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ɂɇȾɂȼɂȾɍȺɅɖɇɈȿ ɁȺȾȺɇɂȿ 1
Ⱦɚɧɚ ɢɧɬɟɪɜɚɥɶɧɚɹ ɜɵɛɨɪɤɚ. Ɍɪɟɛɭɟɬɫɹ:
ɚ) ɩɨɫɬɪɨɢɬɶ ɝɢɫɬɨɝɪɚɦɦɭ ɱɚɫɬɨɬ;
ɛ) ɫɨɫɬɚɜɢɬɶ ɷɦɩɢɪɢɱɟɫɤɢɣ ɪɹɞ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɱɚɫɬɨɬ ɢ ɨɬɧɨɫɢɬɟɥɶɧɵɯ
ɱɚɫɬɨɬ;
ɜ) ɩɨɫɬɪɨɢɬɶ ɩɨɥɢɝɨɧ ɱɚɫɬɨɬ ɢ ɤɭɦɭɥɹɬɢɜɧɭɸ ɤɪɢɜɭɸ;
ɝ) ɧɚɣɬɢ ɷɦɩɢɪɢɱɟɫɤɭɸ ɮɭɧɤɰɢɸ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɢ ɩɨɫɬɪɨɢɬɶ ɟɟ ɝɪɚɮɢɤ;
ɞ) ɧɚɣɬɢ ɦɨɞɭ, ɦɟɞɢɚɧɭ (ɞɜɭɦɹ ɫɩɨɫɨɛɚɦɢ) ɢ ɪɚɡɦɚɯ ɜɚɪɶɢɪɨɜɚɧɢɹ;
ɟ) ɧɚɣɬɢ ɜɵɛɨɪɨɱɧɨɟ ɫɪɟɞɧɟɟ, ɜɵɛɨɪɨɱɧɭɸ ɞɢɫɩɟɪɫɢɸ (ɞɜɭɦɹ ɫɩɨɫɨɛɚɦɢ),
ɜɵɛɨɪɨɱɧɨɟ
ɜɚɪɢɚɰɢɢ; ɤɨɷɮɮɢɰɢɟɧɬ ɚɫɢɦɦɟɬɪɢɢ ɢ ɷɤɫɰɟɫɫ [3].
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ɚɛɫɨɥɸɬɧɨɟ ɢ ɫɪɟɞɧɟɤɜɚɞɪɚɬɢɱɟɫɤɨɟ ɨɬɤɥɨɧɟɧɢɟ; ɤɨɷɮɮɢɰɢɟɧɬɵ
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6–16 16–26 26–36 36–46 46–56 56–66 66–76
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4 11 25 30 15 10 5
12–22 22–32 32–42 42–52 52–62 62–72 72–82
1;ii
3 7 10 40 20 12 8
15–25 25–35 35–45 45–55 55–65 65–75 75–85
1;ii
4 11 25 30 15 10 5
20–30 30–40 40–50 50–60 60–70 70–80 80–90
1;ii
4 6 10 40 20 12 8
25–35 35–45 45–55 55–65 65–75 75–85 85–95
1;ii
4 16 40 25 7 5 3
12–18 18–24 24–30 30–36 36–42 42–48 48–54
1;ii
4 16 20 40 13 4 3
2–6 6–10 10–14 14–18 18–22 22–26 26–30
1;ii
7 11 12 60 5 3 2
7–13 13–19 19–25 25–31 31–37 37–43 43–49
1;ii
3 14 24 40 15 2 2
5–15 15–25 25–35 35–45 45–55 55–65 65–75
1;ii
4 11 25 30 15 10 5
1–9 9–17 17–25 25–33 33–41 41–49 49–57
1;ii
2 16 22 40 15 3 2
4–8 8–12 12–16 16–20 20–24 24–28 28–32
1;ii
3 7 10 40 20 12 8
41
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10–20 20–30 30–40 40–50 50–60 60–70 70–80
1;ii
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5 10 30 25 15 10 5
7–17 17–27 27–37 37–47 47–57 57–67 67–77
1;ii
5 15 40 25 8 4 3
0–12 12–24 24–36 36–48 48–60 60–72 72–84
1
15 5 20 30 10 11 9
-2–4 4–10 10–16 16–22 22–28 28–34 34–40
1
8 10 60 12 5 3 2
-5–5 5–15 15–25 25–35 35–45 45–55 55–65
1
9 6 14 50 10 6 5
-4–6 6–16 16–26 26–36 36–46 46–56 56–66
1
2 3 5 60 12 11 7
0–10 10–20 20–30 30–40 40–50 50–60 60–70
1
3 5 7 25 40 16 4
23–33 33–43 43 –53 53–63 63–73 73–83 83–93
1
2 2 15 40 24 14 3
14–24 24–34 34–44 44–54 54–64 64–74 74–84
1
8 9 10 35 15 11 12
12–16 16–20 20–24 24–28 28–32 32–36 36–40
1
7 11 12 60 5 3 2
1–3 3–5 5–7 7–9 9–11 11–13 13–15
1
3 14 24 40 15 2 2
2–5 5–8 8–11 11–14 14–17 17–20 20–23
1
4 11 25 30 15 10 5
1–7 7–13 13–19 19–25 25–31 31–37 37–43
1
2 16 22 40 15 3 2
4–6 6–8 8–10 10–12 12–14 14–16 16–18
1
3 7 10 40 20 12 8
42
2. ȼɕəȼɅȿɇɂȿ ɊȺɁɅɂɑɂɃ ȼ ɍɊɈȼɇȿ
ɭ
H
ɭ
r
ɂɋɋɅȿȾɍȿɆɈȽɈ ɉɊɂɁɇȺɄȺ
ȼ ɪɟɡɭɥɶɬɚɬɟ ɢɡɭɱɟɧɢɹ ɪɚɡɞɟɥɚ ɫɬɭɞɟɧɬ ɞɨɥɠɟɧ:
– ɭɦɟɬɶ ɚɞɟɤɜɚɬɧɨ ɢɫɩɨɥɶɡɨɜɚɬɶ ɫɬɚɬɢɫɬɢɱɟɫɤɢɟ ɤɪɢɬɟɪɢɢ ɜɵɹɜɥɟɧɢɹ ɪɚɡɥɢ-
ɱɢɣ ɜ ɭɪɨɜɧɟ ɢɫɫɥɟɞɭɟɦɨɝɨ ɩɪɢɡɧɚɤɚ;
– ɜɥɚɞɟɬɶ ɦɟɬɨɞɢɱɟɫɤɢɦ ɚɩɩɚɪɚɬɨɦ ɢ ɛɚɡɨɜɵɦɢ ɧɚɜɵɤɚɦɢ ɜɵɞɜɢɠɟɧɢɹ ɢ ɩɪɨ-
ɜɟɪɤɢ ɝɢɩɨɬɟɡ ɨ ɪɚɡɥɢɱɢɹɯ ɜ ɭɪɨɜɧɟ ɢɡɭɱɚɟɦɨɝɨ ɩɪɢɡɧɚɤɚ.
2.1. ɋɬɚɬɢɫɬɢɱɟɫɤɢɟ ɤɪɢɬɟɪɢɢ ɪɚɡɥɢɱɢɹ
ȼɫɟ ɦɧɨɝɨɨɛɪɚɡɢɟ ɡɚɞɚɱ, ɫ ɤɨɬɨɪɵɦɢ ɩɪɢɯɨɞɢɬɫɹ ɫɬɚɥɤɢɜɚɬɶɫɹ ɷɤɫɩɟɪɢɦɟɧɬɚɬɨɪɭ ɩɪɢ ɩɪɨɜɟɪɤɟ ɝɢɩɨɬɟɡ, ɦɨɠɧɨ ɫɜɟɫɬɢ ɤ ɧɟɫɤɨɥɶɤɢɦ ɝɪɭɩɩɚɦ.
1. ȼɵɹɜɥɟɧɢɟ ɪɚɡɥɢɱɢɣ ɜ ɪɚɫɩɪɟɞɟɥɟɧɢɢ ɩɟɪɟɦɟɧɧɨɣ ɜ ɪɚɡɧɵɯ ɝɪɭɩɩɚɯ
ɢɫɩɵɬɭɟɦɵɯ.
2. ɉɪɨɜɟɪɤɚ ɫɨɜɩɚɞɟɧɢɹ ɷɦɩɢɪɢɱɟɫɤɢɯ ɪɟɡɭɥɶɬɚɬɨɜ ɫ ɬɟɨɪɟɬɢɱɟɫɤɢɦɢ.
3. Ɉɛɧɚɪɭɠɟɧɢɟ ɜɥɢɹɧɢɹ ɮɚɤɬɨɪɚ ɧɚ ɪɚɫɩɪɟɞɟɥɟɧɢɟ ɩɟɪɟɦɟɧɧɨɣ.
4. Ɉɛɧɚɪɭɠɟɧɢɟ ɢɧɬɟɪɟɫɭɸɳɟɝɨ ɢɫɫɥɟɞɨɜɚɬɟɥɹ ɷɮɮɟɤɬɚ ɜ ɨɞɧɨɣ ɢɥɢ ɪɚɡ-
ɧɵɯ ɜɵɛɨɪɤɚɯ
Ʉɪɚɬɤɚɹ ɤɥɚɫɫɢɮɢɤɚɰɢɹ ɡɚɞɚɱ ɢ ɦɟɬɨɞɨɜ ɢɯ ɪɟɲɟɧɢɹ [1] ɩɪɢɜɨɞɢɬɫɹ ɜ
ɬɚɛɥɢɰɟ.
1. ȼɵɹɜɥɟɧɢɟ ɪɚɡɥɢɱɢɣ
ɜ ɭɪɨɜɧɟ ɢɫɫɥɟɞɭɟɦɨɝɨ
ɩɪɢɡɧɚɤɚ
2. Ɉɰɟɧɤɚ ɫɞɜɢɝɚ
ɡɧɚɱɟɧɢɣ ɢɫɫɥɟɞɭɟɦɨɝɨ
ɩɪɢɡɧɚɤɚ
3. ȼɵɹɜɥɟɧɢɟ ɪɚɡɥɢɱɢɣ
ɜ ɪɚɫɩɪɟɞɟɥɟɧɢɢ
ɩɪɢɡɧɚɤɚ
ɢɫɩɵɬɭɟɦɵɯ.
