܠܐ ܨܒܐ ܕܦܢܐ ܠܫܘܐܠܐ ܕܡܥܠܬܐ، ܐܝܢܐ ܕܫܘܪ ܥܠ ܦܐܬܐ، ܐܝܢܐ ܕܠܐ ܡܛܠܗ ܠܓܠܠܐ ܬܪܝܢܐ. ܥܘܩܢܐ ܠܝܠܗ ܕܚܣܝ̈ܪܐ ܝܢܐ – ܝܠܗ ܕܐܝܢܐ ܕܚܣܝܪܐ ܝܠܗ ܠܗ ܠܐ ܡܢ ܐܠܨܘܬܐ ܕܡܐ ܝܠܗ ܠܐܝܢܐ ܕܦܢܐ، ܘܡܛܠ ܗܕܐ ܟܠ ܐܘܪܚܐ ܕܦܘܠܚܢܐ ܥܡ ܚܣܝ̈ܪܐ ܣܝܡܬܐ ܝܠܗ̇ ܥܠ ܥܠܬܐ ܕܚܣܝܪܘܬܐ. ܦܐܬܐ ܟܐܙܠܐ ܒܬܪ ܨܚܚܐ 25 ܕ-Gelman ܘ-Hill: ܐܪܒܥܐ ܡܟܝܢܘ̈ܝܬܐ ܕܚܣܝܪܘܬܐ، ܡܢ ܦܫܝܛܐ ܠܩܫܝܐ؛ ܐܘܪ̈ܚܬܐ ܕܟܫܕܝܐ ܝܗܝ̈ܒܬܐ ܘܡܐ ܟܥܒܕܝ ܒܣܘܟܢܐ؛ ܐܘܪ̈ܚܬܐ ܦܫܝܛ̈ܐ ܕܟܢܛܪܝ ܠܟܠܗܘܢ ܘܡܐ ܟܡܥܩܡܝ؛ ܘܐܘܪܚܐ ܕܐܢܝ ܟܡܠܟܝ – ܡܠܝܐ ܓܕܫܢܝܐ ܡܢ ܡܘܕܝܠ ܕܪܝܓܪܫܢ، ܘܓܘ ܗܘܝ̈ܐ ܕܣܢܝܩܐ ܝܠܗ – ܡܠܝܐ ܣܓܝܐܐ. ܒܚܪܬܐ: ܡܐ ܟܥܒܕܚ ܒܥܒܕܐ، ܡܐ ܣܐܝܛ ܘ-SPSS ܟܥܒܕܝ ܒܝܚܕܝܘܬܗܘܢ، ܘܕܟܝ ܟܬܢܚ.
ܚܣܝܪܐ ܓܕܫܐܝܬ ܓܡܝܪܐܝܬ
ܡܣܬܒܪܢܘܬܐ ܕܚܣܝܪܘܬܐ ܐܦ ܗܝ ܝܠܗ̇ ܩܐ ܟܠܗܘܢ – ܐܝܟ ܕܟܠ ܡܦܢܝܢܐ ܫܕܐܠܗ ܦܨܐ. ܒܣ ܗܝܕܝܟ ܫܩܠܬܐ ܠܐ ܟܥܒܕܐ ܡܣܒ ܒܐܦ̈ܐ. ܚܕ ܚܕ ܓܐܝ̈ܐ.
ܚܣܝܪܐ ܓܕܫܐܝܬ
ܡܣܬܒܪܢܘܬܐ ܕܚܣܝܪܘܬܐ ܬܠܝܐ ܝܠܗ̇ ܒܣ ܒܝܕܥܬܐ ܕܚܙܝܬܐ ܝܠܗ̇ – ܓܢܣܐ ܕܒܪܢܫܐ، ܝܘܠܦܢܐ، ܥܘܡܪܐ. ܡܨܝܚ ܦܠܚܚ ܥܡܗ: ܟܡܥܠܚ ܐܢܝ ܡܫܬܚܠܦ̈ܢܐ ܠܓܘ ܡܘܕܝܠ.
ܚܣܝܪܐ ܠܐ ܓܕܫܐܝܬ
ܬܠܐ ܒܡܐ ܕܠܐ ܡܫܝܚܐ ܝܠܗ، ܝܢ ܒܛܝܡܐ ܚܣܝܪܐ ܓܢܗ – ܐܢܝ ܕܐܝܬ ܠܗܘܢ ܡܥܠܬܐ ܪܡܬܐ ܠܐ ܨܒܝ ܕܬܢܝ ܡܥܠܬܐ. ܠܐ ܡܨܝܐ ܕܡܚܘܝܚ ܕܠܐ؛ ܟܡܒܨܪܚ ܠܗ ܒܥܘܕܪܢܐ ܕܡܢܒ̈ܝܢܐ ܐܚܪ̈ܢܐ.
ܡܠܝܐ (imputation)
ܡܠܝܐ ܕܛܝܡܐ ܚܣܝܪܐ ܒܕܘܟܬܐ ܕܫܩܠܬܐ ܕܗܘܝܐ. ܡܨܥܝܬܐ – ܡܥܩܡܐ؛ ܡܢܒܝܢܘܬܐ ܡܢ ܪܝܓܪܫܢ – ܐܠܝܨܐ ܝܬܝܪ ܡܢ ܡܫܘܚܬܐ؛ ܡܢܒܝܢܘܬܐ + ܛܥܝܘܬܐ ܓܕܫܢܝܬܐ – ܬܪܝܨܐ؛ ܚܕܟܡܐ ܓܐܝ̈ܐ – ܡܠܝܐ ܣܓܝܐܐ.
1. ܩܐ ܡܘܕܝ ܚܣܝܪܐ – ܐܪܒܥܐ ܡܟܝܢܘ̈ܝܬܐ، ܡܢ ܦܫܝܛܐ ܠܩܫܝܐ
ܩܐ ܕܦܣܩܚ ܡܐ ܓܪܓ ܥܒܕܚ ܥܡ ܚܣܝ̈ܪܐ، ܡܘܚܡܐ ܝܠܗ ܕܝܕܥܚ ܩܐ ܡܘܕܝ ܚܣܝ̈ܪܐ ܝܢܐ. Gelman ܘ-Hill (2007، ܦܐܬܐ 530-531) ܟܦܪܫܝ ܒܝܢܝ ܐܪܒܥܐ ܡܟܝܢܘ̈ܝܬܐ. ܚܣܝܪܐ ܓܕܫܐܝܬ ܓܡܝܪܐܝܬ (missing completely at random): ܡܣܬܒܪܢܘܬܐ ܕܚܣܝܪܘܬܐ ܐܦ ܗܝ ܝܠܗ̇ ܩܐ ܟܠ ܚܕܝܘ̈ܬܐ – ܐܝܟ ܕܟܠ ܡܦܢܝܢܐ ܫܕܐܠܗ ܦܨܐ ܘܠܐ ܨܒܐ ܕܦܢܐ ܠܫܘܐܠܐ ܕܡܥܠܬܐ ܐܡܢ ܕܦܠܛܠܗ 6. ܒܣ ܓܘ ܐܗܐ ܗܘܝܐ ܫܕܝܬܐ ܕܗܘ̈ܝܐ ܚܣܝ̈ܪܐ ܠܐ ܟܥܒܕܐ ܡܣܒ ܒܐܦ̈ܐ (bias) ܠܦܐܪ̈ܐ. ܚܣܝܪܐ ܓܕܫܐܝܬ (missing at random): ܣܓܝܐܘܬܐ ܕܚܣܝܪܘܬܐ ܠܐ ܝܠܗ̇ ܓܕܫܢܝܬܐ ܓܡܝܪܐܝܬ، ܘܐܗܐ ܟܡܬܚܙܐ ܓܘ ܝܗܝ̈ܒܬܐ ܓܢܗܝܢ – ܓܘ ܒܘܨܝܐ ܕܡܚܘ̈ܝܢܐ ܟܢܫܝ̈ܐ ܕ-New York، ܡܢ̈ܘܬܐ ܕܠܐ ܦܘܢܝܐ ܥܠ ܡܥܠܬܐ ܦܪ̈ܝܫܐ ܝܢܐ ܒܝܢܝ ܓܘ̈ܕܐ ܕܫܪ̈ܒܬܐ. ܣܝܡܬܐ ܓܘܢܝܬܐ ܒܝܫ ܝܠܗ̇ ܕܡܣܬܒܪܢܘܬܐ ܕܚܣܝܪܘܬܐ ܬܠܝܐ ܝܠܗ̇ ܒܣ ܒܝܕܥܬܐ ܕܐܝܬ: ܐܢ ܓܢܣܐ ܕܒܪܢܫܐ، ܫܪܒܬܐ، ܝܘܠܦܢܐ ܘܥܘܡܪܐ ܪܫܝܡ̈ܐ ܝܢܐ ܩܐ ܟܠܗܘܢ، ܡܥܠܬܐ "ܚܣܝܪܬܐ ܝܠܗ̇ ܓܕܫܐܝܬ" ܐܢ ܠܐ ܦܘܢܝܐ ܬܠܐ ܝܠܗ ܒܣ ܒܐܢܝ. ܘܗܝܕܝܟ ܫܪܝܐ ܝܠܗ ܕܡܦܠܛܚ ܠܗܘ̈ܝܐ ܚܣܝ̈ܪܐ – ܥܡ ܫܪܛܐ ܕܡܘܕܝܠ ܢܛܪ ܥܠ ܟܠ ܡܫܬܚܠܦ̈ܢܐ ܕܟܡܥܒܕܝ ܥܠ ܡܣܬܒܪܢܘܬܐ ܕܚܣܝܪܘܬܐ: ܡܘܕܝܠ ܩܐ ܡܥܠܬܐ ܦܝܫܐ ܣܢܝܩܐ ܕܡܥܠ ܫܪܒܬܐ، ܐܢ ܠܐ ܦܝܫܐ ܥܡ ܡܣܒ ܒܐܦ̈ܐ. ܚܣܝܪܘܬܐ ܕܬܠܝܐ ܒܡܐ ܕܠܐ ܚܙܝܐ ܝܠܗ: ܐܢ ܐܢܫ̈ܐ "ܥܨܒܢ̈ܝܐ" ܒܨܝܪ ܟܦܢܝ ܥܠ ܡܥܠܬܐ، ܥܨܒܢܘܬܐ ܟܡܢܒܝܐ ܠܡܥܠܬܐ، ܘܥܨܒܢܘܬܐ ܠܐ ܡܫܝܚܬܐ ܝܠܗ̇ – ܡܥܠܬܐ ܠܐ ܝܠܗ̇ ܒܝܫ ܚܣܝܪܬܐ ܓܕܫܐܝܬ؛ ܐܝܟ ܗܢܐ ܝܠܗ ܐܦ ܡܬܐܣܝܢܐ ܕܟܫܒܩ ܢܣܝܘܢܐ (experiment) ܡܛܠ ܠܐ ܢܝܚܘܬܐ ܕܠܐ ܡܫܝܚܬܐ ܝܠܗ̇. ܚܣܝܪܘܬܐ ܐܝܟ ܗܕܐ ܓܪܓ ܥܒܕܚ ܠܗ̇ ܡܘܕܝܠ ܓܠܝܐܝܬ، ܝܢ ܡܠܝܚ ܥܡ ܡܣܒ ܒܐܦ̈ܐ. ܚܣܝܪܘܬܐ ܕܬܠܝܐ ܒܛܝܡܐ ܚܣܝܪܐ ܓܢܗ: ܐܢܝ ܕܐܝܬ ܠܗܘܢ ܡܥܠܬܐ ܪܡܬܐ ܒܨܝܪ ܟܓܠܝ ܠܗ̇؛ ܓܘ ܗܘܝܐ ܪܚܝܩܐ – ܟܠ ܐܝܢܐ ܕܟܐܚܕ ܝܬܝܪ ܡܢ ܬܚܘܡܐ ܠܐ ܟܨܒܐ – ܐܗܐ ܦܣܝܩܘܬܐ (censoring) ܝܠܗ̇، ܐܢܐ ܐܦ ܗܘܝܐ ܕܡܣܬܒܪܢܘܬܐ ܩܫܝܐ ܝܠܗ. ܡܨܝܚ ܥܒܕܚ ܡܘܕܝܠ، ܝܢ ܡܒܨܪܚ ܠܥܘܩܢܐ ܒܥܘܕܪܢܐ ܕܡܢܒ̈ܝܢܐ ܐܚܪ̈ܢܐ ܕܟܡܩܪܒܝ ܠܗ ܠ"ܚܣܝܪܐ ܓܕܫܐܝܬ": ܚܘܪ̈ܐ ܘܐܢܝ ܕܐܝܬ ܠܗܘܢ ܫܘܕܥܬܐ ܕܝܘܠܦܢܐ ܝܬܝܪ ܟܐܚܕܝ، ܘܢܛܪܬܐ ܥܠܝܗܘܢ ܩܠܝܠ ܟܡܬܪܨܐ – "ܐܢܐ ܡܨܝܐ ܕܗܘܝܐ ܒܣ ܩܠܝܠ" – ܠܡܢܬܐ ܪܡܬܐ ܕܠܐ ܦܘܢܝܐ ܕܐܢܝ ܕܐܝܬ ܠܗܘܢ ܡܥܠܬܐ ܪܡܬܐ.
ܘܢܘܩܙܐ ܦܣܘܩܬܐ (Gelman & Hill, 2007, p. 531): ܠܐ ܡܨܝܐ ܕܡܚܘܝܚ ܕܝܗܝ̈ܒܬܐ ܚܣܝ̈ܪܬܐ ܝܢܐ ܓܕܫܐܝܬ. "ܡܫܬܚܠܦ̈ܢܐ ܟܡܝܢ̈ܐ" ܕܚܣܝܪܘܬܐ ܡܨܝܐ ܕܬܠܝܐ ܒܝܗܘܢ ܠܐ ܚܙܝ̈ܐ ܝܢܐ – ܡܢ ܬܚܘܡܐ ܕܝܗܘܢ – ܘܡܛܠ ܗܕܐ ܡܢ ܡܬܘܡ ܠܐ ܡܨܝܐ ܕܡܣܠܝܚ ܠܗܘܢ. ܟܣܐܡܚ، ܝܢ ܟܒܚܪܚ ܠܩܘܒܠ ܒܘܨ̈ܝܐ ܐܚܪ̈ܢܐ ܕܥܒܕܠܗܘܢ ܢܛܪܬܐ ܥܠ ܐܢܝ ܕܠܐ ܦܢܝܠܗܘܢ. ܒܥܒܕܐ ܟܡܢܣܚ ܕܡܥܠܚ ܓܘ ܡܘܕܝܠ ܡܢܒ̈ܝܢܐ ܣܓܝ̈ܐܐ ܐܝܟ ܕܡܨܝܐ ܩܐ ܕܣܝܡܬܐ ܗܘܝܐ ܡܬܩܒܠܢܝܬܐ: ܕܣܐܡܚ ܕܠܐ ܦܘܢܝܐ ܥܠ ܡܥܠܬܐ ܬܠܐ ܝܠܗ ܒܣ ܒܓܢܣܐ ܕܒܪܢܫܐ، ܫܪܒܬܐ ܘܝܘܠܦܢܐ ܣܝܡܬܐ ܚܝܠܬܢܬܐ ܝܠܗ̇، ܐܢܐ ܣܓܝ ܡܬܩܒܠܢܝܬܐ ܝܠܗ̇ ܝܬܝܪ ܡܢ ܕܣܐܡܚ ܕܡܣܬܒܪܢܘܬܐ ܩܝܡܬܐ ܝܠܗ̇ ܩܐ ܟܠܗܘܢ.
ܠܘܚܐ 1. ܐܪܒܥܐ ܡܟܝܢܘ̈ܝܬܐ ܕܚܣܝܪܘܬܐ – ܒܡܐ ܬܠܐ ܝܠܗ̇ ܡܣܬܒܪܢܘܬܐ ܕܚܣܝܪܘܬܐ، ܘܡܐ ܟܦܠܛ ܡܢ ܐܗܐ
| ܡܟܝܢܘܬܐ | ܡܣܬܒܪܢܘܬܐ ܕܚܣܝܪܘܬܐ ܬܠܝܐ ܝܠܗ̇ ܒ... | ܡܬܠܐ | ܡܐ ܟܦܠܛ |
|---|---|---|---|
| ܚܣܝܪܐ ܓܕܫܐܝܬ ܓܡܝܪܐܝܬ | ܠܐ ܡܕܡ – ܐܦ ܗܝ ܩܐ ܟܠܗܘܢ | ܠܐ ܨܒܝܢܐ ܠܦܘܬ ܫܕܝܬܐ ܕܦܨܐ | ܫܩܠܬܐ ܠܐ ܟܥܒܕܐ ܡܣܒ ܒܐܦ̈ܐ؛ ܒܣ ܟܡܒܨܪܐ ܠܕܘܡܝܐ |
| ܚܣܝܪܐ ܓܕܫܐܝܬ | ܡܫܬܚܠܦ̈ܢܐ ܕܚܙ̈ܝܐ ܝܢܐ ܩܐ ܟܠܗܘܢ | ܠܐ ܦܘܢܝܐ ܥܠ ܡܥܠܬܐ ܬܠܐ ܝܠܗ ܒܫܪܒܬܐ ܘܒܝܘܠܦܢܐ | ܫܪܝܐ ܝܠܗ ܕܫܩܠܚ ܐܢ ܡܘܕܝܠ ܢܛܪ ܥܠ ܐܢܝ ܡܫܬܚܠܦ̈ܢܐ؛ ܛܒܐ ܝܠܗ ܕܡܠܝܚ ܒܥܘܕܪܢܐ ܕܝܗܘܢ |
| ܬܠܐ ܒܡܐ ܕܠܐ ܚܙܝܐ ܝܠܗ | ܡܫܬܚܠܦܢܐ ܕܠܐ ܡܫܝܚܐ ܝܠܗ ܘܕܟܡܢܒܐ ܠܛܝܡܐ | "ܥܨܒܢܘܬܐ" ܕܠܐ ܡܫܝܚܬܐ ܝܠܗ̇؛ ܠܐ ܢܝܚܘܬܐ ܡܢ ܐܣܝܘܬܐ | ܕܥܒܕܚ ܡܘܕܝܠ ܓܠܝܐܝܬ، ܝܢ ܕܡܠܝܚ ܥܡ ܡܣܒ ܒܐܦ̈ܐ؛ ܕܡܘܣܦܚ ܡܢܒ̈ܝܢܐ |
| ܬܠܐ ܒܛܝܡܐ ܚܣܝܪܐ ܓܢܗ | ܛܝܡܐ ܕܗܘܐ ܦܝܫܐ ܡܫܝܚܐ | ܐܢܝ ܕܐܝܬ ܠܗܘܢ ܡܥܠܬܐ ܪܡܬܐ ܠܐ ܨܒܝ ܕܬܢܝ؛ ܦܣܝܩܘܬܐ (censoring) | ܩܫܝܐ ܡܢ ܟܠ؛ ܡܢܒ̈ܝܢܐ ܟܡܩܪܒܝ ܠ"ܓܕܫܐܝܬ" – ܒܣ ܩܠܝܠ |
ܡܥܝܪܢܘܬܐ. ܠܦܘܬ Gelman ܘ-Hill (2007، ܦܣܩܐ 25.1). "ܚܣܝܪܐ ܓܕܫܐܝܬ" ܠܐ ܟܐܡܪ ܕܚܣܝܪܘܬܐ ܓܕܫܢܝܬܐ ܝܠܗ̇ – ܐܠܐ ܕܡܦܫܩܬܐ ܝܠܗ̇ ܒܝܕ ܡܐ ܕܚܙܝܐ ܝܠܗ؛ ܐܗܝ ܣܝܡܬܐ ܟܡܬܩܪܝܐ ܐܦ ܣܝܡܬܐ ܕ-ignorability (ignorability)، ܡܢ ܐܦ ܗܘ ܙܢܐ ܐܝܟ ܓܘ ܡܦܩܬܐ ܕܥܠ̈ܠܬܐ (causal inference). ܬܪܬܝܢ ܡܟܝܢܘ̈ܝܬܐ ܐܚܪ̈ܝܬܐ ܟܡܬܩܪܝ ܐܟܚܕܐ "ܚܣܝܪܐ ܠܐ ܓܕܫܐܝܬ".
