In this case, interested effect of teacher efficacy (Z) on pupil motivation (y) controlling pupil aptitude (x).

ps. Put it this way, by constant the x, how Z would affect y? This could be linear correlated, as Z does not influence x to influence y.

Looking into this, simple random sample must not be taken. Z population dividing x would affect overall correlation to y.

In this case, there are macro-level that are not discover for the analysis and put to test. This would introduce bias or affect the accuracy of the model if not properly accounted for.

In this case, micro-level must be establish first before two-stage sample is perform with aggregation.

Unless like in this case, there are not multi-level proposition involved, simple random sampling could work.

This would different to first case, there are relation between Z and y, with x and y taken account.

In this case, micro level affect macro level.