quantal response

Think of a class taking a pass/fail exam. You do not measure how brilliant each student is — you simply count how many passed. A quantal response works like that: for each individual the drug either produces the chosen effect or it does not, and the data is the proportion of a population that crosses the line.

Because the endpoint is yes-or-no — asleep or awake, seizure stopped or not, alive or dead — quantal data come from many individuals rather than from one. As you raise the dose, a larger fraction of the population responds, generating a cumulative S-shaped curve whose midpoint defines the ED50 for that effect (and TD50 or LD50 for toxic or lethal endpoints).

Quantal curves are the bridge between pharmacology and safety statistics: they let us compare the dose that helps most people with the dose that harms them, which is exactly what the therapeutic index and margin of safety are built from. They capture biological variability between individuals, something a single graded curve cannot show.