2. ܐܘܪ̈ܚܬܐ ܕܟܫܕܝܐ ܝܗܝ̈ܒܬܐ – ܘܡܐ ܟܥܒܕܝ ܒܣܘܟܢܐ
ܐܘܪ̈ܚܬܐ ܣܓܝ̈ܐܐ ܟܡܦܫܛܝ ܠܥܘܩܢܐ ܒܫܕܝܬܐ ܕܝܗܝ̈ܒܬܐ؛ Gelman ܘ-Hill (2007، ܦܐܬܐ 531-532) ܟܡܚܘܝ ܕܟܝ ܐܗܐ ܟܥܒܕܐ ܡܣܒ ܒܐܦ̈ܐ، ܘܟܡܥܗܕܝ ܕܐܦ ܕܠܐ ܡܣܒ ܒܐܦ̈ܐ – ܛܥ̈ܝܘܬܐ ܬܩܝ̈ܢܬܐ ܟܪܒܝ ܡܛܠ ܕܕܘܡܝܐ ܙܥܘܪܐ ܝܠܗ. ܦܘܫܩܐ ܕܗܘ̈ܝܐ ܓܡܝܪ̈ܐ (complete-case) – ܫܩܠܬܐ ܕܣܕܪܐ ܟܠܗ (listwise deletion): ܟܡܦܠܛܚ ܟܠ ܚܕܝܘܬܐ ܕܚܣܝܪܐ ܠܗ̇ ܛܝܡܐ ܓܘ ܦܐܪܐ ܝܢ ܓܘ ܚܕ ܡܢ ܡܢܒ̈ܝܢܐ؛ R ܘ-SPSS ܟܥܒܕܝ ܐܗܐ ܓܘ ܪܝܓܪܫܢ ܡܢ ܓܢܗܘܢ. ܬܪܝܢ ܥܘ̈ܩܢܐ: ܐܢ ܚܕܝܘ̈ܬܐ ܥܡ ܚܣܝ̈ܪܐ ܦܪ̈ܝܫܐ ܝܢܐ ܛܟܣܢܐܝܬ ܡܢ ܓܡܝܪ̈ܐ – ܡܣܒ ܒܐܦ̈ܐ؛ ܘܐܢ ܐܝܬ ܣܓܝ ܡܫܬܚܠܦ̈ܢܐ ܓܘ ܡܘܕܝܠ – ܦܝܫܝ ܩܠܝܠ ܗܘ̈ܝܐ ܓܡܝܪ̈ܐ، ܘܣܓܝܐܘܬܐ ܕܝܗܝ̈ܒܬܐ ܦܝܫܝ ܫܕܝ̈ܐ ܡܛܠ ܦܘܫܩܐ ܦܫܝܛܐ. ܦܘܫܩܐ ܕܗܘ̈ܝܐ ܕܐܝܬ (available-case) – ܫܩܠܬܐ ܙܘܓܢܝܬܐ (pairwise deletion): ܟܠ ܓܢܒܐ ܟܡܬܒܚܪ ܥܠ ܕܘܡܝܐ ܙܥܘܪܐ ܕܐܝܬ ܠܗ ܝܗܝ̈ܒܬܐ. ܓܘ ܒܘܨܝܐ ܕܫܘܐ̈ܠܐ ܕ-2001 ܟܠܗܘܢ 1,501 ܡܦܢܝ̈ܢܐ ܬܢܝܠܗܘܢ ܝܘܠܦܢܐ ܘ-16% ܠܐ ܨܒܝܠܗܘܢ ܕܬܢܝ ܡܥܠܬܐ – ܗܝܕܝܟ ܟܡܟܢܫܚ ܝܘܠܦܢܐ ܥܠ ܟܠܗܘܢ ܘܡܥܠܬܐ ܥܠ 84%. ܥܘܩܢܐ: ܦܘܫܩ̈ܐ ܦܪ̈ܝܫܐ ܣܡܝܟ̈ܐ ܝܢܐ ܥܠ ܕܘ̈ܡܝܐ ܙܥܘܪ̈ܐ ܦܪ̈ܝܫܐ ܘܠܐ ܡܢ ܐܠܨܘܬܐ ܫܠܡ̈ܐ ܝܢܐ ܚܕ ܥܡ ܚܕ؛ ܘܐܢ ܐܢܝ ܕܠܐ ܦܢܝܠܗܘܢ ܦܪ̈ܝܫܐ ܝܢܐ – ܡܣܒ ܒܐܦ̈ܐ ܐܝܟ ܩܕܡ: 90% ܡܢ ܐܦܪܘ-ܐܡܪܝܟ̈ܝܐ ܐܢܐ ܒܣ 81% ܡܢ ܚܘܪ̈ܐ ܬܢܝܠܗܘܢ ܡܥܠܬܐ، ܘܡܛܠ ܗܕܐ ܟܢܘܫܝܐ ܕܡܥܠܬܐ ܟܡܚܘܐ ܟܢܫܐ ܟܠܢܝܐ (population) ܐܚܪܢܐ ܡܢ ܟܢܘܫܝܐ ܕܝܘܠܦܢܐ. ܐܦ ܫܒܩܬܐ ܕܡܫܬܚܠܦܢܐ ܓܡܝܪܐ ܡܛܠ ܡܢܬܐ ܪܡܬܐ ܕܚܣܝ̈ܪܐ ܦܘܫܩܐ ܕܗܘ̈ܝܐ ܕܐܝܬ ܝܠܗ – ܘܓܘ ܣܘܟܠܐ ܕܥܠ̈ܠܬܐ ܡܨܝܐ ܕܫܒܩ ܡܫܬܚܠܦܢܐ ܕܣܝ̈ܡܬܐ ܣܢܝܩܝ ܠܗ. ܡܬܩܠܢܘܬܐ (weighting) ܕܠܐ ܦܘܢܝܐ: ܡܘܕܝܠ ܕܟܡܢܒܐ ܡܢܝܐ ܦܢܐܠܗ، ܘܗܦܟܐ ܕܡܣܬܒܪܢܘܬܐ ܡܢܒܝܬܐ (predicted probability) ܐܝܟ ܡܬܩܠܐ، ܩܐ ܕܡܕܥܪܚ ܠܕܘܡܝܐ ܓܡܝܪܐ ܕܡܝܘܬܐ (representativeness) – ܟܡܫܓܪܫ ܥܡ ܝܬܝܪ ܡܢ ܚܕ ܡܫܬܚܠܦܢܐ ܚܣܝܪܐ، ܘܛܥ̈ܝܘܬܐ ܬܩܝ̈ܢܬܐ ܟܗܘܝܐ ܠܐ ܩܝ̈ܡܬܐ ܐܡܢ ܕܡܣܬܒܪ̈ܢܘܝܬܐ ܩܪ̈ܝܒܐ ܝܢܐ ܠ-0 ܝܢ ܠ-1.
3. ܐܘܪ̈ܚܬܐ ܦܫܝܛ̈ܐ ܕܟܢܛܪܝ ܠܟܠܗܘܢ – ܘܡܐ ܟܡܥܩܡܝ
ܒܕܘܟܬܐ ܕܫܩܠܬܐ، ܡܨܝܚ ܡܠܝܚ – "ܡܠܝܐ" (impute). ܐܘܪ̈ܚܬܐ ܟܢܛܪܝ ܪܒܘܬܐ ܕܕܘܡܝܐ، ܐܢܐ ܟܒܪܝ ܡܣܒ ܒܐܦ̈ܐ ܡܢ ܙܢܐ ܐܚܪܢܐ، ܘܚܕ ܢܡܘܣܐ ܟܡܬܦܠܚ ܥܠ ܟܠܗܝܢ: ܐܡܢ ܕܟܡܠܝܚ ܛܝܡܐ ܝܚܝܕܝܐ، ܛܥ̈ܝܘܬܐ ܬܩܝ̈ܢܬܐ ܟܦܠܛܝ ܢܚܝ̈ܬܐ ܝܬܝܪ ܡܢ ܡܫܘܚܬܐ، ܡܛܠ ܕܐܝܬ ܣܓܝ ܠܐ ܫܪܝܪܘܬܐ ܥܠ ܛܝܡܐ ܚܣܝܪܐ، ܘܒܓܘܒܝܐ ܕܚܕ ܛܝܡܐ ܟܡܚܘܝܚ ܐܝܟ ܕܝܕܝܥܐ ܝܠܗ ܒܫܪܝܪܘܬܐ (Gelman & Hill, 2007, p. 532). ܚܘܠܦܐ ܒܡܨܥܝܬܐ (mean): ܦܫܝܩܐ ܡܢ ܟܠ – ܘܐܦ ܣܓܝ ܟܡܥܩܡܐ ܠܦܘܠܓܐ (distribution) ܕܡܫܬܚܠܦܢܐ، ܟܡܒܨܪܐ ܠܣܛܝܘܬܐ ܬܩܝܢܬܐ (SD)، ܘ"ܟܓܪܫܐ" ܠܫܘ̈ܥܪܐ ܕܐܣܘܪܐ ܕܚܕ̈ܕܐ (correlation) ܠܨܦܪܐ. Pallant (2020، ܨܚܚܐ 6) ܟܐܡܪܐ ܥܠ ܐܗܝ ܓܘܒܝܐ ܓܘ SPSS: "ܡܢ ܡܬܘܡ ܠܐ ܓܪܓ ܡܬܦܠܚܐ"، ܘ-Field (2024، tip 6.1) ܟܡܦܫܩ ܩܐ ܡܘܕܝ: ܩܐ ܛܝܡܐ ܕܡܘܚܠܦܐ ܝܠܗ ܠܝܬ ܪܘܚܩܐ ܡܢ ܡܨܥܝܬܐ، ܘܛܥܝܘܬܐ ܬܩܝܢܬܐ ܕܡܒܨܪܬܐ ܝܠܗ̇ ܟܒܪܝܐ "ܪܫܝܡܘܬܐ (significance)" ܕܐܝܬܝܗ̇ ܦܐܪܐ ܕܚܘܠܦܐ. ܓܪܫܬܐ ܕܛܝܡܐ ܐܚܪܝܐ ܠܩܕܡ (last value carried