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Apologies if this is a very obvious question, but I have been reading various posts and can't seem to find a good confirmation. In the case of classification, is a classifier's accuracy = 1- test error rate? I get that accuracy is $\frac{TP+TN}{P+N}$, but my question is how exactly are accuracy and test error rate related.

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In principle yes, accuracy is the fraction of properly predicted cases thus 1-the fraction of misclassified cases, that is error (rate). Both terms may be sometimes used in a more vague way, however, and cover different things like class-balanced error/accuracy or even F-score or AUROC -- it is always best to look for/include a proper clarification in the paper or report.

Also note that test error rate implies error on a test set, so it is likely 1-test set accuracy, and there may be other accuracies flying around.

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  • $\begingroup$ Yeah, I think that is the issue I was having is that the terms are used vaguely, and you make a good point that it must be reported in the context of your analysis. Thanks for clarifying! $\endgroup$ – micro_gnomics Jan 16 '15 at 17:57
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@mbq answered:

"1-the fraction of misclassified cases, that is error(rate)"

However, it seems wrong as misclassification and error are the same thing. See below (from http://www.dataschool.io/simple-guide-to-confusion-matrix-terminology/):

Accuracy: Overall, how often is the classifier correct? (TP+TN)/total = (100+50)/165 = 0.91

Misclassification Rate: Overall, how often is it wrong? (FP+FN)/total = (10+5)/165 = 0.09 equivalent to 1 minus Accuracy

also known as "Error Rate"

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