ܦܘܫܩܐ ROC

ܛܥܢܐ ܕܝܗܝ̈ܒܬܐ (loading the data)

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

ܡܫܬܚܠܦ̈ܢܐ ܘܬܘܩ̈ܢܐ (Variables and settings)

ܐܝܡܢ ܡܦܠܚܝܚ (When to use)؟

ܐܝܡܢ ܕܐܝܬ ܬܩܢܐ ܕܕܗܒܐ – ܐܘܪܚܐ ܡܩܒܠܬܐ ܕܦܣܩܚ ܡܢܘ ܓܘ ܗܘܝܐ ܝܠܗ ܘܡܢܘ ܠܐ (ܡܡܠܠܐ ܐܣܝܐ، ܫܒܩܬܐ ܕܝܘܠܦܢܐ ܒܫܪܪܐ، ܡܨܠܚܢܘܬܐ ܓܘ ܒܘܚܪܢܐ) – ܘܡܚܘܝܢܐ ܡܢܝܢܝܐ ܕܣܢܝܩ ܝܠܗ ܕܡܢܒܐ ܠܗ، ܘܟܫܐܠܚ ܟܡܐ ܛܒܐ ܡܚܘܝܢܐ ܟܦܪܫ ܒܝܢܝ ܬܪܬܝܢ ܓܘ̈ܕܐ. ܡܬܠܐ ܥܬܝܩܐ ܝܠܗ ܬܪܝܨܘܬܐ ܕܦܢܩܝܬܐ ܕܫܘܐ̈ܠܐ ܕܡܨܠܠܢܘܬܐ ܩܘܒܠ ܦܘܪܫܢܐ ܕܟܘܪܗܢܐ، ܐܠܐ ܫܘܐܠܐ ܦܬܝܐ ܝܠܗ ܒܙܘܕܐ: Pepe (2003، ܦܐܬܐ 74) ܟܡܥܗܕܐ ܕܣܪܛܐ ܟܦܝܦܐ ROC "ܟܡܚܘܐ ܦܘܪܫܐ ܒܝܢܝ ܬܪܝܢ ܦܘܠܓ̈ܐ"، ܘܡܛܠ ܗܕܐ ܦܝܫܐ ܝܠܗ "ܒܟܠ ܕܘܟܐ ܕܓܘܗ ܦܘܪܫܐ ܒܝܢܝ ܦܘܠܓ̈ܐ ܚܫܝܚܐ ܝܠܗ" – ܡܢܝܢܐ ܕܣܘܟܢܐ ܩܐ ܫܒܩܬܐ ܩܘܒܠ ܫܒܩܬܐ، ܡܣܬܒܪܢܘܬܐ ܡܢܒܝܬܐ ܡܢ ܪܝܓܪܫܢ ܠܘܓܝܣܛܝܩܝܐ ܩܘܒܠ ܦܐܪܐ، ܡܢܝܢܐ ܕܒܘܚܪܢܐ ܕܡܥܠܢܐ ܩܘܒܠ ܡܨܠܚܢܘܬܐ ܓܘ ܝܘܠܦܢܐ.

Pepe (2003، ܦܐܬܐ 73، ܠܘܚܐ 4.1) ܟܡܢܝܐ ܐܪܒܥܐ ܦܘܠܚ̈ܢܐ: ܬܚܘܝܬܐ ܓܡܝܪܬܐ ܕܥܒ̈ܕܐ ܕܡܨܝܐ ܕܗܘܝܢ ܕܡܚܘܝܢܐ؛ ܦܘܚܡܐ ܘܚܘܠܛܐ ܕܒܘܨ̈ܝܐ ܕܦܠܚܠܗܘܢ ܬܚܘ̈ܡܐ ܦܪ̈ܝܫܐ ܕܦܘܪܫܐ؛ ܡܕܒܪܢܘܬܐ ܓܘ ܓܘܒܝܐ ܕܬܚܘܡܐ ܕܦܘܪܫܐ؛ ܘܦܘܚܡܐ ܒܝܢܝ ܡܚܘ̈ܝܢܐ ܕܡܫܝܚ̈ܐ ܝܢܐ ܒܣܒ̈ܠܬܐ ܦܪ̈ܝܫܐ – ܦܢܩܝܬܐ ܕ-27 ܢܘܩ̈ܙܐ ܩܘܒܠ ܣܒܠܬܐ ܕ-1-5. ܐܝܡܢ ܕܡܚܘܝܢܐ ܒܓܢܗ ܕܬܪܝܢ ܛܝ̈ܡܐ ܝܠܗ ܡܢ ܩܕܡ (ܕܙܘܕܐ/ܕܒܨܪܐ)، ܠܝܬ ܣܪܛܐ ܟܦܝܦܐ ܐܠܐ ܚܕ ܢܘܩܙܐ – ܠܘܚܐ 2×2؛ ܒܘܚܪܢܐ ܕܐܣܘܪܐ ܕܝܠܗ – ܓܘ ܦܐܬܐ ܕܟܝ ܡܪܒܥܐ. ܘܡܚܘ̈ܝܢܐ ܕܥܒܕܐ ܕܡܘܕܝܠ ܕܝܘܠܦܢܐ ܕܡܟܝܢܐ – ܥܡ ROC ܩܘܒܠ ܣܪܛܐ ܟܦܝܦܐ ܕ-precision-recall ܓܘ ܓܢܣܐ ܕܠܐ ܡܬܚܙܐ ܣܓܝ – ܓܘ ܦܐܬܐ ܕܡܚܘ̈ܝܢܐ ܕܥܒܕܐ ܘܫܘܪܪܐ ܕܡܘܕܝܠ.

ܗܘܢܐ: ܡܢ ܚܕ ܬܚܘܡܐ ܕܦܘܪܫܐ ܠܟܠ ܬܚܘ̈ܡܐ

ܚܕ ܬܚܘܡܐ ܕܦܘܪܫܐ. ܩܐ ܕܦܣܩܚ ܥܠ ܐܣܐܣܐ ܕܡܢܝܢܐ، ܟܣܝܡܚ ܬܚܘܡܐ ܕܦܘܪܫܐ (cutoff): ܐܝܢܐ ܕܐܝܠܗ ܒܐܬܪܗ "ܕܙܘܕܐ" ܝܠܗ. Pepe (2003، ܦܐܬܐ 67) ܟܡܦܫܩܐ ܕܓܘܒܝܐ ܕܬܚܘܡܐ ܕܦܘܪܫܐ "ܒܕ ܫܚܠܦ ܥܡ ܗܘ̈ܝܐ" – ܥܬܝܪܘܬܐ، ܛܝܡܐ ܕܒܘܚܪܢܐ ܝܢ ܕܐܣܝܘܬܐ، ܩܫܝܘܬܐ ܕܗܘܝܐ – ܘܕܟܣܡܟ ܥܠ ܦܫܪܐ ܡܩܒܠܐ "ܒܝܢܝ ܠܐ ܡܫܟܚܬܐ ܕܗܘܝܐ ܘܡܫܟܚܬܐ ܛܥܝܬܐ ܕܝܠܗ". ܒܬܚܘܡܐ ܝܗܝܒܐ ܟܫܩܠܚ ܠܘܚܐ 2×2 ܘܬܪܝܢ ܡܢܘ̈ܬܐ: ܪܓܝܫܘܬܐ – ܡܢܬܐ ܕܡܫܟܚ̈ܐ ܡܢ ܓܘ ܐܢܝ ܕܐܝܠܗܘܢ ܓܘ ܗܘܝܐ (ܡܢܬܐ ܕܕܙܘܕܐ ܫܪܝܪ̈ܐ، true positives)، ܘܝܚܝܕܝܘܬܐ – ܡܢܬܐ ܕܕܒܨܪܐ ܡܢ ܓܘ ܐܢܝ ܕܠܐ ܝܢܐ ܓܘ ܗܘܝܐ؛ 1 − ܝܚܝܕܝܘܬܐ ܝܠܗ ܡܢܬܐ ܕܕܙܘܕܐ ܛܥ̈ܝܐ (Fawcett, 2006, p. 862).

ܟܠ ܬܚܘ̈ܡܐ. ܣܪܛܐ ܟܦܝܦܐ ܟܢܘܫܝܐ ܝܠܗ ܕܟܠ ܙܘ̈ܓܐ (ܡܢܬܐ ܕܕܙܘܕܐ ܛܥ̈ܝܐ، ܪܓܝܫܘܬܐ) ܕܡܨܝܚ ܕܡܛܚ ܠܗܘܢ ܒܫܘܢܝܐ ܕܬܚܘܡܐ ܕܦܘܪܫܐ (Pepe, 2003, p. 67, Equation 4.3) – "ܡܐܢܐ ܕܒܣ ܟܡܚܘܐ ܦܬܝܘܬܐ ܕܦܫܪ̈ܐ ܕܒܘܚܪܢܐ ܡܨܐ ܕܡܛܐ ܠܗܘܢ". ܙܘܝܬܐ ܣܡܠܝܬܐ ܥܠܝܬܐ، (0, 1)، ܦܘܪܫܐ ܠܓܢ̈ܣܐ ܓܡܝܪܐ ܝܠܗ؛ ܣܪܛܐ ܡܨܠܝܢܐ ܝܠܗ ܚܘܫܒܐ ܓܕܫܢܝܐ – ܐܝܢܐ ܕܟܚܫܒ "ܕܙܘܕܐ" ܓܘ 70% ܕܗܘ̈ܝܐ ܒܕ ܫܩܠ 70% ܪܓܝܫܘܬܐ ܘ-70% ܕܙܘܕܐ ܛܥ̈ܝܐ (Fawcett, 2006, pp. 862-863). ܢܘܩ̈ܙܐ ܒܓܢܒܐ ܣܡܠܝܐ ܕܣܪܛܐ ܟܦܝܦܐ ܬܚܘ̈ܡܐ ܝܢܐ "ܢܛܘܪ̈ܐ" – ܕܙܘܕܐ ܒܣ ܥܡ ܣܗܕ̈ܘܬܐ ܚܝܠܬ̈ܢܝܬܐ، ܩܠܝܠ ܙܘܗܪ̈ܐ ܕܓܠܐ ܘܩܠܝܠ ܡܫܟܚ̈ܬܐ؛ ܒܓܢܒܐ ܝܡܝܢܝܐ ܥܠܝܐ – "ܚܐܪ̈ܐ" (Fawcett, 2006, p. 863).