forward): ܓܘ ܫܘܥܪܐ ܕܥܘܕܪ̈ܢܐ (interventions)، ܕܡܚܠܦܚ ܦܐܪܐ ܚܣܝܪܐ ܒܡܫܘܚܬܐ ܕܫܘܪܝܐ (baseline). ܟܡܬܚܫܒ ܢܛܘܪܐ (conservative)، ܐܢܐ ܡܨܝܐ ܕܗܘܝܐ ܗܦܟܐ: ܡܛܠ ܕܥܪܬܐ ܠܡܨܥܝܬܐ (regression to the mean) ܡܣܟܝܬܐ ܝܠܗ̇ ܢܚܬܬܐ ܓܘ ܬܘܪܨܐ ܕܣܘܟܢܐ ܐܦ ܕܠܐ ܥܘܕܪܢܐ، ܘܡܛܠ ܗܕܐ ܛܝܡܐ ܥܬܝܩܐ ܟܡܬܚܙܐ ܒܝܫܐ ܝܬܝܪ ܡܢ ܫܪܪܐ – ܘܐܢ ܡܢ̈ܘܬܐ ܕܚܣܝ̈ܪܐ ܦܪ̈ܝܫܐ ܝܢܐ ܒܝܢܝ ܓܘ̈ܕܐ، ܫܘܥܪܐ ܕܡܥܒܕܢܘܬܐ ܐܝܬ ܠܗ ܡܣܒ ܒܐܦ̈ܐ ܓܘ ܐܘܪܚܐ ܠܐ ܢܛܘܪܬܐ. ܝܕܥܬܐ ܡܢ ܚܙ̈ܝܬܐ ܩܪ̈ܝܒܐ: ܡܥܠܬܐ ܕܐܒܐ ܡܢ ܬܘܢܝܐ ܕܝܡܐ – ܡܬܩܒܠܢܝܐ، ܐܢܐ ܟܡܥܒܪ ܛܥܝܘܬܐ ܕܡܫܘܚܬܐ، ܘܓܪܓ ܫܐܠܚ ܐܢ ܐܝܬ ܠܡܬܢܝܢܐ ܥܠܬܐ ܕܡܥܩܡ. ܓܢܣܐ "ܚܣܝܪܐ" ܩܐ ܡܢܒܝܢܐ ܕܓܢ̈ܣܐ (categorical): ܦܫܝܛܐ ܘܣܓܝ ܓܐܝ̈ܐ ܡܘܬܪܢܐ. ܡܚܘܝܢܐ ܕܚܣܝܪܘܬܐ ܩܐ ܡܢܒܝܢܐ ܡܬܡܫܚܢܐ (continuous) (ܡܫܬܚܠܦܢܐ dummy "ܚܣܝܪܐ" + ܨܦܪܐ ܝܢ ܡܨܥܝܬܐ ܒܕܘܟܬܐ ܕܛܝܡܐ): ܡܫܡܗܐ ܝܠܗ ܓܘ ܝܕ̈ܥܬܐ ܕܟܢܫܐ، ܐܢܐ ܡܨܠܝܢܐ ܝܠܗ ܕܥܒܕ ܡܣܒ ܒܐܦ̈ܐ ܠܡܢܝ̈ܢܐ ܡܫܘܬܦ̈ܐ ܕܫܪܟܐ ܕܡܢܒ̈ܝܢܐ، ܡܛܠ ܕܟܡܠܨ ܐܦ ܗܝ ܡܨܠܝܢܘܬܐ (slope) ܥܠ ܬܪܬܝܢ ܓܘ̈ܕܐ ܕܚܣܝܪܘܬܐ. ܢܡܘ̈ܣܐ ܕܠܘܓܝܩܐ: ܐܝܢܐ ܕܬܢܐܠܗ ܨܦܪܐ ܝܪ̈ܚܐ ܕܥܒܕܐ – ܡܥܠܬܐ ܕܝܠܗ ܡܢ ܥܒܕܐ ܨܦܪܐ ܝܠܗ̇؛ ܡܠܝܐ ܐܝܟ ܗܢܐ ܠܐ ܟܣܡܟ ܥܠ ܣܝ̈ܡܬܐ ܚܝܠܬܢ̈ܝܬܐ، ܡܛܠ ܕܡܟܝܢܘܬܐ ܕܚܣܝܪܘܬܐ ܝܕܝܥܬܐ ܝܠܗ̇.
4. ܡܠܝܐ ܓܕܫܢܝܐ ܡܢ ܡܘܕܝܠ – ܐܘܪܚܐ ܕ-Gelman ܘ-Hill
ܐܡܢ ܕܚܣܝܪܐ ܝܬܝܪ ܡܢ ܡܢܬܐ ܙܥܘܪܬܐ ܛܒܐ (negligible)، Gelman ܘ-Hill (2007، ܦܣܩܐ 25.4) ܟܓܒܝ ܕܡܠܝܚ ܒܐܘܪܚܐ ܪܫܡܝܬܐ. ܗܘܝܐ ܦܫܝܛܐ: ܚܕ ܡܫܬܚܠܦܢܐ ܥܡ ܚܣܝ̈ܪܐ – ܡܥܠܬܐ – ܘܡܫܬܚܠܦ̈ܢܐ ܕܚܙ̈ܝܐ ܝܢܐ ܩܐ ܟܠܗܘܢ. ܡܠܝܐ ܓܕܫܢܝܐ ܦܫܝܛܐ – ܓܘܒܝܐ ܕܕܘܡܝܐ ܡܢ ܛܝ̈ܡܐ ܕܚܙ̈ܝܐ ܝܢܐ – ܠܐ ܟܚܫܒ ܠܟܠ ܝܕܥܬܐ ܕܐܝܬ ܓܘ ܫܪܟܐ ܕܫܘܐ̈ܠܐ؛ ܐܗܐ ܒܣ ܢܘܩܙܐ ܕܫܘܪܝܐ ܝܠܗ. ܪܝܓܪܫܢ: ܟܡܦܐܐ ܡܘܕܝܠ ܠܗܘ̈ܝܐ ܕܚܙ̈ܝܐ ܝܢܐ ܘܟܡܢܒܝܚ ܠܚܣܝ̈ܪܐ. ܐܢܐ ܡܠܝܐ ܩܝܡܐ (deterministic) – ܡܢܒܝܢܘܬܐ ܓܢܗ̇ – ܟܒܪܐ ܛܝ̈ܡܐ ܐܠܝܨ̈ܐ ܝܬܝܪ ܡܢ ܡܫܘܚܬܐ: ܓܘ ܡܘܕܝܠ ܕܝܗܘܢ R² = .44، ܝܢܝ ܣܛܝܘܬܐ ܬܩܝܢܬܐ ܡܦܫܩܬܐ 66% ܝܠܗ̇ ܡܢ ܕܝܗܝ̈ܒܬܐ، ܘܡܛܠ ܗܕܐ ܛܝ̈ܡܐ ܡܢܒ̈ܝܐ ܒܨܝܪ ܟܡܫܬܚܠܦܝ ܡܢ ܩܕܡ̈ܝܐ – ܘܣܓܝܐܘܬܐ ܕܐܢܝ ܕܠܐ ܦܢܝܠܗܘܢ ܗܘܝ ܡܬܚܙܝ ܐܝܟ ܕܡܥܠܬܐ ܕܝܗܘܢ ܓܘ ܦܠܓܐ ܕܣܒܠܬܐ (scale) ܝܠܗ̇، ܒܛܥܝܘܬܐ (ܦܐܬܐ 536). ܬܘܪܨܐ: ܡܠܝܐ ܓܕܫܢܝܐ ܡܢ ܪܝܓܪܫܢ – ܟܡܘܣܦܚ ܠܡܢܒܝܢܘܬܐ ܛܥܝܘܬܐ ܕܡܢܒܝܢܘܬܐ، ܛܝܡܐ ܓܕܫܢܝܐ ܡܢ ܦܘܠܓܐ ܢܘܪܡܠܝܐ (normal distribution) ܥܡ ܣܛܝܘܬܐ ܬܩܝܢܬܐ ܕܫܪ̈ܟܐ (residuals) – ܘܛܝ̈ܡܐ ܡܠܝ̈ܐ ܟܡܬܦܪܣܝ ܥܠ ܟܠܗ̇ ܦܬܝܘܬܐ (range) ܐܝܟ ܝܗܝ̈ܒܬܐ ܫܪܝܪ̈ܬܐ (ܨܘܪܬܐ 1).
ܨܘܪܬܐ 1. ܡܠܝܐ ܩܝܡܐ ܠܩܘܒܠ ܡܠܝܐ ܓܕܫܢܝܐ
ܣܪܛܐ ܦܫܝܛܐ – ܛܝܡܐ ܕܪܝܓܪܫܢ ܟܡܢܒܐ ܩܐ ܗܘܝܐ ܚܣܝܪܐ؛ ܣܪܛܐ ܙܩܝܦܐ – ܛܝܡܐ ܕܡܘܚܠܦܐ ܝܠܗ. ܝܗܝ̈ܒܬܐ ܥܒܝ̈ܕܬܐ، ܩܐ ܡܚܘܝܢܘܬܐ ܕܐܣܟܝܡܐ
ܡܥܝܪܢܘܬܐ. ܒܪܘܚܐ ܕܨܘܪܬܐ 25.2 ܓܘ Gelman ܘ-Hill (2007، ܦܐܬܐ 537): ܡܠܝܐ ܩܝܡܐ ܝܬܝܒܐ ܝܠܗ ܒܚܬܝܬܘܬܐ ܥܠ ܡܢܒܝܢܘܬܐ ܕܪܝܓܪܫܢ ܘܠܐ ܟܚܫܒ ܠܠܐ ܫܪܝܪܘܬܐ ܕܡܢܒܝܢܘܬܐ؛ ܓܕܫܢܝܐ ܟܡܘܣܦ ܛܥܝܘܬܐ ܕܡܢܒܝܢܘܬܐ ܘܟܡܚܘܐ ܛܒ ܒܝܫ ܦܬܝܘܬܐ (range) ܕܛܝ̈ܡܐ ܓܘ ܝܗܝ̈ܒܬܐ. ܝܗܝ̈ܒܬܐ ܥܒܝ̈ܕܬܐ ܝܢܐ (ܙܪܥܐ ܩܝܡܐ).
