测试样本量问题
各位前辈，新年好！
小弟在做土工材料耐穿刺试验的时候，对试验的样本量这块有些疑惑，
请大家分享一下心得：
在很多测试标准中，如UL94燃烧测试，一般都会规定样本数量不少于5个或者10个，但
在测试标准ASTM D4833中，规定的样本量是根据一个公式计算得出的，如下英文。好像
是基于t检验。
所以我的疑惑如下：
1. 一般测试中规定的样本数量5或者10，依据是什么呢？
2. ASTM D4833中，n = (tv/a)^2=(tv)^2/36 这个公式的依据是什么？
of v based on extensive past records for similar materials
tested in the user’s laboratory, calculate the number of specimens
per unit in the laboratory sample using Eq 1:
n = (tv/a)^2=(tv)^2/36 (1)
where:
n = number of specimens (rounded upward to a whole
number),
v = reliable estimate of the coefficient of variation for
individual observations on similar materials in the
user’s laboratory under conditions of single-operator
precision,
t = value of Student’s test for two-sided limits (see Table
1) a 95 % probability level, and the degrees of
freedom associated with the estimate of v, and
A = 6 % of the average, the value of the allowable variable.
8.2 No Reliable Estimate of v—When there is no reliable
estimate of v in the user’s laboratory, specify the fixed number
of 15 specimens per swatch in the laboratory sample. This
number of specimens is calculated using v = 10 % of the
average, which is a somewhat larger value of v than is usually
found in practice. When a reliable estimate of v for the user’s
laboratory becomes available, Eq 1 will usually require fewer
than 15 specimens per swatch in the laboratory sample.
TABLE 1 Values of Student’s t for Two-Sided Limits and the
95 % ProbabilityA
df t.025 df t.025 df t.025
1 12.706 11 2.201 21 2.080
2 4.303 12 2.179 22 2.074
3 3.182 13 2.160 23 2.069
4 2.776 14 2.145 24 2.064
5 2.571 15 2.131 25 2.060
6 2.447 16 2.120 26 2.056
7 2.365 17 2.110 27 2.052
8 2.306 18 2.101 28 2.048
9 2.262 19 2.093 29 2.045
10 2.228 20 2.086 inf. 1.960
AValues in this table were calculated using Hewlett Packard HP 67/97 Users’
Library Programs 03848D, “One-Sided and Two-Sided Critical Values of Student’s
t” and 00350D, “Improved Normal and Inverse Distribution.” For values at other
than the 95 % probability level, see published tables of critical values of Student’s
t in any standard statistical text. Further use of this table is defined in Practice D
2905.
小弟在做土工材料耐穿刺试验的时候，对试验的样本量这块有些疑惑，
请大家分享一下心得：
在很多测试标准中，如UL94燃烧测试，一般都会规定样本数量不少于5个或者10个，但
在测试标准ASTM D4833中，规定的样本量是根据一个公式计算得出的，如下英文。好像
是基于t检验。
所以我的疑惑如下：
1. 一般测试中规定的样本数量5或者10，依据是什么呢？
2. ASTM D4833中，n = (tv/a)^2=(tv)^2/36 这个公式的依据是什么？
- Number of Specimens
of v based on extensive past records for similar materials
tested in the user’s laboratory, calculate the number of specimens
per unit in the laboratory sample using Eq 1:
n = (tv/a)^2=(tv)^2/36 (1)
where:
n = number of specimens (rounded upward to a whole
number),
v = reliable estimate of the coefficient of variation for
individual observations on similar materials in the
user’s laboratory under conditions of single-operator
precision,
t = value of Student’s test for two-sided limits (see Table
1) a 95 % probability level, and the degrees of
freedom associated with the estimate of v, and
A = 6 % of the average, the value of the allowable variable.
8.2 No Reliable Estimate of v—When there is no reliable
estimate of v in the user’s laboratory, specify the fixed number
of 15 specimens per swatch in the laboratory sample. This
number of specimens is calculated using v = 10 % of the
average, which is a somewhat larger value of v than is usually
found in practice. When a reliable estimate of v for the user’s
laboratory becomes available, Eq 1 will usually require fewer
than 15 specimens per swatch in the laboratory sample.
TABLE 1 Values of Student’s t for Two-Sided Limits and the
95 % ProbabilityA
df t.025 df t.025 df t.025
1 12.706 11 2.201 21 2.080
2 4.303 12 2.179 22 2.074
3 3.182 13 2.160 23 2.069
4 2.776 14 2.145 24 2.064
5 2.571 15 2.131 25 2.060
6 2.447 16 2.120 26 2.056
7 2.365 17 2.110 27 2.052
8 2.306 18 2.101 28 2.048
9 2.262 19 2.093 29 2.045
10 2.228 20 2.086 inf. 1.960
AValues in this table were calculated using Hewlett Packard HP 67/97 Users’
Library Programs 03848D, “One-Sided and Two-Sided Critical Values of Student’s
t” and 00350D, “Improved Normal and Inverse Distribution.” For values at other
than the 95 % probability level, see published tables of critical values of Student’s
t in any standard statistical text. Further use of this table is defined in Practice D
2905.
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