Материал: chap5
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1. ɇɭɥɟɜɚɹ ɝɢɩɨɬɟɡɚ ɇ0 ɫɨɫɬɨɢɬ ɜ ɬɨɦ, ɱɬɨ N ij |
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ɞɥɹ ɜɫɟɯ i ɢ j. Ƚɢɩɨɬɟɡɚ |
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ɡɚɤɥɸɱɚɟɬɫɹ ɜ ɬɨɦ, ɱɬɨ ɧɚɣɞɟɬɫɹ ɯɨɬɹ ɛɵ ɨɞɧɚ ɩɚɪɚ i ɢ j ɬɚɤɚɹ, ɱɬɨ N ij |
z N( xi )N( y j |
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Ʉɪɢɬɢɱɟɫɤɚɹ ɬɨɱɤɚ ɨɩɪɟɞɟɥɹɟɬɫɹ |
ɞɥɹ ɡɚɞɚɧɧɨɝɨ ɢɫɫɥɟɞɨɜɚɬɟɥɟɦ ɭɪɨɜɧɹ ɡɧɚɱɢɦɨɫɬɢ q ɢ ɞɥɹ |
(k—1) (l—1) ɫɬɟɩɟɧɟɣ ɫɜɨɛɨɞɵ ɩɨ |
ɬɚɛɥɢɰɟ Ȼ ɉɪɢɥɨɠɟɧɢɹ 3. |
Ⱦɨɜɟɪɢɬɟɥɶɧɵɟ ɢɧɬɟɪɜɚɥɵ |
ɞɥɹ F2 ɧɟ ɜɵɱɢɫɥɹɸɬɫɹ. ɉɪɢɦɟɪ 35. Ɂɧɚɱɟɧɢɟ F2, |
ɪɚɫɫɱɢɬɚɧɧɨɟ ɞɥɹ ɬɚɛɥɢɰɵ 21 (ɝɥ. II, §2), ɪɚɜɧɨ 92,2. ɉɨɫɤɨɥɶɤɭ (k—1) (l—1)=10, F02 ɞɥɹ 1%- ɝɨ ɭɪɨɜɧɹ ɡɧɚɱɢɦɨɫɬɢ ɪɚɜɧɨ 23,21. ɋɥɟɞɨɜɚɬɟɥɶɧɨ, F2 ɢ ɜɫɟ ɪɚɫɫɱɢɬɚɧɧɵɟ ɧɚ ɟɝɨ ɨɫɧɨɜɟ ɤɨɷɮɮɢɰɢɟɧɬɵ ɡɧɚɱɢɦɵ.
ɍɩɪɚɠɧɟɧɢɟ 96. Ⱦɥɹ ɬɚɛɥɢɰɵ 5u8 ɛɵɥɨ ɩɨɥɭɱɟɧɨ ɡɧɚɱɟɧɢɟ, ɪɚɜɧɨɟ 45,4. Ɂɧɚɱɢɦɨ ɥɢ ɷɬɨ ɡɧɚɱɟɧɢɟ ɧɚ ɭɪɨɜɧɟ 5%? Ɉɬɜɟɬ: ɞɚ.
9. Ɂɧɚɱɢɦɨɫɬɶ ɪɚɡɥɢɱɢɣ r1 ɢ r2
ɂɡ ɞɜɭɯ ɛɟɫɤɨɧɟɱɧɵɯ ɝɟɧɟɪɚɥɶɧɵɯ ɫɨɜɨɤɭɩɧɨɫɬɟɣ ɢɡɜɥɟɱɟɧɵ ɜɵɛɨɪɤɢ ɨɛɴɟɦɚ ɩ1 ɢ ɩ2 ɢ
ɞɥɹ ɧɟɤɨɬɨɪɵɯ ɩɪɢɡɧɚɤɨɜ ɏ ɢ Y ɜ ɤɚɠɞɨɣ ɢɡ ɜɵɛɨɪɨɤ ɪɚɫɫɱɢɬɚɧɵ ɜɵɛɨɪɨɱɧɵɟ ɤɨɷɮɮɢɰɢɟɧɬɵ ɤɨɪɪɟɥɹɰɢɢ r1B ɢ r2B.
1.H 0 : r1Ƚ = r2Ƚ
2.H 1 : r1Ƚ z r2Ƚ
2.Ⱦɥɹ ɩɪɨɜɟɪɤɢ ɝɢɩɨɬɟɡɵ ɇ0 ɩɪɢɦɟɧɹɟɬɫɹ z-ɩɪɟɨɛɪɚɡɨɜɚɧɢɟ Ɏɢɲɟɪɚ — ɫɦ. ɮɨɪɦɭɥɭ
(V,8,2). ȼɵɱɢɫɥɹɟɦ r:
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Ɇɨɠɧɨ ɞɨɤɚɡɚɬɶ, ɱɬɨ z ɢɦɟɟɬ ɧɨɪɦɚɥɶɧɨɟ ɪɚɫɩɪɟɞɟɥɟɧɢɟ ɫ ɧɭɥɟɜɵɦ ɫɪɟɞɧɢɦ ɢ ɟɞɢɧɢɱɧɨɣ ɞɢɫɩɟɪɫɢɟɣ, ɟɫɥɢ ɜɟɪɧɚ ɝɢɩɨɬɟɡɚ ɇ0.