ܒܣ ܛܟܣܐ ܚܫܝܚܐ ܝܠܗ. ܣܪܛܐ ܟܦܝܦܐ ܠܐ ܟܡܫܬܚܠܦ ܒܚܕ ܫܘܢܝܐ ܕܣܠܩ ܕܡܢܝܢܐ (Pepe, 2003، ܦܐܬܐ 69، ܦܐܪܐ 4.1)، ܘܣܪܛܐ ܟܦܝܦܐ ܡܢ ܢܣܝܘܢܐ "ܦܘܢܩܣܝܘܢ ܝܠܗ ܕܕܪ̈ܓܐ ܕܛܟܣܐ ܒܠܚܘܕ" (Pepe, 2003, p. 98). ܡܛܠ ܗܕܐ ܟܦܚܡܚ ܒܗ ܡܚܘ̈ܝܢܐ ܒܚܕܝܘ̈ܬܐ ܦܪ̈ܝܫܐ، ܘܡܛܠ ܗܕܐ ܦܐܝܐ ܝܠܗ ܐܦ ܩܐ ܡܢܝܢܐ ܕܛܟܣܐ ܥܡ ܩܠܝܠ ܛܝ̈ܡܐ – ܗܝܓ ܣܪܛܐ ܟܦܝܦܐ ܕܪ̈ܓܐ ܕܪ̈ܓܐ ܝܠܗ، ܥܡ ܫܘܪ̈ܐ ܪ̈ܒܐ ܘܦܣ̈ܩܐ ܡܨܠܝ̈ܢܐ ܒܕܘ̈ܟܝܬܐ ܕܓܘܗܝܢ ܐܝܬ ܛܝ̈ܡܐ ܫܘ̈ܝܐ ܒܝܢܝ ܐܝܢܐ ܕܐܝܠܗ ܓܘ ܗܘܝܐ ܘܐܝܢܐ ܕܠܐ (Pepe, 2003, p. 98).

ܫܛܝܚܘܬܐ ܬܚܘܬ ܣܪܛܐ ܟܦܝܦܐ

ܫܛܝܚܘܬܐ ܬܚܘܬ ܣܪܛܐ ܟܦܝܦܐ (area under the curve، AUC) ܝܠܗ 1 ܓܘ ܡܚܘܝܢܐ ܓܡܝܪܐ ܘ-0.5 ܓܘ ܡܚܘܝܢܐ ܕܠܐ ܡܘܕܥܢܘܬܐ (Pepe, 2003, p. 77). ܐܝܬܠܗ ܬܪܝܢ ܩܪ̈ܝܢܐ، ܘܡܒܘ̈ܥܐ ܦܠܝܓ̈ܐ ܝܢܐ ܥܠ ܐܝܢܐ ܛܒܐ ܝܠܗ – ܘܡܛܠ ܗܕܐ "ܐܦ ܐܗܐ ܘܐܦ ܐܗܐ":

ܡܣܬܒܪܢܘܬܐ ܕܛܟܣܐ ܬܪܝܨܐ. ܫܛܝܚܘܬܐ ܝܠܗ ܡܣܬܒܪܢܘܬܐ ܕܡܫܬܘܬܦܢܐ ܓܕܫܢܝܐ ܡܢ ܓܘܕܐ ܕܗܘܝܐ ܫܩܠ ܡܢܝܢܐ ܪܡܐ ܒܙܘܕܐ ܡܢ ܡܫܬܘܬܦܢܐ ܓܕܫܢܝܐ ܡܢ ܓܘܕܐ ܐܚܪܬܐ (Hanley & McNeil, 1982, p. 29; Fawcett, 2006, p. 868)، ܘܐܗܐ ܒܚܬܝܬܘܬܐ ܝܠܗ ܟܡܝܘܬܐ ܕܟܫܥܪ ܒܘܚܪܢܐ ܕMann-Whitney (Wilcoxon ܩܐ ܬܪܝܢ ܕܘ̈ܡܝܐ): ܫܛܝܚܘܬܐ ܬܚܘܬ ܣܪܛܐ ܟܦܝܦܐ ܡܢ ܢܣܝܘܢܐ ܫܘܝܐ ܝܠܗ ܠܣܛܐܛܝܣܛܝܩ U ܦܠܝܓܐ ܥܠ ܡܢܝܢܐ ܕܙܘ̈ܓܐ (Pepe, 2003، ܦܐܬܐ 103، ܦܐܪܐ 5.3؛ Hanley & McNeil, 1982، ܦܐܬܐ 31-32). ܛܝܡܐ ܫܘܝܐ ܒܝܢܝ ܬܪܝܢ ܡܫܬܘܬܦ̈ܢܐ ܟܡܬܡܢܐ ܐܝܟ ܦܠܓܐ. Hanley ܘ-McNeil (1982، ܦܐܬܐ 31) ܟܡܚܫܚܝ ܕܐܗܐ ܐܣܘܪܐ "ܠܐ ܟܣܝܡ ܡܕܡ ܥܠ ܐܣܟܝܡܐ ܕܦܘܠܓ̈ܐ" – ܠܐ ܐܝܟ ܫܛܝܚܘܬܐ ܕܣܪܛܐ ܟܦܝܦܐ ܫܥܝܥܐ، ܕܟܣܡܟ ܥܠ ܬܪܝܢ ܦܘܠܓ̈ܐ ܢܘܪܡܠܝ̈ܐ.

ܪܓܝܫܘܬܐ ܡܨܥܝܬܐ. Pepe (2003، ܦܐܬܐ 78-79) ܠܐ ܝܠܗ ܡܦܝܣܬܐ: ܛܟܣܐ ܬܪܝܨܐ ܕܙܘܓܐ "ܠܐ ܝܠܗ ܡܦܝܣܢܐ ܒܝܚܝܕܝܘܬܐ" ܐܝܟ ܫܘܐܠܐ ܐܣܝܐ – ܟܝܢܝܐ ܝܠܗ ܓܘ ܢܣܝܘܢܐ ܕܓܘܒܝܐ ܡܛܠܨܐ ܡܢ ܙܘܓܐ ܕܨܘܪ̈ܬܐ، ܠܐ ܓܘ ܦܘܠܚܢܐ ܕܒܘܚܪܢܐ – ܘܗܝ ܟܓܒܝܐ ܕܩܪܝܐ ܠܫܛܝܚܘܬܐ "ܐܝܟ ܪܓܝܫܘܬܐ ܡܨܥܝܬܐ، ܥܠ ܟܠܗ ܦܬܝܘܬܐ ܕܡܢܘ̈ܬܐ ܕܕܙܘܕܐ ܛܥ̈ܝܐ". ܬܪܝܢ ܩܪ̈ܝܢܐ ܬܪܝ̈ܨܐ ܝܢܐ ܒܚܘܫܒܢܐ؛ ܩܕܡܝܐ ܦܫܝܩܐ ܝܠܗ ܩܐ ܡܦܫܩܬܐ، ܬܪܝܢܐ ܟܡܥܗܕ ܕܫܛܝܚܘܬܐ ܟܥܒܕܐ ܡܨܥܝܬܐ ܐܦ ܥܠ ܬܚܘ̈ܡܐ ܕܚܕ ܠܐ ܒܕ ܡܦܠܚ ܠܗܘܢ.

ܡܘܕܝ ܫܛܝܚܘܬܐ ܟܛܫܝܐ. ܬܪܝܢ ܡܚܘ̈ܝܢܐ ܥܡ ܐܗܝ ܫܛܝܚܘܬܐ ܡܨܝ ܕܗܘܝ ܒܣܓܝ ܦܪ̈ܝܫܐ ܓܘ ܐܬܪܐ ܕܚܫܝܚܐ ܝܠܗ ܩܐܠܘܟܘܢ: "ܡܨܐ ܕܗܘܐ ܕܡܘܕܝܠ ܕܦܘܪܫܐ (classifier) ܥܡ AUC ܪܡܐ ܥܒܕ ܒܝܫ ܒܙܘܕܐ ܓܘ ܚܕ ܐܬܪܐ ܕܚܠܐ ܕ-ROC ܡܢ ܡܘܕܝܠ ܕܦܘܪܫܐ ܥܡ AUC ܬܚܬܝܐ" (Fawcett, 2006, p. 868)، ܘܡܢ ܣܪܛܐ ܟܦܝܦܐ ܛܒܐ ܒܙܘܕܐ ܒܟܠ ܕܘܟܐ ܟܐܬܝܐ ܫܛܝܚܘܬܐ ܪܒܬܐ ܒܙܘܕܐ، ܐܠܐ "ܗܘܦܟܐ ܠܐ ܝܠܗ ܒܐܢܢܩܝ ܬܪܝܨܐ" (Pepe, 2003, p. 77). ܓܘ ܡܨܠܠܢܘܬܐ ܕܟܢܫܐ ܟܠܢܝܐ، ܡܬܠܐ، ܒܣ ܬܚܘ̈ܡܐ ܥܡ ܩܠܝܠ ܕܙܘܕܐ ܛܥ̈ܝܐ ܡܨܝܐ ܕܡܬܦܠܚܝ، ܘܬܡܐ ܒܣ ܡܢܬܐ ܣܡܠܝܬܐ ܕܣܪܛܐ ܟܦܝܦܐ ܚܫܝܚܬܐ ܝܠܗ (Pepe, 2003, p. 75) – ܩܐ ܐܗܐ ܐܝܬ ܫܛܝܚܘܬܐ ܡܢܬܢܝܬܐ (pAUC; Pepe, 2003, p. 79)، ܕܐܗܐ ܦܐܬܐ ܠܐ ܟܚܫܒܐ ܠܗ. ܡܛܠ ܗܕܐ ܐܗܐ ܦܐܬܐ ܟܡܚܘܐ ܒܟܠ ܙܒܢ ܣܪܛܐ ܟܦܝܦܐ ܘܠܐ ܒܣ ܫܛܝܚܘܬܐ. ܡܢܝܢܐ ܡܫܘܬܦܐ ܕ-Gini، ܕܟܡܬܚܙܐ ܓܘ ܣܦܪ̈ܘܬܐ ܕܝܘܠܦܢܐ ܕܡܟܝܢܐ، ܝܠܗ 2·AUC − 1 (Hand & Till, 2001، ܐܝܟ ܕܡܬܦܪܣܝ ܓܘ Fawcett, 2006، ܦܐܬܐ 868).

