Stratified two-stage cluster sampling design 

First stage: sampling schools

• Selection probability proportional to the size of the school (PPS)
• Optional: stratification of schools according to (demographic) variables of interest (e.g., school type or source of funding, level of urbanization, region of the country), either explicit or implicit
• Random-start fixed-interval systematic sampling
• Schools sampled at the same time for field trial and main data collection
• For each sampled school, two replacement schools were assigned where possible

Second stage (students): sampling classes

Within schools agreeing to participate:

• Systematic random sampling was used to select one or more classes from the sampled school in the target grade.
• Each class had an equal selection probability within the school.
• If a selected class was smaller than half of the average class size, a pseudo-class was created with other classes.
• All students within a selected class were asked to participate.

General notes

• Sampling of schools was conducted by the sampling team at IEA Hamburg.
• Sampling procedures within the center/school were carried out by the national study centers, using the Within-school Sampling Software for Windows (WinW3S) provided by IEA.