2.1 母集団と標本
clear
set seed 2022
set obs 100
generate x = rnormal(50, 10)
list x
+----------+
| x |
|----------|
1. | 54.72184 |
2. | 57.83728 |
3. | 54.85993 |
4. | 64.43429 |
5. | 28.463 |
|----------|
6. | 46.86906 |
7. | 54.04034 |
8. | 43.09037 |
9. | 43.55874 |
10. | 67.44601 |
|----------|
11. | 65.16725 |
12. | 45.85949 |
13. | 69.22049 |
14. | 52.78434 |
15. | 51.74491 |
|----------|
16. | 51.55506 |
17. | 59.95332 |
18. | 39.3822 |
19. | 45.14891 |
20. | 41.70154 |
|----------|
21. | 55.55453 |
22. | 36.13799 |
23. | 51.67796 |
24. | 54.6027 |
25. | 39.50498 |
|----------|
26. | 42.91825 |
27. | 49.60077 |
28. | 60.91685 |
29. | 53.24129 |
30. | 59.11747 |
|----------|
31. | 63.41263 |
32. | 65.53846 |
33. | 54.42587 |
34. | 54.49843 |
35. | 31.52787 |
|----------|
36. | 51.61845 |
37. | 46.18401 |
38. | 54.8383 |
39. | 52.29193 |
40. | 43.75826 |
|----------|
41. | 57.47549 |
42. | 59.45118 |
43. | 48.10275 |
44. | 54.0606 |
45. | 41.1449 |
|----------|
46. | 44.57216 |
47. | 40.63018 |
48. | 54.38108 |
49. | 54.39209 |
50. | 66.16985 |
|----------|
51. | 49.45791 |
52. | 71.02126 |
53. | 50.3375 |
54. | 52.88632 |
55. | 45.25692 |
|----------|
56. | 36.40867 |
57. | 43.52808 |
58. | 48.95045 |
59. | 46.06606 |
60. | 50.77587 |
|----------|
61. | 36.0733 |
62. | 56.27862 |
63. | 45.95923 |
64. | 48.35371 |
65. | 47.45552 |
|----------|
66. | 64.44137 |
67. | 51.39878 |
68. | 46.63072 |
69. | 41.59076 |
70. | 49.48847 |
|----------|
71. | 46.62038 |
72. | 38.88836 |
73. | 33.08361 |
74. | 49.27411 |
75. | 45.50976 |
|----------|
76. | 52.08639 |
77. | 34.54663 |
78. | 53.93042 |
79. | 37.40854 |
80. | 49.52537 |
|----------|
81. | 13.65156 |
82. | 62.04644 |
83. | 55.87931 |
84. | 70.52183 |
85. | 55.12461 |
|----------|
86. | 52.93826 |
87. | 55.92964 |
88. | 63.00453 |
89. | 59.47496 |
90. | 52.97406 |
|----------|
91. | 74.39547 |
92. | 67.05323 |
93. | 34.03576 |
94. | 50.66547 |
95. | 44.32327 |
|----------|
96. | 45.39636 |
97. | 64.69812 |
98. | 60.00776 |
99. | 53.95464 |
100. | 41.24168 |
+----------+
clear
set seed 2022
set obs 1000
generate x = (_n - 1) / 10
generate y = normalden(x, 50, 10)
line y x
clear
scalar z = (60 - 50) / 10
scalar x = normal(z)
display x
.84134475
2.2 無作為抽出
clear
set seed 2022
set obs 100
generate Z = rnormal(50, 10)
histogram Z
list Z in 1/10, separator(0)
+----------+
| Z |
|----------|
1. | 54.72184 |
2. | 57.83728 |
3. | 54.85993 |
4. | 64.43429 |
5. | 28.463 |
6. | 46.86906 |
7. | 54.04034 |
8. | 43.09037 |
9. | 43.55874 |
10. | 67.44601 |
+----------+
list Z if inlist(_n, 5, 10, 100)
+----------+
| Z |
|----------|
5. | 28.463 |
10. | 67.44601 |
100. | 41.24168 |
+----------+
quietly summarize Z
display r(max)
74.39547
+----------+
| Z |
|----------|
91. | 74.39547 |
+----------+
13.651556
+----------+
| Z |
|----------|
81. | 13.65156 |
+----------+
50.801357
Z
-------------------------------------------------------------
Percentiles Smallest
1% 21.05728 13.65156