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3.Ʉɪɢɬɢɱɟɫɤɢɟ ɬɨɱɤɢ ɩɨ ɡɚɞɚɧɧɨɦɭ ɭɪɨɜɧɸ ɡɧɚɱɢɦɨɫɬɢ q ɨɩɪɟɞɟɥɹɸɬɫɹ ɩɨ ɬɚɛɥɢɰɟ Ⱥ ɉɪɢɥɨɠɟɧɢɹ 3.
4.ɇɚɣɞɟɧɧɵɟ ɜ ɩ. 3 ɤɪɢɬɢɱɟɫɤɢɟ ɬɨɱɤɢ ɦɨɝɭɬ ɛɵɬɶ ɢɫɩɨɥɶɡɨɜɚɧɵ ɞɥɹ ɩɨɫɬɪɨɟɧɢɹ ɞɨɜɟɪɢɬɟɥɶɧɵɯ ɢɧɬɟɪɜɚɥɨɜ ɫ ɞɨɜɟɪɢɬɟɥɶɧɨɣ ɜɟɪɨɹɬɧɨɫɬɶɸ 1 — q:
z1B z2B z |
1 1 z1Ƚ z2Ƚ z1B z2B z |
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n1 3 n2 3 |
n1 3 n2 3 |
ɉɨɫɥɟ ɬɨɝɨ, ɤɚɤ ɧɚɣɞɟɧɵ ɤɪɢɬɢɱɟɫɤɢɟ ɬɨɱɤɢ ɞɥɹ z, ɨɧɢ ɩɪɟɨɛɪɚɡɭɸɬɫɹ ɜ ɤɪɢɬɢɱɟɫɤɢɟ ɬɨɱɤɢ ɞɥɹ r ɩɨ ɮɨɪɦɭɥɟ (V,8,3) ɢɥɢ ɫ ɩɨɦɨɳɶɸ ɬɚɛɥɢɰɵ Ʉ ɉɪɢɥɨɠɟɧɢɹ 3.
5. ɉɪɢɦɟɪ 36. ȼ ɢɫɫɥɟɞɨɜɚɧɢɢ ɜɥɢɹɧɢɹ ɩɪɟɫɬɢɠɚ ɩɪɨɮɟɫɫɢɣ ɫɪɟɞɢ ɲɤɨɥɶɧɢɤɨɜ ɧɚ ɩɪɢɜɥɟɤɚɬɟɥɶɧɨɫɬɶ ɩɪɨɮɟɫɫɢɢ34 ɛɵɥɚ ɜɵɞɜɢɧɭɬɚ ɝɢɩɨɬɟɡɚ, ɱɬɨ ɩɪɟɫɬɢɠ ɨɤɚɡɵɜɚɟɬ ɛɨɥɶɲɟɟ ɜɥɢɹɧɢɟ ɧɚ ɩɪɢɜɥɟɤɚɬɟɥɶɧɨɫɬɶ ɩɪɨɮɟɫɫɢɢ ɞɥɹ ɲɤɨɥɶɧɢɤɨɜ ɢɡ ɫɟɦɟɣ ɢɧɬɟɥɥɢɝɟɧɰɢɢ, ɱɟɦ ɞɥɹ ɲɤɨɥɶɧɢɤɨɜ ɢɡ ɫɟɦɟɣ ɪɚɛɨɱɢɯ. Ⱦɥɹ ɩɪɨɜɟɪɤɢ ɷɬɨɝɨ ɩɪɟɞɩɨɥɨɠɟɧɢɹ ɛɵɥɨ ɩɪɨɜɟɞɟɧɨ ɪɟɩɪɟɡɟɧɬɚɬɢɜɧɨɟ ɞɥɹ ɝ. Ʉɢɟɜɚ ɢɫɫɥɟɞɨɜɚɧɢɟ ɲɤɨɥɶɧɢɤɨɜ 10-ɯ ɤɥɚɫɫɨɜ, ɜ ɯɨɞɟ ɤɨɬɨɪɨɝɨ ɞɥɹ 43 ɩɪɨɮɟɫɫɢɣ ɛɵɥɢ ɩɨɥɭɱɟɧɵ ɨɰɟɧɤɢ ɩɪɟɫɬɢɠɚ ɢ ɩɪɢɜɥɟɤɚɬɟɥɶɧɨɫɬɢ ɢɯ ɞɥɹ ɲɤɨɥɶɧɢɤɨɜ. ɋɜɹɡɶ ɩɪɟɫɬɢɠɚ ɢ ɩɪɢɜɥɟɤɚɬɟɥɶɧɨɫɬɢ ɯɚɪɚɤɬɟɪɢɡɨɜɚɥɚɫɶ ɤɨɷɮɮɢɰɢɟɧɬɨɦ ɤɨɪɪɟɥɹɰɢɢ ɷɬɢɯ
34 ɑɟɪɧɨɜɨɥɟɧɤɨ ȼ. Ɏ., Ɉɫɫɨɜɫɤɢɣ ȼ. Ʌ., ɉɚɧɢɨɬɬɨ ȼ. ɂ. ɉɪɟɫɬɢɠ ɩɪɨɮɟɫɫɢɣ ɢ ɩɪɨɛɥɟɦɵ ɫɨɰɢɚɥɶɧɨ-
ɩɪɨɮɟɫɫɢɨɧɚɥɶɧɨɣ ɨɪɢɟɧɬɚɰɢɢ ɦɨɥɨɞɟɠɢ. Ʉɢɟɜ, 1979, ɫ. 146, 147.