ܫܛܝܚܘܬܐ ܬܚܘܬ 0.5. "ܚܕ ܡܘܕܝܠ ܕܦܘܪܫܐ ܫܪܝܪܐ ܠܐ ܣܢܝܩ ܝܠܗ ܕܫܩܠ AUC ܬܚܘܬ 0.5" (Fawcett, 2006, p. 868): ܡܚܘܝܢܐ ܬܚܘܬ ܣܪܛܐ ܡܨܠܝܢܐ "ܐܝܬܠܗ ܡܘܕܥܢܘܬܐ ܦܝܫܬܐ، ܐܠܐ ܟܦܠܚ ܒܗ ܠܐ ܬܪܝܨܐܝܬ" (Flach & Wu, 2003، ܐܝܟ ܕܡܬܦܪܣܝ ܓܘ Fawcett, 2006، ܦܐܬܐ 863) – ܩܪܝܒܐ ܒܟܠ ܙܒܢ ܐܘܪܚܐ ܗܘܦܟܐ ܣܝܡܐ ܝܠܗ. ܐܗܐ ܦܐܬܐ ܟܙܗܪܐ ܓܘ ܗܘܝܐ ܕܐܗܐ ܙܢܐ.

ܛܥܝܘܬܐ ܬܩܝܢܬܐ، ܬܚܘܡܐ ܕܬܘܟܠܢܐ ܘܒܘܚܪܢܐ

ܛܥܝܘܬܐ ܬܩܝܢܬܐ ܕ-DeLong. DeLong، DeLong ܘ-Clarke-Pearson (1988، ܦܐܬܐ 839-840) ܟܦܪܩܝ ܫܛܝܚܘܬܐ ܠ"ܡܢܘ̈ܬܐ ܕܒܢܝܢܐ" (structural components): ܩܐ ܟܠ ܡܫܬܘܬܦܢܐ ܡܢ ܓܘܕܐ ܕܗܘܝܐ – ܡܢܬܐ ܕܡܫܬܘܬܦ̈ܢܐ ܡܢ ܓܘܕܐ ܐܚܪܬܐ ܕܐܝܠܗ ܥܒܪ ܥܠܝܗܘܢ؛ ܩܐ ܟܠ ܡܫܬܘܬܦܢܐ ܡܢ ܓܘܕܐ ܐܚܪܬܐ – ܡܢܬܐ ܕܡܫܬܘܬܦ̈ܢܐ ܡܢ ܓܘܕܐ ܕܗܘܝܐ ܕܥܒܪܝ ܥܠܝܗ. ܫܘܚܠܦܐ ܕܫܛܝܚܘܬܐ ܝܠܗ ܫܘܚܠܦܐ ܕܡܢܘ̈ܬܐ ܩܕܡܝ̈ܐ ܦܠܝܓܐ ܥܠ ܡܢܝܢܐ ܕܡܫܬܘܬܦ̈ܢܐ ܥܡ ܗܘܝܐ، ܘܙܘܕܐ ܫܘܚܠܦܐ ܕܐܚܪ̈ܝܐ ܦܠܝܓܐ ܥܠ ܡܢܝܢܐ ܕܡܫܬܘܬܦ̈ܢܐ ܕܦܘܚܡܐ. Pepe (2003، ܦܐܬܐ 105-106) ܟܩܪܝܐ ܠܐܢܝ ܡܢܘ̈ܬܐ "placement values" – ܐܝܟܐ ܟܠ ܡܢܝܢܐ ܣܝܡܐ ܝܠܗ ܓܘ ܦܘܠܓܐ ܕܓܘܕܐ ܐܚܪܬܐ – ܘܟܚܙܝܐ ܠܗܘܢ ܐܝܟ ܚܕ ܪܥܝܢܐ "ܫܬܐܣܢܝܐ ܩܐ ܦܘܫܩܐ ROC". ܐܗܐ ܝܠܗ ܛܥܝܘܬܐ ܬܩܝܢܬܐ ܪܫܝܬܐ ܓܘ ܐܗܐ ܦܐܬܐ، ܘܐܗܝ ܕ-R ܟܚܫܒ (pROC).

ܛܥܝܘܬܐ ܬܩܝܢܬܐ ܕ-Hanley ܘ-McNeil. ܡܬܘܪܓܡܐ ܥܬܝܩܐ (Hanley & McNeil, 1982, p. 32, Equation 1) ܟܣܡܟ ܥܠ ܬܪܬܝܢ ܡܣܬܒܪ̈ܢܘܝܬܐ: Q₁ – ܕܬܪܝܢ ܡܫܬܘܬܦ̈ܢܐ ܡܢ ܓܘܕܐ ܕܗܘܝܐ ܬܪܘܝܗܝ ܥܒܪܝ ܥܠ ܡܫܬܘܬܦܢܐ ܡܢ ܓܘܕܐ ܐܚܪܬܐ، ܘ-Q₂ – ܕܡܫܬܘܬܦܢܐ ܡܢ ܓܘܕܐ ܕܗܘܝܐ ܥܒܪ ܥܠ ܬܪܝܢ ܡܢ ܓܘܕܐ ܐܚܪܬܐ. ܐܗܐ ܦܐܬܐ ܟܚܫܒܐ ܠܗܝܢ ܡܢ ܝܗܝ̈ܒܬܐ، ܥܡ ܛܝ̈ܡܐ ܫܘ̈ܝܐ ܐܝܟ ܓܘ ܠܘܚܐ II ܕܡܐܡܪܐ (ܦܐܬܐ 31)، ܘܐܗܐ ܝܠܗ ܛܥܝܘܬܐ ܬܩܝܢܬܐ ܕ-PSPP ܟܛܒܥ. ܬܪܝܢ ܡܬܘܪ̈ܓܡܐ ܩܪܝ̈ܒܐ ܝܢܐ ܩܪܝܒܐ ܒܟܠ ܙܒܢ. Hanley ܘ-McNeil (1982، ܦܐܬܐ 33، ܡܬܘܪܓܡܐ 2) ܡܘܩܪܒܠܗܘܢ ܐܦ ܩܘܪܒܐ ܕܬܠܐ ܒܣ ܒܫܛܝܚܘܬܐ – Q₁ = θ/(2 − θ)، Q₂ = 2θ²/(1 + θ) – ܩܐ ܬܘܩܢܐ ܕܪܒܘܬܐ ܕܕܘܡܝܐ ܩܕܡ ܕܐܝܬ ܝܗܝ̈ܒܬܐ؛ ܠܘܚܐ III ܓܘ ܡܐܡܪܐ (ܦܐܬܐ 34) ܟܝܗܒ ܡܢܝ̈ܢܐ ܕܡܫܬܘܬܦ̈ܢܐ ܕܣܢܝܩܝ ܝܢܐ ܩܐ ܦܘܚܡܐ ܒܝܢܝ ܬܪܬܝܢ ܫܛܝ̈ܚܘܬܐ.

ܬܚܘܡܐ ܕܬܘܟܠܢܐ – ܬܪܝܢ ܙܢ̈ܐ، "ܐܦ ܐܗܐ ܘܐܦ ܐܗܐ". ܐܗܐ ܕܡܬܚܙܐ ܣܓܝ – ܫܛܝܚܘܬܐ ܘܙܘܕܐ ܘܒܨܪܐ 1.96 ܛܥܝ̈ܘܬܐ ܬܩܝܢ̈ܬܐ (DeLong)، ܐܝܟ ܒ-R. ܐܠܐ ܫܛܝܚܘܬܐ ܟܪܝܬܐ ܝܠܗ ܒ-1، ܘܐܝܡܢ ܕܩܪܝܒܬܐ ܝܠܗ ܠ-1 ܦܘܠܓܐ ܕܝܠܗ "ܡܨܠܝܐ ܝܠܗ ܠܦܐܬܐ ܕ-0.5" (Hanley & McNeil, 1982, p. 34)، ܘܬܚܘܡܐ ܫܘܝܐ ܠܬܪܝܢ ܓܢ̈ܒܐ ܡܨܐ ܕܥܒܪ ܡܢ 1 (ܐܗܐ ܦܐܬܐ ܟܦܣܩܐ ܠܗ ܒ-1، ܐܝܟ R). Pepe (2003، ܦܐܬܐ 107) ܟܡܩܪܒܐ ܬܚܘܡܐ ܒܣܒܠܬܐ ܕܠܘܓܝܬ – ܠܐ ܫܘܝܐ ܠܬܪܝܢ ܓܢ̈ܒܐ، ܒܟܠ ܙܒܢ ܒܝܢܝ 0 ܘ-1 – ܘܟܡܚܘܝܐ ܒܢܣܝܘܢܐ ܕܚܘܫܒܢܐ (simulation) ܕܓܘ ܕܘ̈ܡܝܐ ܙܥܘ̈ܪܐ ܘܫܛܝ̈ܚܘܬܐ ܪ̈ܡܐ ܟܣܝܘܬܐ ܕܝܠܗ ܛܒܬܐ ܝܠܗ ܒܙܘܕܐ (ܠܘܚܐ 5.1)؛ "ܒܫܪܪܐ ܟܡܦܝܣܚ" ܥܠܝܗ. ܐܗܐ ܦܐܬܐ ܟܡܚܘܐ ܬܪܘܝܗܝ؛ ܦܣܩܐ ܕܡܫܟܚ̈ܢܘܬܐ ܟܦܠܚܐ ܒ-DeLong ܫܘܝܐ ܠܬܪܝܢ ܓܢ̈ܒܐ، ܕܡܨܝܚ ܕܬܢܚ ܠܗ ܒ-R ܘܒ-SPSS، ܘܒܫܛܝܚܘܬܐ ܕ-.90 ܘܒܐܬܪܗ ܝܢ ܓܘ ܓܘܕܐ ܕܒܨܝܪ ܡܢ 30 ܡܫܬܘܬܦ̈ܢܐ – ܛܒܐ ܝܠܗ ܕܡܬܢܐ ܬܚܘܡܐ ܕܠܘܓܝܬ.

