A nine-year-old is taller than seven-year-olds. Establishing this by comparing different age groups at one time is an example of

Comparing different age groups at one point in time is a cross-sectional study.

Vertical studies is not a standard research design label.

Experimental studies manipulate a variable, absent here.

Case studies probe a single unit intensively.

Cross-sectional design substitutes age groups for the passage of time.

It is quicker than longitudinal but cannot track individual change.