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ɨɰɟɧɨɤ. Ɉɤɚɡɚɥɨɫɶ, ɱɬɨ ɷɬɨɬ ɤɨɷɮɮɢɰɢɟɧɬ ɞɥɹ ɲɤɨɥɶɧɢɤɨɜ ɢɡ ɫɟɦɟɣ ɢɧɬɟɥɥɢɝɟɧɬɨɜ ɪɚɜɟɧ 0,94, ɚ ɢɡ ɫɟɦɟɣ ɪɚɛɨɱɢɯ 0,82. Ⱦɚɸɬ ɥɢ ɷɬɢ ɞɚɧɧɵɟ ɨɫɧɨɜɚɧɢɟ ɡɚɤɥɸɱɢɬɶ, ɱɬɨ ɝɢɩɨɬɟɡɚ ɩɨɞɬɜɟɪɞɢɥɚɫɶ? ɉɪɨɜɟɪɢɦ ɡɧɚɱɢɦɨɫɬɶ ɪɚɡɥɢɱɢɣ: ɩ1=n2=43, rB1 = 0,94, rB2 = 0,82. ɑɬɨɛɵ ɜɨɫɩɨɥɶɡɨɜɚɬɶɫɹ ɮɨɪɦɭɥɨɣ (V,9,1), ɩɪɨɜɨɞɢɦ ɫɧɚɱɚɥɚ z-ɩɪɟɨɛɪɚɡɨɜɚɧɢɟ Ɏɢɲɟɪɚ ɩɨ ɮɨɪɦɭɥɟ (V,8,2) ɢɥɢ ɩɨ ɬɚɛɥɢɰɟ Ʉ ɉɪɢɥɨɠɟɧɢɹ 3: z1 = 1,738, z2 == 1,157. Ɍɨɝɞɚ ɩɨɥɭɱɢɦ:
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ɉɨɫɤɨɥɶɤɭ ɩɨɥɭɱɟɧɧɨɟ ɡɧɚɱɟɧɢɟ ɜɵɲɟ, ɱɟɦ 2,58, ɦɨɠɧɨ ɭɬɜɟɪɠɞɚɬɶ, ɱɬɨ ɪɚɡɥɢɱɢɹ ɡɧɚɱɢɦɵ ɧɚɭɪɨɜɧɟ 1%, ɢ ɝɢɩɨɬɟɡɚ
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ɢɫɫɥɟɞɨɜɚɬɟɥɟɣ, ɫɥɟɞɨɜɚɬɟɥɶɧɨ, ɩɨɥɭɱɢɥɚ ɷɦɩɢɪɢɱɟɫɤɨɟ ɩɨɞɬɜɟɪɠɞɟɧɢɟ.