Ɂɚɞɚɱɢ ɍɫɥɨɜɢɹ Ɇɟɬɨɞɵ
Ʉɪɢɬɟɪɢɣ Ɇɚɤɧɚɦɚɪɵ
ɚ) ɞɜɟ ɜɵɛɨɪɤɢ
ɢɫɩɵɬɭɟɦɵɯ
ɛ) ɬɪɢ ɢ ɛɨɥɟɟ
ɜɵɛɨɪɨɤ ɢɫɩɵɬ
ɚ) ɞɜɚ ɡɚɦɟɪɚ
ɧɚ ɨɞɧɨɣ ɢ ɬɨɣ ɠɟ
ɜɵɛɨɪɤɟ ɢɫɩɵɬɭɟɦɵɯ
ɛ) ɬɪɢ ɢ ɛɨɥɟɟ
ɡɚɦɟɪɨɜ ɧɚ ɨɞɧɨɣ
ɢ ɬɨɣ ɠɟ ɜɵɛɨɪɤɟ
ɢɫɩɵɬ
ɟɦɵɯ
ɚ) ɩɪɢ ɫɨɩɨɫɬɚɜɥɟɧɢɢ
ɷɦɩɢɪɢɱɟɫɤɨɝɨ
ɪɚɫɩɪɟɞɟɥɟɧɢɹ
ɫ ɬɟɨɪɟɬɢɱɟɫɤɢɦ
ɛ) ɩɪɢ ɫɨɩɨɫɬɚɜɥɟɧɢɢ
ɞɜɭɯ ɷɦɩɢɪɢɱɟɫɤɢɯ
ɪɚɫɩɪɟɞɟɥɟɧɢɣ
Q – ɤɪɢɬɟɪɢɣ Ɋɨɡɟɧɛɚɭɦɚ
U – ɤɪɢɬɟɪɢɣ Ɇɚɧɧɚ – ɍɢɬɧɢ
*
ij
– ɤɪɢɬɟɪɢɣ (ɭɝɥɨɜɨɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɟ
Ɏɢɲɟɪɚ)
S – ɤɪɢɬɟɪɢɣ ɬɟɧɞɟɧɰɢɣ Ⱦɠɨɧɤɢɪɚ
ɟɦɵɯ
43
– ɤɪɢɬɟɪɢɣ Ʉɪɭɫɤɚɥɚ – ɍɨɥɥɢɫɚ
T – ɤɪɢɬɟɪɢɣ ȼɢɥɤɨɤɫɨɧɚ
G – ɤɪɢɬɟɪɢɣ ɡɧɚɤɨɜ
*
ij
– ɤɪɢɬɟɪɢɣ (ɭɝɥɨɜɨɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɟ
Ɏɢɲɟɪɚ)
t – ɤɪɢɬɟɪɢɣ ɋɬɶɸɞɟɧɬɚ
2
F
– ɤɪɢɬɟɪɢɣ Ɏɪɢɞɦɚɧɚ
L – ɤɪɢɬɟɪɢɣ ɬɟɧɞɟɧɰɢɣ ɉɟɣɞɠɚ
t – ɤɪɢɬɟɪɢɣ ɋɬɶɸɞɟɧɬɚ
2
F
– ɤɪɢɬɟɪɢɣ ɉɢɪɫɨɧɚ
Ȝ – ɤɪɢɬɟɪɢɣ Ʉɨɥɦɨɝɨɪɨɜɚ – ɋɦɢɪɧɨɜɚ
m – ɛɢɧɨɦɢɚɥɶɧɵɣ ɤɪɢɬɟɪɢɣ
2
F
– ɤɪɢɬɟɪɢɣ ɉɢɪɫɨɧɚ
Ȝ – ɤɪɢɬɟɪɢɣ Ʉɨɥɦɨɝɨɪɨɜɚ – ɋɦɢɪɧɨɜɚ
*
– ɤɪɢɬɟɪɢɣ (ɭɝɥɨɜɨɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɟ
ij
Ɏɢɲɟɪɚ)
Ɂɚɞɚɱɢ ɍɫɥɨɜɢɹ Ɇɟɬɨɞɵ
ɭ
ɇ
ɇ
Ʉɨɷɮɮɢɰɢɟɧɬ ɤɨɪɪɟɥɹɰɢɢ ɉɢɪɫɨɧɚ
Ʉɨɷɮɮɢɰɢɟɧɬ ɤɨɪɪɟɥɹɰɢɢ Ʉɟɧɞɚɥɥɚ
Ȼɢɫɟɪɢɚɥɶɧɵɣ ɤɨɷɮɮɢɰɢɟɧɬ
ɤɨɪɪɟɥɹɰɢɢ
Ʉɨɪɪɟɥɹɰɢɨɧɧɨɟ ɨɬɧɨɲɟɧɢɟ ɉɢɪɫɨɧɚ
– ɤɨɷɮɮɢɰɢɟɧɬ ɪɚɧɝɨɜɨɣ
r
s
ɤɨɪɪɟɥɹɰɢɢ ɋɩɢɪɦɟɧɚ
– ɤɨɷɮɮɢɰɢɟɧɬ ɪɚɧɝɨɜɨɣ
r
s
ɤɨɪɪɟɥɹɰɢɢ ɋɩɢɪɦɟɧɚ
Ʉɨɷɮɮɢɰɢɟɧɬ ɤɨɪɪɟɥɹɰɢɢ ɉɢɪɫɨɧɚ
Ɇɧɨɠɟɫɬɜɟɧɧɚɹ ɢ ɱɚɫɬɧɚɹ ɤɨɪɪɟɥɹɰɢɹ
Ʌɢɧɟɣɧɚɹ, ɤɪɢɜɨɥɢɧɟɣɧɚɹ
ɢ ɦɧɨɠɟɫɬɜɟɧɧɚɹ ɪɟɝɪɟɫɫɢɹ
Ɏɚɤɬɨɪɧɵɣ ɢ ɤɥɚɫɬɟɪɧɵɣ ɚɧɚɥɢɡɵ
S – ɤɪɢɬɟɪɢɣ ɬɟɧɞɟɧɰɢɣ Ⱦɠɨɧɤɢɪɚ
L – ɤɪɢɬɟɪɢɣ ɬɟɧɞɟɧɰɢɣ ɉɟɣɞɠɚ
Ɉɞɧɨɮɚɤɬɨɪɧɵɣ ɞɢɫɩɟɪɫɢɨɧɧɵɣ
ɚɧɚɥɢɡ Ɏɢɲɟɪɚ
Ɇɧɨɠɟɫɬɜɟɧɧɨɟ ɫɪɚɜɧɟɧɢɟ
ɧɟɡɚɜɢɫɢɦɵɯ ɜɵɛɨɪɨɤ
Ⱦɜɭɯɮɚɤɬɨɪɧɵɣ ɞɢɫɩɟɪɫɢɨɧɧɵɣ
ɚɧɚɥɢɡ Ɏɢɲɟɪɚ
4. ȼɵɹɜɥɟɧɢɟ ɫɬɟɩɟɧɢ
ɫɨɝɥɚɫɨɜɚɧɧɨɫɬɢ
ɢɡɦɟɧɟɧɢɣ
5. Ⱥɧɚɥɢɡ ɢɡɦɟɧɟɧɢɣ
ɩɪɢɡɧɚɤɚ ɩɨɞ ɜɥɢɹɧɢɟɦ
ɤɨɧɬɪɨɥɢɪɭɟɦɵɯ
ɭɫɥɨɜɢɣ
ɚ) ɞɜɭɯ ɩɪɢɡɧɚɤɨɜ
ɛ) ɞɜɭɯ ɢɟɪɚɪɯɢɣ
ɢɥɢ ɩɪɨɮɢɥɟɣ
ɚ) ɩɨɞ ɜɥɢɹɧɢɟɦ
ɨɞɧɨɝɨ ɮɚɤɬɨɪɚ
ɛ) ɩɨɞ ɜɥɢɹɧɢɟɦ ɞɜɭɯ
ɮɚɤɬɨɪɨɜ
ɨɞɧɨɜɪɟɦɟɧɧɨ
Ⱦɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ ɫɪɚɜɧɟɧɢɹ ɪɟɡɭɥɶɬɚɬɨɜ ɨɛɫɥɟɞɨɜɚɧɢɹ ɩɫɢɯɨɥɨɝɢɱɟɫɤɨɝɨ ɩɪɢɡɧɚɤɚ ɜ ɪɚɡɧɵɯ ɭɫɥɨɜɢɹɯ ɢɡɦɟɪɟɧɢɹ (ɧɚɩɪɢɦɟɪ, ɞɨ ɢ ɩɨɫɥɟ ɜɨɡɞɟɣɫɬɜɢɹ) ɢɥɢ ɨɛɫɥɟɞɨɜɚɧɢɹ ɤɨɧɬɪɨɥɶɧɨɣ ɢ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨɣ ɝɪɭɩɩ ɢɫɩɨɥɶɡɭɟɬɫɹ
ɛɨɥɶɲɨɣ ɧɚɛɨɪ ɫɬɚɬɢɫɬɢɱɟɫɤɢɯ ɫɩɨɫɨɛɨɜ, ɧɚɡɵɜɚɟɦɵɯ ɜ ɧɚɢɛɨɥɟɟ ɨɛɳɟɦ ɜɢɞɟ
ɤɪɢɬɟɪɢɹɦɢ ɪɚɡɥɢɱɢɣ. ɗɬɢ ɤɪɢɬɟɪɢɢ ɩɨɡɜɨɥɹɸɬ ɨɰɟɧɢɬɶ ɫɬɟɩɟɧɶ ɫɬɚɬɢɫɬɢɱɟ-
ɫɤɨɣ ɞɨɫɬɨɜɟɪɧɨɫɬɢ ɪɚɡɥɢɱɢɣ ɦɟɠɞɭ ɪɚɡɧɨɨɛɪɚɡɧɵɦɢ ɩɨɤɚɡɚɬɟɥɹɦɢ, ɢɡɦɟɪɟɧɧɵɦɢ ɫɨɝɥɚɫɧɨ ɩɥɚɧɭ ɩɪɨɜɟɞɟɧɢɹ ɩɫɢɯɨɥɨɝɢɱɟɫɤɨɝɨ ɢɫɫɥɟɞɨɜɚɧɢɹ.
ȼɫɟ ɤɪɢɬɟɪɢɢ ɨɛɥɚɞɚɸɬ ɨɛɳɟɣ
1.