ܬܠܬܐ ܡܥܝܪ̈ܢܘܝܬܐ ܥܒܕܢܝ̈ܬܐ ܡܢܝܗܘܢ. ܐܝܢܝ ܡܢܒ̈ܝܢܐ؟ ܟܠ ܡܐ ܕܟܡܢܒܐ – ܐܦ ܦܐܪ̈ܐ ܕܡܫܬܚܠܦܢܐ ܚܣܝܪܐ: ܢܘܟܪܝܐ ܝܠܗ ܕܥܒܕܚ ܡܘܕܝܠ ܩܐ ܡܥܠܬܐ ܠܦܘܬ ܫܩܠܬܐ ܕܥܘܕܪܢܐ ܕܡܕܝܢܬܐ (benefits)، ܕܡܢܬܐ ܡܢܗ ܦܐܪܐ ܝܠܗ ܕܡܥܠܬܐ، ܐܢܐ ܩܐ ܡܠܝܐ ܐܗܐ ܡܬܩܒܠܢܐ ܝܠܗ – ܢܝܫܐ ܠܝܠܗ ܡܦܩܬܐ ܕܥܠ̈ܠܬܐ ܐܠܐ ܡܢܒܝܢܘܬܐ ܚܬܝܬܬܐ، ܘܫܪܝܐ ܝܠܗ ܕܡܦܠܚܚ ܟܠ ܡܥܠܢܐ ܕܟܡܫܡܫ ܠܗ̇ (ܦܐܬܐ 537). ܡܫܘܚܬܐ (scale): ܐܢܝ ܟܥܒܕܝ ܡܘܕܝܠ ܩܐ ܫܪܫܐ ܕܡܥܠܬܐ، ܘ"ܟܩܛܥܝ" (topcode) ܛܝ̈ܡܐ ܪ̈ܡܐ – ܠܐ ܩܐ ܕܡܬܪܨܝ ܝܗܝ̈ܒܬܐ ܐܠܐ ܩܐ ܕܡܫܦܪܝ ܡܢܒܝܢܘܬܐ ܓܘ ܦܬܝܘܬܐ ܕܡܘܚܡܐ ܝܠܗ̇. ܨܦܪܐ ܝܢ ܠܥܠ ܡܢ ܨܦܪܐ: ܐܡܢ ܕܡܫܬܚܠܦܢܐ ܡܨܝܐ ܕܗܘܝܐ ܨܦܪܐ (ܠܐ ܦܠܚܠܗ) ܝܢ ܠܥܠ ܡܢ ܨܦܪܐ، ܟܡܠܝܚ ܒܬܪܝܢ ܕܪ̈ܓܐ – ܪܝܓܪܫܢ ܠܘܓܝܣܛܝܩܝܐ ܩܐ ܫܘܐܠܐ ܐܢ ܠܥܠ ܡܢ ܨܦܪܐ ܝܠܗ، ܘܪܝܓܪܫܢ ܣܪܛܢܝܐ ܩܐ ܛܝܡܐ ܕܠܥܠ ܡܢ ܨܦܪܐ (ܦܐܬܐ 537-538). ܘܐܝܬ ܐܦ ܫܘܝܢܐ (hot-deck): ܩܐ ܟܠ ܚܕܝܘܬܐ ܚܣܝܪܬܐ ܟܡܫܟܚܚ ܚܕܝܘܬܐ ܕܕܡܝܐ ܓܘ ܝܗܝ̈ܒܬܐ ܕܚܙ̈ܝܐ ܝܢܐ ܘܟܫܩܠܚ ܛܝܡܐ ܕܝܠܗ̇ – ܢܘܣܚܐ ܠܐ ܦܪܡܝܛܪܝܐ (nonparametric) ܕܪܝܓܪܫܢ؛ ܡܬܠܐ ܕܝܗܘܢ – ܡܠܝܐ ܕܥܠ̈ܠܬܐ ܕܣܘܟܢܐ ܩܐ ܬܝ̈ܩܐ ܕܠܐ ܫܪ̈ܝܐ ܡܢ ܚܡܫܐ ܬܝ̈ܩܐ ܫܪ̈ܝܐ ܕܕܡܝ̈ܐ ܝܢܐ ܡܢ ܟܠ.
5. ܚܕܟܡܐ ܡܫܬܚܠܦ̈ܢܐ ܚܣܝ̈ܪܐ – ܘܡܠܝܐ ܣܓܝܐܐ
ܟܠܝܘܡ ܚܣܝ̈ܪܐ ܒܕܝܪ̈ܐ ܝܢܐ ܓܘ ܚܕܟܡܐ ܡܫܬܚܠܦ̈ܢܐ، ܘܠܐ ܡܨܝܐ ܕܡܩܝܡܚ ܚܕ ܡܫܬܚܠܦܢܐ ܠܩܘܒܠ ܡܢܒ̈ܝܢܐ ܓܡܝܪ̈ܐ (Gelman & Hill, 2007, Section 25.5). ܬܪܬܝܢ ܐܘܪ̈ܚܬܐ: ܚܕ ܡܘܕܝܠ ܕܣܓܝ ܡܫܬܚܠܦ̈ܢܐ ܩܐ ܟܠ ܡܫܬܚܠܦ̈ܢܐ ܚܣܝ̈ܪܐ – ܒܥܒܕܐ ܡܘܕܝܠ "ܡܢ ܪܦܐ" (ܢܘܪܡܠܝܐ ܕܣܓܝ ܡܫܬܚܠܦ̈ܢܐ) ܕܬܘܟܢ̈ܝܬܐ ܟܡܪܗܛܝ ܒܚܕ ܕܚܝܬܐ ܕܩܘܦܬܐ، "ܡܠܝ̈ܐ ܒܣ ܛܒ̈ܐ ܝܢܐ ܐܝܟ ܡܘܕܝܠ ܘܡܛܠ ܗܕܐ ܓܪܓ ܡܒܚܪܚ ܠܗܘܢ – ܐܢܐ ܐܗܐ ܢܘܩܙܐ ܛܒܐ ܕܫܘܪܝܐ ܝܠܗ"؛ ܝܢ ܡܠܝܐ ܕܡܬܢܐ (iterative): ܟܡܠܝܚ ܓܫܝܡܐܝܬ، ܘܒܬܪܗ ܩܐ ܟܠ ܡܫܬܚܠܦܢܐ ܚܣܝܪܐ ܒܕܘܪܗ ܟܡܦܐܐ ܪܝܓܪܫܢ ܥܠ ܟܠ ܫܪܟܐ (ܥܡ ܛܝ̈ܡܐ ܕܗܫܐ ܡܠܝ̈ܐ ܝܢܐ)، ܟܡܠܝܚ ܓܕܫܐܝܬ، ܘܟܕܥܪܚ ܗܠ ܟܢܫܬܐ (convergence). ܝܘܬܪܢܗ̇ – ܟܠ ܪܝܓܪܫܢ ܡܦܗܡܐ ܝܠܗ ܒܦܪܝܫܘܬܐ ܘܡܨܝܚ ܡܥܠܚ ܥܒ̈ܕܐ ܕܚܕ̈ܕܐ (interactions)؛ ܚܘܣܪܢܗ̇ – ܓܪܓ ܫܪܪܚ ܕܡܘܕܝ̈ܠܐ ܫܠܡ̈ܐ ܝܢܐ (ܠܐ ܡܠܝܐ ܕܥܘܡܪܐ ܠܦܘܬ ܡܥܠܬܐ ܘܒܬܪܗ ܫܒܩܬܐ ܕܥܘܡܪܐ ܓܘ ܡܠܝܐ ܕܡܥܠܬܐ)، ܘܒܟܠ ܗܘܝܐ: ܕܚܙܝܚ ܠ-histograms ܘܨܘܪ̈ܬܐ ܕܒܕܪܐ ܕܛܝ̈ܡܐ ܕܚܙ̈ܝܐ ܝܢܐ ܠܩܘܒܠ ܐܢܝ ܕܡܠܝ̈ܐ ܝܢܐ، ܩܐ ܕܫܪܪܚ ܕܡܠܝ̈ܐ ܡܬܩܒܠܢ̈ܐ ܝܢܐ (ܦܐܬܐ 540).
ܡܠܝܐ ܣܓܝܐܐ (multiple imputation; Section 25.7, p. 542): ܒܕܘܟܬܐ ܕܚܕ ܛܝܡܐ ܡܠܝܐ – ܚܕܟܡܐ (ܡܬܠܐ ܚܡܫܐ)، ܟܠ ܚܕ ܡܢ ܡܘܕܝܠ ܩܠܝܠ ܦܪܝܫܐ، ܕܟܡܚܘܝ ܠܐ ܒܣ ܫܘܚܠܦܐ (variance) ܕܓܘܒܝܐ ܕܕܘܡܝܐ ܐܠܐ ܐܦ ܠܐ ܫܪܝܪܘܬܐ ܥܠ ܡܢܝ̈ܢܐ ܡܫܘܬܦ̈ܐ ܕܡܘܕܝܠ ܕܡܠܝܐ. ܟܡܪܗܛܚ ܦܘܫܩܐ ܥܡܝܐ ܥܠ ܟܠ ܚܕ ܡܢ ܚܡܫܐ ܦܐܝ̈ܠܐ ܕܝܗܝ̈ܒܬܐ ܡܠܝ̈ܐ، ܘܟܡܚܝܕܚ: ܫܘܥܪܐ ܐܚܪܝܐ ܝܠܗ ܡܨܥܝܬܐ ܕܫܘ̈ܥܪܐ، ܘܫܘܚܠܦܐ ܟܡܚܠܛ ܫܘܚܠܦܐ ܓܘ ܡܠܝ̈ܐ (ܡܨܥܝܬܐ ܕܡܪ̈ܒܥܐ ܕܛܥ̈ܝܘܬܐ ܬܩܝ̈ܢܬܐ) ܥܡ ܫܘܚܠܦܐ ܒܝܢܝ ܡܠܝ̈ܐ (ܟܡܐ ܫܘ̈ܥܪܐ ܦܪ̈ܝܫܐ ܝܢܐ ܚܕ ܡܢ ܚܕ)، ܥܡ ܬܘܪܨܐ ܙܥܘܪܐ ܩܐ ܡܢܝܢܐ ܕܡܠܝ̈ܐ. ܗܕܟ ܛܥܝܘܬܐ ܬܩܝܢܬܐ ܟܡܚܘܝܐ ܕܠܐ ܝܕܥܚ ܗܘܐ ܠܛܝ̈ܡܐ ܚܣܝ̈ܪܐ – ܡܐ ܕܡܠܝܐ ܝܚܝܕܝܐ ܟܡܛܫܐ. Pallant (2020، ܨܚܚܐ 6) ܟܡܝܬܝܐ ܡܬܠܐ ܡܢ Tabachnick ܘ-Fidell ܕܡܠܝܐ ܣܓܝܐܐ ܐܕܝܘܡ "ܐܘܪܚܐ ܡܝܩܪܬܐ ܡܢ ܟܠ" ܝܠܗ̇ ܩܐ ܦܘܠܚܢܐ ܥܡ ܚܣܝ̈ܪܐ.
