ꯔꯨꯂꯦꯠ ꯂꯦꯕ · ꯂꯦꯕ · ꯁ꯭ꯇꯦꯇꯤꯁ꯭ꯇꯤꯛꯁ · ꯃꯤꯅꯤꯠ 8

ꯀꯥꯏ-ꯁ꯭ꯀ꯭ꯋꯦꯌꯔ ꯇꯦꯁ꯭ꯠ

“ꯃꯁꯤꯡ 37 ꯑꯁꯤ ꯆꯨꯝꯃꯤꯟꯅꯕ ꯆꯛꯔ ꯑꯃꯅ ꯄꯨꯊꯣꯛꯀꯗꯕ ꯑꯗꯨꯅꯤ ꯔꯥ?” ꯍꯥꯌꯕꯒꯤ ꯃꯥꯏꯄꯥꯀꯄꯒꯤ ꯇꯦꯁ꯭ꯠ꯫

ꯊꯨꯅ ꯄꯥꯎꯈꯨꯝ

ꯄꯣꯀꯦꯠ 37 ꯄꯨꯝꯅꯃꯛꯇ χ² = Σ (ꯎꯈꯤꯕ − ꯐꯪꯒꯗꯕ)² / ꯐꯪꯒꯗꯕ꯫ p-ꯚꯦꯜꯌꯨ ꯑꯃꯥ ꯐꯪꯅꯕ ꯃꯁꯤꯕꯨ ꯗꯤꯒ꯭ꯔꯤ ꯑꯣꯐ ꯐ꯭ꯔꯤꯗꯝ 36 ꯒꯤ ꯀꯥꯏ-ꯁ꯭ꯀ꯭ꯋꯦꯌꯔ ꯗꯤꯁ꯭ꯇ꯭ꯔꯤꯕ꯭ꯌꯨꯁꯅꯒꯥ ꯆꯥꯡꯗꯝꯕꯤꯌꯨ꯫