5% 34.29119 28.463
10% 38.14845 31.52787 Obs 100
25% 44.86053 33.08361 Sum of wgt. 100
50% 51.58675 Mean 50.80136
Largest Std. dev. 10.16443
75% 55.90447 69.22049
90% 64.56974 70.52183 Variance 103.3157
95% 67.24962 71.02126 Skewness -.3428058
99% 72.70837 74.39547 Kurtosis 3.903721
2.3 平均と大数の法則
clear
set seed 2022
postfile sim means1000 using means1000, replace
forvalues i = 1/1000 {
quietly capture drop x
quietly set obs 100
quietly generate x = rnormal(50, 10)
quietly summarize x
post sim (r(mean))
}
postclose sim
use means1000, clear
summarize means1000
Variable | Obs Mean Std. dev. Min Max
-------------+---------------------------------------------------------
means1000 | 1,000 49.98582 .9900411 46.95685 53.6977
clear
set seed 2022
postfile sim means1000 using means1000, replace
forvalues i = 1/1000 {
quietly capture drop x
quietly set obs 10000
quietly generate x = rnormal(50, 10)
quietly summarize x
post sim (r(mean))
}
postclose sim
use means1000, clear
summarize means1000
Variable | Obs Mean Std. dev. Min Max
-------------+---------------------------------------------------------
means1000 | 1,000 49.99832 .1024485 49.68475 50.34666
clear
set seed 2022
set obs 10
generate x = ceil(runiform(0, 6))
quietly summarize x
display r(mean)
2.8
clear
set seed 2022
postfile sim means1000 using means1000, replace
forvalues i = 1/1000 {
quietly capture drop x
quietly set obs 1000
quietly generate x = ceil(runiform(0, 6))
quietly summarize x
post sim (r(mean))
}
postclose sim
use means1000, clear
summarize means1000
Variable | Obs Mean Std. dev. Min Max
-------------+---------------------------------------------------------
means1000 | 1,000 3.499558 .0546235 3.329 3.681
clear
set seed 2022
postfile sim means1000 using means1000, replace
forvalues i = 1/1000 {
quietly capture drop x
quietly set obs 10000
quietly generate x = ceil(runiform(0, 6))
quietly summarize x
post sim (r(mean))
}
postclose sim
use means1000, clear
summarize means1000
Variable | Obs Mean Std. dev. Min Max
-------------+---------------------------------------------------------
means1000 | 1,000 3.499559 .0166011 3.4576 3.5529
2.4 分散と標準偏差
clear
set seed 2022
set obs 1000
generate x = rnormal(50, 10)
quietly summarize x
display r(Var)
101.28133
10.063862
clear
set seed 2022
postfile sim sds1000 using sds1000, replace
forvalues i = 1/1000 {
quietly capture drop x
quietly set obs 1000
quietly generate x = rnormal(50, 10)
quietly summarize x
post sim (r(sd))
}
postclose sim
use sds1000, clear
summarize sds1000
Variable | Obs Mean Std. dev. Min Max
-------------+---------------------------------------------------------
sds1000 | 1,000 10.00502 .2271609 9.258702 10.732
2.5 相関係数と共分散
clear
set seed 2022
set obs 100
generate x = rnormal(50, 10)
generate y = rnormal(50, 10)
twoway (scatter y x)
(obs=100)
| x y
-------------+------------------
x | 1.0000
y | -0.1192 1.0000
(obs=100)
| x z
-------------+------------------
x | 1.0000
z | 0.7088 1.0000