Ɏɨɪɦɭɥɢɪɭɟɬɫɹ ɧɭɥɟɜɚɹ ɝɢɩɨɬɟɡɚ ɇ
Ɏɨɪɦɭɥɢɪɭɟɬɫɹ ɚɥɶɬɟɪɧɚɬɢɜɧɚɹ ɝɢɩɨɬɟɡɚ ɇ
2.
ȼɵɛɢɪɚɟɬɫɹ ɤɪɢɬɟɪɢɣ (ɫɬɚɬɢɫɬɢɤɚ) ɞɥɹ ɜɵɛɨɪɚ ɦɟɠɞɭ ɇ
3.
4.
ɍɫɬɚɧɚɜɥɢɜɚɟɬɫɹ ɤɪɢɬɢɱɟɫɤɚɹ ɨɛɥɚɫɬɶ.
ɥɨɝɢɱɟɫɤɨɣ ɫɬɪɭɤɬɭɪɨɣ:
.
0
.
1
ɢ ɇ1.
0
ɂɧɬɟɪɩɪɟɬɚɰɢɹ ɪɚɡɥɢɱɧɵɯ ɭɪɨɜɧɟɣ ɡɧɚɱɢɦɨɫɬɢ ɩɪɢɜɟɞɟɧɚ ɜ ɬɚɛɥɢɰɟ.
ɍɪɨɜɟɧɶ ɡɧɚɱɢɦɨɫɬɢ Ɋɟɲɟɧɢɟ ȼɨɡɦɨɠɧɵɣ ɫɬɚɬɢɫɬɢɱɟɫɤɢɣ ɜɵɜɨɞ
ȡ > 0,1
ȡ 0,1
ȡ 0,05
ȡ 0,01
ɉɪɢɧɢɦɚɟɬɫɹ ɇ0
ɋɨɦɧɟɧɢɹ ɜ ɢɫɬɢɧɧɨɫɬɢ
ɇ
, ɧɟɨɩɪɟɞɟɥɟɧɧɨɫɬɶ
0
Ɂɧɚɱɢɦɨɫɬɶ,
ɨɬɤɥɨɧɟɧɢɟ
ȼɵɫɨɤɚɹ ɡɧɚɱɢɦɨɫɬɶ,
ɨɬɤɥɨɧɟɧɢɟ
0
0
ɋɬɚɬɢɫɬɢɱɟɫɤɢ ɞɨɫɬɨɜɟɪɧɵɟ ɪɚɡɥɢɱɢɹ
ɧɟ ɨɛɧɚɪ
Ɋɚɡɥɢɱɢɹ ɨɛɧɚɪɭɠɟɧɵ ɧɚ ɭɪɨɜɧɟ
ɫɬɚɬɢɫɬɢɱɟɫɤɨɣ ɬɟɧɞɟɧɰɢɢ
Ɉɛɧɚɪɭɠɟɧɵ ɫɬɚɬɢɫɬɢɱɟɫɤɢ
ɞɨɫɬɨɜɟɪɧɵɟ (ɡɧɚɱɢɦɵɟ) ɪɚɡɥɢɱɢɹ
Ɋɚɡɥɢɱɢɹ ɨɛɧɚɪɭɠɟɧɵ ɧɚ ɜɵɫɨɤɨɦ
ɭɪɨɜɧɟ ɫɬɚɬɢɫɬɢɱɟɫɤɨɣ ɡɧɚɱɢɦɨɫɬɢ
44
ɠɟɧɵ
Ȼɨɥɶɲɨɟ ɪɚɡɧɨɨɛɪɚɡɢɟ ɤɪɢɬɟɪɢɟɜ ɪɚɡɥɢɱɢɹ ɩɪɟɞɨɫɬɚɜɥɹɟɬ ɫɥɟɞɭɸɳɢɟ ɜɨɡɦɨɠɧɨɫɬɢ: ɜɵɛɢɪɚɬɶ ɤɪɢɬɟɪɢɣ, ɚɞɟɤɜɚɬɧɵɣ ɬɢɩɭ ɲɤɚɥɵ, ɜ ɤɨɬɨɪɨɣ ɩɨɥɭɱɟɧɵ
ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɟ ɞɚɧɧɵɟ; ɪɚɛɨɬɚɬɶ ɫɨ ɫɜɹɡɧɵɦɢ (ɡɚɜɢɫɢɦɵɦɢ) ɢ ɧɟɫɜɹɡɧɵɦɢ
(ɧɟɡɚɜɢɫɢɦɵɦɢ) ɜɵɛɨɪɤɚɦɢ; ɪɚɛɨɬɚɬɶ ɫ ɧɟɪɚɜɧɵɦɢ ɩɨ ɨɛɴɟɦɭ ɜɵɛɨɪɤɚɦɢ; ɜɵɛɢɪɚɬɶ ɢɡ ɤɪɢɬɟɪɢɟɜ ɪɚɡɧɵɟ ɩɨ ɦɨɳɧɨɫɬɢ (ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɰɟɥɟɣ ɢɫɫɥɟɞɨɜɚɧɢɹ).
ɉɚɪɚɦɟɬɪɢɱɟɫɤɢɣ ɤɪɢɬɟɪɢɣ ɪɚɡɥɢɱɢɹ ɨɫɧɨɜɚɧ ɧɚ ɤɨɧɤɪɟɬɧɨɦ ɬɢɩɟ ɪɚɫ-
ɩɪɟɞɟɥɟɧɢɹ ɝɟɧɟɪɚɥɶɧɨɣ ɫɨɜɨɤɭɩɧɨɫɬɢ (ɤɚɤ ɩɪɚɜɢɥɨ, ɧɨɪɦɚɥɶɧɨɦ) ɢɥɢ ɢɫɩɨɥɶɡɭɟɬ ɩɚɪɚɦɟɬɪɵ ɷɬɨɣ ɫɨɜɨɤɭɩɧɨɫɬɢ.
ɇɟɩɚɪɚɦɟɬɪɢɱɟɫɤɢɣ ɤɪɢɬɟɪɢɣ ɪɚɡɥɢɱɢɹ ɧɟ ɛɚɡɢɪɭɟɬɫɹ ɧɚ ɩɪɟɞɩɨɥɨɠɟ-
ɧɢɢ ɨ ɬɢɩɟ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɝɟɧɟɪɚɥɶɧɨɣ ɫɨɜɨɤɭɩɧɨɫɬɢ ɢ ɧɟ ɢɫɩɨɥɶɡɭɟɬ ɩɚɪɚɦɟɬɪɵ ɷɬɨɣ ɫɨɜɨɤɭɩɧɨɫɬɢ.
ɉɪɢ ɩɨɞɝɨɬɨɜɤɟ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨɝɨ ɢɫɫɥɟɞɨɜɚɧɢɹ ɩɫɢɯɨɥɨɝ ɞɨɥɠɟɧ ɡɚɪɚɧɟɟ ɡɚɩɥɚɧɢɪɨɜɚɬɶ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɫɨɩɨɫɬɚɜɥɹɟɦɵɯ ɜɵɛɨɪɨɤ (ɩɪɟɠɞɟ ɜɫɟɝɨ
ɫɜɹɡɧɨɫɬɶ/ɧɟɫɜɹɡɧɨɫɬɶ ɢ ɨɞɧɨɪɨɞɧɨɫɬɶ), ɢɯ ɜɟɥɢɱɢɧɭ (ɨɛɴɟɦ), ɬɢɩ ɢɡɦɟɪɢɬɟɥɶɧɨɣ ɲɤɚɥɵ ɢ ɜɢɞ ɢɫɩɨɥɶɡɭɟɦɨɝɨ ɤɪɢɬɟɪɢɹ ɪɚɡɥɢɱɢɹ. ɉɨɫɥɟɞɨɜɚɬɟɥɶɧɨ
ɷɬɨ ɦɨɠ-
ɧɨ ɩɪɟɞɫɬɚɜɢɬɶ ɜ ɜɢɞɟ ɫɥɟɞɭɸɳɢɯ ɷɬɚɩɨɜ:
– ɨɩɪɟɞɟɥɢɬɶ, ɹɜɥɹɟɬɫɹ ɥɢ ɜɵɛɨɪɤɚ ɫɜɹɡɧɨɣ ɢɥɢ ɧɟɫɜɹɡɧɨɣ;
– ɨɩɪɟɞɟɥɢɬɶ ɨɞɧɨɪɨɞɧɨɫɬɶ / ɧɟɨɞɧɨɪɨɞɧɨɫɬɶ ɜɵɛɨɪɤɢ;
– ɨɰɟɧɢɬɶ ɨɛɴɟɦ ɜɵɛɨɪɤɢ ɢ, ɡɧɚɹ ɨɝɪɚɧɢɱɟɧɢɹ ɤɚɠɞɨɝɨ ɤɪɢɬɟɪɢɹ ɩɨ ɨɛɴɟ-
ɦɭ, ɜɵɛɪɚɬɶ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɣ ɤɪɢɬɟɪɢɣ.
ɐɟɥɟɫɨɨɛɪɚɡɧɟɟ ɧɚɱɢɧɚɬɶ ɪɚɛɨɬɭ ɫ ɜɵɛɨɪɚ ɧɚɢɦɟɧɟɟ ɬɪɭɞɨɟɦɤɨɝɨ ɤɪɢɬɟɪɢɹ. ȿɫɥɢ ɢɫɩɨɥɶɡɭɟɦɵɣ ɤɪɢɬɟɪɢɣ ɧɟ ɜɵɹɜɢɥ ɪɚɡɥɢɱɢɹ, ɬɨ
ɫɥɟɞɭɟɬ ɩɪɢɦɟɧɢɬɶ
ɛɨɥɟɟ ɦɨɳɧɵɣ, ɧɨ ɨɞɧɨɜɪɟɦɟɧɧɨ ɢ ɛɨɥɟɟ ɬɪɭɞɨɟɦɤɢɣ ɤɪɢɬɟɪɢɣ.