ꯁ꯭ꯇꯦꯇꯤꯁ꯭ꯇꯤꯛ
Σ (O−E)²/E
df
36
5% ꯗ ꯀ꯭ꯔꯤꯇꯤꯀꯦꯜ
51.0
1% ꯗ ꯀ꯭ꯔꯤꯇꯤꯀꯦꯜ
58.6

ꯃꯁꯤ ꯊꯤꯕ

ꯄꯣꯀꯦꯠꯈꯨꯠꯂꯥꯏꯄꯣꯀꯦꯠꯔꯣꯇꯔꯗ ꯂꯩꯕ ꯃꯁꯤꯡ ꯏꯔꯕ ꯀꯣꯠ 37 ꯒꯤ ꯃꯅꯨꯡꯗ ꯑꯃꯥ꯫ ꯑꯇꯣꯞꯄ ꯃꯃꯤꯡ: ꯁ꯭ꯂꯣꯠ, ꯀꯞ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯈꯨꯗꯤꯡꯒꯤ ꯐꯪꯒꯗꯕ ꯃꯁꯤꯡ ꯑꯗꯨ n/37 ꯅꯤ꯫ ꯄꯣꯀꯦꯠ ꯈꯨꯗꯤꯡꯃꯛꯀꯤꯗꯃꯛ ꯎꯈꯤꯕ ꯑꯃꯁꯨꯡ ꯐꯪꯒꯗꯕꯒꯤ ꯈꯦꯠꯅꯕ ꯑꯗꯨ ꯁ꯭ꯀ꯭ꯋꯦꯌꯔ ꯇꯧꯕꯤꯌꯨ ꯑꯃꯁꯨꯡ ꯐꯪꯒꯗꯕꯅ ꯈꯥꯌꯕꯤꯌꯨ; ꯁꯔꯨꯛ 37 ꯑꯗꯨ ꯄꯨꯟꯁꯤꯟꯕꯤꯌꯨ꯫ ꯆꯨꯝꯃꯤꯟꯅꯕ ꯆꯛꯔ ꯑꯃꯅ ꯑꯦꯚꯔꯦꯖꯗ 36 ꯃꯇꯧꯒꯤ ꯚꯦꯜꯌꯨꯁꯤꯡ ꯄꯤ (ꯗꯤꯒ꯭ꯔꯤ ꯑꯣꯐ ꯐ꯭ꯔꯤꯗꯝꯂꯦꯕꯗꯤꯒ꯭ꯔꯤ ꯑꯣꯐ ꯐ꯭ꯔꯤꯗꯝꯁ꯭ꯇꯦꯇꯤꯁ꯭ꯇꯤꯛ ꯑꯃꯗ ꯃꯔꯤ ꯂꯩꯅꯗꯕ ꯚꯦꯂꯨꯁꯤꯡꯒꯤ ꯃꯁꯤꯡ꯫ ꯄꯣꯀꯦꯠ 37 ꯒꯤ ꯀꯥꯏ-ꯁ꯭ꯀ꯭ꯋꯦꯌꯔ ꯇꯦꯁ꯭ꯠ ꯑꯃꯗ ꯃꯁꯤ 36 ꯅꯤ, ꯃꯔꯃꯗꯤ ꯊꯤꯕ ꯃꯁꯤꯡꯁꯤꯡ ꯄꯨꯟꯁꯤꯟꯂꯕꯗ ꯃꯄꯨꯡ ꯑꯗꯨ ꯑꯣꯏꯒꯗꯕꯅꯤ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ →), ꯁ꯭ꯇꯦꯟꯗꯔꯗ ꯗꯤꯚꯤꯌꯦꯁꯟꯃꯦꯊꯃꯦꯇꯤꯛꯁꯁ꯭ꯇꯦꯟꯗꯔꯗ ꯗꯤꯚꯤꯌꯦꯁꯟꯚꯦꯌꯔꯤꯌꯦꯟꯁꯀꯤ ꯁ꯭ꯀ꯭ꯋꯦꯌꯔ ꯔꯨꯠ; ꯃꯍꯩ ꯑꯃꯅ ꯐꯪꯒꯗꯕ ꯃꯃꯜꯗꯒꯤ ꯌꯥꯝꯅ ꯂꯥꯞꯄ ꯃꯑꯣꯡ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯈꯔꯥ 8.5꯫ 51.0 ꯗꯒꯤ ꯍꯦꯟꯕ ꯑꯁꯤ 5% ꯂꯦꯚꯦꯂꯗ ꯃꯔꯨꯑꯣꯏ; 58.6 ꯗꯒꯤ ꯍꯦꯟꯕ ꯑꯁꯤ 1% ꯗ꯫ ꯍꯨꯏꯜ ꯕꯥꯏꯌꯥꯁ ꯑꯦꯅꯥꯂꯥꯏꯖꯔꯅ ꯔꯦꯒ꯭ꯌꯨꯂꯥꯔꯥꯏꯖ ꯇꯧꯔꯕ ꯏꯟꯀꯝꯞ꯭ꯂꯤꯠ ꯒꯥꯃꯥ ꯐꯉ꯭ꯀꯁꯅꯗꯒꯤ ꯁ꯭ꯇꯦꯇꯤꯁ꯭ꯇꯤꯛ ꯑꯃꯁꯨꯡ ꯆꯨꯝꯕ p-ꯚꯦꯜꯌꯨꯂꯦꯕp-ꯚꯦꯜꯌꯨꯆꯛꯔ ꯑꯗꯨ ꯆꯨꯝꯃꯤꯟꯅꯔꯕꯗꯤ ꯎꯈꯤꯕ ꯑꯗꯨꯗꯒꯤ ꯍꯟꯊꯗꯕ ꯂꯥꯞꯊꯣꯛꯄ ꯑꯃꯥ ꯎꯕꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯑꯗꯨ ꯊꯤ꯫

ꯁ꯭ꯄꯤꯟ nꯄꯣꯀꯦꯠ ꯈꯨꯗꯤꯡꯗ ꯐꯪꯒꯗꯕꯄꯣꯀꯦꯠ ꯈꯨꯗꯤꯡꯒꯤ σ+2σ ꯗ ꯂꯩꯕ ꯄꯣꯀꯦꯠ+3σ ꯗ ꯂꯩꯕ ꯄꯣꯀꯦꯠ
370103.11619
1,000275.13742
3,7001009.9120130
10,00027016.2303319
37,0001,00031.21,0621,094
σ ≈ √(n·p·(1−p)), p = 1/37꯫ ꯁ꯭ꯄꯤꯟ 1,000 ꯗ ꯂꯥꯀꯄ 37 ꯂꯩꯕ ꯄꯣꯀꯦꯠ ꯑꯃꯥ ꯑꯈꯟꯅꯕ ꯅꯠꯇꯦ; 42 ꯂꯩꯕ ꯑꯃꯒꯤꯗꯃꯛ ꯑꯅꯤꯁꯨꯕ ꯁꯦꯝꯄꯜ ꯑꯃꯒꯤ ꯃꯃꯜ ꯂꯩ꯫