6. ܡܐ ܟܥܒܕܚ ܒܥܒܕܐ – ܡܕܒܪܢܐ ܕܦܣܩܐ
ܛܟܣܐ ܕܦܠܛ ܡܢ ܨܚܚܐ، ܐܝܟ ܡܕܒܪܢܐ ܕܣܐܝܛ (ܦܣ̈ܩܐ – ܕܒܘܨܝܬܐ ܝܢܐ): ܩܕܡܐ ܟܡܢܝܚ – ܟܡܐ ܚܣܝܪܐ ܓܘ ܟܠ ܡܫܬܚܠܦܢܐ، ܘܒܐܝܢܐ ܛܘܦܣܐ (ܐܦ ܐܢܝ ܐܢܫ̈ܐ؟ ܚܕ ܫܘܐܠܐ؟) – ܘܟܒܚܪܚ ܐܢ ܐܝܬ ܢܡܘܣܐ ܕܠܘܓܝܩܐ ܕܟܡܠܐ ܕܠܐ ܣܝ̈ܡܬܐ (ܨܦܪܐ ܝܪ̈ܚܐ ܕܥܒܕܐ – ܨܦܪܐ ܡܥܠܬܐ؛ "ܠܐ ܡܘܚܡܐ" ܕܠܐ ܝܠܗ ܚܣܝܪܐ). ܒܬܪܗ ܟܫܐܠܚ ܩܐ ܡܘܕܝ: ܡܢܝܐ ܠܐ ܦܢܐܠܗ، ܘܐܢ ܐܗܐ ܐܣܝܪܐ ܝܠܗ ܥܡ ܡܫܬܚܠܦ̈ܢܐ ܕܡܫܝ̈ܚܐ ܝܢܐ – ܠܘܚܐ ܕܣܓܝܐܘ̈ܬܐ (frequency table) ܕ"ܦܢܐܠܗ / ܠܐ ܦܢܐܠܗ" ܠܩܘܒܠ ܓܢܣܐ ܕܒܪܢܫܐ، ܥܘܡܪܐ، ܝܘܠܦܢܐ (ܟܝ ܡܪܒܥܐ (chi-square)) ܝܠܗ ܒܘܚܪܢܐ ܦܫܝܛܐ ܕ-Gelman ܘ-Hill (ܬܘܪܓܠܐ 25.1). ܘܒܬܪܗ ܠܦܘܬ ܡܫܘܚܬܐ: ܚܣܝܪܘܬܐ ܙܥܘܪܬܐ ܘܒܕܝܪܬܐ – ܫܩܠܬܐ ܙܘܓܢܝܬܐ، ܥܡ ܬܘܢܝܐ ܕ-N ܩܐ ܟܠ ܦܘܫܩܐ؛ ܓܘ ܡܘܕܝܠ ܕܪܝܓܪܫܢ ܥܡ ܚܕܟܡܐ ܡܢܒ̈ܝܢܐ – ܕܥܗܕܚ ܕܫܩܠܬܐ ܕܣܕܪܐ ܟܠܗ ܟܦܠܛܐ ܟܠ ܐܝܢܐ ܕܚܣܝܪܐ ܠܗ ܡܕܡ، ܘܕܡܥܠܚ ܓܘ ܡܘܕܝܠ ܠܡܫܬܚܠܦ̈ܢܐ ܕܟܡܢܒܝ ܠܐ ܦܘܢܝܐ. ܚܣܝܪܘܬܐ ܪܒܬܐ ܓܘ ܡܫܬܚܠܦܢܐ ܪܫܝܐ – ܡܠܝܐ ܓܕܫܢܝܐ ܡܢ ܪܝܓܪܫܢ ܥܡ ܟܠ ܡܢܒ̈ܝܢܐ ܕܐܝܬ، ܝܢ ܡܠܝܐ ܣܓܝܐܐ، ܘܬܘܢܝܐ ܥܠ ܐܘܪܚܐ. ܚܣܝܪܘܬܐ ܕܬܠܝܐ ܒܛܝܡܐ ܓܢܗ (ܡܥܠܬܐ، ܬܘܪ̈ܨܐ ܪܓܝܫ̈ܐ) – ܠܝܬ ܫܪܝܐ ܣܛܐܛܝܣܛܝܩܝܐ ܕܟܝܐ: ܟܡܘܣܦܚ ܡܢܒ̈ܝܢܐ، ܟܬܢܚ ܣܝܡܬܐ ܘܟܒܚܪܚ ܪܓܝܫܘܬܐ (sensitivity) – ܡܐ ܟܗܘܐ ܠܦܐܪܐ ܓܘ ܡܠܝ̈ܐ ܦܪ̈ܝܫܐ. ܘܒܟܠ ܗܘܝܐ: ܠܐ ܡܨܥܝܬܐ، ܠܐ ܓܪܫܬܐ ܕܛܝܡܐ ܐܚܪܝܐ، ܘܠܐ ܡܠܝܐ ܝܚܝܕܝܐ ܕܟܡܬܬܢܐ ܐܝܟ ܕܛܝ̈ܡܐ ܡܫܝ̈ܚܐ ܗܘܝ.
ܠܘܚܐ 2. ܐܘܪ̈ܚܬܐ – ܡܐ ܟܠ ܚܕܐ ܟܢܛܪܐ، ܡܐ ܟܡܥܩܡܐ، ܘܐܝܡܢ ܡܬܩܒܠܢܝܬܐ ܝܠܗ̇
| ܐܘܪܚܐ | ܡܐ ܟܡܥܩܡܐ | ܐܝܡܢ ܡܬܩܒܠܢܝܬܐ | ܓܘ ܣܐܝܛ / ܓܘ ܬܘܟܢܝܬܐ |
|---|---|---|---|
| ܫܩܠܬܐ ܕܣܕܪܐ ܟܠܗ (ܗܘ̈ܝܐ ܓܡܝܪ̈ܐ) | ܡܣܒ ܒܐܦ̈ܐ ܐܢ ܚܣܝ̈ܪܐ ܦܪ̈ܝܫܐ ܝܢܐ؛ ܕܘܡܝܐ ܙܥܘܪܐ ܣܓܝ ܥܡ ܣܓܝ ܡܫܬܚܠܦ̈ܢܐ | ܚܣܝܪܘܬܐ ܙܥܘܪܬܐ ܘܓܕܫܢܝܬܐ ܓܡܝܪܐܝܬ؛ ܐܡܢ ܕܟܒܥܝܚ ܕܘܡܝܐ ܙܥܘܪܐ ܕܦܢܐܠܗ ܥܠ ܟܠ ܡܕܡ | ܓܘܒܝܐ ܡܩܕܡܐ ܕܪܝܓܪܫܢ ܓܘ SPSS ܘܓܘ R |
| ܫܩܠܬܐ ܙܘܓܢܝܬܐ (ܗܘ̈ܝܐ ܕܐܝܬ) | ܦܘܫܩ̈ܐ ܥܠ ܕܘ̈ܡܝܐ ܙܥܘܪ̈ܐ ܦܪ̈ܝܫܐ؛ ܐܦ ܗܘ ܡܣܒ ܒܐܦ̈ܐ ܐܢ ܚܣܝ̈ܪܐ ܦܪ̈ܝܫܐ ܝܢܐ | ܚܣܝܪܘܬܐ ܙܥܘܪܬܐ ܘܒܕܝܪܬܐ؛ ܐܣܘܪ̈ܐ ܕܚܕ̈ܕܐ ܘܬܚܘܝܬܐ | ܐܣܘܪ̈ܐ ܕܚܕ̈ܕܐ – N ܩܐ ܟܠ ܙܘܓܐ؛ ܡܠܟܐ ܕ-Pallant ܩܐ Options |
| ܚܘܠܦܐ ܒܡܨܥܝܬܐ | ܟܡܒܨܪܐ ܠܣܛܝܘܬܐ ܬܩܝܢܬܐ ܘܛܥܝܘܬܐ ܬܩܝܢܬܐ؛ ܟܓܪܫܐ ܠܐܣܘܪ̈ܐ ܕܚܕ̈ܕܐ ܠܨܦܪܐ | ܡܢ ܡܬܘܡ ܠܐ | ܐܝܬ ܓܘ Options ܕ-SPSS – ܠܐ ܪܫܡܝܬܘܢ |
| ܓܪܫܬܐ ܕܛܝܡܐ ܐܚܪܝܐ | ܡܨܝܐ ܕܗܘܝܐ ܠܐ ܢܛܘܪܬܐ (ܕܥܪܬܐ ܠܡܨܥܝܬܐ) | ܠܐ ܐܝܟ ܓܘܒܝܐ ܡܩܕܡܐ | – |
| ܓܢܣܐ "ܚܣܝܪܐ" ܩܐ ܡܢܒܝܢܐ ܕܓܢ̈ܣܐ | ܩܠܝܠ؛ ܟܡܘܣܦܐ ܓܘܕܐ | ܣܓܝ ܓܐܝ̈ܐ ܡܘܬܪܢܐ | ܪܡܙܢܘܬܐ ܓܘ ܦܐܝܠ، ܩܕܡ ܦܘܫܩܐ |
| ܡܚܘܝܢܐ ܕܚܣܝܪܘܬܐ + ܨܦܪܐ/ܡܨܥܝܬܐ ܩܐ ܡܢܒܝܢܐ ܡܬܡܫܚܢܐ | ܟܥܒܕ ܡܣܒ ܒܐܦ̈ܐ ܠܡܢܝ̈ܢܐ ܡܫܘܬܦ̈ܐ ܕܫܪܟܐ ܕܡܢܒ̈ܝܢܐ | ܒܣ ܥܡ ܥܒ̈ܕܐ ܕܚܕ̈ܕܐ – ܘܗܝܕܝܟ ܩܪܝܒܐ ܠܗܘ̈ܝܐ ܓܡܝܪ̈ܐ | – |
| ܡܠܝܐ ܩܝܡܐ ܡܢ ܪܝܓܪܫܢ | ܫܘܚܠܦܐ ܐܠܝܨܐ ܝܬܝܪ ܡܢ ܡܫܘܚܬܐ؛ ܛܥ̈ܝܘܬܐ ܬܩܝ̈ܢܬܐ ܢܚܝ̈ܬܐ ܝܬܝܪ ܡܢ ܡܫܘܚܬܐ | ܠܐ – ܒܣ ܐܝܟ ܕܪܓܐ ܠܘܬ ܓܕܫܢܝܐ | – |