ȿɫɥɢ ɜ ɪɚɫɩɨɪɹɠɟɧɢɢ ɩɫɢɯɨɥɨɝɚ ɢɦɟɟɬɫɹ ɧɟɫɤɨɥɶɤɨ ɤɪɢɬɟɪɢɟɜ, ɬɨ ɫɥɟɞɭɟɬ
ɜɵɛɢɪɚɬɶ ɬɟ ɢɡ ɧɢɯ, ɤɨɬɨɪɵɟ ɧɚɢɛɨɥɟɟ ɩɨɥɧɨ ɢɫɩɨɥɶɡɭɸɬ ɢɧɮɨɪɦɚɰɢɸ, ɫɨɞɟɪɠɚɳɭɸɫɹ ɜ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɯ ɞɚɧɧɵɯ.
2.2. ɇɟɩɚɪɚɦɟɬɪɢɱɟɫɤɢɟ ɤɪɢɬɟɪɢɢ ɞɥɹ ɧɟɫɜɹɡɧɵɯ ɜɵɛɨɪɨɤ
ɇɟɫɜɹɡɧɵɟ ɢɥɢ ɧɟɡɚɜɢɫɢɦɵɟ ɜɵɛɨɪɤɢ ɨɛɪɚɡɭɸɬɫɹ, ɤɨɝɞɚ ɜ ɰɟɥɹɯ ɷɤɫɩɟɪɢɦɟɧɬɚ ɞɥɹ ɫɪɚɜɧɟɧɢɹ ɩɪɢɜɥɟɤɚɸɬɫɹ ɞɚɧɧɵɟ ɞɜɭɯ ɢɥɢ ɛɨɥɟɟ ɜɵɛɨɪɨɤ, ɩɪɢɱɟɦ ɷɬɢ
ɜɵɛɨɪɤɢ ɦɨɝɭɬ ɛɵɬɶ ɜɡɹɬɵ ɢɡ ɨɞɧɨɣ ɢɥɢ ɢɡ ɪɚɡɧɵɯ ɝɟɧɟɪɚɥɶɧɵɯ ɫɨɜɨɤɭɩɧɨɫɬɟɣ.
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɞɥɹ ɧɟɫɜɹɡɧɵɯ ɜɵɛɨɪɨɤ ɯɚɪɚɤɬɟɪɧɨ, ɱɬɨ ɜ ɧɢɯ ɨɛɹɡɚɬɟɥɶɧɨ ɜɯɨɞɹɬ ɪɚɡɧɵɟ ɢɫɩɵɬɭɟɦɵɟ. Ⱦɥɹ ɨɰɟɧɤɢ ɞɨɫɬɨɜɟɪɧɨɫɬɢ ɪɚɡɥɢɱɢɣ ɦɟɠɞɭ
ɧɟɫɜɹɡɧɵɦɢ ɜɵɛɨɪɤɚɦɢ ɢɫɩɨɥɶɡɭɟɬɫɹ ɪɹɞ ɧɟɩɚɪɚɦɟɬɪɢɱɟɫɤɢɯ ɤɪɢɬɟɪɢɟɜ. Ɋɚɫɫɦɨɬɪɢɦ ɧɟɤɨɬɨɪɵɟ ɢɡ ɧɢɯ.
Q-ɤɪɢɬɟɪɢɣ Ɋɨɡɟɧɛɚɭɦɚ
Ʉɪɢɬɟɪɢɣ ɢɫɩɨɥɶɡɭɟɬɫɹ ɞɥɹ ɨɰɟɧɤɢ ɪɚɡɥɢɱɢɣ ɦɟɠɞɭ ɞɜɭɦɹ ɜɵɛɨɪɤɚɦɢ ɩɨ
ɭɪɨɜɧɸ ɤɚɤɨɝɨ-ɥɢɛɨ ɤɨɥɢɱɟɫɬɜɟɧɧɨ ɢɡɦɟɪɟɧɧɨɝɨ ɩɪɢɡɧɚɤɚ [5].
ȼɵɞɜɢɝɚɸɬɫɹ
H
: ɍɪɨɜɟɧɶ ɩɪɢɡɧɚɤɚ ɜ ɜɵɛɨɪɤɟ 1 ɧɟ ɩɪɟɜɵɲɚɟɬ ɭɪɨɜɧɹ ɩɪɢɡɧɚɤɚ ɜ ɜɵ-
0
ɝɢɩɨɬɟɡɵ:
ɛɨɪɤɟ 2.
45
H
: ɍɪɨɜɟɧɶ ɩɪɢɡɧɚɤɚ ɜ ɜɵɛɨɪɤɟ 1 ɩɪɟɜɵɲɚɟɬ ɭɪɨɜɟɧɶ ɩɪɢɡɧɚɤɚ ɜ ɜɵɛɨɪ-
1
ɤɟ 2.
ɇɚ ɪɢɫɭɧɤɟ 2 ɩɪɟɞɫɬɚɜɥɟɧɨ ɬɪɢ ɜɚɪɢɚɧɬɚ ɫɨɨɬɧɨɲɟɧɢɹ ɪɹɞɨɜ ɡɧɚɱɟɧɢɣ ɜ
ɞɜɭɯ ɜɵɛɨɪɤɚɯ. ȼ ɜɚɪɢɚɧɬɟ (ɚ) ɜɫɟ ɡɧɚɱɟɧɢɹ ɩɟɪɜɨɝɨ ɪɹɞɚ ɜɵɲɟ ɜɫɟɯ ɡɧɚɱɟɧɢɣ
ɜɬɨɪɨɝɨ ɪɹɞɚ. Ɋɚɡɥɢɱɢɹ, ɛɟɡɭɫɥɨɜɧɨ, ɞɨɫɬɨɜɟɪɧɵ ɩɪɢ ɫɨɛɥɸɞɟɧɢɢ ɭɫɥɨɜɢɹ, ɱɬɨ
n
, n2 11. ȼ ɜɚɪɢɚɧɬɟ (ɛ), ɧɚɩɪɨɬɢɜ, ɨɛɚ ɪɹɞɚ ɧɚɯɨɞɹɬɫɹ ɧɚ ɨɞɧɨɦ ɢ ɬɨɦ ɠɟ
1
ɭɪɨɜɧɟ: ɪɚɡɥɢɱɢɹ ɧɟɞɨɫɬɨɜɟɪɧɵ. ȼ ɜɚɪɢɚɧɬɟ (ɜ) ɪɹɞɵ ɱɚɫɬɢɱɧɨ ɩɟɪɟɤɪɟɳɢɜɚɸɬɫɹ, ɧɨ ɜɫɟ ɠɟ ɩɟɪɜɵɣ ɪɹɞ ɨɤɚɡɵɜɚɟɬɫɹ ɝɨɪɚɡɞɨ ɜɵɲɟ ɜɬɨɪɨɝɨ.
S
Ⱦɨɫɬɚɬɨɱɧɨ ɥɢ ɜɟɥɢɤɢ ɡɨɧɵ
ɬɨɪɵɟ ɜɵɲɟ ɦɚɤɫɢɦɚɥɶɧɨɝɨ ɡɧɚɱɟɧɢɹ ɜɬɨɪɨɝɨ ɪɹɞɚ,
ɢ S2 (S1 – ɡɨɧɚ ɡɧɚɱɟɧɢɣ ɩɟɪɜɨɝɨ ɪɹɞɚ, ɤɨ-
1
S
– ɡɨɧɚ ɡɧɚɱɟɧɢɣ ɜɬɨɪɨɝɨ
2
ɪɹɞɚ, ɤɨɬɨɪɵɟ ɦɟɧɶɲɟ ɦɢɧɢɦɚɥɶɧɨɝɨ ɡɧɚɱɟɧɢɹ ɩɟɪɜɨɝɨ ɪɹɞɚ), ɜ ɫɭɦɦɟ ɫɨɫɬɚɜɥɹɸɳɢɟ
ɱɟɫɤɢɟ ɡɧɚɱɟɧɢɹ
Q, ɦɨɠɧɨ ɨɩɪɟɞɟɥɢɬɶ ɩɨ ɬɚɛɥɢɰɟ 3 ɉɪɢɥɨɠɟɧɢɹ, ɝɞɟ ɩɪɢɜɟɞɟɧɵ ɤɪɢɬɢ-
Q ɞɥɹ ɪɚɡɧɵɯ n. ɑɟɦ ɜɟɥɢɱɢɧɚ Q ɛɨɥɶɲɟ, ɬɟɦ ɛɨɥɟɟ ɞɨɫɬɨɜɟɪ-
ɧɵɟ ɪɚɡɥɢɱɢɹ ɦɨɠɧɨ ɤɨɧɫɬɚɬɢɪɨɜɚɬɶ.
ɚ)
Ɋɹɞ 1
Ɋɹɞ 2
S1
S
2
ɛ)
Ɋɹɞ 1 Ɋɹɞ 2
=0
S
1
S
=0
2
ɜ)
Ɋɹɞ 1
Ɋɹɞ 2
S1
S
2
Ɋɢɫ. 2. ȼɨɡɦɨɠɧɵɟ ɫɨɨɬɧɨɲɟɧɢɹ ɪɹɞɨɜ ɡɧɚɱɟɧɢɣ ɜ ɞɜɭɯ ɜɵɛɨɪɤɚɯ
Ɉɝɪɚɧɢɱɟɧɢɹ ɤɪɢɬɟɪɢɹ Q.
1. ɂɡɦɟɪɟɧɢɟ ɞɨɥɠɧɨ ɛɵɬɶ ɩɪɨɜɟɞɟɧɨ ɜ ɲɤɚɥɟ ɩɨɪɹɞɤɚ, ɢɧɬɟɪɜɚɥɨɜ ɢɥɢ
ɨɬɧɨɲɟɧɢɣ.
2.
ȼɵɛɨɪɤɢ ɞɨɥɠɧɵ ɛɵɬɶ ɧɟɡɚɜɢɫɢɦɵɦɢ.
