Two things determine whether you say "yes, I detected it." One is how separable the signal is from background noise — sensitivity, measured as d′ (d-prime). The other is where you place your decision threshold — the criterion, c. They're independent. You can have sharp senses and a strict threshold, or blunt senses and a liberal one.
The distributions below show what internal sensory evidence looks like on noise-alone trials (blue) and signal-present trials (amber). The dashed line is the criterion. Everything to its right produces a "yes." Drag it left or right. Adjust d′ with the slider. Watch the four outcome regions shift — and watch where you land on the ROC curve.
The ROC curve traces every possible operating point for a given d′ — one point per criterion position. The white dot is where you are now. Curves for other d′ values are shown in gray. A curve that hugs the upper-left corner means better sensitivity: you can achieve high hit rates without inflating false alarms.
This means a single hit rate number is not interpretable alone. An observer who hits 80% of the time might have sharp senses and a strict criterion, or moderate senses and a liberal one. You can't tell from the hit rate. You need the false alarm rate too — and ideally the full ROC curve, which is what reveals the underlying d′.
The criterion is a policy, not a percept. It encodes the relative cost of misses versus false alarms. Two people with identical sensory access to the world can respond very differently, simply because they disagree about what kind of error to avoid.