ܐܢ ܫܛܝܚܘܬܐ ܪܒܬܐ ܝܠܗ ܡܢ 0.5؟ ܐܗܐ ܦܐܬܐ ܟܡܬܢܝܐ z ܘ-p ܩܐ ܗܘܦܘܬܣܝܣ ܕܣܦܝܩܘܬܐ ܕܡܚܘܝܢܐ ܠܐ ܟܦܪܫ (ܫܛܝܚܘܬܐ 0.5)، ܥܡ ܛܥܝܘܬܐ ܬܩܝܢܬܐ ܬܚܘܬ ܗܘܦܘܬܣܝܣ ܕܣܦܝܩܘܬܐ – ܐܗܐ ܝܠܗ ܒܘܚܪܢܐ ܕ-Mann-Whitney ܒܩܘܪܒܐ ܢܘܪܡܠܝܐ، ܕܠܐ ܬܘܪܨܐ ܩܐ ܛܝ̈ܡܐ ܫܘ̈ܝܐ، ܘܐܗܐ ܝܠܗ Asymptotic Sig. ܕ-PSPP. ܥܡ ܬܘܪܨܐ ܩܐ ܛܝ̈ܡܐ ܫܘ̈ܝܐ (ܦܐܬܐ ܕMann-Whitney) p ܒܨܝܪ ܝܠܗ ܩܠܝܠ. ܒܘܚܪܢܐ ܕܐܗܐ ܙܢܐ ܟܦܢܐ ܠܫܘܐܠܐ ܡܟܝܟܐ: ܓܘ ܕܘܡܝܐ ܪܒܐ ܐܦ ܫܛܝܚܘܬܐ ܕ-.58 "ܪܫܝܡܬܐ" ܝܠܗ، ܘܡܛܠ ܗܕܐ ܡܐ ܕܟܡܬܢܚ ܝܠܗ ܫܛܝܚܘܬܐ ܘܬܚܘܡܐ ܕܬܘܟܠܢܐ ܕܝܠܗ.

ܓܘܒܝܐ ܕܬܚܘܡܐ ܕܦܘܪܫܐ

ܡܚܘܝܢܐ ܕ-Youden. J = ܪܓܝܫܘܬܐ + ܝܚܝܕܝܘܬܐ − 1، ܗܢܘ ܪܘܚܩܐ ܙܩܝܦܐ ܒܝܢܝ ܣܪܛܐ ܟܦܝܦܐ ܘܣܪܛܐ ܡܨܠܝܢܐ؛ ܬܚܘܡܐ ܕܦܘܪܫܐ ܕܟܡܪܒܐ ܠܗ ܡܢ ܟܠܗ ܝܠܗ ܓܘܒܝܐ ܡܩܕܡܐ (default) ܕܐܗܐ ܦܐܬܐ. Pepe (2003، ܦܐܬܐ 80) ܟܡܚܘܝܐ ܠܗ ܐܝܟ ܟܢܘܫܝܐ ܕܡܘܩܪܒܐ ܝܠܗ "ܐܝܡܢ ܕܛܝܡܐ ܕܛܥܝ̈ܘܬܐ ܕܕܙܘܕܐ ܛܥ̈ܝܐ ܕܡܐ ܝܠܗ ܒܪܒܘܬܐ ܠܐܗܐ ܕܕܒܨܪܐ ܛܥ̈ܝܐ" – ܘܐܗܐ ܣܝܡܬܐ ܝܠܗ، ܠܐ ܫܪܪܐ. ܐܝܡܢ ܕܛܝ̈ܡܐ ܦܪ̈ܝܫܐ ܝܢܐ، ܬܚܘܡܐ ܬܪܝܨܐ ܬܠܐ ܝܠܗ ܒܛܝ̈ܡܐ ܘܒܣܓܝܐܘܬܐ ܕܗܘܝܐ (Pepe, 2003، ܦܐܬܐ 72، ܦܐܪܐ 4.5؛ Fawcett, 2006، ܦܐܬܐ 867، "iso-performance lines"): ܓܘ ܡܨܠܠܢܘܬܐ ܩܐ ܗܘܝܐ ܕܣܘܟܢܐ ܟܓܒܚ ܪܓܝܫܘܬܐ ܪܡܬܐ ܐܦ ܒܛܝܡܐ ܕܙܘܗܪ̈ܐ ܕܓܠܐ؛ ܩܕܡ ܥܘܕܪܢܐ ܝܩܝܪܐ ܒܛܝܡܐ – ܗܘܦܟܐ. ܡܛܠ ܗܕܐ ܐܗܐ ܦܐܬܐ ܟܡܨܐ ܕܒܚܪܚ ܟܠ ܬܚܘܡܐ، ܘܟܡܚܘܐ ܟܠ ܬܚܘ̈ܡܐ ܓܘ ܠܘܚܐ ܓܡܝܪܐ. ܘܐܢ ܐܝܬ ܬܚܘܡܐ ܡܩܒܠܐ ܓܘ ܣܦܪ̈ܘܬܐ ܩܐ ܡܚܘܝܢܐ – ܟܡܬܢܚ ܠܗ، ܘܠܐ ܬܚܘܡܐ ܕܡܫܟܚܐ ܝܠܗ ܓܘ ܝܗܝ̈ܒܬܐ.

ܬܚܘܡܐ ܕܓܒܝܐ ܝܠܗ ܥܠ ܝܗܝ̈ܒܬܐ ܡܣܒܪܢܐ (optimistic) ܝܠܗ. ܬܚܘܡܐ ܕ-Youden ܓܒܝܐ ܝܠܗ ܕܦܐܝܐ ܒܚܬܝܬܘܬܐ ܠܐܗܐ ܕܘܡܝܐ، ܘܡܛܠ ܗܕܐ ܪܓܝܫܘܬܐ ܘܝܚܝܕܝܘܬܐ ܓܘܗ ܪ̈ܡܐ ܝܢܐ ܩܠܝܠ ܡܢ ܡܐ ܕܒܕ ܡܬܛܝܐ ܓܘ ܕܘܡܝܐ ܚܕܬܐ. ܠܦܘܬ ܥܝܕܐ ܕܣܐܝܛ، ܬܚܘܡܐ ܕܓܒܝܐ ܝܠܗ ܥܠ ܝܗܝ̈ܒܬܐ ܟܡܬܢܚ ܠܗ ܐܝܟ ܡܫܟܚܢܘܬܐ ܩܕܡܝܬܐ، ܘܥܒ̈ܕܐ ܕܝܠܗ ܟܫܪܪܚ ܠܗܘܢ ܓܘ ܕܘܡܝܐ ܐܚܪܢܐ (ܥܠ ܫܘܪܪܐ ܥܠ ܝܗܝ̈ܒܬܐ ܚܕ̈ܬܬܐ – ܦܐܬܐ ܕܡܚܘ̈ܝܢܐ ܕܥܒܕܐ ܘܫܘܪܪܐ ܕܡܘܕܝܠ).

ܡܘܕܝ ܟܚܫܒܚ ܓܘ ܬܚܘܡܐ. ܪܓܝܫܘܬܐ ܘܝܚܝܕܝܘܬܐ ܥܡ ܬܚܘܡܐ ܕܬܘܟܠܢܐ ܚܬܝܬܐ (Clopper-Pearson) – Pepe (2003، ܦܐܬܐ 22) ܟܓܒܝܐ ܐܘܪ̈ܚܬܐ ܚܬܝܬ̈ܐ ܝܢ ܠܘܓܝܣܛܝܩ̈ܝܐ، ܡܛܠ ܕܓܘ ܒܘܚܪ̈ܢܐ ܛܒ̈ܐ ܡܢܘ̈ܬܐ ܩܪܝ̈ܒܐ ܝܢܐ ܠܣܘܦܐ، ܘܬܚܘܡܐ ܢܘܪܡܠܝܐ ܫܘܝܐ ܠܬܪܝܢ ܓܢ̈ܒܐ "ܡܨܐ ܕܥܒܪ ܡܢ (0, 1)". ܚܫܝܚܐ ܝܠܗ ܕܡܬܢܚ ܬܪܘܝܗܝ، ܘܠܐ ܚܬܝܬܘܬܐ ܟܠܢܝܬܐ: ܬܪܬܝܢ ܛܥܝ̈ܘܬܐ ܦܪ̈ܝܫܐ ܝܢܐ ܒܛܝܡܐ ܕܝܠܗܝܢ، ܘܚܬܝܬܘܬܐ ܟܠܢܝܬܐ ܬܠܝܐ ܝܠܗ ܒܣܓܝܐܘܬܐ – ܒܘܚܪܢܐ ܕܟܦܪܫ ܟܠܗܘܢ ܐܝܟ ܕܒܨܪܐ ܒܕ ܫܩܠ ܚܬܝܬܘܬܐ ܪܡܬܐ ܓܘ ܗܘܝܐ ܕܠܐ ܡܬܚܙܐ ܣܓܝ (Pepe, 2003, p. 15). ܦܘܚ̈ܡܐ ܕܡܬܚܙܝܢܘܬܐ (LR+ = ܪܓܝܫܘܬܐ/(1 − ܝܚܝܕܝܘܬܐ)، LR− = (1 − ܪܓܝܫܘܬܐ)/ܝܚܝܕܝܘܬܐ) ܟܐܡܪܝ ܟܡܐ ܓܗ̈ܐ ܦܐܪܐ ܕܙܘܕܐ ܝܢ ܕܒܨܪܐ ܟܡܫܚܠܦ ܣܟܘ̈ܝܐ ܕܗܘܝܐ، ܘܠܐ ܬܠܝ̈ܐ ܝܢܐ ܒܣܓܝܐܘܬܐ (Pepe, 2003, p. 20, Table 2.2)؛ ܬܚܘܡܐ ܕܬܘܟܠܢܐ ܕܝܠܗܘܢ – ܒܣܒܠܬܐ ܕܠܘܓ (Pepe, 2003، ܦܐܬܐ 24، ܦܐܪܐ 2.5).

