Question at position 38 Multiple Choice Question: When is accuracy a good metric for evaluating the performance of a classifier? When there is high class imbalance.When the dataset is large.When false positives and false negatives have different costs.When classes are approximately equally distributed and the cost of misclassification is the same for each class.When the dataset is small.

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BlackTom AI · Accepted Answer

First, let's restate the question and all the options to set the stage for analysis.
Question: When is accuracy a good metric for evaluating the performance of a classifier? 
Options:
1) When there is high class imbalance.
2) When the dataset is large.
3) When false positives and false negatives have different costs.
4) When classes are approximately equally distributed and the cost of misclassification is the same for each class.
5) When the dataset is small.

Now, evaluate each option in turn, noting how accuracy behaves under different conditions.
Option 1: 'When there is high class imbalance.' In situations with severe class imbalance, a classifier could achieve high accuracy by simply predicting the majority class every time, which would be misleading about true performance on the minority class. Therefore, accuracy is not a reliable metric here.
Option 2: 'When the dataset is large.' A large dataset helps reduce sampling error, but it does not by itself make accuracy a good metric. If the class distribution is imbalanced or the costs of misclassification differ across classes, accuracy can still be misleading even with many examples.
Option 3: 'When false positives and false negatives have different costs.' This implies that the relative importances of FP and FN are unequal, so accuracy, which treats FP and FN equally, becomes a poor measure of performance for cost-sensitive objectives. Other metrics like weighted cost, F1, or ROC-AUC are often preferred in such cases.
Option 4: 'When classes are approximately equally distributed and the cost of misclassification is the same for each class.' This scenario aligns well with the assumptions under which accuracy is a meaningful and informative metric: balanced classes and equal misclassification costs ensure that each misclassification contributes equally to the error, making overall accuracy a good summary of performance.
Option 5: 'When the dataset is small.' With a small dataset, accuracy estimates can be highly variable and unreliable due to high variance; thus, relying on accuracy alone may be misleading. Other approaches or metrics might be more informative in small-sample settings.

Putting these considerations together, the scenario that supports accuracy as a good performance metric is the one in which there is balance between classes and uniform misclassification costs. The other options describe conditions where accuracy can be deceptive or insufficient as a sole measure of performance.

In summary, the reasoning aligns with the idea that accuracy is most informative when class distributions are approximately equal and misclassification costs are identical across classes, while it can be misleading under imbalance, cost asymmetry, or small sample noise.

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