Experimental unit

The experimental unit is whatever the randomization acts on: the smallest thing in the study that could have been sent to a different treatment on its own. That is the test to apply, and it is what sets the sample size. An experiment's $n$ is the number of experimental units, never the number of measurements taken.

The unit is often not a person. A district compares two reading schedules across 6 classes of 25 students, giving the new schedule to 3 whole classes and leaving 3 on the old one. The schedule was handed to a class, so the class is the experimental unit and the study has 6 units, 3 per group. Treat the 150 students as the units instead and the $\sqrt{n}$ in the standard error becomes $\sqrt{75}$ rather than $\sqrt{3}$, while the conservative degrees of freedom for a two-sample $t$ comparison go from 2, where $t^* = 4.303$, to 74, where $t^* = 1.993$. The interval that comes out is several times too narrow, and the p-value with it.

The sentence to stop writing is "the experiment had 150 subjects." It had 6 experimental units and 150 observational units. Two students in the same class share a teacher, a room, and an hour of the day, so their responses are not independent, and independence is exactly what the analysis assumes. Counting them separately manufactures evidence that was never collected.

The two kinds of unit come apart in the other direction too. If one runner's time is recorded on five separate days under a single assigned shoe, there are five observations and still one experimental unit. Measuring more often makes that runner's estimate steadier; it does not add runners.

Topic 1.13, Experimental Design, lists replication among the four elements of a well-designed experiment, and replication is counted in units: three classes per treatment is replication of three, not of seventy-five.