ܛܝ̈ܡܐ ܡܢܒ̈ܝܢܐ ܘܣܓܝܐܘܬܐ. ܛܝܡܐ ܡܢܒܝܢܐ ܕܙܘܕܐ – ܡܢ ܓܘ ܐܢܝ ܕܦܪܝܫ̈ܐ ܝܢܐ ܐܝܟ ܕܙܘܕܐ، ܟܡܐ ܒܫܪܪܐ ܓܘ ܗܘܝܐ ܝܢܐ؛ ܕܒܨܪܐ – ܡܢ ܓܘ ܕܒܨܪܐ، ܟܡܐ ܒܫܪܪܐ ܠܐ. ܐܢܝ ܝܢܐ ܡܐ ܕܚܫܝܚܐ ܝܠܗ ܩܐ ܐܝܢܐ ܕܫܩܠܠܗ ܦܐܪܐ، ܐܠܐ "ܬܠܝ̈ܐ ܝܢܐ ܠܐ ܒܣ ܒܥܒ̈ܕܐ ܕܒܘܚܪܢܐ... ܐܠܐ ܐܦ ܒܣܓܝܐܘܬܐ ܕܗܘܝܐ" (Pepe, 2003, p. 16). ܐܝܡܢ ܕܕܘܡܝܐ ܒܢܝܐ ܝܠܗ ܡܢ ܡܢܝܢܐ ܩܝܡܐ ܕܡܫܬܘܬܦ̈ܢܐ ܥܡ ܗܘܝܐ ܘܕܡܫܬܘܬܦ̈ܢܐ ܕܦܘܚܡܐ، ܡܢܬܐ ܓܘ ܕܘܡܝܐ "ܒܕ ܫܥܪ ܒܝܬܝܪܘܬܐ ܛܝܡܐ ܡܢܒܝܢܐ ܕܙܘܕܐ" (Pepe, 2003, p. 25). ܡܛܠ ܗܕܐ ܟܬܘܒܘܢ ܣܓܝܐܘܬܐ ܕܗܘܝܐ ܓܘ ܟܢܫܐ ܟܠܢܝܐ ܕܓܘܗ ܡܚܘܝܢܐ ܒܕ ܡܬܦܠܚ، ܘܐܗܐ ܦܐܬܐ ܒܕ ܚܫܒܐ ܛܝ̈ܡܐ ܡܢܒ̈ܝܢܐ ܓܘܗ ܠܦܘܬ ܢܡܘܣܐ ܕ-Bayes. ܣܪܛܐ ܟܦܝܦܐ ROC ܒܓܢܗ، ܒܪܡ، "ܠܐ ܝܠܗ ܪܓܝܫܐ ܠܫܘܚܠܦ̈ܐ ܓܘ ܦܘܠܓܐ ܕܓܢ̈ܣܐ" (Fawcett, 2006, p. 864).

ܦܘܚܡܐ ܕܡܚܘ̈ܝܢܐ

ܐܝܡܢ ܕܟܡܐ ܡܚܘ̈ܝܢܐ ܡܫܝܚ̈ܐ ܝܢܐ ܥܠ ܐܢܝ ܡܫܬܘܬܦ̈ܢܐ، ܫܛܝ̈ܚܘܬܐ ܕܝܠܗܘܢ ܐܣܝܪ̈ܐ ܝܢܐ ܚܕ ܥܡ ܚܕ – ܐܢܝ ܐܢܫ̈ܐ "ܦܫܝܩ̈ܐ" ܘ"ܥܣܩ̈ܐ" ܝܢܐ ܩܐ ܟܠ ܡܚܘ̈ܝܢܐ – ܘܦܘܚܡܐ ܕܠܐ ܟܚܫܒ ܐܗܐ ܛܥܝܐ ܝܠܗ. DeLong ܘܚܒܪ̈ܘܗܝ (1988) ܦܬܚܠܗܘܢ ܩܐ ܐܗܐ ܐܘܪܚܐ ܠܐ ܦܪܡܝܛܪܝܬܐ: ܡܐܛܪܝܟܣ ܕܫܘܚܠ̈ܦܐ ܡܫܘܬ̈ܦܐ ܕܫܛܝ̈ܚܘܬܐ ܡܢ ܡܢܘ̈ܬܐ ܕܒܢܝܢܐ، ܘܒܘܚܪܢܐ ܕܟܝ ܡܪܒܥܐ ܩܐ ܟܠ ܣܘܩܒܠܐ (contrast) ܒܝܢܝ ܐܢܝ (ܦܐܬܐ 840-841، ܡܬܘܪܓܡܐ 5). ܩܐ ܙܘܓܐ ܕܡܚܘ̈ܝܢܐ – z ܩܐ ܦܘܪܫܢܐ ܒܝܢܝ ܫܛܝ̈ܚܘܬܐ، ܥܡ ܬܚܘܡܐ ܕܬܘܟܠܢܐ (Pepe, 2003، ܦܐܬܐ 108، ܦܐܪܐ 5.6)؛ ܩܐ ܬܠܬܐ ܘܒܐܬܪܗ – ܒܘܚܪܢܐ ܟܠܢܝܐ ܩܐ ܫܘܝܘܬܐ ܕܟܠ ܫܛܝ̈ܚܘܬܐ (k − 1 ܕܪ̈ܓܐ ܕܚܐܪܘܬܐ)، ܘܒܬܪܗ ܟܠ ܙܘ̈ܓܐ، ܥܡ ܬܘܪܨܐ ܕ-Holm ܩܐ ܦܘܚ̈ܡܐ ܣܓܝ̈ܐܐ ܠܦܘܬ ܥܝܕܐ ܕܣܐܝܛ. ܡܚܘܝܢܐ ܒܐܘܪܚܐ ܗܘܦܟܐ (ܫܝܢܐ ܕܢܦܫܐ ܩܘܒܠ ܢܝ̈ܫܢܐ ܕܟܘܪܗܢܐ) ܟܥܐܠ ܠܦܘܚܡܐ ܒܬܪ ܗܘܦܟܐ ܕܪܘܫܡܐ، ܐܝܟ ܕܥܒܕܠܗܘܢ DeLong ܘܚܒܪ̈ܘܗܝ ܥܡ ܡܢܝܢܐ ܕܝܠܗܘܢ (ܦܐܬܐ 842).

ܝܘܠܦܢܐ ܕܡܬܠܐ ܕܝܠܗܘܢ (ܦܐܬܐ 844): ܡܢܝܢܐ ܝܚܝܕܝܐ ܩܐ ܡܢܒܝܢܘܬܐ ܕܡܨܠܚܢܘܬܐ ܕܓܪܚܬܐ ܠܐ ܗܘܐ ܛܒܐ ܒܙܘܕܐ ܡܢ ܬܪܝܢ ܡܚܘ̈ܝܢܐ ܕܡܐܟܘܠܬܐ ܥܝܕܝ̈ܐ، ܐܠܐ "ܚܝܠܐ ܣܛܐܛܝܣܛܝܩܝܐ ܓܘ ܐܗܐ ܗܘܝܐ ܡܨܐ ܕܗܘܐ ܒܣܓܝ ܙܥܘܪܐ ܡܛܠ ܪܒܘܬܐ ܙܥܘܪܬܐ ܕܕܘܡܝܐ" – 49 ܟܘܪܗܢ̈ܝܬܐ. ܠܐ ܐܝܬܘܬܐ ܕܦܘܪܫܢܐ ܪܫܝܡܐ ܒܝܢܝ ܫܛܝ̈ܚܘܬܐ ܓܘ ܕܘܡܝܐ ܙܥܘܪܐ ܠܐ ܝܠܗ ܚܘܝܐ ܕܡܚܘ̈ܝܢܐ ܫܘ̈ܝܐ ܝܢܐ. ܐܝܡܢ ܕܡܚܘ̈ܝܢܐ ܡܫܝܚ̈ܐ ܝܢܐ ܥܠ ܓܘ̈ܕܐ ܦܪ̈ܝܫܐ ܕܡܫܬܘܬܦ̈ܢܐ، ܫܘܚܠܦܐ ܕܦܘܪܫܢܐ ܒܣ ܓܘܡܪܐ ܝܠܗ ܕܫܘܚܠ̈ܦܐ (Pepe, 2003, p. 108) – ܐܗܐ ܦܐܬܐ ܠܐ ܟܚܫܒܐ ܦܘܚܡܐ ܕܐܗܐ ܙܢܐ.

ܩܪܝܢܐ ܕܡܦܩܢܐ (How to read the output)

ܠܘܚܐ 1 – ܫܛܝܚܘܬܐ ܬܚܘܬ ܣܪܛܐ ܟܦܝܦܐ: ܩܐ ܟܠ ܡܚܘܝܢܐ – ܐܘܪܚܐ، ܫܛܝܚܘܬܐ، ܛܥܝ̈ܘܬܐ ܬܩܝܢ̈ܬܐ (DeLong; Hanley & McNeil)، ܬܪܝܢ ܬܚܘ̈ܡܐ ܕܬܘܟܠܢܐ، ܘ-z ܘ-p ܩܘܒܠ 0.5. ܨܘܪܬܐ 1 – ܣܪ̈ܛܐ ܟܦܝܦ̈ܐ، ܥܡ ܣܪܛܐ ܡܨܠܝܢܐ ܘܬܚܘܡܐ ܕ-Youden ܕܟܠ ܡܚܘܝܢܐ.

ܠܘܚܐ 2 – ܬܚܘܡܐ ܕܦܘܪܫܐ ܠܦܘܬ ܡܚܘܝܢܐ ܕ-Youden: ܩܐ ܟܠ ܡܚܘܝܢܐ – ܬܚܘܡܐ (ܕܙܘܕܐ ܐܢ ܡܢܝܢܐ ܪܡܐ ܝܠܗ ܡܢܗ ܝܢ ܫܘܝܐ ܠܗ؛ ܓܘ ܡܚܘܝܢܐ ܒܐܘܪܚܐ ܗܘܦܟܐ – ܬܚܬܝܐ ܝܢ ܫܘܝܐ)، ܪܓܝܫܘܬܐ ܘܝܚܝܕܝܘܬܐ ܥܡ ܬܚܘ̈ܡܐ ܕܬܘܟܠܢܐ، J، ܛܝ̈ܡܐ ܡܢܒ̈ܝܢܐ ܘܦܘܚ̈ܡܐ ܕܡܬܚܙܝܢܘܬܐ. ܬܚܘ̈ܡܐ ܢܘܩ̈ܙܐ ܡܨܥ̈ܝܐ ܝܢܐ ܒܝܢܝ ܛܝ̈ܡܐ ܩܪܝ̈ܒܐ، ܐܝܟ ܒ-SPSS ܘܒ-R، ܘܡܛܠ ܗܕܐ ܬܚܘܡܐ ܕ-10.5 ܓܘ ܦܢܩܝܬܐ ܕܡܢܝ̈ܢܐ ܫܠܡ̈ܐ ܟܐܡܪ "11 ܘܒܐܬܪܗ".

