There are three methods for testing for variation in an individual level variable between macro units that increase in complexity. The first is to compare the distribution of the micro level variable across macro units. With ratio or interval level measures, this typically takes the form of comparing the means for each macro unit.

If you are interested in a categorical variable then it would usually be more appropriate to inspect the frequency distribution of the micro variable separately for each macro unit.

A second method helps in situations where there are large number of macro units, and it is known as analysis of variance (or ANOVA). This technique can be used for ratio or interval level variables, and it can be used to calculate how much of the variance in a micro variable is due to variation between macro units and how much is variance within macro units.

Not only can ANOVA give the researcher a good idea of how much variation there is at the macro level (both absolutely and relative to that at the micro level), but it will calculate whether the macro level variation is statistically significant, i.e. whether it is sufficiently large that you can be confident it didn't simply arise by chance assuming there are no differences in the means of the micro variable for each macro unit in the real world.

ANOVA cannot be used with categorical dependent variables.

A third method for assessing the between macro unit variation for a micro variables is to fit a multilevel model with no explanatory variables but random effects for the macro units. This technique can be extended for use with categorical as well as interval and ratio level micro variables. Multilevel modelling is covered in Unit 5 of this series.