ꯊꯤꯔꯕ ꯈꯨꯗꯝ ꯑꯃꯥ

ꯁ꯭ꯄꯤꯟ 1,000꯫ ꯄꯣꯀꯦꯠ ꯀꯨꯟꯊꯔꯥꯇꯔꯨꯛ ꯑꯁꯤ ꯂꯥꯀꯄ 20 ꯗꯒꯤ 34 ꯒꯤ ꯃꯔꯛꯇ ꯂꯩ; ꯄꯣꯀꯦꯠ 8 ꯗ 41 ꯂꯩ꯫ ꯐꯪꯒꯗꯕꯗꯤ 27.03 ꯅꯤ꯫ ꯄꯣꯀꯦꯠ 8 ꯒꯤ ꯁꯔꯨꯛ ꯈꯛꯇꯗꯤ (41 − 27.03)²/27.03 = 7.2꯫ ꯑꯇꯣꯞꯄ ꯁꯔꯨꯛ 36 ꯑꯗꯨꯒꯤ ꯄꯨꯟꯁꯤꯟꯕ 38 (ꯃꯇꯝ ꯌꯥꯝꯅ ꯎꯕ) ꯍꯥꯌꯅ ꯂꯧꯁꯤ꯫ df 36 ꯗ χ² = 45.2, p ≈ 0.14꯫ ꯃꯔꯨꯑꯣꯏꯗꯦ: ꯆꯨꯝꯃꯤꯟꯅꯕ ꯆꯛꯔ ꯑꯃꯅ ꯑꯃꯨꯛ ꯇꯔꯦꯠꯇ ꯑꯃꯨꯛ ꯃꯁꯤ ꯇꯧꯏ꯫ ꯄꯣꯀꯦꯠ 8 ꯑꯁꯤ ꯌꯦꯡꯁꯤꯟꯒꯗꯕ ꯑꯃꯅꯤ, ꯊꯤꯗꯣꯛꯄ ꯑꯃꯥ ꯅꯠꯇꯦ, ꯑꯃꯁꯨꯡ ꯄꯥꯎꯈꯨꯝ ꯑꯗꯨꯗꯤ ꯍꯦꯟꯅꯥ ꯁ꯭ꯄꯤꯟ ꯂꯤꯁꯤꯡ ꯑꯃꯅꯤ꯫

ꯂꯧꯁꯤꯡꯁꯤꯡ

ꯃꯔꯤ ꯂꯩꯅꯗꯕ ꯁ꯭ꯄꯤꯟꯁꯤꯡꯃꯦꯊꯃꯦꯇꯤꯛꯁꯃꯔꯤ ꯂꯩꯅꯗꯕ ꯁ꯭ꯄꯤꯟꯁꯤꯡꯍꯥꯟꯅꯒꯤ ꯃꯍꯩ ꯀꯔꯤꯒꯨꯝꯕ ꯑꯣꯏꯔꯕꯁꯨ ꯁ꯭ꯄꯤꯟ ꯈꯨꯗꯤꯡꯃꯛꯀꯤ ꯊꯣꯛꯄꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕ ꯃꯥꯟꯅꯩ꯫ ꯋꯦꯕꯁꯥꯏꯠ ꯑꯁꯤꯒꯤ ꯊꯤꯕ ꯈꯨꯗꯤꯡꯃꯛꯀꯤ ꯌꯨꯝꯐꯝꯅꯤ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ →, ꯑꯃꯁꯨꯡ ꯄꯣꯀꯦꯠ ꯈꯨꯗꯤꯡꯗ ꯈ꯭ꯕꯥꯏꯗꯒꯤ ꯅꯦꯝꯕꯗ 5 ꯐꯪꯒꯗꯕ ꯃꯁꯤꯡ, ꯃꯁꯤꯒꯤ ꯑꯔꯊꯗꯤ ꯇꯦꯁ꯭ꯠ ꯑꯁꯤ ꯆꯨꯝꯅꯕꯒꯤꯗꯃꯛ n ≥ 185 ꯑꯣꯏꯒꯗꯕꯅꯤ ꯑꯃꯁꯨꯡ ꯀꯥꯟꯅꯕ ꯂꯩꯅꯕꯒꯤꯗꯃꯛ ꯌꯥꯝꯅ ꯍꯦꯟꯅꯥ꯫ ꯆꯛꯔ ꯀꯌꯥꯒꯤ ꯁ꯭ꯄꯤꯟꯁꯤꯡ ꯄꯨꯟꯁꯤꯟꯕꯅ ꯑꯍꯥꯅꯕ ꯂꯧꯁꯤꯡ ꯑꯗꯨꯒꯤ ꯊꯋꯥꯌꯗ ꯊꯨꯒꯥꯏ (ꯅꯍꯥꯛꯅ ꯆꯛꯔ ꯑꯃꯥ ꯅꯠꯇꯅ ꯌꯥꯎꯃꯤꯟꯅꯕ ꯑꯃꯥ ꯇꯦꯁ꯭ꯠ ꯇꯧꯔꯤ)꯫ ꯗꯤꯂꯔꯒꯤ ꯁꯥꯏꯅꯦꯆꯔꯒꯤ ꯊꯧꯒꯜ ꯑꯃꯅ ꯃꯁꯤ ꯑꯁꯦꯡꯕꯗ ꯊꯨꯒꯥꯏꯒꯅꯤ, ꯑꯃꯁꯨꯡ ꯍꯛꯆꯥꯡꯒꯤ ꯃꯑꯣꯡꯗ ꯄꯣꯀꯦꯠ ꯑꯃꯠꯇ ꯍꯦꯟꯅꯥ ꯂꯥꯀꯍꯟꯗꯅ χ² ꯍꯦꯅꯒꯠꯍꯅꯒꯅꯤ꯫