ܒܘܚܪܢܐ ܕܬܚܘܡܐ: ܟܓܒܚ ܡܚܘܝܢܐ ܘܟܟܬܒܚ ܬܚܘܡܐ، ܘܟܫܩܠܚ ܠܘܚܐ 3 – ܠܘܚܐ 2×2 ܘܟܠ ܡܚܘ̈ܝܢܐ ܓܘ ܐܗܐ ܬܚܘܡܐ، ܥܡ ܛܝ̈ܡܐ ܡܢܒ̈ܝܢܐ ܒܣܓܝܐܘܬܐ ܕܟܬܒܠܘܟܘܢ. ܬܚܘܬܗ، ܒܡܚܝܬܐ – ܟܠ ܬܚܘ̈ܡܐ ܕܡܚܘܝܢܐ. ܠܘܚܐ 4 – ܦܘܚܡܐ ܕܫܛܝ̈ܚܘܬܐ (ܐܝܡܢ ܕܓܒܝ̈ܐ ܝܢܐ ܬܪܝܢ ܡܚܘ̈ܝܢܐ ܝܢ ܒܙܘܕܐ): ܦܘܪܫܢܐ ܒܝܢܝ ܟܠ ܙܘܓܐ، ܛܥܝܘܬܐ ܬܩܝܢܬܐ، ܬܚܘܡܐ ܕܬܘܟܠܢܐ، z، p، p ܡܬܘܪܨܐ ܠܦܘܬ Holm، ܘܐܣܘܪܐ ܕܚܕ̈ܕܐ ܒܝܢܝ ܫܛܝ̈ܚܘܬܐ؛ ܓܘ ܡܥܝܪܢܘܬܐ – ܒܘܚܪܢܐ ܟܠܢܝܐ.

ܫܪ̈ܛܐ ܘܙܘܗܪ̈ܐ (Assumptions and warnings)

ܬܩܢܐ ܕܕܗܒܐ ܬܪܝܨܐ ܝܠܗ. ܟܠܗ ܚܘܫܒܢܐ ܟܣܝܡ ܕܡܫܬܚܠܦܢܐ ܕܗܘܝܐ ܠܐ ܟܛܥܐ. Pepe (2003، ܦܐܬܐ 6-7، ܠܘܚܐ 1.3) ܟܡܢܝܐ ܡܣܒ ܒܐܦ̈ܐ (bias) ܕܡܬܚܙܝܢ ܣܓܝ ܓܘ ܒܘܨ̈ܝܐ ܕܐܗܐ ܙܢܐ: ܬܩܢܐ ܕܕܗܒܐ ܠܐ ܓܡܝܪܐ؛ ܡܣܒ ܒܐܦ̈ܐ ܕܫܘܪܪܐ (verification bias) – ܒܣ ܡܢܬܐ ܡܢ ܡܫܬܘܬܦ̈ܢܐ، ܘܠܐ ܓܕܫܢܐܝܬ، ܒܚܝܪ̈ܐ ܝܢܐ ܒܬܩܢܐ ܕܕܗܒܐ؛ ܡܣܒ ܒܐܦ̈ܐ ܕ-spectrum (spectrum bias) – "ܛܥܝܘܬܐ ܕܡܬܚܙܝܐ ܣܓܝ ܝܠܗ ܕܓܒܚ ܡܫܬܘܬܦ̈ܢܐ ܓܘ ܗܘܝܐ ܩܫܝܐ ܝܢ ܥܬܝܩܐ ܘܡܫܬܘܬܦ̈ܢܐ ܕܦܘܚܡܐ ܚܠܝܡ̈ܐ ܒܙܘܕܐ ܡܢ ܡܨܥܝܬܐ"، ܡܐ ܕ"ܡܨܐ ܕܡܪܒܐ ܚܬܝܬܘܬܐ ܕܡܬܚܙܝܐ ܕܒܘܚܪܢܐ"؛ ܘܡܣܒ ܒܐܦ̈ܐ ܕܦܘܫܩܐ (interpretation bias) – ܐܝܡܢ ܕܐܝܢܐ ܕܟܦܣܩ ܗܘܝܐ ܟܝܕܥ ܦܐܪܐ ܕܡܚܘܝܢܐ، ܝܢ ܗܘܦܟܐ (ܦܐܬܐ 5-6).

ܡܫܬܘܬܦ̈ܢܐ ܠܐ ܬܠܝ̈ܐ. ܛܥܝ̈ܘܬܐ ܬܩܝܢ̈ܬܐ ܟܣܝܡܝ ܕܟܠ ܡܫܬܘܬܦܢܐ ܟܝܗܒ ܚܕ ܚܙܝܬܐ. ܐܝܡܢ ܕܐܝܬ ܟܡܐ ܚܙ̈ܝܬܐ ܩܐ ܡܫܬܘܬܦܢܐ (ܬܪܬܝܢ ܥܝ̈ܢܐ، ܟܡܐ ܒܘܚܪ̈ܢܐ ܩܐ ܬܠܡܝܕܐ)، Pepe (2003، ܦܐܬܐ 104) ܟܡܦܝܣܐ ܥܠ ܒܘܛܣܛܪܐܦ (bootstrap) ܓܘ ܪܡܐ ܕܡܫܬܘܬܦܢܐ – ܕܐܗܐ ܦܐܬܐ ܠܐ ܟܪܗܛܐ ܠܗ.

ܛܝ̈ܡܐ ܫܘ̈ܝܐ. ܓܘ ܡܢܝ̈ܢܐ ܥܡ ܩܠܝܠ ܛܝ̈ܡܐ ܐܝܬ ܣܓܝ ܛܝ̈ܡܐ ܫܘ̈ܝܐ (ties)، ܘ-Fawcett (2006، ܦܐܬܐ 867) ܟܙܗܪ ܕܐܢ ܠܐ ܟܥܒܕܚ ܡܨܥܝܬܐ ܕܝܠܗܘܢ، ܣܪܛܐ ܟܦܝܦܐ ܬܠܐ ܝܠܗ ܒܛܟܣܐ ܕܓܘܗ ܡܫܬܘܬܦ̈ܢܐ ܟܡܬܚܙܝ ܓܘ ܦܐܝܠ، ܘ"ܛܟ̈ܣܐ ܦܪ̈ܝܫܐ ܡܨܝ ܕܝܗܒܝ ܣܪ̈ܛܐ ܟܦܝܦ̈ܐ ܕܒܣܓܝ ܡܛܥܝܢܝ̈ܐ ܝܢܐ". ܐܗܐ ܦܐܬܐ ܟܥܒܕܐ ܡܨܥܝܬܐ ܕܝܠܗܘܢ: ܛܝܡܐ ܫܘܝܐ ܒܝܢܝ ܡܫܬܘܬܦܢܐ ܥܡ ܗܘܝܐ ܘܡܫܬܘܬܦܢܐ ܕܦܘܚܡܐ ܟܡܬܡܢܐ ܐܝܟ ܦܠܓܐ، ܘܣܪܛܐ ܟܦܝܦܐ ܟܥܒܪ ܒܣܪܛܐ ܡܨܠܝܢܐ.

ܐܘܪܚܐ ܦܣܝܩܐ ܝܠܗ ܡܢ ܩܕܡ. ܦܪ̈ܘܓܪܡܐ ܕܟܓܒܝ ܐܘܪܚܐ "ܒܓܢܗ" ܠܦܘܬ ܝܗܝ̈ܒܬܐ ܟܗܦܟܝ ܟܠ ܡܚܘܝܢܐ ܟܪܝܗܐ ܠܫܛܝܚܘܬܐ ܒܐܬܪܐ ܕ-0.5. ܐܗܐ ܦܐܬܐ ܠܐ ܟܥܒܕܐ ܐܗܐ: ܐܘܪܚܐ ܦܣܩܐ ܕܝܘܟܘܢ ܝܠܗ، ܠܦܘܬ ܡܐ ܕܡܚܘܝܢܐ ܣܢܝܩ ܝܠܗ ܕܡܫܚ، ܘܫܛܝܚܘܬܐ ܬܚܘܬ 0.5 ܟܡܬܚܙܝܐ ܐܝܟ ܕܐܝܠܗ، ܥܡ ܙܘܗܪܐ.

ܟܪܝܘ̈ܬܐ ܥܒܕ̈ܢܝܬܐ. ܛܝ̈ܡܐ ܚܣܝ̈ܪܐ: ܫܩܠܬܐ ܕܣܕܪܐ ܟܠܗ (listwise deletion) ܥܠ ܡܫܬܚܠܦܢܐ ܕܗܘܝܐ ܘܥܠ ܟܠ ܡܚܘ̈ܝܢܐ ܕܓܒܝ̈ܐ ܝܢܐ (ܐܗܐ ܦܐܬܐ ܟܡܘܕܥܐ ܟܡܐ ܫܩܝܠ̈ܐ ܝܢܐ). ܣܢܝܩܘܬܐ ܐܝܬ ܠܚܡܫܐ ܡܫܬܘܬܦ̈ܢܐ ܠܦܚܘܬ ܓܘ ܟܠ ܓܘܕܐ؛ ܒܒܨܝܪ ܡܢ 30 ܓܘ ܓܘܕܐ – ܬܚܘ̈ܡܐ ܕܬܘܟܠܢܐ ܩܪܝܒ̈ܝܐ (asymptotic) ܒܨܝܪ ܚܬܝܬ̈ܐ ܝܢܐ (Pepe, 2003, p. 107, Table 5.1). ܫܛܝܚܘܬܐ ܕ-1 (ܦܘܪܫܐ ܓܡܝܪܐ) – ܛܥܝܘܬܐ ܬܩܝܢܬܐ 0 ܘܬܚܘܡܐ ܕܬܘܟܠܢܐ ܕܠܐ ܣܘܟܠܐ ܝܠܗ، ܘܐܗܐ ܦܐܬܐ ܟܙܗܪܐ؛ ܩܐ ܬܚܘ̈ܡܐ ܚܬܝܬ̈ܐ ܓܘ ܗܘܝܐ ܕܐܗܐ ܙܢܐ Pepe (2003، ܦܐܬܐ 107) ܟܡܫܕܪܐ ܠ-Obuchowski ܘ-Lieber (2002، ܐܝܟ ܕܡܬܦܪܣܝ ܬܡܐ). ܡܘܕܝ ܠܐ ܟܚܫܒܐ ܐܗܐ ܦܐܬܐ: ܣܪܛܐ ܟܦܝܦܐ ܫܥܝܥܐ (binormal)، ܫܛܝܚܘܬܐ ܡܢܬܢܝܬܐ، ܬܚܘ̈ܡܐ ܕܬܘܟܠܢܐ ܩܐ ܣܪܛܐ ܟܦܝܦܐ ܟܠܗ، ܦܘܚܡܐ ܒܝܢܝ ܓܘ̈ܕܐ ܠܐ ܬܠܝ̈ܐ، ܘ-ROC ܩܐ ܒܙܘܕܐ ܡܢ ܬܪܬܝܢ ܓܘ̈ܕܐ.