Ⱦɥɹ ɷɬɨɝɨ ɠɟ ɭɪɨɜɧɹ ɡɧɚɱɢɦɨɫɬɢ (ɬ.ɟ. ɞɥɹ 99% ɞɨɜɟɪɢɬɟɥɶɧɨɣ ɜɟɪɨɹɬɧɨɫɬɢ) ɧɚɣɞɟɦ ɞɨɜɟɪɢɬɟɥɶɧɵɣ ɢɧɬɟɪɜɚɥ:
1,738 1,157 2,58 |
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Ƚ 1,738 |
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ɢɥɢ 0,004 < z1Ƚ z2Ƚ < 1,158
ɉɟɪɟɜɨɞɹ z ɜ r ɩɨ ɮɨɪɦɭɥɟ (V,8,3) ɢɥɢ ɩɨ ɬɚɛɥɢɰɟ Ʉ ɉɪɢɥɨɠɟɧɢɹ 3, ɩɨɥɭɱɚɟɦ:
0,004< z1Ƚ z2Ƚ <0,820
6. ɍɩɪɚɠɧɟɧɢɟ 97. ȼ ɩɪɢɦɟɪɟ ɢ ɭɩɪɚɠɧɟɧɢɢ § 8 Ⱥ ɩɪɢɜɟɞɟɧɵ ɪɟɡɭɥɶɬɚɬɵ ɢɫɫɥɟɞɨɜɚɧɢɹ35, ɩɨɤɚɡɚɜɲɟɝɨ, ɱɬɨ ɤɨɷɮɮɢɰɢɟɧɬ ɤɨɪɪɟɥɹɰɢɢ ɦɟɠɞɭ ɭɞɨɜɥɟɬɜɨɪɟɧɧɨɫɬɹɦɢ ɪɚɛɨɬɨɣ ɢ ɩɪɨɮɟɫɫɢɟɣ 89 ɪɭɤɨɜɨɞɢɬɟɥɟɣ ɝɪɭɩɩ ɪɚɜɟɧ 0,23, ɚ ɷɬɨɬ ɠɟ ɤɨɷɮɮɢɰɢɟɧɬ, ɪɚɫɫɱɢɬɚɧɧɵɣ ɩɨ ɨɰɟɧɤɚɦ 52 ɝɥɚɜɧɵɯ ɢɧɠɟɧɟɪɨɜ ɩɪɨɟɤɬɚ, ɪɚɜɟɧ 0,51. Ⱦɨɫɬɚɬɨɱɧɵ ɥɢ ɷɬɢ ɪɚɡɥɢɱɢɹ, ɱɬɨɛɵ ɭɬɜɟɪɠɞɚɬɶ, ɱɬɨ ɛɨɥɟɟ ɜɵɫɨɤɨɟ ɞɨɥɠɧɨɫɬɧɨɟ ɩɨɥɨɠɟɧɢɟ ɩɨɡɜɨɥɹɟɬ ɩɨɥɧɟɟ ɪɟɚɥɢɡɨɜɚɬɶ ɩɪɨɮɟɫɫɢɨɧɚɥɶɧɵɟ ɨɠɢɞɚɧɢɹ, ɡɧɚɱɢɦɨ ɥɢ ɪɚɡɥɢɱɢɟ ɩɨɥɭɱɟɧɧɵɯ ɤɨɷɮɮɢɰɢɟɧɬɨɜ ɤɨɪɪɟɥɹɰɢɢ? ɉɪɨɜɟɪɢɬɶ ɧɚ 5%-ɦ ɭɪɨɜɧɟ ɡɧɚɱɢɦɨɫɬɢ ɢ ɩɨɫɬɪɨɢɬɶ ɞɥɹ ɪɚɡɧɨɫɬɢ ɤɨɷɮɮɢɰɢɟɧɬɨɜ ɞɨɜɟɪɢɬɟɥɶɧɵɣ ɢɧɬɟɪɜɚɥ.
Ɉɬɜɟɬ: ɪɚɡɥɢɱɢɟ ɧɟɡɧɚɱɢɦɨ (z = 1,83), -0,022< |
r Ƚ |
r Ƚ |
<0,592. Ɉɬɦɟɬɢɦ ɫɜɹɡɶ ɝɢɩɨɬɟɡ |
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ɫ ɞɨɜɟɪɢɬɟɥɶɧɵɦɢ ɢɧɬɟɪɜɚɥɚɦɢ: ɟɫɥɢ ɇ0 ɩɪɢɧɢɦɚɟɬɫɹ, ɬɨ ɞɨɜɟɪɢɬɟɥɶɧɵɣ ɢɧɬɟɪɜɚɥ ɫɨɞɟɪɠɢɬ 0; ɟɫɥɢ ɇ0 ɨɬɜɟɪɝɚɟɬɫɹ — ɬɨ ɧɟ ɫɨɞɟɪɠɢɬ. Ʉɚɤ ɜɢɞɢɦ, ɜ ɞɚɧɧɨɦ ɫɥɭɱɚɟ ɞɨɜɟɪɢɬɟɥɶɧɵɣ ɢɧɬɟɪɜɚɥ ɫɨɞɟɪɠɢɬ 0.
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35 ɋɨɰɢɚɥɶɧɨ-ɩɫɢɯɨɥɨɝɢɱɟɫɤɢɣ ɩɨɪɬɪɟɬ ɢɧɠɟɧɟɪɚ. Ɇ., 1977, ɬɚɛɥ. 11, ɫ. 149
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