3. ȼ ɤɚɠɞɨɣ ɢɡ ɫɨɩɨɫɬɚɜɥɹɟɦɵɯ ɜɵɛɨɪɨɤ ɞɨɥɠɧɨ ɛɵɬɶ ɧɟ ɦɟɧɟɟ 11 ɧɚɛɥɸɞɟɧɢɣ. ɉɪɢ ɷɬɨɦ ɨɛɴɟɦɵ ɜɵɛɨɪɨɤ ɞɨɥɠɧɵ ɩɪɢɦɟɪɧɨ ɫɨɜɩɚɞɚɬɶ. ȿ. ȼ. Ƚɭɛɥɟɪɨɦ
(Ƚɭɛɥɟɪ ȿ. ȼ., 1978, ɫ. 75) ɭɤɚɡɵɜɚɸɬɫɹ ɫɥɟɞɭɸɳɢɟ ɩɪɚɜɢɥɚ:
ɚ) ɟɫɥɢ ɜ ɨɛɟɢɯ ɜɵɛɨɪɤɚɯ ɦɟɧɶɲɟ 50 ɧɚɛɥɸɞɟɧɢɣ, ɬɨ ɚɛɫɨɥɸɬɧɚɹ ɜɟɥɢɱɢ-
ɧɚ ɪɚɡɧɨɫɬɢ ɦɟɠɞɭ
n
ɢ n2 ɧɟ ɞɨɥɠɧɚ ɛɵɬɶ ɛɨɥɶɲɟ 10 ɧɚɛɥɸɞɟɧɢɣ;
1
ɛ) ɟɫɥɢ ɜ ɤɚɠɞɨɣ ɢɡ ɜɵɛɨɪɨɤ ɛɨɥɶɲɟ 51 ɧɚɛɥɸɞɟɧɢɹ, ɧɨ ɦɟɧɶɲɟ 100, ɬɨ
ɚɛɫɨɥɸɬɧɚɹ ɜɟɥɢɱɢɧɚ ɪɚɡɧɨɫɬɢ ɦɟɠɞɭ
n
ɢ n2 ɧɟ ɞɨɥɠɧɚ ɛɵɬɶ ɛɨɥɶɲɟ 20 ɧɚɛɥɸ-
1
ɞɟɧɢɣ;
ɜ) ɟɫɥɢ ɜ ɤɚɠɞɨɣ ɢɡ ɜɵɛɨɪɨɤ ɛɨɥɶɲɟ 100 ɧɚɛɥɸɞɟɧɢɣ, ɬɨ ɞɨɩɭɫɤɚɟɬɫɹ,
ɱɬɨɛɵ ɨɞɧɚ ɢɡ ɜɵɛɨɪɨɤ ɛɵɥɚ ɛɨɥɶɲɟ ɞɪɭɝɨɣ ɧɟ ɛɨɥɟɟ ɱɟɦ ɜ 1,5–2 ɪɚɡɚ.
4. Ⱦɢɚɩɚɡɨɧɵ ɪɚɡɛɪɨɫɚ ɡɧɚɱɟɧɢɣ ɜ ɞɜɭɯ ɜɵɛɨɪɤɚɯ ɞɨɥɠɧɵ ɧɟ ɫɨɜɩɚɞɚɬɶ
ɦɟɠɞɭ ɫɨɛɨɣ, ɜ ɩɪɨɬɢɜɧɨɦ ɫɥɭɱɚɟ ɩɪɢɦɟɧɟɧɢɟ ɤɪɢɬɟɪɢɹ ɛɟɫɫɦɵɫɥɟɧɧɨ.
Ⱥɥɝɨɪɢɬɦ ɩɨɞɫɱɟɬɚ Q-ɤɪɢɬɟɪɢɹ Ɋɨɡɟɧɛɚɭɦɚ.
1. ɉɪɨɜɟɪɢɬɶ, ɜɵɩɨɥɧɹɸɬɫɹ ɥɢ ɨɝɪɚɧɢɱɟɧɢɹ: n
46
, n
11, n1 § n2.
1
2
2. ɍɩɨɪɹɞɨɱɢɬɶ ɡɧɚɱɟɧɢɹ ɨɬɞɟɥɶɧɨ ɜ ɤɚɠɞɨɣ ɜɵɛɨɪɤɟ ɩɨ ɫɬɟɩɟɧɢ ɭɛɵɜɚ-
ɧɢɹ ɩɪɢɡɧɚɤɚ. ɋɱɢɬɚɬɶ ɜɵɛɨɪɤɨɣ 1 ɬɭ ɜɵɛɨɪɤɭ, ɡɧɚɱɟɧɢɹ ɜ ɤɨɬɨɪɨɣ ɩɪɟɞɩɨɥɨɠɢɬɟɥɶɧɨ ɜɵɲɟ, ɚ ɜɵɛɨɪɤɨɣ 2 ɬɭ, ɝɞɟ ɡɧɚɱɟɧɢɹ ɩɪɟɞɩɨɥɨɠɢɬɟɥɶɧɨ ɧɢɠɟ.
3. Ɉɩɪɟɞɟɥɢɬɶ ɦɚɤɫɢɦɚɥɶɧɨɟ ɡɧɚɱɟɧɢɟ ɜ ɜɵɛɨɪɤɟ 2.
4. ɉɨɞɫɱɢɬɚɬɶ ɤɨɥɢɱɟɫɬɜɨ ɡɧɚɱɟɧɢɣ ɜ ɜɵɛɨɪɤɟ 1, ɤɨɬɨɪɵɟ ɜɵɲɟ ɦɚɤɫɢ-
S
ɦɚɥɶɧɨɝɨ ɡɧɚɱɟɧɢɹ ɜ ɜɵɛɨɪɤɟ 2. Ɉɛɨɡɧɚɱɢɬɶ ɩɨɥɭɱɟɧɧɭɸ ɜɟɥɢɱɢɧɭ ɤɚɤ
.
1
5. Ɉɩɪɟɞɟɥɢɬɶ ɦɢɧɢɦɚɥɶɧɨɟ ɡɧɚɱɟɧɢɟ ɜ ɜɵɛɨɪɤɟ 1.
6. ɉɨɞɫɱɢɬɚɬɶ ɤɨɥɢɱɟɫɬɜɨ ɡɧɚɱɟɧɢɣ ɜ ɜɵɛɨɪɤɟ 2, ɤɨɬɨɪɵɟ ɧɢɠɟ ɦɢɧɢɦɚɥɶɧɨɝɨ ɡɧɚɱɟɧɢɹ ɜɵɛɨɪɤɢ. Ɉɛɨɡɧɚɱɢɬɶ ɩɨɥɭɱɟɧɧɭɸ ɜɟɥɢɱɢɧɭ ɤɚɤ
7. ɉɨɞɫɱɢɬɚɬɶ ɷɦɩɢɪɢɱɟɫɤɨɟ ɡɧɚɱɟɧɢɟ
Q ɩɨ ɮɨɪɦɭɥɟ Q = S
8. ɉɨ ɬɚɛɥɢɰɟ 5 ɉɪɢɥɨɠɟɧɢɹ ɨɩɪɟɞɟɥɢɬɶ ɤɪɢɬɢɱɟɫɤɢɟ ɡɧɚɱɟɧɢɹ
n
ɞɚɧɧɵɯ
Q
ɫ
ɢ n2. ȿɫɥɢ Q
1
9. ɉɪɢ
= 8 (ȡ 0,05) ɢ Q
ɤɪ
n
ɦɟɪɟ, ɪɚɜɧɹɟɬɫɹ
, n2 > 26 ɫɨɩɨɫɬɚɜɢɬɶ ɩɨɥɭɱɟɧɧɨɟ ɷɦɩɢɪɢɱɟɫɤɨɟ ɡɧɚɱɟɧɢɟ
1
Q
ɪɚɜɧɨ Q
ɷɦɩ
= 10 (ȡ 0,01). ȿɫɥɢ Q
ɤɪ
= 8, ɇ0 ɨɬɜɟɪɝɚɟɬɫɹ.
ɤp
0,05
ɢɥɢ ɩɪɟɜɵɲɚɟɬ ɟɝɨ, ɇ0 ɨɬɜɟɪɝɚɟɬɫɹ.
ɩɪɟɜɵɲɚɟɬ ɢɥɢ, ɩɨ ɤɪɚɣɧɟɣ
ɷɦɩ
+ S2.
1
S
.
2
Q ɞɥɹ
Ɂɚɦɟɱɚɧɢɟ. ȿɫɥɢ ɷɦɩɢɪɢɱɟɫɤɚɹ ɜɟɥɢɱɢɧɚ ɤɪɢɬɟɪɢɹ ɫɨɜɩɚɞɚɟɬ ɫ ɝɪɚɧɢɰɟɣ
ɡɨɧɵ ɧɟɡɧɚɱɢɦɨɫɬɢ, ɦɨɠɧɨ ɥɢɲɶ ɭɬɜɟɪɠɞɚɬɶ, ɱɬɨ ɪɚɡɥɢɱɢɹ ɞɨɫɬɨɜɟɪɧɵ ɩɪɢ
ȡ 0,05, ɟɫɥɢ ɨɧɨ ɨɤɚɡɵɜɚɟɬɫɹ ɦɟɠɞɭ ɞɜɭɦɹ ɤɪɢɬɢɱɟɫɤɢɦɢ ɡɧɚɱɟɧɢɹɦɢ, ɬɨ
ȡ < 0,05. ȿɫɥɢ ɷɦɩɢɪɢɱɟɫɤɨɟ ɡɧɚɱɟɧɢɟ ɤɪɢɬɟɪɢɹ ɨɤɚɡɵɜɚɟɬɫɹ ɧɚ ɝɪɚɧɢɰɟ ɡɨɧɵ
ɡɧɚɱɢɦɨɫɬɢ, ɬɨ
ȡ 0,01, ɜ ɡɨɧɟ ɡɧɚɱɢɦɨɫɬɢ – ȡ < 0,01.
U-ɤɪɢɬɟɪɢɣ ȼɢɥɤɨɤɫɨɧɚ – Ɇɚɧɧɚ – ɍɢɬɧɢ
Ʉɪɢɬɟɪɢɣ ɩɪɟɞɧɚɡɧɚɱɟɧ ɞɥɹ ɨɰɟɧɤɢ ɪɚɡɥɢɱɢɣ ɦɟɠɞɭ ɞɜɭɦɹ ɜɵɛɨɪɤɚɦɢ ɩɨ
ɭɪɨɜɧɸ ɤɚɤɨɝɨ-ɥɢɛɨ ɤɨɥɢɱɟɫɬɜɟɧɧɨ ɢɡɦɟɪɟɧɧɨɝɨ ɩɪɢɡɧɚɤɚ. ɉɨɡɜɨɥɹɟɬ ɜɵɹɜɥɹɬɶ
ɪɚɡɥɢɱɢɹ ɦɟɠɞɭ
ɦɚɥɵɦɢ ɜɵɛɨɪɤɚɦɢ, ɤɨɝɞɚ n1, n
3 ɢɥɢ n1 = 2, n2 5, ɢ ɹɜɥɹɟɬ-
2
ɫɹ ɛɨɥɟɟ ɦɨɳɧɵɦ, ɱɟɦ ɤɪɢɬɟɪɢɣ Ɋɨɡɟɧɛɚɭɦɚ.
