【分享】重新再学一遍 : Numerical Values

有些概念确实需要好好学习,常常以为自己很明白,可是当给别人解释的时候才知道自己原来只是一知半解

同感。 以上资料我十年前已看过, 现在重新再学一遍, 又有新体会。

Why the concept of Exact Value and Inexact Value is important? Here is my experience:

I know that the average of 0.13, 0.25, 0.19, 0.32,0.41 is

(0.13+0.25+0.19+0.32+0.41)/5=0.26

I would not report that the average = 0.3 by taking into account of the number of significant figure of 5 (i.e. n.s.f.=1 for the number 5), but I did not know the reason in the past. Now, I know that 5 is an exact value, so the rules of arithmetic operation for significant figures do not apply.

(There is another opinion that although 5 is an exact value, if the concept of significant figure must be imposed on it, 5 has infinite number of significant figures, i.e. 5=5.0000……00000)

I am thinking whether the limiting value (极限值, 或称界限值) specified in the testing standard is an exact value. If it is an exact value, I need not consider the number of significant values when I report the measured value, only consider the precision as indicated by the limiting value.

例: 极限值=0.030%, 测定值=0.1573%

My opinion:

(1) 我不认为0.030%是一个有2位有效数字的数, because it is an exact value
(2) 0.030%显示了精度要求为千分位

Therefore:

(A) 我不会报0.16%, 這会損失精度, 亦与有效数字的概念无关(see (1) above)。
(B) 我也不会报0.1573%, 这会太长而无助于判定是否合格

我会报0.157%

非精确的数字是否就是我们长讲的有效数字位数

Inexact value ≠ significant figure, I think that significant figure is one of the attributes of inexact value. I am still studying this subject and unable make the precise definitions for them. Perhaps, the following example may illustrate their difference:

If the population of a city is 1.030×10⁶ in government survey record and when it is printed as 1030000 in the newspaper, I would have the following description about the value 1030000:

1030000 is an inexact value (人口统计时是以千为单位的, 不会精确至几百几十的)

1030000 是一个7位数

1030000 具有4位有效数字

1030000中 1,0,3,0 是有效数字, 最右的三个0是定位0

我似乎在鑽牛角尖, 但我的工作之一是计量, 对一些有关数字的基本概念不能不理啊。

最近要新写一个关于修约的SOP，有两个参考，一个是国标，注重有效数字，标准多少有效数字就多少位数（我们以前就这么干）；一个是国外某企业的SOP，注重仪器和方法本身的精度，打算倾向后者。但是这么写的话，又牵涉到仪器方法的相关SOP里面的内容，工程比较大。犹豫不决中。

以我的经验，可以在这个修约的SOP中用一句话规定：所有修约的程序以本SOP为准。
仪器方法的相关SOP以后再逐步修订。

“标准多少有效数字就多少位数”?

The problem is how do you interpret “位”. In the past month, I studied the “significant figure” again and found that there are two meanings of “位”, i.e. “number” and “place”. Example:

(A) 0.00235 : 3位有效数字 (number of significant figures = 3)

(B) 0.00235 : 精确至小数後5位 (5 decimal places)

http://bbs.instrument.com.cn/shtml/20100608/2599734/ 中提到 “药典明确规定了结果的有效位数要和标准一致啊！！”, 这个“位数要和标准一致”中的“位数”应是(B)“place”. If this interpretation is accepted, there is no difference between 国标 and 国外某企业的SOP. (GB/T 8170-2008 Clause 4.3.3.1中用的字是“数位”一致, my interpretation is “in agreement with the places of the limiting value”)

I am writing a notes about the Significant Figure, and really really want to know the exact wording in 中国药典

= = = = = =

My suggestion to your SOP about rounding is “the rounding of the measured value should be in agreement with the limiting value” 轻轻带过, 留有演译的余地;

or more specific “the rounding of the measured value should be in agreement with the places of the limiting value” so as to be in line with GB/T 8170-2008 Clause 4.3.3.1

or “in accordance with xxxxxx unless otherwise specified”

恩，谢谢微寒老师的建议。其实我现在面对的与其说是数字的修约问题，不如说是数据报告习惯的问题。除了对外的药品企业外，我看到的一般情况就是，仪器检测出多少数据就是多少。比如，一个液相检测杂质报告0.0005%，实际情况是，这个仪器或方法根本没有这样的检出限，但是如果你报告<0.01%（假设检出限是0.01%），领导就不认可。非得让你写个确切的数字。

我们现在的规定是：按照有效数字的位数，检测标准有多少位，结果就报告多少位，如果有100%或0的情况，就往下多保留一位，直至不为100%或0为止.没提检出限这回事。

另：微寒老师的论坛内另外个帖子的链接，我的google浏览器打开后，每次点关闭这个页面，浏览器就崩溃一次。

A quantitative result sometimes or to some extent would become a qualitative indication.

领导要照顾一些非专业客户(或专业客户的非专业领导), 让报告填上数字, 令报告看起来有根有据, 亦无可厚非。 行内人会明白, any value below the detection limit is only an indication. An indication of 非常非常少的杂质。



( “飞流直下三千尺”, 这个三千不是真的quantitative value of 3000, but a qualitative indication of 高。 所以, 能科学地出一份报告固然好, 若要报一个小于检出限的数值作为indication, 也不是不能自园其说的。)