Unit 10 Accuracy and Precision

Unit 10 Accuracy and Precision

第十单元 准确度和精度

Can you make a measurement that’s very precise, but not very accurate? Can a number be

你能够进行一次非常精确地测量，但是它并不非常准确？ 一个数字可以是

accurate, but not very precise? Let’s find out the difference between these two terms; you’ll see

准确的，但是它并不十分精确？让我们一起找出这两者之间的区别；你将会看到

that precision and accuracy are really two different things. A measurement can be precise but

精度和准确度确实是两个不同的东西。 一个测量可以有精度但它并不准确

inaccurate, as well as accurate but imprecise. For example, if a measurement was made with much

，同样地，它可以有准确直但不具备精度。例如，假如在一台高精度的仪器非常

care using a highly refined instrument, repeated reading of the same quantity

would agree closely

仔细地测量之后，等量重复地读取观测值，那么这些观测值彼此之间将非常接近

and thus precision would exist. But if the instrument contained one or more undetected,

，精度也得到了保障。但是，假如这些仪器包含有一个甚至更多没有被检测，

uncorrected systematic errors, the results would be inaccurate. In contrast, it is possible that the

没有被改正的系统误差，这些测出来的结果将是不准确的。相比之下，用一台精度稍微没有

mean of several repeated measurements of this same quantity, using a less refined (but calibrated)

那么高的（但有校准过的）仪器进行等量重复测量时，测量值的平均数（中数）能更接近于

method, could be closer to the true value and thus this procedure would yield more accurate

真值也是可能的，因此这种方法也可以使测量值将达到更加准确的结果，即使

results even though there was less agreement among the readings.

这些数据当中有一些是不太符合的读数。

Perhaps the easiest way to illustrate the difference between accuracy and precision is to use the

也许阐述准确度和精度之间的不同点最简单的方法是用枪手打靶心的例子来近似。

analogy of marksman, to whom the “truth” represents the bull’s-eye.

Precision: The degree of refinement in the performance of an operation, or the degree of

精度：是测量操作中的精确程度，或者是用测量仪器和测量方法

perfection in the instruments and methods used to obtain a result, or an indication of the

获取观测结果的完美程度，也可以是重复测量结果的均一的指示程度。

uniformity or reproducibility of a result. Precision relates to the quality of an operation by which a

精度和获取测量结果的操作的质量有关，

result is obtained, and is distinguished from accuracy, which relates to the quality of the result.

它和准确度要加以区别，准确度和观测结果的质量联系起来。

Figure 1 shows uniformity achieved by the marksman who is skilled by very small scatter. It

图1显示了枪手非常有技巧地在一个离散度很小地获取均一的结果。它描述了很好的

illustrates the excellent precision. However, as the shots are far from the center, caused by the bent

精度。 但是，由于射击和靶心的距离比较远，造成了视线的弯曲

sight (systematic error),they are completely inaccurate. With the knowledge gained by observation

（系统误差），射击结果就变得完全不准确了。 通过观察射击结果可以知道，射击手

of the results, the marksman can apply a systematic adjustment (aim higher and to the left of his

除了他固有的一套射击方法和器材达到了已有的精度外还可以使用一个系统的改正

（向指定

intended target, or have his equipment adjusted) to achieve more accurate results in addition to the

目标瞄的高一点和往左边一点，或者是让他的射击器材调整）来获取更加准确的结果，

precision that his methodology and equipment have already attained. Such a situation can arise in

类似地状况，可以应用到电子测距仪的实践之中生产出

practice when a piece of EDM equipment produces a set of measurements all agreeing to a few

一系列能够达到毫米精度（高精度）的测量结果，

millimeters (high precision) but, due to an operation fault and lack of calibration, the

但是，由于缺乏仪器校准的操作，

measurements are all incorrect by several meters (low accuracy).