ȼɵɞɜɢɝɚɸɬɫɹ ɫɥɟɞɭɸɳɢɟ
H
: ɍɪɨɜɟɧɶ ɩɪɢɡɧɚɤɚ ɜ ɝɪɭɩɩɟ 2 ɧɟ ɧɢɠɟ ɭɪɨɜɧɹ ɩɪɢɡɧɚɤɚ ɜ ɝɪɭɩɩɟ 1.
0
H
: ɍɪɨɜɟɧɶ ɩɪɢɡɧɚɤɚ ɜ ɝɪɭɩɩɟ 2 ɧɢɠɟ ɭɪɨɜɧɹ ɩɪɢɡɧɚɤɚ ɜ ɝɪɭɩɩɟ 1.
1
ɝɢɩɨɬɟɡɵ:
Ɋɚɫɫɦɨɬɪɢɦ ɬɪɢ ɢɡ ɦɧɨɠɟɫɬɜɚ ɜɨɡɦɨɠɧɵɯ ɜɚɪɢɚɧɬɨɜ ɫɨɨɬɧɨɲɟɧɢɹ ɞɜɭɯ
ɪɹɞɨɜ ɡɧɚɱɟɧɢɣ (ɪɢɫɭɧɨɤ 3).
ɚ)
Ɋɹɞ 1
Ɋɹɞ 2
ɛ)
Ɋɹɞ 1
Ɋɹɞ 2
ɜ)
Ɋɹɞ 1
Ɋɹɞ 2
Ɋɢɫ. 3. ȼɨɡɦɨɠɧɵɟ ɜɚɪɢɚɧɬɵ ɫɨɨɬɧɨɲɟɧɢɹ ɞɜɭɯ ɪɹɞɨɜ ɡɧɚɱɟɧɢɣ
ȼ ɜɚɪɢɚɧɬɟ (ɚ) ɪɹɞɵ ɩɨɱɬɢ ɧɟ ɩɟɪɟɤɪɟɳɢɜɚɸɬɫɹ. Ɉɛɥɚɫɬɶ ɧɚɥɨɠɟɧɢɹ
ɫɥɢɲɤɨɦ ɦɚɥɚ, ɱɬɨɛɵ ɫɤɪɚɞɵɜɚɬɶ ɪɚɡɥɢɱɢɹ ɦɟɠɞɭ ɪɹɞɚɦɢ. ȿɫɬɶ ɲɚɧɫ, ɱɬɨ ɪɚɡɥɢɱɢɹ ɦɟɠɞɭ ɧɢɦɢ ɞɨɫɬɨɜɟɪɧɵ. ȼ ɜɚɪɢɚɧɬɟ (ɛ) ɜɬɨɪɨɣ ɪɹɞ ɬɨɠɟ ɧɢɠɟ ɩɟɪɜɨɝɨ,
47
ɧɨ ɢ ɨɛɥɚɫɬɶ ɩɟɪɟɤɪɟɳɢɜɚɸɳɢɯɫɹ ɡɧɚɱɟɧɢɣ ɭ ɞɜɭɯ ɪɹɞɨɜ ɞɨɫɬɚɬɨɱɧɨ ɨɛɲɢɪɧɚ,
ɧɨ ɦɨɠɟɬ ɧɟ ɞɨɫɬɢɝɚɬɶ ɤɪɢɬɢɱɟɫɤɨɣ ɜɟɥɢɱɢɧɵ, ɤɨɝɞɚ ɪɚɡɥɢɱɢɹ ɩɪɢɞɟɬɫɹ ɩɪɢɡɧɚɬɶ ɧɟɫɭɳɟɫɬɜɟɧɧɵɦɢ. ȼ ɜɚɪɢɚɧɬɟ (ɜ) ɨɛɥɚɫɬɶ ɧɚɥɨɠɟɧɢɹ ɧɚɫɬɨɥɶɤɨ ɨɛɲɢɪɧɚ,
ɱɬɨ ɪɚɡɥɢɱɢɹ ɦɟɠɞɭ ɪɹɞɚɦɢ ɫɤɪɚɞɵɜɚɸɬɫɹ.
Ɉɝɪɚɧɢɱɟɧɢɹ U-ɤɪɢɬɟɪɢɹ.
1. ɂɡɦɟɪɟɧɢɟ ɞɨɥɠɧɨ ɛɵɬɶ ɩɪɨɜɟɞɟɧɨ ɜ ɲɤɚɥɟ ɢɧɬɟɪɜɚɥɨɜ ɢɥɢ ɨɬɧɨɲɟ-
ɧɢɣ.
ȼɵɛɨɪɤɢ ɞɨɥɠɧɵ ɛɵɬɶ ɧɟɡɚɜɢɫɢɦɵɦɢ.
2.
3. ȼ ɤɚɠɞɨɣ ɜɵɛɨɪɤɟ ɞɨɥɠɧɨ ɛɵɬɶ ɧɟ ɦɟɧɟɟ 3 ɧɚɛɥɸɞɟɧɢɣ:
n
= 2, n2 5.
1
n1, n
3 ɢɥɢ
2
4. ȼ ɤɚɠɞɨɣ ɜɵɛɨɪɤɟ ɞɨɥɠɧɨ ɛɵɬɶ ɧɟ ɛɨɥɟɟ 60 ɧɚɛɥɸɞɟɧɢɣ, ɯɨɬɹ ɭɠɟ ɩɪɢ
n1, n
20 ɪɚɧɠɢɪɨɜɚɧɢɟ ɫɬɚɧɨɜɢɬɫɹ ɬɪɭɞɨɟɦɤɢɦ. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɥɭɱɲɟ ɢɫɩɨɥɶ-
2
ɡɨɜɚɬɶ ɞɪɭɝɨɣ ɤɪɢɬɟɪɢɣ, ɧɚɩɪɢɦɟɪ ɭɝɥɨɜɨɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɟ Ɏɢɲɟɪɚ ɜ ɤɨɦɛɢɧɚ-
Ȝ-ɤɪɢɬɟɪɢɟɦ.
ɰɢɢ ɫ
Ⱥɥɝɨɪɢɬɦ ɩɨɞɫɱɟɬɚ U-ɤɪɢɬɟɪɢɹ.
1. ɉɨɥɭɱɟɧɧɵɟ ɞɚɧɧɵɟ ɧɟɨɛɯɨɞɢɦɨ ɩɪɟɞɫɬɚɜɢɬɶ ɤɚɤ ɨɞɢɧ ɪɹɞ ɢ ɭɩɨɪɹɞɨ-
ɱɢɬɶ ɟɝɨ ɩɨ ɜɨɡɪɚɫɬɚɧɢɸ ɜɯɨɞɹɳɢɯ ɜ ɧɟɝɨ ɜɟɥɢɱɢɧ.
ɉɪɨɪɚɧɠɢɪɨɜɚɬɶ ɡɧɚɱɟɧɢɹ, ɩɪɢɩɢɫɵɜɚɹ ɦɟɧɶɲɟɦɭ ɡɧɚɱɟɧɢɸ ɦɟɧɶɲɢɣ
2.
ɪɚɧɝ. ȼɫɟɝɨ ɪɚɧɝɨɜ ɩɨɥɭɱɢɬɫɹ (
3.
ɉɨɞɫɱɢɬɚɬɶ ɫɭɦɦɭ ɪɚɧɝɨɜ ɨɬɞɟɥɶɧɨ ɩɨ ɤɚɠɞɨɣ ɝɪɭɩɩɟ. ɉɪɨɜɟɪɢɬɶ, ɫɨɜ-
n1+ n
).
2
ɩɚɞɚɟɬ ɥɢ ɨɛɳɚɹ ɫɭɦɦɚ ɪɚɧɝɨɜ ɫ ɪɚɫɱɟɬɧɨɣ.
4.
Ɉɩɪɟɞɟɥɢɬɶ ɛɨɥɶɲɭɸ ɢɡ ɞɜɭɯ ɪɚɧɝɨɜɵɯ ɫɭɦɦ.
5.
Ɉɩɪɟɞɟɥɢɬɶ ɡɧɚɱɟɧɢɟ U ɩɨ ɮɨɪɦɭɥɟ:
ɷɦɩ
nnU
21 x
xx
2
,
T
)1(
nn
n
– ɤɨɥɢɱɟɫɬɜɨ ɢɫɩɵɬɭɟɦɵɯ ɜ ɝɪɭɩɩɟ 1;
ɝɞɟ
1
n
– ɤɨɥɢɱɟɫɬɜɨ ɢɫɩɵɬɭɟɦɵɯ ɜ ɝɪɭɩɩɟ 2;
2
n
– ɤɨɥɢɱɟɫɬɜɨ ɢɫɩɵɬɭɟɦɵɯ ɜ ɝɪɭɩɩɟ ɫ ɛɨɥɶɲɟɣ ɪɚɧɝɨɜɨɣ ɫɭɦɦɨɣ;
x
Ɍ
– ɛɨɥɶɲɚɹ ɢɡ ɞɜɭɯ ɪɚɧɝɨɜɵɯ ɫɭɦɦ.
ɯ
6. Ɉɩɪɟɞɟɥɢɬɶ ɤɪɢɬɢɱɟɫɤɢɟ ɡɧɚɱɟɧɢɹ
ɧɢɹ. ȿɫɥɢ
ɇ
ɨɬɜɟɪɝɚɟɬɫɹ.
0
UU !
