Refer to the exhibit: [Image of PV+ vs depth chart on page 2] On the Gains Chart, what is the correct interpretation of the horizontal reference line?

Question

Options

• Athe proportion of cases that cannot be classified
• Bthe probability of a false negative
• Cthe probability of a false positive
• Dthe prior event rate

• A
  3% (1)
• B
  90% (27)
• C
  7% (2)

Explanation

Important caveat before the explanation: Based on standard data mining and predictive modeling literature, the correct answer for this question is almost certainly D (the prior event rate), not B. This appears to be an error in the answer key. Here is why:

On a Gains Chart (or PV+ vs. depth chart), the horizontal reference line marks the prior event rate - the baseline proportion of positive cases in the full dataset. This line represents what PV+ would equal if your model had no discriminating power and you simply guessed at random; it's the "naive baseline." Options A, B, and C are wrong because the horizontal line is not about unclassifiable cases (A), false negative probability (B), or false positive probability (C) - those metrics are not directly encoded as a flat horizontal baseline across the entire chart.

Why B is suspicious: The false negative probability (1 − sensitivity) is a threshold-specific metric, not a single horizontal reference spanning the whole chart. It would not naturally appear as a fixed baseline on a PV+ vs. depth plot.

Memory tip: Think of the horizontal line as the "coin flip line" - it shows how well you'd do with no model at all (just the base rate). If your model's curve is above this line, you're beating random chance.

Recommendation: Double-check your source material or instructor, as D is the textbook answer for this concept. If your exam uses B, it may reflect a non-standard definition specific to that course.

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