Accuracy and Precision - in Binary Classification

In Binary Classification

Accuracy is also used as a statistical measure of how well a binary classification test correctly identifies or excludes a condition.

That is, the accuracy is the proportion of true results (both true positives and true negatives) in the population. It is a parameter of the test.

On the other hand, precision or positive predictive value is defined as the proportion of the true positives against all the positive results (both true positives and false positives)

An accuracy of 100% means that the measured values are exactly the same as the given values.

Also see Sensitivity and specificity.

Accuracy may be determined from Sensitivity and Specificity, provided Prevalence is known, using the equation:

The accuracy paradox for predictive analytics states that predictive models with a given level of accuracy may have greater predictive power than models with higher accuracy. It may be better to avoid the accuracy metric in favor of other metrics such as precision and recall. In situations where the minority class is more important, F-measure may be more appropriate, especially in situations with very skewed class imbalance.

Another useful performance measure is the balanced accuracy which avoids inflated performance estimates on imbalanced datasets. It is defined as the arithmetic mean of sensitivity and specificity, or the average accuracy obtained on either class:

If the classifier performs equally well on either class, this term reduces to the conventional accuracy (i.e., the number of correct predictions divided by the total number of predictions). In contrast, if the conventional accuracy is above chance only because the classifier takes advantage of an imbalanced test set, then the balanced accuracy, as appropriate, will drop to chance. A closely related chance corrected measure is:

while a direct approach to debiasing and renormalizing Accuracy is Cohen's_kappa whilst Informedness has been shown to be a Kappa family debiased renormalization of Recall. Informedness and Kappa have the advantage that chance level is defined to be 0, and they have the form of a probability. Informedness has the stronger property that it is the probability that an informed decision is made (rather than a guess), when positive. When negative this is still true for the absolutely value of Informedness, but the information has been used to force an incorrect response.