这些测出来的结果都是达到米级精度（低精度）不正确的测量值。

Accuracy: The degree of conformity of a final measured value, with respect to the true value as

准确度：最终测量值，被公认的标准取值（真值）符合的程度。

defined by accepted standard (the “truth”). Figure 2 shows the shots achieved by the marksman

表2显示的是射击手在一个较大的离散范围里的射击结果。

with a wide scatter. It illustrates that the bent sight is now corrected, i.e. the systematic errors are

它描述的是现在的弯曲视线已经被改正的，也就是系统误差已经最小化了，

minimized, and the marksman has approached the “truth”, although without great precision. It

虽然没有较高的精度，但射击手的射击结果已经接近“正中”（靶心）。

may be that the marksman will need to change the equipment or methodology used to obtain the

假如想提高射击的精度，射击手需要改变射击器材和射击方法，

result if a greater degree of precision is required, as he has reached the

limitations associated with

直到他的设备和方法都达到了极限的时候为止。

his equipment and methodology.

In Figure 3, the shots are clustered near the center of the target. It represents results indicating both

在图3中，射击的结果成群地聚集在目标的中心。它同时显示出了结果的准确度

accuracy and precision. In this case, the marksman has probably made one of the systematic

和精度。 既然这样，射击手很可能通过他的射击结果有精度但没有准确值时

adjustments that were indicated by his attainment of precision without accuracy. The degree of

采取了其中一个系统调整。 射击的结果的精度没有很大的改变，但是和图1相比，它的

precision has not changed greatly, but its conformity with the “truth” has improved over the results

结果的准确值都提高了并且趋近于真值。

obtained in Figure 1. The scatter is, of course, due to the unavoidable random errors.

离散是必然存在的，因为随机误差是没有办法避免的。

So from the analysis of precision and accuracy, several important facts should be mentioned as

所以从精度和准确度比较的分析中，下面几个重要的事实应该引起注意：

follows. (1) Scatter is an “indicator of precision”: the wider the scatter of a set of results about the

（1）离散程度是“精度的指标”：离散程度越大结果值，和离散程度小的

mean, the less reliable they will be compared with results having a small scatter. (2) Precision

结果值相比就显得越不可靠。

must not be confused with accuracy; the former is a relative grouping without regard to the

（2）精度和准确度一定不能混淆，前者是一个相关联的组并不考虑它和真值的接近

nearness to the truth, whilst the latter denotes absolute nearness to the truth.

(3) Precision may be

情况，同时后者描述的是和真值的绝对靠近的情况。（3）

regarded as an index of accuracy only when all sources of error, other than random errors, have

只有当所有的误差原因除了随机误差都被消除后精度才可以被当做准确度的指标。

been eliminated.

An example that explains the difference between precision and accuracy better than any other in

一个在测量中可以比其他例子更好地解释精度和准确度之间的不同点的是有关

surveying has to do with error of closure in traversing. Many surveyors seem to think that error of

导线闭合差的例子。许多测量员认为闭合差的检查的是工作的的准确的。

closure checks the accuracy of the work. Wrong! Error of closure primarily checks the precision,

这种想法完全是错的！闭合差主要是用来检查测量精度的，而不是准确度。

not the accuracy. It checks accuracy only in that it can find blunders. But, since it cannot detect

它只在能找到粗差的情况下检查准确度。但是，由于它不能够检测

systematic errors in the distances, it cannot fully check accuracy.

距离当中的系统误差，它就不能够完全检查准确度。

In surveying, the need for greater precision usually leads to greater costs. To obtain a higher

在测量中，需要更高的精度往往导致更多的花费。为了获取更好的精度，

degree of precision, it may be necessary to use more sophisticated (costly) equipment or a more

或许将要用到更昂贵，更精密的测量仪器设备或者通过耗费更长的时间来达到要求。

time-consuming methodology. The surveyor must determine what methodology and resultant

在即将来临的任务之前，测量员必须做好决定并控制好精度要求来满足

precision is needed to achieve the accuracy required for a task at hand.

一定的准确度。

Accuracy is telling the truth… Precision is telling the same story over and over again.

准确度讲的是真值……精度也是再重复地讲同样的事情。