What are better alternative to this equation %Error = (|Exact-Measured|/Exact)*100?

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I am trying to find the %Accuracy, in which I used this equation:
%Accuracy = 100-%Error.



So far, I have faced two problems with this equation:



  1. When the Exact Value is Zero, the fraction can’t be used -> Solved by adding the same value to both Exact and Measured, to avoid the null denominator


  2. When the Measured value is twice bigger or smaller, the %Accuracy value will be in negative values, In which I don't see the meaning behind it.


For example:



if:
Exact = 20;
Measured = 25;
%Accuracy = 75%;



But, when:
Exact = 20;
Measured = 45;
%Accuracy = -25%;



What is the meaning of -25%? and How to change the range of [0-100], to take the values that are outside of it accurately?




measurement-theory




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    According to the equation you wrote, for the second scenario, $%Error = dfrac120 times 100 = 5%$ and hence accuracy is $95%$.
    – Aniruddha Deshmukh
    Aug 22 at 8:34











  • Thanks for your answer, it was a mistake of mine. The question is edited now, as the thing I am looking for is how to know the meaning of measured numbers that are twice bigger than the exact measurement. Can you help me in answering this question? Appreciated :)
    – Tarek Albawab
    Aug 22 at 8:52














up vote
0
down vote

favorite
1












I am trying to find the %Accuracy, in which I used this equation:
%Accuracy = 100-%Error.



So far, I have faced two problems with this equation:



  1. When the Exact Value is Zero, the fraction can’t be used -> Solved by adding the same value to both Exact and Measured, to avoid the null denominator


  2. When the Measured value is twice bigger or smaller, the %Accuracy value will be in negative values, In which I don't see the meaning behind it.


For example:



if:
Exact = 20;
Measured = 25;
%Accuracy = 75%;



But, when:
Exact = 20;
Measured = 45;
%Accuracy = -25%;



What is the meaning of -25%? and How to change the range of [0-100], to take the values that are outside of it accurately?




measurement-theory




share|cite|improve this question


















  • 1




    According to the equation you wrote, for the second scenario, $%Error = dfrac120 times 100 = 5%$ and hence accuracy is $95%$.
    – Aniruddha Deshmukh
    Aug 22 at 8:34











  • Thanks for your answer, it was a mistake of mine. The question is edited now, as the thing I am looking for is how to know the meaning of measured numbers that are twice bigger than the exact measurement. Can you help me in answering this question? Appreciated :)
    – Tarek Albawab
    Aug 22 at 8:52












up vote
0
down vote

favorite
1









up vote
0
down vote

favorite
1






1





I am trying to find the %Accuracy, in which I used this equation:
%Accuracy = 100-%Error.



So far, I have faced two problems with this equation:



  1. When the Exact Value is Zero, the fraction can’t be used -> Solved by adding the same value to both Exact and Measured, to avoid the null denominator


  2. When the Measured value is twice bigger or smaller, the %Accuracy value will be in negative values, In which I don't see the meaning behind it.


For example:



if:
Exact = 20;
Measured = 25;
%Accuracy = 75%;



But, when:
Exact = 20;
Measured = 45;
%Accuracy = -25%;



What is the meaning of -25%? and How to change the range of [0-100], to take the values that are outside of it accurately?




measurement-theory




share|cite|improve this question














I am trying to find the %Accuracy, in which I used this equation:
%Accuracy = 100-%Error.



So far, I have faced two problems with this equation:



  1. When the Exact Value is Zero, the fraction can’t be used -> Solved by adding the same value to both Exact and Measured, to avoid the null denominator


  2. When the Measured value is twice bigger or smaller, the %Accuracy value will be in negative values, In which I don't see the meaning behind it.


For example:



if:
Exact = 20;
Measured = 25;
%Accuracy = 75%;



But, when:
Exact = 20;
Measured = 45;
%Accuracy = -25%;



What is the meaning of -25%? and How to change the range of [0-100], to take the values that are outside of it accurately?





measurement-theory





share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Aug 22 at 9:04

























asked Aug 22 at 8:28









Tarek Albawab

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  • 1




    According to the equation you wrote, for the second scenario, $%Error = dfrac120 times 100 = 5%$ and hence accuracy is $95%$.
    – Aniruddha Deshmukh
    Aug 22 at 8:34











  • Thanks for your answer, it was a mistake of mine. The question is edited now, as the thing I am looking for is how to know the meaning of measured numbers that are twice bigger than the exact measurement. Can you help me in answering this question? Appreciated :)
    – Tarek Albawab
    Aug 22 at 8:52












  • 1




    According to the equation you wrote, for the second scenario, $%Error = dfrac120 times 100 = 5%$ and hence accuracy is $95%$.
    – Aniruddha Deshmukh
    Aug 22 at 8:34