| ܡܠܝܐ ܓܕܫܢܝܐ ܡܢ ܪܝܓܪܫܢ | ܛܥ̈ܝܘܬܐ ܬܩܝ̈ܢܬܐ ܗܠܝܐ ܩܠܝܠ ܢܚܝ̈ܬܐ ܝܢܐ (ܡܠܝܐ ܝܚܝܕܝܐ) | ܚܣܝܪܘܬܐ ܪܒܬܐ ܓܘ ܚܕ ܡܫܬܚܠܦܢܐ؛ ܟܠ ܡܢܒ̈ܝܢܐ ܕܐܝܬ | R – ܚܕܟܡܐ ܣܕܪ̈ܐ (Gelman & Hill, Section 25.4) |
| ܡܠܝܐ ܣܓܝܐܐ | ܒܨܝܪ ܡܢ ܟܠ؛ ܣܢܝܩܐ ܝܠܗ̇ ܠܡܘܕܝܠ ܡܬܩܒܠܢܐ ܘܒܘܚܪܢܐ | ܚܣܝܪܘܬܐ ܪܒܬܐ ܓܘ ܚܕܟܡܐ ܡܫܬܚܠܦ̈ܢܐ؛ ܐܡܢ ܕܟܬܢܚ ܒܘܚܪ̈ܢܐ ܘܬܚܘ̈ܡܐ ܕܬܘܟܠܢܐ | R – ܪܝܓܪ̈ܫܢܐ ܕܟܡܬܚܠܛܝ (Van Buuren et al., 1999, as cited in Gelman & Hill)؛ SPSS – ܐܘܪܚܐ Missing Value Analysis (Pallant, 2020, Chapter 6) |
ܡܥܝܪܢܘܬܐ. ܠܦܘܬ Gelman ܘ-Hill (2007، ܦܣ̈ܩܐ 25.2-25.7)، Pallant (2020، ܨܚܚܐ 6) ܘ-Field (2024، tip 6.1). ܥܡܘܕܐ "ܐܝܡܢ ܡܬܩܒܠܢܝܬܐ" ܟܢܘܫܝܐ ܝܠܗ ܕܣܐܝܛ، ܠܐ ܡܬܠܐ.
7. ܓܘ ܣܐܝܛ ܘܓܘ SPSS – ܡܐ ܟܗܘܐ ܠܚܣܝ̈ܪܐ ܕܠܐ ܕܒܥܐܠܘܟܘܢ
ܓܘ ܛܘܦܣܐ ܬܩܝܢܐ ܕܣܐܝܛ ܩܠܝܬܐ ܣܦܝܩܬܐ (empty cell) ܚܣܝܪܐ ܝܠܗ̇. ܡܐܛܪܝܟܣ ܕܐܣܘܪ̈ܐ ܕܚܕ̈ܕܐ ܟܚܫܒܐ ܟܠ ܙܘܓܐ ܥܠ ܐܝܢܐ ܕܐܝܬ ܠܗ ܬܪܝܢ ܛܝ̈ܡܐ (ܫܩܠܬܐ ܙܘܓܢܝܬܐ) ܘܟܬܢܐ N ܩܐ ܟܠ ܙܘܓܐ – ܘܡܛܠ ܗܕܐ N ܟܡܫܬܚܠܦ ܒܝܢܝ ܩܠ̈ܝܬܐ ܕܠܘܚܐ، ܘܐܗܐ ܝܕܥܬܐ ܝܠܗ̇، ܠܐ ܛܥܝܘܬܐ. ܫܪܝܪܘܬܐ ܒܝܢܝ ܪܡܙ̈ܢܐ ܟܦܠܚܐ ܥܡ ܚܣܝ̈ܪܐ ܒܬܪܬܝܢ ܐܘܪ̈ܚܬܐ ܦܪ̈ܝܫܬܐ ܒܨܒܝܢܐ: κ ܕ-Cohen ܥܠ ܚܕܝܘ̈ܬܐ ܕܪܡܝܙ̈ܐ ܝܢܐ ܒܝܕ ܬܪܝܢ ܪܡܙ̈ܢܐ ܒܣ، ܘ-α ܕ-Krippendorff ܥܠ ܟܠ ܛܝܡܐ ܕܐܝܬ ܠܗ ܙܘܓܐ ܓܘ ܚܕܝܘܬܐ ܕܝܠܗ – ܦܘܪܫܢܐ ܒܝܢܝ N-ܐ ܡܘܚܙܝܐ ܝܠܗ ܓܘ ܠܘܚܐ. ܡܢ SPSS ܠܐܩܣܠ ܟܡܥܒܪ ܪ̈ܡܙܐ ܕܚܣܝܪܘܬܐ ܕܬܚܝܡ̈ܐ ܝܢܐ ܓܘ SPSS (user-missing) ܐܝܟ ܩܠ̈ܝܬܐ ܣܦܝ̈ܩܬܐ – ܘܟܡܙܗܪ ܐܡܢ ܕܪܡܙܐ ܐܝܟ "ܐܚܪܢܐ، ܟܬܘܒ/ܟܬܘܒܝ" ܝܢ "ܠܐ ܨܒܐ/ܨܒܝܐ ܠܡܦܢܝܐ" ܠܐ ܬܚܝܡܐ ܝܠܗ ܐܝܟ ܚܣܝܪܐ ܘܡܛܠ ܗܕܐ ܦܝܫܐ ܥܒܪܐ ܐܝܟ ܛܝܡܐ ܬܪܝܨܐ (valid value)، ܐܝܟ ܕܗܘܐ ܓܘ ܦܐܝܠ ܕܡܬܠܐ ܓܘ ܬܫܥܐ ܡܫܬܚܠܦ̈ܢܐ. ܓܘ SPSS، Pallant (2020، ܨܚܚܐ 6) ܟܡܠܟܐ ܕܕܚܝܚ ܟܠܝܘܡ ܥܠ Options ܘܒܚܪܚ ܡܐ ܪܫܝܡܐ ܝܠܗ، ܡܛܠ ܕܓܘܒܝܐ ܡܩܕܡܐ ܟܡܫܬܚܠܦ ܒܝܢܝ ܐܘܪ̈ܚܬܐ: ܫܩܠܬܐ ܙܘܓܢܝܬܐ ܐܠܐ ܐܢ ܐܝܬ ܥܠܬܐ ܛܒܬܐ؛ ܕܣܕܪܐ ܟܠܗ ܒܣ ܐܡܢ ܕܟܒܥܝܚ ܕܘܡܝܐ ܙܥܘܪܐ ܕܦܢܐܠܗ ܥܠ ܟܠ ܡܕܡ؛ ܚܘܠܦܐ ܒܡܨܥܝܬܐ – ܡܢ ܡܬܘܡ ܠܐ. ܠܐܘܪܚܐ Missing Value Analysis ܐܗܝ ܟܡܫܕܪܐ ܐܝܢܐ ܕܟܒܥܐ ܡܠܝܐ ܘܛܘ̈ܦܣܐ ܕܚܣܝܪܘܬܐ.
8. ܐܝܟܢ ܟܡܬܢܚ
ܡܢܬܐ ܕܚܣܝܪܘܬܐ ܩܐ ܟܠ ܡܫܬܚܠܦܢܐ ܪܝܫܝܐ، ܘܐܢ ܐܝܬ ܐܣܟܝܡܐ – ܡܢ ܠܐ ܦܢܐ (ܒܘܚܪܢܐ ܡܢ ܦܣܩܐ 6)؛ ܡܘܕܝ ܝܠܗ ܫܪܛܐ ܥܠ ܡܝܟܐܢܝܙܡ (mechanism) ܘܥܠ ܡܘܕܝ ܣܡܝܟܐ ܝܠܗ؛ ܐܘܪܚܐ: "ܫܩܠܬܐ ܙܘܓܢܝܬܐ؛ N ܩܐ ܟܠ ܦܘܫܩܐ ܡܬܢܝܐ ܝܠܗ ܓܘ ܠܘ̈ܚܐ"، ܝܢ "ܡܠܝܐ ܣܓܝܐܐ ܕܛܝ̈ܡܐ ܚܣܝ̈ܪܐ (multiple imputation)، ܚܡܫܐ ܦܐܝܠ̈ܐ، ܡܘܕܝܠ ܕܡܠܝܐ ܥܠܝܠܐ ܝܠܗ X، Y، Z؛ ܫܘ̈ܥܪܐ ܘܛܥ̈ܝܘܬܐ ܬܩܝ̈ܢܬܐ ܚܘܝܕ̈ܐ ܝܢܐ ܠܦܘܬ Gelman ܘ-Hill (2007، ܦܣܩܐ 25.7)"؛ ܘܡܘܕܝ ܟܗܘܐ ܠܫܘܠܡܐ ܓܘ ܦܘܫܩܐ ܕܚܙ̈ܝܬܐ ܓܡܝܪ̈ܬܐ (complete cases) ܩܘܒܠ ܡܠܝܐ – ܐܢ ܫܠܡܝ، ܟܐܡܪܚ ܗܕܟܐ؛ ܐܢ ܠܐ، ܐܗܐ ܡܫܟܚܢܘܬܐ ܝܠܗ̇. ܛܝܡܐ ܕܡܠܝܐ ܝܠܗ ܠܦܘܬ ܢܡܘܣܐ ܠܘܓܝܩܝܐ ܟܡܬܢܚ ܠܗ ܐܝܟ ܡܠܝܐ (ܥܣܪܐ ܡܦܢܝ̈ܢܐ ܥܡ ܨܦܪܐ ܝܪ̈ܚܐ ܕܥܒܕܐ – ܡܥܠܬܐ ܨܦܪܐ)، ܠܐ ܐܝܟ ܡܫܘܚܬܐ.
