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I read the material on the difference betweeen accuracy and precision, but it makes me feel confused. Can I define accuracy as: \begin{equation} accuracy=\frac{TruePositive+TrueNegative}{TruePositive+TrueNegative+FalsePositive+FlaseNegative} \end{equation}

So in machine learning, what is the difference between accuracy and precision?

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    $\begingroup$ This picture is a good way to internalize the difference. (In machine learning, accuracy vs. precision is actually analogous to bias vs. variance, if you are familiar with that.) $\endgroup$ – GeoMatt22 Oct 14 '16 at 4:04
  • $\begingroup$ @GeoMatt22, thank you, can I define accuracy as :\begin{equation} accuracy=\frac{TruePositive+TrueNegative}{TruePositive+TrueNegative+FalsePositive+FlaseNegative} \end{equation} $\endgroup$ – GoingMyWay Oct 14 '16 at 4:25
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    $\begingroup$ Aaah, now I see your confusion. "Accuracy" and "precision" are general terms throughout science (and have the sense indicated by the bullseye diagrams I linked to before). However in the particular context of Binary Classification these terms have very specific definitions. The chart at that Wikipedia page gives these. (Note that this context is more specialized than just "machine learning".) $\endgroup$ – GeoMatt22 Oct 14 '16 at 4:34
  • $\begingroup$ Just for reference, I made my comments into an answer. (We have far too many "unanswered questions" already that are answered in the comments!) $\endgroup$ – GeoMatt22 Oct 14 '16 at 4:57
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(Just for reference, I am posting my comments as an answer. Note that the first version of the question did not include the formula.)

"Accuracy" and "precision" are general terms throughout science. A good way to internalize the difference are the common "bullseye diagrams". In machine learning/statistics as a whole, accuracy vs. precision is analogous to bias vs. variance.

However in the particular context of Binary Classification* these terms have very specific definitions. The chart at that Wikipedia page gives these, which are $$\mathrm{Accuracy}=\frac{\mathrm{True}}{\mathrm{Total}} \text{ , } \mathrm{Precision}=\frac{\mathrm{True\;Positive}}{\mathrm{All\;Positive}} $$ i.e. the fraction of cases that are correctly classified vs. the fraction of positives that are true.

(*Note that this context is much more specialized than simply "machine learning".)

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