ꯔꯨꯂꯦꯠ ꯗꯤꯂꯔꯒꯤ ꯁꯥꯏꯅꯦꯆꯔꯃꯔꯤ ꯂꯩꯅꯗꯕ ꯔꯨꯂꯦꯠ ꯁ꯭ꯄꯤꯟꯁꯤꯡ

ꯄꯤꯌꯔꯁꯟ ꯑꯃꯁꯨꯡ ꯃꯣꯟꯇꯦ ꯀꯥꯔꯂꯣ

ꯀꯥꯔꯜ ꯄꯤꯌꯔꯁꯟ (Karl Pearson) ꯅ 1900 ꯗ ꯇꯦꯁ꯭ꯠ ꯑꯁꯤ ꯐꯣꯡꯗꯣꯀꯈꯤ, ꯑꯃꯁꯨꯡ ꯃꯍꯥꯛꯀꯤ ꯑꯍꯥꯅꯕ ꯊꯤꯔꯕ ꯈꯨꯗꯃꯁꯤꯡꯒꯤ ꯃꯅꯨꯡꯗ ꯑꯃꯗꯤ ꯏꯔꯝꯕ ꯃꯣꯟꯇꯦ ꯀꯥꯔꯂꯣ ꯔꯨꯂꯦꯠ ꯁ꯭ꯄꯤꯟ 26,306 ꯅꯤ, ꯃꯈꯣꯌ ꯑꯁꯤ ꯂꯥꯀꯏꯕ ꯑꯣꯏꯅꯕ ꯌꯥꯝꯅ ꯃꯥꯟꯅꯗꯕꯅꯤ ꯍꯥꯌꯅ ꯃꯍꯥꯛꯅ ꯐꯪꯈꯤ ꯑꯃꯁꯨꯡ “ꯃꯣꯟꯇꯦ ꯀꯥꯔꯂꯣꯒꯤ ꯔꯨꯂꯦꯠ… ꯂꯥꯀꯏꯕꯒꯤ ꯁꯥꯟꯅꯕ ꯑꯃꯥ ꯅꯠꯇꯦ” ꯍꯥꯌꯅ ꯂꯥꯑꯣꯊꯣꯀꯈꯤ꯫ ꯃꯇꯨꯡꯒꯤ ꯏꯕꯥ ꯃꯤꯁꯤꯡꯅ ꯄꯤꯔꯤꯡ ꯑꯃꯒꯤꯗꯃꯛ ꯁ꯭ꯄꯤꯟꯁꯤꯡ ꯏꯈꯤꯕ ꯖꯔꯅꯥꯂꯤꯁ꯭ꯇꯁꯤꯡꯅ ꯃꯈꯣꯌꯒꯤ ꯀꯌꯥ ꯁꯦꯝꯖꯤꯟꯈꯤ ꯍꯥꯌꯅ ꯂꯦꯞꯈꯤ, ꯃꯁꯤ ꯗꯦꯇꯥ ꯀꯗꯥꯏꯗꯒꯤ ꯂꯥꯀꯈꯤꯕꯅꯣ ꯍꯥꯌꯕꯒꯤ ꯃꯇꯥꯡꯗ ꯃꯁꯥꯒꯤ ꯇꯝꯕꯤꯕ ꯑꯃꯅꯤ꯫

ꯇꯦꯁ꯭ꯠ ꯑꯃꯁꯨꯡ ꯆꯛꯔ
1900

ꯄꯤꯌꯔꯁꯅꯅ ꯃꯣꯟꯇꯦ ꯀꯥꯔꯂꯣꯒꯤ ꯁ꯭ꯄꯤꯟꯁꯤꯡ ꯈꯨꯗꯝ ꯑꯣꯏꯅ ꯂꯧꯗꯨꯅ ꯀꯥꯏ-ꯁ꯭ꯀ꯭ꯋꯦꯌꯔ ꯒꯨꯗꯅꯦꯁ-ꯑꯣꯐ-ꯐꯤꯠ ꯇꯦꯁ꯭ꯠ ꯐꯣꯡꯗꯣꯀꯏ꯫

