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phy131studiof17:lectures:error [2017/08/28 09:25]
mdawber [Visual Comparison of Types of Error]
phy131studiof17:lectures:error [2017/08/28 09:26] (current)
mdawber [Visual Comparison of Types of Error]
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 Think of the round object as an archery target. ​ The archer shoots some number of arrows at it, and each dot shows where one landed. ​ Now think of the "​bull'​s eye" -- the larger black dot in the center -- as the "​true"​ value of some quantity that's being measured, and think of each arrow-dot as a measurement of that quantity. ​ The problem is that the one doing the measurements does not know the "​true"​ value of the quantity; s/he's trying to determine it experimentally,​ and this means there must be uncertainty associated with the experimentally determined value. ​ Note that each archery target -- we'll call them 1,2,3,4 from left to right -- shows a different distribution of arrow-hit/​measurements.  ​ Think of the round object as an archery target. ​ The archer shoots some number of arrows at it, and each dot shows where one landed. ​ Now think of the "​bull'​s eye" -- the larger black dot in the center -- as the "​true"​ value of some quantity that's being measured, and think of each arrow-dot as a measurement of that quantity. ​ The problem is that the one doing the measurements does not know the "​true"​ value of the quantity; s/he's trying to determine it experimentally,​ and this means there must be uncertainty associated with the experimentally determined value. ​ Note that each archery target -- we'll call them 1,2,3,4 from left to right -- shows a different distribution of arrow-hit/​measurements.  ​
  
-In number 1 the measurements cluster pretty tightly: we say that the statistical (random) error is small, and the terminology we introduce for that is, "These measurements are precise."​ However, the center of their distribution is far from the bull's eye: we say that there is a large systematic ​+In number 1 the measurements cluster tightly, and one can see that the center of their distribution is very close to the bull's eye.  These measurements have a small statistical error __and__ a small systematic error. ​ In a few words, "These measurements are precise and accurate." ​  
 + 
 +In number 2 the measurements cluster pretty tightly: we say that the statistical (random) error is small, and the terminology we introduce for that is, "These measurements are precise."​ However, the center of their distribution is far from the bull's eye: we say that there is a large systematic ​
 error, and the terminology we introduce for that is, "These measurements are not accurate." ​ In a few words, "These measurements are precise but inaccurate."  ​ error, and the terminology we introduce for that is, "These measurements are not accurate." ​ In a few words, "These measurements are precise but inaccurate."  ​
  
-In number ​the measurements do not cluster tightly, but one can see that the center of their distribution is not far from the bull's eye.  These measurements have a large statistical error but a small systematic error. ​ In a few words, "These measurements are imprecise but accurate."  ​+In number ​the measurements do not cluster tightly, but one can see that the center of their distribution is not far from the bull's eye.  These measurements have a large statistical error but a small systematic error. ​ In a few words, "These measurements are imprecise but accurate."  ​
  
-In number ​the measurements do not cluster tightly, and one can see that the center of their distribution is not close to the bull's eye.  These measurements have a large statistical error __and__ a large systematic error. ​ In a few words, "These measurements are imprecise and inaccurate."  ​+In number ​the measurements do not cluster tightly, and one can see that the center of their distribution is not close to the bull's eye.  These measurements have a large statistical error __and__ a large systematic error. ​ In a few words, "These measurements are imprecise and inaccurate."  ​
  
-In number 4 the measurements cluster tightly, and one can see that the center of their distribution is very close to the bull's eye.  These measurements have a small statistical error __and__ a small systematic error. ​ In a few words, "These measurements are precise and accurate."  ​ 
  
 Here is a crucial point: You can always know your measurements achieve a high level of __precision__ if they cluster tightly, and you can quantify "how precise"​ they are.  But this tells you nothing about how accurate they are.  To aim properly, an archer needs to know where the bull's eye is, but suppose, in our analogy, a white sheet is put up to block view of the target. ​ Not knowing where the bull's eye is, the archer'​s shots could still cluster tightly but there'​s no way of the archer knowing __without additional information__ where they are with respect to the bull's eye.  The accuracy is unknown.  ​ Here is a crucial point: You can always know your measurements achieve a high level of __precision__ if they cluster tightly, and you can quantify "how precise"​ they are.  But this tells you nothing about how accurate they are.  To aim properly, an archer needs to know where the bull's eye is, but suppose, in our analogy, a white sheet is put up to block view of the target. ​ Not knowing where the bull's eye is, the archer'​s shots could still cluster tightly but there'​s no way of the archer knowing __without additional information__ where they are with respect to the bull's eye.  The accuracy is unknown.  ​
phy131studiof17/lectures/error.txt · Last modified: 2017/08/28 09:26 by mdawber
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