If our research question postulates that the correlation between two micro variables might be different in different kinds of macro unit, before linking the micro to the macro data, you can see whether there is any variation between macro units in the correlation between to variables.

When one or both of the variables of interest is categorical there are a variety of different strategies for assessing the pattern of association. If both are categorical, the most basic is to consider a cross-tabulation of the two variables. This could then be produced separately for each macro unit. However, comparing a series of tables is often awkward and so researchers frequently use summary statistics that measure the strength of certain aspects of the pattern of association. If both of the variables are binary, then a logistic regression analysis can be used to calculate the odds ratio for the table. If separate bivariate logistic regression analyses are run for each macro unit it is possible to compare the odds ratios and their confidence intervals. This approach can also be used if there is an interval or ratio level explanatory variable, and a binary dependent variable.

As with inspection of the macro unit means or frequency distributions of micro variables, assessing large numbers of correlation coefficients or odds ratios becomes increasingly difficult as the number of macro units grows. Anova does not provide a solution in this case, however, there are multilevel models, known as random-coefficient models that allow the researcher to assess the extent to which a linear or logistic regression coefficient varies between macro units. These models are discussed in depth in Unit 6 of this series.