1900 ꯁꯨꯕ

ꯁ꯭ꯄꯤꯟꯒꯤ ꯗꯦꯇꯥꯗ ꯆꯤꯡꯅꯕ ꯄꯣꯛꯂꯀꯏ; ꯏꯕꯥ ꯃꯤꯁꯤꯡꯅ ꯁ꯭ꯇ꯭ꯔꯤꯛꯁꯤꯡ ꯁꯦꯝꯖꯤꯟꯈꯤꯕꯥ ꯃꯑꯣꯡ ꯎꯏ꯫

1920 ꯁꯨꯕ

ꯐꯤꯁꯔꯅ ꯗꯤꯒ꯭ꯔꯤ ꯑꯣꯐ ꯐ꯭ꯔꯤꯗꯝ ꯃꯑꯣꯡ ꯃꯇꯧ ꯂꯩꯅ ꯁꯦꯝꯃꯤ; 5% ꯒꯤ ꯆꯠꯅꯕꯤ ꯑꯗꯨ ꯂꯦꯞꯂꯛꯏ꯫

1940–50 ꯁꯨꯕ

ꯁ꯭ꯇꯦꯇꯤꯁ꯭ꯇꯤꯁꯤꯌꯥꯅꯁꯤꯡꯅ ꯃꯥꯟꯅꯕꯒꯤ ꯇꯦꯁ꯭ꯇꯁꯤꯡꯒꯤꯗꯃꯛ ꯔꯨꯂꯦꯠ ꯁ꯭ꯄꯤꯟꯁꯤꯡ ꯂꯥꯏꯔꯤꯀꯀꯤ ꯗꯦꯇꯥ ꯑꯣꯏꯅ ꯁꯤꯖꯤꯟꯅꯩ꯫

1990 ꯁꯨꯕ

ꯒꯥꯔꯁꯤꯌꯥ-ꯄꯦꯂꯥꯌꯣ ꯏꯃꯨꯡꯅ ꯑꯁꯦꯡꯕ ꯏꯈꯤꯕ ꯗꯦꯇꯥꯒꯥ ꯂꯣꯌꯅꯅ ꯃꯑꯣꯡ ꯑꯁꯤ ꯁꯤꯖꯤꯟꯅꯩ ꯑꯃꯁꯨꯡ ꯃꯥꯗ꯭ꯔꯤꯗꯇ ꯃꯥꯏꯄꯥꯀꯏ꯫

ꯉꯁꯤ

ꯀꯦꯁꯤꯅꯣꯁꯤꯡꯅ ꯃꯈꯣꯌꯒꯤ ꯆꯛꯔꯁꯤꯡꯗ ꯃꯇꯝ ꯃꯇꯝꯒꯤ ꯌꯦꯡꯁꯤꯟꯕꯒꯤ ꯃꯅꯨꯡꯗ ꯇꯦꯁ꯭ꯠ ꯑꯗꯨꯃꯛ ꯆꯂꯥꯏ꯫

ꯄꯤꯌꯔꯁꯅꯒꯤ 1900 ꯒꯤ ꯇꯦꯁ꯭ꯇꯅ ꯃꯣꯟꯇꯦ ꯀꯥꯔꯂꯣꯒꯤ ꯁ꯭ꯄꯤꯟꯁꯤꯡ ꯌꯥꯝꯅ ꯃꯥꯟꯅꯗꯕꯅꯤ ꯍꯥꯌꯅ ꯐꯪꯈꯤ; ꯄꯤꯔꯤꯡꯒꯤ ꯏꯕꯥ ꯃꯤꯁꯤꯡꯅ ꯃꯈꯣꯌꯒꯤ ꯀꯌꯥ ꯁꯦꯝꯖꯤꯟꯈꯤ꯫