ܛܥܝ̈ܘܬܐ ܕܡܬܚܙܝܢ ܣܓܝ (Common mistakes)
"ܚܣܝ̈ܪܐ ܓܕܫܢ̈ܝܐ ܝܢܐ" – ܕܠܐ ܒܘܚܪܢܐ. ܠܘܚܐ ܚܕ ܕܦܢܐ/ܠܐ-ܦܢܐ ܩܘܒܠ ܡܫܬܚܠܦ̈ܢܐ ܕܪܩܥܐ ܟܡܚܘܐ ܐܢ ܚܣܝܪܘܬܐ ܬܠܝܬܐ ܝܠܗ̇ ܒܡܐ ܕܡܫܝܚܐ ܝܠܗ. ܐܢ ܐܝܢ – ܫܩܠܬܐ ܦܫܝܛܬܐ ܟܡܥܠܐ ܡܣܒ ܒܐܦ̈ܐ (bias).
ܚܠܦܬܐ ܒܡܨܥܝܬܐ. ܟܡܙܥܪܐ ܠܫܘܚܠܦܐ ܘܟܒܪܐ ܪܫܝܡܘܬܐ ܕܓܠܬܐ؛ Pallant: ܚܕ ܓܗܐ ܠܐ.
ܫܩܠܬܐ ܕܟܠ ܡܢ ܕܚܣܝܪܐ ܝܠܗ ܡܕܡ – ܓܘ ܪܝܓܪܫܢ ܥܡ ܥܣܪܐ ܡܢܒ̈ܝܢܐ. ܟܦܝܫܚ ܥܡ ܦܠܓܐ ܕܕܘܡܝܐ، ܘܠܐ ܝܕܝܥܐ ܝܠܗ ܐܝܢܐ ܦܠܓܐ. ܟܡܢܝܚ ܟܡܐ ܦܝܫܝܠܗܘܢ ܩܕܡ ܕܡܦܫܩܚ.
ܡܠܝܐ ܕܛܝܡܐ ܝܚܝܕܝܐ ܘܬܘܢܝܐ ܐܝܟ ܕܡܫܝܚܐ ܗܘܐ. ܛܥ̈ܝܘܬܐ ܬܩܝ̈ܢܬܐ ܢܚܝ̈ܬܐ ܝܢܐ ܒܙܘܕܐ ܡܢ ܟܝܢܐ ܕܐܘܪܚܐ. ܡܠܝܐ ܣܓܝܐܐ، ܝܢ ܒܨܘܪܐ ܬܘܢܝܐ ܕܛܝ̈ܡܐ ܡܠܝ̈ܐ ܝܢܐ.
ܡܢܒܝܢܘܬܐ ܡܢ ܪܝܓܪܫܢ ܘܡܫܒܩܬܐ ܕܛܥܝܘܬܐ. ܟܠ ܠܐ-ܡܦܢܝ̈ܢܐ "ܓܘ ܡܨܥܬܐ" – ܡܕܡ ܕܓܠܬܐ (artifact) ܕܡܢܒܝܢܘܬܐ ܕܠܐ ܒܕܪܐ. ܟܡܘܣܦܚ ܛܥܝܘܬܐ ܕܡܢܒܝܢܘܬܐ.
ܙܕܥܬܐ ܡܢ ܦܘܠܚܢܐ ܕ"ܦܐܪ̈ܐ" ܐܝܟ ܡܢܒ̈ܝܢܐ ܩܐ ܡܠܝܐ. ܩܐ ܡܠܝܐ ܢܝܫܐ ܝܠܗ ܡܢܒܝܢܘܬܐ، ܘܟܠ ܡܕܡ ܕܟܡܢܒܐ ܫܠܝܛܐ ܝܠܗ.
ܦܘܠܚܢܐ ܒܪܡܙܐ "ܠܐ ܨܒܐ ܠܡܦܢܝܐ" ܐܝܟ ܛܝܡܐ. 99 ܕܠܐ ܬܚܝܡܐ ܝܠܗ ܐܝܟ ܚܣܝܪܐ ܟܥܐܠ ܓܘ ܡܨܥܝܬܐ. ܟܒܚܪܚ ܓܘ ܡܦܫܩܢܐ (legend) ܩܕܡ ܟܠ ܡܕܡ.
ܛܥܝܬܐ ܕ-N ܫܚܠܦܠܗ. ܫܩܠܬܐ ܙܘܓܢܝܬܐ ܟܐܡܪܐ N ܐܚܪܢܐ ܩܐ ܟܠ ܦܘܫܩܐ – ܟܡܬܢܚ ܠܗ، ܘܠܐ ܟܢܣܚܚ N ܕܕܘܡܝܐ ܓܡܝܪܐ.
ܪܫܝܡܬܐ ܕܒܘܚܪܢܐ – ܩܕܡ ܪܗܛܐ ܥܡ ܛܝ̈ܡܐ ܚܣܝ̈ܪܐ
| ܫܘܐܠܐ | ܩܡܘܕܝ ܐܗܐ ܚܫܝܚܐ ܝܠܗ |
|---|---|
| ܟܠ ܪ̈ܡܙܐ ܕܚܣܝܪܘܬܐ (99، "ܠܐ ܨܒܐ ܠܡܦܢܝܐ"، "ܠܐ ܐܣܝܪܐ") ܬܚܝܡ̈ܐ ܝܢܐ ܐܝܟ ܚܣܝ̈ܪܐ ܓܘ ܡܦܫܩܢܐ – ܘܠܐ ܐܝܟ ܛܝ̈ܡܐ؟ | ܐܢ ܠܐ، ܟܥܐܠܝ ܓܘ ܚܘܫܒܢܐ (ܦܣܩܐ 7). |
| ܟܡܐ ܚܣܝܪܐ ܝܠܗ ܓܘ ܟܠ ܡܫܬܚܠܦܢܐ؟ ܒܐܝܢܐ ܐܣܟܝܡܐ؟ | ܩܠܝܠ ܘܡܒܕܪܐ ܩܘܒܠ ܣܓܝ ܘܟܢܝܫܐ – ܐܘܪ̈ܚܬܐ ܐܚܪ̈ܢܝܬܐ (ܦܣܩܐ 6). |
| ܐܝܬ ܢܡܘܣܐ ܠܘܓܝܩܝܐ ܕܟܡܠܐ ܕܠܐ ܫܪ̈ܛܐ؟ | ܨܦܪܐ ܝܪ̈ܚܐ ܕܥܒܕܐ ← ܨܦܪܐ ܡܥܠܬܐ (ܦܣܩܐ 3). |
| ܡܢ ܠܐ ܦܢܐ – ܐܣܝܪܐ ܝܠܗ ܥܡ ܓܢܣܐ، ܥܘܡܪܐ، ܡܪܕܘܬܐ؟ (ܟܝ ܡܪܒܥܐ) | ܐܢ ܐܝܢ – ܠܐ "ܓܕܫܢܝܐ ܓܡܝܪܐܝܬ"، ܘܡܘܕܝܠ ܓܪܓ ܕܡܥܠܐ ܠܐܢܝ ܡܫܬܚܠܦ̈ܢܐ (ܦܣܩܐ 1). |
| ܡܨܝܐ ܕܚܣܝܪܘܬܐ ܬܠܝܬܐ ܝܠܗ̇ ܒܛܝܡܐ ܒܓܢܗ؟ | ܡܥܠܬܐ، ܥܒ̈ܕܐ ܪܓܝܫ̈ܐ – ܠܝܬ ܫܪܝܐ ܕܟܝܐ؛ ܟܡܬܢܚ ܘܟܥܒܕܚ ܦܘܫܩܐ ܕܪܓܝܫܘܬܐ (ܦܣ̈ܩܐ 1، 6). |
| ܓܘ Options ܕ-SPSS – ܡܘܕܝ ܓܒܝܐ ܝܠܗ؟ ܕܣܕܪܐ ܟܠܗ / ܙܘܓܢܝܬܐ / ܡܨܥܝܬܐ؟ | ܓܘܒܝܐ ܡܩܕܡܐ ܟܫܚܠܦ ܒܝܢܝ ܦܘܠܚ̈ܢܐ؛ ܡܨܥܝܬܐ – ܚܕ ܓܗܐ ܠܐ (ܦܣܩܐ 7). |
| ܐܢ ܡܠܐܠܘܟܘܢ – ܓܕܫܢܐܝܬ؟ ܣܓܝܐܐ؟ ܛܝ̈ܡܐ ܡܠܝ̈ܐ ܒܚܝܪ̈ܐ ܝܢܐ ܓܘ ܨܘܪܬܐ ܩܘܒܠ ܛܝ̈ܡܐ ܚܙ̈ܝܐ؟ | ܦܣܝܩܐ (deterministic) ܥܩܐ ܝܠܗ ܒܙܘܕܐ؛ ܝܚܝܕܝܐ ܟܡܙܥܪܐ ܛܥ̈ܝܘܬܐ ܬܩܝ̈ܢܬܐ (ܦܣ̈ܩܐ 4-5). |
| N ܩܐ ܟܠ ܦܘܫܩܐ ܡܬܢܝܐ ܝܠܗ؟ ܫܘܠܡܐ ܐܗܘ ܓܢܗ ܝܠܗ ܥܡ ܡܠܝܐ ܘܕܠܐ ܡܠܝܐ؟ | ܦܘܪܫܢܐ ܡܫܟܚܢܘܬܐ ܝܠܗ̇ (ܦܣܩܐ 8). |
ܡܒܘ̈ܥܐ
Field, A. (2024). Discovering statistics using IBM SPSS statistics (6th ed.). SAGE.
Gelman, A., & Hill, J. (2007). Data analysis using regression and multilevel/hierarchical models. Cambridge University Press.
Pallant, J. (2020). SPSS survival manual: A step by step guide to data analysis using IBM SPSS (7th ed.). Routledge.