  • Thanks for your answer, it was a mistake of mine. The question is edited now, as the thing I am looking for is how to know the meaning of measured numbers that are twice bigger than the exact measurement. Can you help me in answering this question? Appreciated :)
    – Tarek Albawab
    Aug 22 at 8:52







1




1




According to the equation you wrote, for the second scenario, $%Error = dfrac120 times 100 = 5%$ and hence accuracy is $95%$.
– Aniruddha Deshmukh
Aug 22 at 8:34





According to the equation you wrote, for the second scenario, $%Error = dfrac120 times 100 = 5%$ and hence accuracy is $95%$.
– Aniruddha Deshmukh
Aug 22 at 8:34













Thanks for your answer, it was a mistake of mine. The question is edited now, as the thing I am looking for is how to know the meaning of measured numbers that are twice bigger than the exact measurement. Can you help me in answering this question? Appreciated :)
– Tarek Albawab
Aug 22 at 8:52




Thanks for your answer, it was a mistake of mine. The question is edited now, as the thing I am looking for is how to know the meaning of measured numbers that are twice bigger than the exact measurement. Can you help me in answering this question? Appreciated :)
– Tarek Albawab
Aug 22 at 8:52










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For your problem 1, if the exact answer is zero, then a miss is as good as a mile. That is, any measured value other than zero is equally wrong. For your problem 2, there is a better way. If x and y are two non-zero real numbers, then define



%Error := 100 * min(1, 2 * abs(x - y) / (abs(x) + abs(y))), while if only one number is zero the %Error := 100%, and if both are zero then %Error := 0%. With this definition %Error is always between 0% and 100%. Now your definition of %Accuracy = 100-%Error behaves as you would expect.



If this is too radical for you then just slightly adjust your original equation to %Error = min(1, |Exact - Measured| / Exact) * 100.






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    For your problem 1, if the exact answer is zero, then a miss is as good as a mile. That is, any measured value other than zero is equally wrong. For your problem 2, there is a better way. If x and y are two non-zero real numbers, then define



    %Error := 100 * min(1, 2 * abs(x - y) / (abs(x) + abs(y))), while if only one number is zero the %Error := 100%, and if both are zero then %Error := 0%. With this definition %Error is always between 0% and 100%. Now your definition of %Accuracy = 100-%Error behaves as you would expect.



    If this is too radical for you then just slightly adjust your original equation to %Error = min(1, |Exact - Measured| / Exact) * 100.






    share|cite|improve this answer


























      up vote
      0
      down vote













      For your problem 1, if the exact answer is zero, then a miss is as good as a mile. That is, any measured value other than zero is equally wrong. For your problem 2, there is a better way. If x and y are two non-zero real numbers, then define



      %Error := 100 * min(1, 2 * abs(x - y) / (abs(x) + abs(y))), while if only one number is zero the %Error := 100%, and if both are zero then %Error := 0%. With this definition %Error is always between 0% and 100%. Now your definition of %Accuracy = 100-%Error behaves as you would expect.



      If this is too radical for you then just slightly adjust your original equation to %Error = min(1, |Exact - Measured| / Exact) * 100.






      share|cite|improve this answer
























        up vote
        0
        down vote










        up vote
        0
        down vote









        For your problem 1, if the exact answer is zero, then a miss is as good as a mile. That is, any measured value other than zero is equally wrong. For your problem 2, there is a better way. If x and y are two non-zero real numbers, then define



        %Error := 100 * min(1, 2 * abs(x - y) / (abs(x) + abs(y))), while if only one number is zero the %Error := 100%, and if both are zero then %Error := 0%. With this definition %Error is always between 0% and 100%. Now your definition of %Accuracy = 100-%Error behaves as you would expect.



        If this is too radical for you then just slightly adjust your original equation to %Error = min(1, |Exact - Measured| / Exact) * 100.






        share|cite|improve this answer














        For your problem 1, if the exact answer is zero, then a miss is as good as a mile. That is, any measured value other than zero is equally wrong. For your problem 2, there is a better way. If x and y are two non-zero real numbers, then define



        %Error := 100 * min(1, 2 * abs(x - y) / (abs(x) + abs(y))), while if only one number is zero the %Error := 100%, and if both are zero then %Error := 0%. With this definition %Error is always between 0% and 100%. Now your definition of %Accuracy = 100-%Error behaves as you would expect.



        If this is too radical for you then just slightly adjust your original equation to %Error = min(1, |Exact - Measured| / Exact) * 100.







        share|cite|improve this answer














        share|cite|improve this answer



        share|cite|improve this answer








        edited Aug 22 at 19:59

























        answered Aug 22 at 19:49









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