ꯃꯣꯟꯇꯦ ꯀꯥꯔꯂꯣ ꯔꯨꯂꯦꯠ

ꯑꯁꯦꯡꯕ ꯇꯦꯁ꯭ꯠ ꯑꯃꯥ: ꯂꯥꯁ ꯚꯦꯒꯥꯁꯇ ꯑꯣꯇꯣꯃꯦꯇꯤꯛ ꯆꯛꯔꯁꯤꯡ

ꯁꯥꯟꯅꯔꯤꯕꯁꯤꯡꯅ ꯃꯇꯝ ꯌꯥꯝꯅ ꯑꯣꯇꯣꯃꯦꯇꯤꯛ ꯆꯛꯔ ꯑꯃꯅ ꯕꯣꯜꯈꯨꯠꯂꯥꯏꯕꯣꯜꯔꯣꯇꯔꯒꯤ ꯃꯥꯌꯣꯛꯇ ꯇ꯭ꯔꯦꯛꯇ ꯊꯥꯗꯣꯛꯄ ꯑꯄꯤꯛꯄ ꯕꯣꯜ꯫ ꯍꯧꯖꯤꯛꯀꯤ ꯕꯣꯜꯁꯤꯡ ꯑꯥꯏꯚꯣꯔꯤꯟ ꯅꯠꯔꯒ ꯇꯦꯐ꯭ꯂꯣꯅꯅ ꯁꯦꯝꯃꯤ, 18–21 mm꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯑꯗꯨ ꯑꯆꯧꯕ ꯕꯦꯠꯁꯤꯡꯗꯒꯤ ꯂꯥꯞꯅ ꯆꯠꯍꯜꯂꯤ ꯍꯥꯌꯅ ꯆꯤꯡꯅꯩ꯫ 2017 ꯒꯤ ꯑꯦꯅꯥꯂꯥꯏꯁꯤꯁ ꯑꯃꯅ ꯂꯥꯁ ꯚꯦꯒꯥꯁꯇ ꯂꯩꯕ ꯏꯟꯇꯔꯕ꯭ꯂꯣꯛ (Interblock) ꯀꯤ ꯗꯤꯂꯔ ꯂꯩꯇꯕ ꯗꯕꯜ ꯖꯤꯔꯣꯆꯛꯔꯖꯤꯔꯣꯆꯞ ꯃꯥꯟꯅꯕ, ꯗꯖꯟ ꯅꯠꯔꯒ ꯀꯂꯝ ꯕꯦꯠ ꯑꯃꯠꯇꯅ ꯀꯨꯞꯇꯕ ꯑꯁꯪꯕ ꯄꯣꯀꯦꯠ ꯑꯃꯈꯛꯇ; ꯍꯥꯎꯁ ꯑꯦꯖꯀꯤ ꯍꯧꯔꯀꯐꯝꯅꯤ꯫ ꯑꯇꯣꯞꯄ ꯃꯃꯤꯡ: ꯁꯤꯡꯒꯜ ꯖꯤꯔꯣ, 0꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯆꯛꯔꯁꯤꯡꯗ ꯆꯤꯡꯅꯕ ꯑꯁꯤ ꯇꯦꯁ꯭ꯠ ꯇꯧꯈꯤ, ꯌꯨꯝꯂꯣꯟꯅꯕ ꯃꯁꯤꯡ ꯃꯉꯥꯒꯤ ꯁꯔꯨꯛ ꯑꯃꯗ ꯕꯦꯠ ꯊꯃꯗꯨꯅ, ꯍꯨꯏꯜ ꯀ꯭ꯂꯣꯀꯔ ꯑꯃꯅ ꯊꯝꯕ ꯃꯈꯂꯒꯤ ꯕꯦꯠ꯫ ꯁ꯭ꯄꯤꯟ 299 ꯗ ꯁꯔꯨꯛ ꯑꯗꯨ 39.3 ꯐꯪꯒꯗꯕꯒꯤ ꯃꯍꯨꯠꯇ ꯑꯃꯨꯛ 29 ꯃꯥꯏꯄꯥꯀꯈꯤ, ꯆꯨꯝꯃꯤꯟꯅꯕ ꯆꯛꯔ ꯑꯃꯅ ꯃꯇꯃꯒꯤ 4% ꯃꯇꯧꯗ ꯄꯨꯊꯣꯀꯄ ꯍꯟꯊꯕ ꯑꯃꯥ꯫ ꯄꯣꯀꯦꯠ 38 ꯄꯨꯝꯅꯃꯛꯇ ꯀꯥꯏ-ꯁ꯭ꯀ꯭ꯋꯦꯌꯔ ꯑꯁꯤ ꯗꯤꯒ꯭ꯔꯤ ꯑꯣꯐ ꯐ꯭ꯔꯤꯗꯝ 37 ꯗ 45.29 ꯑꯣꯏꯈꯤ: p = 16.5%꯫ ꯆꯛꯔ ꯑꯍꯨꯃꯗ ꯁ꯭ꯄꯤꯟ 1,204 ꯒꯤ ꯑꯅꯤꯁꯨꯕ ꯁꯦꯝꯄꯜ ꯑꯃꯅ χ² = 34.79, p = 57% ꯄꯤꯈꯤ, ꯑꯃꯁꯨꯡ ꯌꯦꯡꯈꯤꯕ ꯀꯔꯤꯒꯨꯝꯕ ꯆꯥꯡꯒꯤ ꯁꯔꯨꯛ ꯑꯃꯠꯇ ꯃꯔꯨꯑꯣꯏꯈꯤꯗꯦ꯫ ꯁꯦꯝꯄꯜ ꯑꯅꯤꯃꯛ ꯄꯨꯟꯅ, ꯁ꯭ꯄꯤꯟ 1,503, ꯅ χ² = 41.75, p = 27% ꯄꯤꯈꯤ꯫ ꯋꯥꯔꯦꯞ ꯑꯗꯨꯗꯤ ꯂꯥꯞꯅ ꯆꯠꯍꯟꯕꯒꯤ ꯈꯨꯠꯊꯥꯡ ꯂꯩꯇꯦ ꯍꯥꯌꯕꯅꯤ꯫ ꯑꯍꯥꯅꯕ ꯁꯦꯝꯄꯜ ꯈꯛꯇꯗꯤ ꯆꯤꯡꯅꯕ ꯄꯣꯀꯍꯟꯕ ꯃꯑꯣꯡ ꯎꯈꯤ; ꯑꯅꯤꯁꯨꯕ ꯑꯗꯨꯅ ꯃꯁꯤ ꯂꯦꯞꯊꯣꯀꯈꯤ꯫

