A confusion matrix is created for data that were oversampled due to a rare target. What values are not affected by this oversampling?

Question

Options

• ASensitivity and PV+
• BSpecificity and PV-
• CPV+ and PV-
• DSensitivity and Specificity

• A
  4% (1)
• B
  4% (1)
• C
  8% (2)
• D
  83% (20)

Explanation

Sensitivity and Specificity are unaffected because they are conditioned on the true class. Sensitivity = TP/(TP+FN) uses only the actual-positive row, and Specificity = TN/(TN+FP) uses only the actual-negative row. Oversampling multiplies positive instances proportionally, so both the numerator and denominator of Sensitivity scale together - the ratio doesn't change. The negative class is untouched, so Specificity is also unchanged.

Why the distractors fail:

• A (Sensitivity and PV+): PV+ = TP/(TP+FP). Oversampling inflates TP while FP stays the same, so PV+ rises artificially - it is affected.
• B (Specificity and PV-): PV- = TN/(TN+FN). Oversampling inflates FN while TN stays fixed, so PV- drops artificially - it is affected.
• C (PV+ and PV-): Both predictive values depend on prevalence (the proportion of positives in the sample), which oversampling directly manipulates - so both are affected.

Memory tip: Think of Sensitivity and Specificity as "row metrics" - they live entirely within one true-class row of the confusion matrix and never cross rows. Predictive values are "column metrics" that mix both classes, so they shift whenever class balance (prevalence) changes, as oversampling does.

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