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

ܒ-SPSS Statistics: Analyze › Classify › ROC Curve (ܓܘ ܢܘ̈ܣܚܐ ܥܬܝܩ̈ܐ – Analyze › ROC Curve)؛ ܟܡܥܒܪܚ ܡܚܘ̈ܝܢܐ ܠ-Test Variable، ܡܫܬܚܠܦܢܐ ܕܗܘܝܐ ܠ-State Variable ܘܟܟܬܒܚ ܛܝܡܐ ܕܟܡܚܘܐ ܗܘܝܐ؛ ܟܪܫܡܚ ROC Curve، With diagonal reference line، Standard error and confidence interval ܘ-Coordinate points of the ROC Curve. ܐܘܪܚܐ ܦܣܝܩܐ ܝܠܗ ܓܘ Options › Test Direction – ܚܕ ܩܐ ܟܠܗ ܦܘܩܕܢܐ، ܘܡܛܠ ܗܕܐ ܣܝܢܬܐܟܣ ܕܐܗܐ ܦܐܬܐ ܟܡܦܩܐ ܟܪܗܛ ܦܘܩܕܢܐ ܦܪܝܫܐ ܩܐ ܡܚܘ̈ܝܢܐ ܒܐܘܪܚܐ ܗܘܦܟܐ. ܐܘܪ̈ܚܬܐ ܡܘܕܥܢܘܬܐ ܟܠܢܝܬܐ ܝܢܐ ܥܠ ܦܪܘܓܪܡܐ؛ ܣܝܢܬܐܟܣ ܠܐ ܝܠܗ ܪܗܛܐ ܒ-SPSS.

ܐܗܘ ܦܘܩܕܢܐ (ROC) ܐܝܬ ܐܦ ܒ-PSPP، ܚܠܦܐ ܕܡܓܢ، ܘܪܗܛܐ ܝܠܗ ܥܠ ܦܐܝܠ ܕܡܬܠܐ: ܫܛܝܚܘܬܐ ܘ-Std. Error ܫܘ̈ܝܐ ܝܢܐ ܠܐܗܐ ܦܐܬܐ (Std. Error ܕ-Hanley ܘ-McNeil ܝܠܗ، ܥܡܘܕܐ "SE (H-M)" ܓܘ ܠܘܚܐ 1)، ܘܐܗܟܐ ܐܦ Asymptotic Sig.؛ ܐܠܐ ܬܚܘ̈ܡܐ ܕ-PSPP ܟܛܒܥ ܬܚܘܬ "95%" ܪܚܝܩ̈ܐ ܝܢܐ ܡܢ ܫܛܝܚܘܬܐ 1.645 ܛܥܝ̈ܘܬܐ ܬܩܝܢ̈ܬܐ ܘܠܐ 1.96 – ܗܢܘ ܬܚܘܡܐ ܕ-90% – ܘܒܐܘܪܚܐ TESTPOS(SMALL) ܟܡܕܥܪ NaN ܩܐ ܛܥܝܘܬܐ ܬܩܝܢܬܐ ܘܩܐ ܬܚܘܡܐ. ܒ-PSPP – ܫܩܘܠܘܢ ܬܚܘ̈ܡܐ ܕܬܘܟܠܢܐ ܡܢ ܐܗܐ ܦܐܬܐ. ܦܘܚܡܐ ܒܝܢܝ ܫܛܝ̈ܚܘܬܐ ܠܐ ܝܠܗ ܡܢܬܐ ܕܦܘܩܕܢܐ ROC؛ ܐܝܠܗ ܓܘ ܣܩܪܝܦܬ R ܕܬܚܬ.

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

ܓܪܒܐ pROC: roc ܟܒܢܐ ܣܪܛܐ ܟܦܝܦܐ (levels – ܛܝܡܐ ܕܒܨܪܐ ܘܒܬܪܗ ܕܙܘܕܐ؛ direction = "<" – ܛܝܡܐ ܪܡܐ ܟܡܣܗܕ ܥܠ ܗܘܝܐ، ">" – ܛܝܡܐ ܬܚܬܝܐ؛ ܕܠܐ direction ܓܪܒܐ ܟܓܒܝܐ ܐܘܪܚܐ ܠܦܘܬ ܝܗܝ̈ܒܬܐ – ܚܙܝܡܘܢ ܓܘ ܫܪ̈ܛܐ)، ci.auc ܟܝܗܒ ܫܛܝܚܘܬܐ ܘܬܚܘܡܐ ܕܬܘܟܠܢܐ ܕ-DeLong، coords – ܬܚܘܡܐ ܠܦܘܬ Youden ܘܟܠ ܬܚܘ̈ܡܐ، ܘ-roc.test – ܦܘܚܡܐ ܙܘܓܢܝܐ ܕ-DeLong. ܐܗܐ ܦܐܬܐ ܡܫܪܪܐ ܝܠܗ ܩܘܒܠ ܓܪܒܐ: ܫܛܝܚܘܬܐ، ܛܥܝܘܬܐ ܬܩܝܢܬܐ، ܬܚܘܡܐ ܕܬܘܟܠܢܐ، ܟܠ ܢܘܩ̈ܙܐ ܕܣܪܛܐ ܟܦܝܦܐ، ܬܚܘܡܐ ܕ-Youden، ܦܘܚ̈ܡܐ ܘܒܘܚܪܢܐ ܟܠܢܝܐ. ܣܩܪܝܦܬ ܪܗܛܐ ܝܠܗ ܐܝܟ ܕܐܝܠܗ ܥܠ ܦܐܝܠ ܕܡܬܠܐ (ܛܝ̈ܡܐ ܓܘ ܡܥܝܪ̈ܢܘܬܐ).

# ܦܘܫܩܐ ROC – ܦܪܘܦܣܘܪ ܣܛܐܛ. ܐܗܐ ܦܐܝܠ ܢܛܝܪܐ ܝܠܗ ܒ-UTF-8؛ ܟܠ ܣܕܪܐ ܕܡܥܝܪܢܘܬܐ ܟܫܪܐ ܒܡܠܬܐ ܕܣܘܪܝܬ
library(readxl)    # ܩܪܝܢܐ ܕܐܩܣܠ
library(pROC)      # ܣܪ̈ܛܐ ܟܦܝܦ̈ܐ ROC، ܫܛܝܚܘܬܐ، ܬܚܘ̈ܡܐ ܕܬܘܟܠܢܐ ܘܦܘܚܡܐ ܕ-DeLong

# ܛܥܢܐ: ܛܘܦܣܐ ܬܩܝܢܐ – ܣܕܪܐ = ܡܫܬܘܬܦܢܐ، ܥܡܘܕܐ = ܡܫܬܚܠܦܢܐ؛ ܓܠܝܘܢܐ "Data"
d <- read_excel("C:/Rdata/DATA_roc_example_eng.xlsx", sheet = "Data")
v <- c("diagnosis", "screen_long", "screen_short", "wellbeing")
d <- d[complete.cases(d[, v]), ]                        # ܫܩܠܬܐ ܕܣܕܪܐ ܟܠܗ: 218 ܡܢ 220 – ܐܢܝ ܡܫܬܘܬܦ̈ܢܐ ܩܐ ܟܠ ܣܪ̈ܛܐ ܟܦܝܦ̈ܐ

# ܣܪܛܐ ܟܦܝܦܐ ܩܐ ܟܠ ܡܚܘܝܢܐ؛ levels = c(ܕܒܨܪܐ، ܕܙܘܕܐ)؛ direction "<" – ܛܝܡܐ ܪܡܐ ܟܡܣܗܕ ܥܠ ܗܘܝܐ، ">" – ܛܝܡܐ ܬܚܬܝܐ
r_long  <- roc(d$diagnosis, d$screen_long,  levels = c(0, 1), direction = "<")
r_short <- roc(d$diagnosis, d$screen_short, levels = c(0, 1), direction = "<")
r_well  <- roc(d$diagnosis, d$wellbeing,    levels = c(0, 1), direction = ">")

# ܫܛܝܚܘܬܐ ܘܬܚܘܡܐ ܕܬܘܟܠܢܐ ܕ-DeLong
ci.auc(r_long); ci.auc(r_short); ci.auc(r_well)       # ܫܛܝܚܘܬܐ: .817 [.757, .876]; .762 [.693, .831]; .677 [.596, .759]
sqrt(var(r_long))                                      # ܛܥܝܘܬܐ ܬܩܝܢܬܐ (DeLong): .030

# ܬܚܘܡܐ ܠܦܘܬ Youden، ܘܡܘܕܝ ܟܗܘܐ ܓܘܗ
coords(r_long, "best", best.method = "youden",
       ret = c("threshold", "sensitivity", "specificity", "ppv", "npv"))   # ܬܚܘܡܐ 10.5: ܪܓܝܫܘܬܐ .875، ܝܚܝܕܝܘܬܐ .676
binom.test(42, 48)$conf.int                            # ܬܚܘܡܐ ܕܬܘܟܠܢܐ ܚܬܝܬܐ ܩܐ ܪܓܝܫܘܬܐ ܓܘ ܬܚܘܡܐ: [.748, .953]
coords(r_long, "all", transpose = FALSE)               # ܟܠ ܬܚܘ̈ܡܐ

# ܦܘܚܡܐ ܙܘܓܢܝܐ ܕܫܛܝ̈ܚܘܬܐ (ܐܢܝ ܡܫܬܘܬܦ̈ܢܐ) – DeLong
roc.test(r_long, r_short, method = "delong", paired = TRUE)   # ܦܘܪܫܢܐ .055 [.007, .103], z = 2.25, p = .025
# ܫܝܢܐ ܕܢܦܫܐ ܒܐܘܪܚܐ ܗܘܦܟܐ: ܦܘܚܡܐ ܥܠ ܡܫܬܚܠܦܢܐ ܒܗܘܦܟܐ ܕܪܘܫܡܐ، ܩܐ ܕܟܠ ܣܪ̈ܛܐ ܟܦܝܦ̈ܐ ܗܘܝ ܒܐܗܘ ܐܘܪܚܐ (DeLong et al., 1988، ܦܐܬܐ 842)
r_well2 <- roc(d$diagnosis, -d$wellbeing, levels = c(0, 1), direction = "<")
roc.test(r_long, r_well2, method = "delong", paired = TRUE)   # ܦܘܪܫܢܐ .140 [.062, .217], z = 3.54, p < .001