ꯁꯦꯝꯄꯜꯁ꯭ꯄꯤꯟχ²dfp
ꯑꯍꯥꯅꯕ29945.293716.5%
ꯑꯅꯤꯁꯨꯕ, ꯆꯛꯔ ꯑꯍꯨꯝ1,20434.793757%
ꯑꯅꯤꯃꯛ1,50341.753727%
ꯃꯁꯤꯡꯁꯤꯡ ꯑꯁꯤ 2017 ꯒꯤ ꯑꯦꯅꯥꯂꯥꯏꯁꯤꯁ ꯑꯗꯨꯗꯒꯤꯅꯤ; p-ꯚꯦꯜꯌꯨ ꯈꯨꯗꯤꯡꯃꯛ ꯃꯁꯥꯒꯤ χ² ꯗꯒꯤ ꯊꯣꯀꯏ꯫ ꯗꯕꯜ ꯖꯤꯔꯣ ꯆꯛꯔ ꯑꯃꯗ ꯄꯣꯀꯦꯠ 38 ꯂꯩ, ꯃꯔꯝ ꯑꯗꯨꯅ ꯗꯤꯒ꯭ꯔꯤ ꯑꯣꯐ ꯐ꯭ꯔꯤꯗꯝ 37꯫

ꯀꯥꯏ-ꯁ꯭ꯀ꯭ꯋꯦꯌꯔꯒꯤ ꯃꯊꯛꯇ

ꯆꯤꯡꯅꯕ ꯄꯣꯀꯂꯤꯕ ꯄꯣꯀꯦꯠ ꯑꯃꯈꯛꯀꯤꯗꯃꯛ ꯕꯥꯏꯅꯣꯃꯤꯑꯦꯜ ꯇꯦꯁ꯭ꯠ ꯑꯃꯅ ꯍꯦꯟꯅꯥ ꯃꯄꯥꯡ ꯀꯅꯕꯅꯤ꯫ ꯆꯤꯡꯅꯕ ꯄꯣꯀꯂꯤꯕ ꯁꯔꯨꯛ ꯑꯃꯒꯤꯗꯃꯛ ꯁꯦꯛꯇꯔ ꯑꯦꯅꯥꯂꯥꯏꯁꯤꯁꯀꯤ ꯂꯃꯥꯏꯗ ꯂꯩꯕ ꯁꯦꯛꯇꯔꯆꯛꯔꯁꯦꯛꯇꯔꯆꯛꯔꯗ ꯃꯔꯛ ꯂꯩꯇꯅ ꯃꯈꯥ ꯆꯠꯅꯅ ꯂꯩꯕ ꯄꯣꯀꯦꯠꯁꯤꯡꯒꯤ ꯁꯔꯨꯛ, ꯂꯦꯑꯥꯎꯠꯇ ꯂꯩꯕ ꯀꯥꯡꯂꯨꯞ ꯑꯃꯗꯒꯤ ꯇꯣꯉꯥꯟꯅ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → z-ꯇꯦꯁ꯭ꯠ꯫ ꯀꯥꯏ-ꯁ꯭ꯀ꯭ꯋꯦꯌꯔ ꯑꯁꯤ ꯑꯣꯝꯅꯤꯕꯁ ꯇꯦꯁ꯭ꯠꯅꯤ: ꯀꯔꯤꯒꯨꯝꯕ ꯑꯃꯥ ꯆꯨꯝꯗꯦ ꯍꯥꯌꯕ ꯇꯥꯀꯏ, ꯀꯔꯤꯅꯣ ꯍꯥꯌꯕꯗꯨ ꯍꯥꯌꯗꯦ꯫ ꯑꯍꯥꯅꯕꯗ ꯃꯁꯤ ꯁꯤꯖꯤꯟꯅꯕꯤꯌꯨ, ꯃꯇꯨꯡꯗ ꯌꯦꯡꯕꯤꯌꯨ꯫

ꯁꯦꯛꯇꯔ ꯑꯦꯅꯥꯂꯥꯏꯁꯤꯁ

ꯐꯣꯔꯃꯨꯂꯥ

χ² = Σᵢ (Oᵢ − Eᵢ)² / Eᵢ
Eᵢ = n / 37 · df = 36
ꯀ꯭ꯔꯤꯇꯤꯀꯦꯜ ꯚꯦꯜꯌꯨꯁꯤꯡ: 51.0 (5%) · 58.6 (1%)

ꯋꯥꯍꯪꯁꯤꯡ

ꯀꯔꯤꯒꯤ ꯗꯤꯒ꯭ꯔꯤ ꯑꯣꯐ ꯐ꯭ꯔꯤꯗꯝ 37 ꯅꯠꯇꯅ 36?