, ɬɨ ɧɟɬ ɨɫɧɨɜɚɧɢɣ ɨɬɜɟɪɝɧɭɬɶ ɇ0. ȼ ɩɪɨɬɢɜɧɨɦ ɫɥɭɱɚɟ
05,0ɤɪɷɦɩ
U-ɤɪɢɬɟɪɢɹ ɩɨ ɬɚɛɥɢɰɟ 6 ɉɪɢɥɨɠɟ-
ɉɪɚɜɢɥɚ ɪɚɧɠɢɪɨɜɚɧɢɹ:
ɧɚɢɦɟɧɶɲɟɦɭ ɱɢɫɥɨɜɨɦɭ ɡɧɚɱɟɧɢɸ ɩɪɢɫɜɚɢɜɚɟɬɫɹ ɪɚɧɝ 1;
ɧɚɢɛɨɥɶɲɟɦɭ ɱɢɫɥɨɜɨɦɭ ɡɧɚɱɟɧɢɸ ɩɪɢɫɜɚɢɜɚɟɬɫɹ ɪɚɧɝ, ɪɚɜɧɵɣ ɤɨɥɢ-
ɱɟɫɬɜɭ ɪɚɧɠɢɪɭɟɦɵɯ ɜɟɥɢɱɢɧ;
ɟɫɥɢ ɧɟɫɤɨɥɶɤɨ ɢɫɯɨɞɧɵɯ ɱɢɫɥɨɜɵɯ ɡɧɚɱɟɧɢɣ ɪɚɜɧɵ, ɬɨ ɢɦ ɩɪɢɫɜɚɢɜɚ-
ɟɬɫɹ ɪɚɧɝ, ɪɚɜɧɵɣ ɫɪɟɞɧɟɣ ɜɟɥɢɱɢɧɟ ɬɟɯ ɪɚɧɝɨɜ, ɤɨɬɨɪɵɟ ɨɧɢ ɩɨɥɭɱɢɥɢ ɛɵ, ɟɫɥɢ
ɛɵ ɫɬɨɹɥɢ ɩɨ ɩɨɪɹɞɤɭ ɞɪɭɝ ɡɚ ɞɪɭɝɨɦ ɢ ɧɟ ɛɵɥɢ ɛɵ ɪɚɜɧɵ;
ɨɛɳɚɹ ɫɭɦɦɚ ɪɟɚɥɶɧɵɯ ɪɚɧɝɨɜ ɞɨɥɠɧɚ ɫɨɜɩɚɞɚɬɶ ɫ ɪɚɫɱɟɬɧɨɣ, ɨɩɪɟɞɟ-
ɥɹɟɦɨɣ ɩɨ ɮɨɪɦɭɥɟ
48
)1( NN
,
2
N – ɤɨɥɢɱɟɫɬɜɨ ɪɚɧɠɢɪɭɟɦɵɯ ɩɪɢɡɧɚɤɨɜ;
ɝɞɟ
ɧɟ ɪɟɤɨɦɟɧɞɭɟɬɫɹ ɪɚɧɠɢɪɨɜɚɬɶ ɛɨɥɟɟ ɱɟɦ 20 ɜɟɥɢɱɢɧ, ɬɚɤ ɤɚɤ ɜ ɷɬɨɦ
ɫɥɭɱɚɟ ɪɚɧɠɢɪɨɜɚɧɢɟ ɜ ɰɟɥɨɦ ɨɤɚɡɵɜɚɟɬɫɹ ɦɚɥɨɭɫɬɨɣɱɢɜɵɦ;
ɩɪɢ ɧɟɨɛɯɨɞɢɦɨɫɬɢ ɪɚɧɠɢɪɨɜɚɧɢɹ ɞɨɫɬɚɬɨɱɧɨ ɛɨɥɶɲɨɝɨ ɱɢɫɥɚ ɨɛɴɟɤ-
ɬɨɜ ɢɯ ɫɥɟɞɭɟɬ ɨɛɴɟɞɢɧɹɬɶ ɩɨ ɤɚɤɨɦɭ-ɥɢɛɨ ɩɪɢɡɧɚɤɭ ɜ ɞɨɫɬɚɬɨɱɧɨ ɨɞɧɨɪɨɞɧɵɟ
ɤɥɚɫɫɵ, ɚ ɡɚɬɟɦ ɭɠɟ ɪɚɧɠɢɪɨɜɚɬɶ ɩɨɥɭɱɟɧɧɵɟ ɤɥɚɫɫɵ.
U-ɤɪɢɬɟɪɢɣ ɩɪɢɦɟɧɹɟɬɫɹ ɢ ɞɥɹ ɫɜɹɡɧɵɯ ɜɵɛɨɪɨɤ, ɩɪɢ ɷɬɨɦ ɨɧɢ ɪɚɫɫɦɚɬ-
ɪɢɜɚɸɬɫɹ ɤɚɤ ɧɟɡɚɜɢɫɢɦɵɟ. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɜɨɡɦɨɠɧɨ ɩɨɥɭɱɟɧɢɟ ɡɧɚɱɢɦɵɯ ɪɚɡɥɢɱɢɣ ɩɨ
U-ɤɪɢɬɟɪɢɸ, ɜ ɬɨ ɜɪɟɦɹ ɤɚɤ ɫɩɟɰɢɚɥɶɧɨ ɩɪɟɞɧɚɡɧɚɱɟɧɧɵɟ ɞɥɹ ɫɜɹɡɧɵɯ
ɜɵɛɨɪɨɤ ɤɪɢɬɟɪɢɢ ɦɨɝɭɬ ɢ ɧɟ ɨɛɧɚɪɭɠɢɬɶ ɡɧɚɱɢɦɵɯ ɪɚɡɥɢɱɢɣ.
ɇ-ɤɪɢɬɟɪɢɣ Ʉɪɭɫɤɚɥɚ – ɍɨɥɥɢɫɚ
Ʉɪɢɬɟɪɢɣ ɩɪɟɞɧɚɡɧɚɱɟɧ ɞɥɹ ɨɰɟɧɤɢ ɪɚɡɥɢɱɢɣ ɩɨ ɫɬɟɩɟɧɢ ɜɵɪɚɠɟɧɧɨɫɬɢ
ɚɧɚɥɢɡɢɪɭɟɦɨɝɨ ɩɪɢɡɧɚɤɚ ɨɞɧɨɜɪɟɦɟɧɧɨ ɦɟɠɞɭ ɬɪɟɦɹ, ɱɟɬɵɪɶɦɹ ɢ ɛɨɥɟɟ ɜɵɛɨɪɤɚɦɢ. Ɉɧ ɩɨɡɜɨɥɹɟɬ ɭɫɬɚɧɨɜɢɬɶ, ɱɬɨ ɭɪɨɜɟɧɶ ɩɪɢɡɧɚɤɚ ɢɡɦɟɧɹɟɬɫɹ ɩɪɢ ɩɟɪɟɯɨɞɟ ɨɬ ɝɪɭɩɩɵ ɤ ɝɪɭɩɩɟ, ɧɨ ɧɟ ɭɤɚɡɵɜɚɟɬ ɧɚ ɧɚɩɪɚɜɥɟɧɢɟ ɷɬɢɯ ɢɡɦɟɧɟɧɢɣ.
ȼɵɞɜɢɝɚɸɬɫɹ
H
: Ɇɟɠɞɭ ɜɵɛɨɪɤɚɦɢ ɫɭɳɟɫɬɜɭɸɬ ɥɢɲɶ ɫɥɭɱɚɣɧɵɟ ɪɚɡɥɢɱɢɹ ɩɨ ɭɪɨɜɧɸ
0
ɝɢɩɨɬɟɡɵ:
ɢɫɫɥɟɞɭɟɦɨɝɨ ɩɪɢɡɧɚɤɚ.
H
: Ɇɟɠɞɭ ɜɵɛɨɪɤɚɦɢ ɫɭɳɟɫɬɜɭɸɬ ɧɟɫɥɭɱɚɣɧɵɟ ɪɚɡɥɢɱɢɹ ɩɨ ɭɪɨɜɧɸ ɢɫ-
1
ɫɥɟɞɭɟɦɨɝɨ ɩɪɢɡɧɚɤɚ.
ɇ-ɤɪɢɬɟɪɢɣ ɨɰɟɧɢɜɚɟɬ ɨɛɳɭɸ ɫɭɦɦɭ ɩɟɪɟɤɪɟɳɢɜɚɸɳɢɯɫɹ ɡɨɧ ɩɪɢ ɫɨɩɨ-
ɫɬɚɜɥɟɧɢɢ ɜɫɟɯ ɨɛɫɥɟɞɨɜɚɧɧɵɯ ɜɵɛɨɪɨɤ.
Ɉɝɪɚɧɢɱɟɧɢɹ ɇ-ɤɪɢɬɟɪɢɹ.
1. ɂɡɦɟɪɟɧɢɟ ɞɨɥɠɧɨ ɛɵɬɶ ɩɪɨɜɟɞɟɧɨ ɜ ɲɤɚɥɟ ɩɨɪɹɞɤɚ, ɢɧɬɟɪɜɚɥɨɜ ɢɥɢ
ɨɬɧɨɲɟɧɢɣ.
2.
ȼɵɛɨɪɤɢ ɞɨɥɠɧɵ ɛɵɬɶ ɧɟɡɚɜɢɫɢɦɵɦɢ.
Ⱦɨɩɭɫɤɚɟɬɫɹ ɪɚɡɧɨɟ ɱɢɫɥɨ ɢɫɩɵɬɭɟɦɵɯ ɜ ɫɨɩɨɫɬɚɜɥɹɟɦɵɯ ɜɵɛɨɪɤɚɯ.
3.
4.
ɉɪɢ ɫɨɩɨɫɬɚɜɥɟɧɢɢ ɬɪɟɯ ɜɵɛɨɪɨɤ ɞɨɩɭɫɤɚɟɬɫɹ, ɱɬɨɛɵ ɜ ɨɞɧɨɣ ɢɡ ɧɢɯ
ɛɵɥɨ
n = 3, ɚ ɜ ɞɜɭɯ ɞɪɭɝɢɯ n = 2. ȼ ɬɚɤɨɦ ɫɥɭɱɚɟ ɪɚɡɥɢɱɢɹ ɦɨɝɭɬ ɛɵɬɶ ɡɚɮɢɤɫɢ-
ɪɨɜɚɧɵ ɥɢɲɶ ɧɚ 5 % ɭɪɨɜɧɟ ɡɧɚɱɢɦɨɫɬɢ. Ⱦɥɹ ɛɨɥɟɟ ɜɵɫɨɤɨɝɨ ɭɪɨɜɧɹ ɡɧɚɱɢɦɨɫɬɢ ɜɚɠɧɨ ɫɨɨɬɧɨɲɟɧɢɟ ɱɢɫɥɚ ɧɚɛɥɸɞɟɧɢɣ 4 : 2 : 2.
5.