# ܨܘܪܬܐ
plot(r_long, legacy.axes = TRUE, print.auc = TRUE)
lines(r_short, col = "darkorange"); lines(r_well, col = "darkgreen")

ܬܘܢܝܐ ܕܡܫܟܚ̈ܢܘܬܐ (reporting the results)

ܟܡܬܢܚ ܬܩܢܐ ܕܕܗܒܐ ܘܡܢܝܢܐ ܕܡܫܬܘܬܦ̈ܢܐ ܓܘ ܟܠ ܓܘܕܐ؛ ܩܐ ܟܠ ܡܚܘܝܢܐ – ܐܘܪܚܐ، ܫܛܝܚܘܬܐ ܘܬܚܘܡܐ ܕܬܘܟܠܢܐ (ܘܐܝܢܐ)؛ ܬܚܘܡܐ ܕܦܘܪܫܐ ܘܐܝܟܢܐ ܓܒܝܐ ܝܠܗ – ܡܢ ܩܕܡ ܡܢ ܣܦܪ̈ܘܬܐ ܝܢ ܥܠ ܝܗܝ̈ܒܬܐ – ܥܡ ܪܓܝܫܘܬܐ ܘܝܚܝܕܝܘܬܐ ܘܬܚܘ̈ܡܐ ܕܬܘܟܠܢܐ ܕܝܠܗܝܢ؛ ܛܝ̈ܡܐ ܡܢܒ̈ܝܢܐ ܒܣ ܥܡ ܣܓܝܐܘܬܐ ܕܓܘܗ ܚܫܝܒ̈ܐ ܝܢܐ؛ ܘܓܘ ܦܘܚܡܐ – ܒܘܚܪܢܐ (DeLong، ܙܘܓܢܝܐ)، ܦܘܪܫܢܐ ܘܬܚܘܡܐ ܕܬܘܟܠܢܐ ܕܝܠܗ. ܡܢܝ̈ܢܐ ܒܨܘܪܬܐ ܕ-APA: ܕܠܐ ܨܦܪܐ ܩܕܡ ܢܘܩܙܐ ܓܘ ܫܛܝܚܘܬܐ، ܓܘ ܪܓܝܫܘܬܐ ܘܓܘ ܝܚܝܕܝܘܬܐ، ܕܠܐ ܡܨܝܐ ܕܥܒܪܝ ܡܢ 1 (APA, 2020, Section 6.36)، ܘ-p ܒܬܠܬܐ ܡܢܝ̈ܢܐ. ܦܣܩܐ ܕܐܗܐ ܦܐܬܐ ܟܡܦܩܐ ܢܘܩܙܐ ܕܫܘܪܝܐ ܝܠܗ – ܟܡܫܠܡܚ ܓܘܗ ܣܝܩܐ ܘܣܘܟܠܐ.

ܛܥܝ̈ܘܬܐ ܕܡܬܚܙܝܢ ܣܓܝ (Common mistakes)

ܡܬܢܝܐ ܕܫܛܝܚܘܬܐ ܒܠܚܘܕ. ܫܛܝܚܘܬܐ ܕ-.82 ܟܥܒܕܐ ܡܨܥܝܬܐ ܥܠ ܟܠ ܬܚܘ̈ܡܐ، ܥܡ ܐܢܝ ܕܚܕ ܠܐ ܒܕ ܡܦܠܚ ܠܗܘܢ (Pepe, 2003, pp. 78-79; Fawcett, 2006, p. 868)، ܘܡܐ ܕܟܦܣܩܚ ܥܠܝܗ ܒܫܪܪܐ ܬܚܘܡܐ ܝܠܗ. ܟܡܬܢܚ ܫܛܝܚܘܬܐ، ܣܪܛܐ ܟܦܝܦܐ، ܘܪܓܝܫܘܬܐ ܘܝܚܝܕܝܘܬܐ ܓܘ ܬܚܘܡܐ. ܘܗܘܦܟܐ – ܡܬܢܝܐ ܕܚܕ ܢܘܩܙܐ ܒܠܚܘܕ: ܬܘܢܝܐ ܕܪܓܝܫܘܬܐ ܘܝܚܝܕܝܘܬܐ ܓܘ ܚܕ ܬܚܘܡܐ ܝܚܝܕܝܐ "ܟܪܝܐ ܝܠܗ ܓܠܝܐܝܬ" (Pepe, 2003, p. 71).

ܡܬܢܝܐ ܕܚܬܝܬܘܬܐ ܟܠܢܝܬܐ ܒܕܘܟܬ ܪܓܝܫܘܬܐ ܘܝܚܝܕܝܘܬܐ – ܓܘ ܗܘܝܐ ܕܠܐ ܡܬܚܙܐ ܣܓܝ ܪܡܬܐ ܝܠܗ ܐܦ ܩܐ ܒܘܚܪܢܐ ܕܠܐ ܛܝܡܐ (Pepe, 2003, p. 15).

ܡܬܢܝܐ ܕܛܝܡܐ ܡܢܒܝܢܐ ܕܙܘܕܐ ܡܢ ܕܘܡܝܐ ܕܡܫܬܘܬܦ̈ܢܐ ܥܡ ܗܘܝܐ ܘܡܫܬܘܬܦ̈ܢܐ ܕܦܘܚܡܐ ܐܝܟ ܕܐܝܠܗ ܩܐ ܟܢܫܐ ܟܠܢܝܐ – ܡܢܦܚܐ ܝܠܗ (Pepe, 2003, p. 25).

ܡܚܘܝܐ ܕܬܚܘܡܐ ܕ-Youden ܐܝܟ "ܬܚܘܡܐ ܛܒܐ ܡܢ ܟܠܗ" – ܛܒܐ ܡܢ ܟܠܗ ܝܠܗ ܒܣ ܐܝܡܢ ܕܩܐ ܬܪܬܝܢ ܛܥܝ̈ܘܬܐ ܐܝܬ ܐܗܘ ܛܝܡܐ، ܘܒܣ ܓܘ ܕܘܡܝܐ ܕܓܘܗ ܡܫܟܚܐ ܝܠܗ.

ܦܘܚܡܐ ܕܫܛܝ̈ܚܘܬܐ ܕܡܚܘ̈ܝܢܐ ܕܡܫܝܚ̈ܐ ܝܢܐ ܥܠ ܐܢܝ ܡܫܬܘܬܦ̈ܢܐ ܒܒܘܚܪܢܐ ܩܐ ܓܘ̈ܕܐ ܠܐ ܬܠܝ̈ܐ، ܝܢ ܠܦܘܬ ܚܠܛܘܬܐ ܕܬܚܘ̈ܡܐ ܕܬܘܟܠܢܐ – ܦܘܚܡܐ ܬܪܝܨܐ ܙܘܓܢܝܐ ܝܠܗ (DeLong et al., 1988).

ܫܒܩܬܐ ܠܦܪܘܓܪܡܐ ܕܓܒܝܐ ܐܘܪܚܐ – ܘܡܬܢܝܐ ܕ"AUC = .58" ܩܐ ܡܚܘܝܢܐ ܕܒܫܪܪܐ ܟܡܢܒܐ ܗܘܦܟܐ ܡܢ ܡܐ ܕܬܘܩܢܐ ܝܠܗ، ܝܢ ܕܠܐ ܟܡܢܒܐ ܡܕܡ.

ܓܘܒܝܐ ܕܬܚܘܡܐ، ܘܒܬܪܗ "ܫܘܪܪܐ" ܕܝܠܗ ܥܠ ܐܢܝ ܝܗܝ̈ܒܬܐ – ܕܠܐ ܕܘܡܝܐ ܐܚܪܢܐ، ܡܢܝ̈ܢܐ ܓܘ ܬܚܘܡܐ ܡܣܒܪ̈ܢܐ ܝܢܐ.

ܡܒܘ̈ܥܐ

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

DeLong, E. R., DeLong, D. M., & Clarke-Pearson, D. L. (1988). Comparing the areas under two or more correlated receiver operating characteristic curves: A nonparametric approach. Biometrics, 44(3), 837-845. https://doi.org/10.2307/2531595

Fawcett, T. (2006). An introduction to ROC analysis. Pattern Recognition Letters, 27(8), 861-874. https://doi.org/10.1016/j.patrec.2005.10.010

Hanley, J. A., & McNeil, B. J. (1982). The meaning and use of the area under a receiver operating characteristic (ROC) curve. Radiology, 143(1), 29-36. https://doi.org/10.1148/radiology.143.1.7063747

Pepe, M. S. (2003). The statistical evaluation of medical tests for classification and prediction. Oxford University Press.

Hand ܘ-Till (2001) ܘ-Flach ܘ-Wu (2003) – ܐܝܟ ܕܡܬܦܪܣܝ ܓܘ Fawcett (2006)؛ Obuchowski ܘ-Lieber (2002) – ܐܝܟ ܕܡܬܦܪܣܝ ܓܘ Pepe (2003). ܠܦܘܬ ܢܡܘܣܐ ܕܣܐܝܛ، ܓܘ ܪܫܝܡܬܐ ܕܡܒܘ̈ܥܐ ܒܣ ܡܒܘ̈ܥܐ ܕܩܪܝ̈ܐ ܝܢܐ ܓܘ ܡܒܘܥܐ ܟܡܬܚܙܝ؛ ܡܬܦܪ̈ܣܢܘܬܐ ܠܦܘܬ ܦܐܬܐ ܛܒܝܥܬܐ. ܚܘܫܒܢܐ ܓܘ ܐܗܐ ܦܐܬܐ ܡܫܪܪܐ ܝܠܗ ܩܘܒܠ R 4.3.3 ܘܓܪܒܐ pROC 1.18.5 (roc، ci.auc، coords، roc.test، cov)، ܩܘܒܠ binom.test، ܘܩܘܒܠ ܦܘܩܕܢܐ ROC ܕ-PSPP 2.0؛ ܘܩܘܒܠ ܡܢܝ̈ܢܐ ܕܓܘ ܡܒܘ̈ܥܐ – 0.893 ܘܛܥܝܘܬܐ ܬܩܝܢܬܐ 0.032 ܓܘ ܠܘܚܐ II ܕ-Hanley ܘ-McNeil (1982، ܦܐܬܐ 31).