ꯃꯁꯤꯡ 37 ꯑꯗꯨ ꯄꯨꯟꯁꯤꯟꯕꯗ n ꯑꯣꯏꯒꯗꯕꯅꯤ, ꯃꯔꯝ ꯑꯗꯨꯅ 36 ꯈꯛ ꯅꯤꯡꯊꯤꯖꯅ ꯍꯣꯡꯕ ꯌꯥꯏ꯫

ꯃꯄꯥꯡ ꯀꯅꯕ ꯕꯥꯏꯌꯥꯁ ꯂꯩꯕ ꯆꯛꯔ ꯑꯃꯅ χ² ꯀꯌꯥ ꯎꯠꯀꯅꯤ?

ꯁ꯭ꯄꯤꯟ 10,000 ꯗ ꯄꯣꯀꯦꯠ ꯑꯃꯥ 1/25 ꯗ ꯂꯥꯀꯄ ꯆꯛꯔ ꯑꯃꯅ ꯄꯣꯀꯦꯠ ꯑꯗꯨꯒꯤ ꯁꯔꯨꯛ ꯈꯛꯇꯗ 60 ꯃꯇꯧ ꯄꯤꯒꯅꯤ; χ² 100 ꯃꯇꯧ, p ꯑꯁꯦꯡꯕꯗ ꯁꯨꯟꯌ꯫

ꯁ꯭ꯄꯤꯟ 200 ꯗ ꯃꯁꯤ ꯆꯂꯥꯏꯕ ꯌꯥꯕ꯭ꯔꯥ?

ꯇꯦꯛꯅꯤꯀꯦꯜ ꯑꯣꯏꯅ ꯌꯥꯏ, ꯄꯣꯀꯦꯠ ꯈꯨꯗꯤꯡꯗ 5.4 ꯐꯪꯒꯗꯕꯒꯥ ꯂꯣꯌꯅꯅ꯫ ꯄꯣꯀꯦꯠ ꯑꯃꯥ ꯒ꯭ꯂꯨꯅ ꯊꯤꯡꯖꯤꯜꯂꯕ ꯆꯛꯔ ꯑꯃꯗꯒꯤ ꯍꯦꯟꯗꯅ ꯃꯁꯤꯅ ꯀꯔꯤꯁꯨ ꯊꯤꯗꯣꯛꯂꯣꯏ꯫

ꯅꯣꯛꯅꯕꯒꯤ ꯀꯃꯤꯛ

ꯑꯉꯀꯄꯁꯤꯡꯒꯤ ꯁ꯭ꯀ꯭ꯋꯦꯌꯔ ꯄꯨꯟꯁꯤꯟꯕꯤꯌꯨ꯫ 51.0 ꯒ ꯆꯥꯡꯗꯝꯕꯤꯌꯨ꯫

ꯑꯉꯀꯄꯁꯤꯡꯒꯤ ꯁ꯭ꯀ꯭ꯋꯦꯌꯔ ꯄꯨꯟꯁꯤꯟꯕꯤꯌꯨ꯫ 51.0 ꯒ ꯆꯥꯡꯗꯝꯕꯤꯌꯨ꯫

ꯍꯧꯔꯛꯐꯃꯁꯤꯡ

  1. Pearson, K. “On the criterion that a given system of deviations from the probable…” Philosophical Magazine 50(302), 1900꯫
  2. Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 1. Wiley, ꯑꯦꯗꯤꯁꯟ 3, 1968꯫ ꯖꯨꯌꯥ ꯁꯥꯟꯅꯔꯤꯕꯒꯤ ꯃꯥꯡꯍꯟ ꯇꯥꯀꯍꯟꯕ, ꯆꯦꯞꯇꯔ XIV꯫
  3. Wizard of Odds. “Organic Roulette Experiment.” ꯃꯥꯔꯆ 2017; ꯑꯣꯒꯁ꯭ꯠ 3, 2026ꯗ ꯑꯅꯧꯅ ꯁꯦꯃꯈꯤ꯫
ꯌꯦꯡꯁꯤꯅꯈꯤꯕ 2026-09-28ꯃꯣꯗꯦꯜ: ꯌꯨꯔꯣꯄꯤꯌꯟ, ꯁꯤꯡꯒꯜ ꯖꯤꯔꯣꯃꯦꯊꯗꯣꯂꯣꯖꯤ ↗ꯍꯧꯔꯛꯐꯃꯁꯤꯡ ↗