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Balanced accuracy averages sensitivity and specificity in binary classification, giving each class equal weight.
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Formula
Dimensionless; unadjusted binary score ranges from 0 to 1
| Symbol | Meaning | Unit |
|---|---|---|
| True positive predictions | count | |
| Missed positive cases | count | |
| Correct negative predictions | count | |
| False positive predictions | count |
\mathrm{BA}=\frac{1}{2}\left(\frac{TP}{TP+FN}+\frac{TN}{TN+FP}\right)In binary classification, balanced accuracy is the mean of positive-class recall and negative-class recall: (TPR+TNR)/2. This prevents a large majority class from dominating the score as it can with ordinary accuracy. In multiclass settings, it is commonly the macro-average of per-class recall. A chance-adjusted variant is a separate definition. If a class is absent from the evaluation set, its recall is undefined and the handling convention should be reported.
In binary classification, balanced accuracy is the mean of positive-class recall and negative-class recall: (TPR+TNR)/2. This prevents a large majority class from dominating the score as it can with ordinary accuracy. In multiclass settings, it is commonly the macro-average of per-class recall. A chance-adjusted variant is a separate definition. If a class is absent from the evaluation set, its recall is undefined and the handling convention should be reported.
Balanced accuracy averages sensitivity and specificity in binary classification, giving each class equal weight.
Defining relation
The equation states the defining relation within its stated domain.
Use the example for Balanced accuracy to explain which inputs determine the requested output.
The example connects concrete inputs to its result.
Balanced accuracy averages sensitivity and specificity in binary classification, giving each class equal weight.
The relation applies only under its stated assumptions.
Applying the relation to a different case without checking its stated assumptions.
Check the validity range before substituting values: In binary classification, balanced accuracy is the mean of positive-class recall and negative-class recall: (TPR+TNR)/2. This prevents a large majority class from dominating the score as it can with ordinary.
Formula cluster
Balanced accuracy averages sensitivity and specificity in binary classification, giving each class equal weight.
With TP=80, FN=20, TN=45 and FP=5, TPR=0.8 and TNR=0.9, so balanced accuracy is 0.85.
Compare classification performance when class frequencies are uneven and inspect per-class recall.
Here is how to work through a typical Balanced accuracy (BA = (TPR + TNR)/2) task step by step:
Task
Use the example for Balanced accuracy to explain which inputs determine the requested output.
Solution path
The example connects concrete inputs to its result.
Balanced accuracy averages sensitivity and specificity in binary classification, giving each class equal weight.
The relation applies only under its stated assumptions.
The relation \mathrm{BA}=\frac{1}{2}\left(\frac{TP}{TP+FN}+\frac{TN}{TN+FP}\right) summarizes Balanced accuracy averages sensitivity and specificity in binary classification, giving each class equal weight. Read it as a model for defined quantities, not as an automatic claim about every real situation. In the example With TP=80, FN=20, TN=45 and FP=5, TPR=0.8 and TNR=0.9, so balanced accuracy is 0.85., symbols are connected to concrete values and the result is interpreted in context. Validity limit: In binary classification, balanced accuracy is the mean of positive-class recall and negative-class recall: (TPR+TNR)/2. This prevents a large majority class from dominating the score as it can with ordinary Source: scikit-learn, Model Evaluation Guide, “Balanced accuracy score”.
First write down the requested quantity and all given values with their symbols. Substitute them into the defining relation and check unit consistency. The example With TP=80, FN=20, TN=45 and FP=5, TPR=0.8 and TNR=0.9, so balanced accuracy is 0.85. provides a worked check: formula and result must have compatible scale and meaning; round only at the end. Validity limit: In binary classification, balanced accuracy is the mean of positive-class recall and negative-class recall: (TPR+TNR)/2. This prevents a large majority class from dominating the score as it can with ordinary Source: scikit-learn, Model Evaluation Guide, “Balanced accuracy score”.
The formula applies only when quantities are defined as in the source and background. Check boundary cases, measurement conditions and whether an approximation rather than equality is intended. Substitution can be algebraically correct yet technically wrong when assumptions fail or the population or system boundary changes. Validity limit: In binary classification, balanced accuracy is the mean of positive-class recall and negative-class recall: (TPR+TNR)/2. This prevents a large majority class from dominating the score as it can with ordinary Source: scikit-learn, Model Evaluation Guide, “Balanced accuracy score”.
The stated units are: Dimensionless; unadjusted binary score ranges from 0 to 1. Convert values to a consistent unit system before substitution; counts, percentages and dimensionless ratios are not interchangeable. The variable list states the role of each symbol. Dimensional analysis catches many errors but does not replace checking the formula's assumptions. Validity limit: In binary classification, balanced accuracy is the mean of positive-class recall and negative-class recall: (TPR+TNR)/2. This prevents a large majority class from dominating the score as it can with ordinary Source: scikit-learn, Model Evaluation Guide, “Balanced accuracy score”.
Comparison helps when both quantities address the same question but emphasize different properties. Report the definition, input data, threshold or averaging with the value. The source scikit-learn, Model Evaluation Guide, “Balanced accuracy score”. supports the definition used here; other conventions can differ. Choose the measure to match the learning or analysis goal. Validity limit: In binary classification, balanced accuracy is the mean of positive-class recall and negative-class recall: (TPR+TNR)/2. This prevents a large majority class from dominating the score as it can with ordinary Source: scikit-learn, Model Evaluation Guide, “Balanced accuracy score”.
Quanta exam set
Curated exam set for "Balanced accuracy":
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Which formula describes Balanced accuracy?
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How do you rearrange Balanced accuracy for Defining relation?
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Which common mistake happens with Balanced accuracy?
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