Ɍɚɛɥɢɰɚ 7 ɉɪɢɥɨɠɟɧɢɹ ɩɪɟɞɭɫɦɨɬɪɟɧɚ ɬɨɥɶɤɨ ɞɥɹ ɬɪɟɯ ɜɵɛɨɪɨɤ ɢ
. ɉɪɢ ɛɨɥɶɲɟɦ ɤɨɥɢɱɟɫɬɜɟ ɜɵɛɨɪɨɤ ɢ ɪɚɡɧɨɦ ɱɢɫɥɟ ɢɫɩɵɬɭɟɦɵɯ
5},,{
dnnn
321
2
ɜ ɤɚɠɞɨɣ ɜɵɛɨɪɤɟ ɩɨɥɶɡɭɸɬɫɹ ɬɚɛɥɢɰɟɣ ɤɪɢɬɢɱɟɫɤɢɯ ɡɧɚɱɟɧɢɣ ɤɪɢɬɟɪɢɹ
ɱɢɫɥɨɦ ɫɬɟɩɟɧɟɣ
ɉɪɢ ɦɧɨɠɟɫɬɜɟɧɧɨɦ ɫɨɩɨɫɬɚɜɥɟɧɢɢ ɜɵɛɨɪɨɤ ɞɨɫɬɨɜɟɪɧɵɟ ɪɚɡɥɢɱɢɹ
6.
Ȟ = ɫ – 1, ɝɞɟ ɫ – ɱɢɫɥɨ ɫɨɩɨɫɬɚɜɥɹɟɦɵɯ ɜɵɛɨɪɨɤ.
F
, ɫ
ɦɟɠɞɭ ɤɚɤɨɣ-ɥɢɛɨ ɩɚɪɨɣ ɢɥɢ ɩɚɪɚɦɢ ɦɨɝɭɬ ɨɤɚɡɚɬɶɫɹ ɫɬɟɪɬɵɦɢ. Ⱦɥɹ ɩɨɩɚɪɧɵɯ
ɫɨɩɨɫɬɚɜɥɟɧɢɣ ɢɫɩɨɥɶɡɭɸɬɫɹ ɤɪɢɬɟɪɢɢ ɞɥɹ ɞɜɭɯ ɜɵɛɨɪɨɤ.
49
Ⱥɥɝɨɪɢɬɦ ɩɨɞɫɱɟɬɚ ɇ-ɤɪɢɬɟɪɢɹ.
1. ɉɨɥɭɱɟɧɧɵɟ ɞɚɧɧɵɟ ɧɟɨɛɯɨɞɢɦɨ ɩɪɟɞɫɬɚɜɢɬɶ ɤɚɤ ɨɞɢɧ ɪɹɞ ɢ ɭɩɨɪɹɞɨ-
ɱɢɬɶ ɟɝɨ ɩɨ ɜɨɡɪɚɫɬɚɧɢɸ ɜɯɨɞɹɳɢɯ ɜ ɧɟɝɨ ɜɟɥɢɱɢɧ.
2.
ɉɪɨɪɚɧɠɢɪɨɜɚɬɶ ɡɧɚɱɟɧɢɹ.
3.
ɉɨɞɫɱɢɬɚɬɶ ɫɭɦɦɭ ɪɚɧɝɨɜ ɨɬɞɟɥɶɧɨ ɩɨ ɤɚɠɞɨɣ ɝɪɭɩɩɟ. ɉɪɨɜɟɪɢɬɶ, ɫɨɜ-
ɩɚɞɚɟɬ ɥɢ ɨɛɳɚɹ ɫɭɦɦɚ ɪɚɧɝɨɜ ɫ ɪɚɫɱɟɬɧɨɣ.
Ɉɩɪɟɞɟɥɢɬɶ ɡɧɚɱɟɧɢɟ ɇ ɩɨ ɮɨɪɦɭɥɟ:
4.
5.
2
H
NN
12
)1(3
T
j
¦
)1(
n
j
N
,
N – ɨɛɳɟɟ ɱɢɫɥɨ ɢɫɩɵɬɭɟɦɵɯ ɜ ɨɛɴɟɞɢɧɟɧɧɨɣ ɜɵɛɨɪɤɟ;
ɝɞɟ
– ɤɨɥɢɱɟɫɬɜɨ ɢɫɩɵɬɭɟɦɵɯ ɜ ɤɚɠɞɨɣ ɜɵɛɨɪɤɟ;
n
j
– ɫɭɦɦɵ ɪɚɧɝɨɜ ɩɨ ɤɚɠɞɨɣ ɜɵɛɨɪɤɟ.
T
j
ɉɪɢ ɱɢɫɥɟ ɝɪɭɩɩ ɫ = 3,
6.
, ɨɩɪɟɞɟɥɢɬɶ ɤɪɢɬɢɱɟɫɤɢɟ ɡɧɚɱɟ-
5},,{
dnnn
321
ɧɢɹ ɢ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɣ ɢɦ ɭɪɨɜɟɧɶ ɡɧɚɱɢɦɨɫɬɢ ɩɨ ɬɚɛɥɢɰɟ 7 ɉɪɢɥɨɠɟɧɢɹ. ȿɫɥɢ
ɇH t
ɉɪɢ ɱɢɫɥɟ ɝɪɭɩɩ ɫ > 3 ɢɥɢ
2
F
ɱɟɧɢɹ
ɩɨ ɬɚɛɥɢɰɟ 8 ɉɪɢɥɨɠɟɧɢɹ. ȿɫɥɢ
, ɬɨ ɧɭɥɟɜɚɹ ɝɢɩɨɬɟɡɚ ɇ0 ɨɬɜɟɪɝɚɟɬɫɹ.
05,0ɤɪɷɦɩ
, ɨɩɪɟɞɟɥɢɬɶ ɤɪɢɬɢɱɟɫɤɢɟ ɡɧɚ-
5},,{
!nnn
321
H , ɬɨ ɧɭɥɟɜɚɹ ɝɢɩɨɬɟɡɚ ɇ
ɷɦɩ
2
F
t
ɨɬɜɟɪɝɚɟɬɫɹ.
S-ɤɪɢɬɟɪɢɣ ɬɟɧɞɟɧɰɢɣ Ⱦɠɨɧɤɢɪɚ
ɗɬɨɬ ɤɪɢɬɟɪɢɣ ɨɪɢɟɧɬɢɪɨɜɚɧ ɧɚ ɜɵɹɜɥɟɧɢɟ ɬɟɧɞɟɧɰɢɣ ɢɡɦɟɧɟɧɢɹ ɩɪɢɡɧɚɤɚ ɩɪɢ ɩɟɪɟɯɨɞɟ ɨɬ ɜɵɛɨɪɤɢ ɤ ɜɵɛɨɪɤɟ ɩɪɢ ɫɨɩɨɫɬɚɜɥɟɧɢɢ ɨɬ 3 ɞɨ 6 ɜɵɛɨɪɨɤ.
ɂɧɬɟɪɩɪɟɬɚɰɢɹ ɩɨɥɭɱɟɧɧɵɯ ɪɟɡɭɥɶɬɚɬɨɜ ɡɚɜɢɫɢɬ ɨɬ ɬɨɝɨ, ɩɨ ɤɚɤɨɦɭ ɩɪɢɧɰɢɩɭ
ɛɵɥɢ ɨɛɪɚɡɨɜɚɧɵ ɢɫɫɥɟɞɭɟɦɵɟ ɜɵɛɨɪɤɢ.
1.
ȿɫɥɢ ɜɵɛɨɪɤɢ ɪɚɡɥɢɱɚɸɬɫɹ ɩɨ ɤɚɱɟɫɬɜɟɧɧɵɦ ɩɪɢɡɧɚɤɚɦ (ɩɪɨɮɟɫɫɢɹ,
ɧɚɰɢɨɧɚɥɶɧɨɫɬɶ ɢ ɬ. ɩ.), ɬɨ ɫ ɩɨɦɨɳɶɸ
ɩɨ
ɤɨɥɢɱɟɫɬɜɟɧɧɨɦɭ ɩɪɢɡɧɚɤɭ (ɤɪɟɚɬɢɜɧɨɫɬɶ, ɝɢɛɤɨɫɬɶ ɢ ɬ. ɩ.).
2.
ȿɫɥɢ ɜɵɛɨɪɤɢ ɪɚɡɥɢɱɚɸɬɫɹ ɢɥɢ ɫɩɟɰɢɚɥɶɧɨ ɫɝɪɭɩɩɢɪɨɜɚɧɵ ɩɨ ɤɨɥɢɱɟ-
ɫɬɜɟɧɧɨɦɭ
ɩɪɢɡɧɚɤɭ (ɜɨɡɪɚɫɬ, ɫɬɚɠ ɪɚɛɨɬɵ ɢ ɞɪ.), ɬɨ, ɭɩɨɪɹɞɨɱɢɜɚɹ ɢɯ ɩɨ ɞɪɭ-
ɝɨɦɭ ɤɨɥɢɱɟɫɬɜɟɧɧɨɦɭ ɩɪɢɡɧɚɤɭ, ɭɫɬɚɧɚɜɥɢɜɚɟɬɫɹ ɦɟɪɚ ɫɜɹɡɢ
ɥɢɱɟɫɬɜɟɧɧɵɦɢ ɩɪɢɡɧɚɤɚɦɢ
ȼɵɞɜɢɝɚɸɬɫɹ
H
: Ɍɟɧɞɟɧɰɢɹ ɜɨɡɪɚɫɬɚɧɢɹ ɡɧɚɱɟɧɢɣ ɩɪɢɡɧɚɤɚ ɩɪɢ ɩɟɪɟɯɨɞɟ ɨɬ ɜɵɛɨɪɤɢ ɤ
0
ɝɢɩɨɬɟɡɵ:
.
S-ɤɪɢɬɟɪɢɹ ɦɨɠɧɨ ɭɩɨɪɹɞɨɱɢɬɶ ɜɵɛɨɪɤɢ
ɦɟɠɞɭ ɞɜɭɦɹ ɤɨ-
ɜɵɛɨɪɤɟ ɹɜɥɹɟɬɫɹ ɫɥɭɱɚɣɧɨɣ.
H
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ɜɵɛɨɪɤɟ ɧɟ ɹɜɥɹɟɬɫɹ ɫɥɭɱɚɣɧɨɣ.
S-ɤɪɢɬɟɪɢɣ ɩɨɡɜɨɥɹɟɬ ɨɩɪɟɞɟɥɢɬɶ, ɞɨɫɬɚɬɨɱɧɨ ɥɢ ɜɟɥɢɤɚ ɫɭɦɦɚɪɧɚɹ ɡɨɧɚ
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