# Correlation of aggregated data - is it valid

This is a common analysis situation which I've come across, but it makes me feel a little uneasy. Its finding the correlation of 2 variables after they have been aggregated. I haven't got any concrete numbers (they're commercially sensitive), but here are 2 examples:

In a call centre we have speed to answering the phone (variable A) for the past 12 months (n=12) and customer satisfaction (variable B), again for the past 12 months. What does the correlation between the 2 variables aggregated by month tell us? If it was a strong negative correlation, say -0.9, does it mean that slow answers lower customer satisfaction

Example 2:

Suppose a company ran a staff satisfaction survey on its 30 departments (n=30). It measured the staff turnover (variable A) and staff satisfaction aggregated for the department (variable B). What does the correlation between the 2 variables mean?

Robinson (1950) described this as the ecological fallacy Robinson, W.S. (1950) Ecological correlations and behaviour of individuals. American Sociological Review 15: 351-7

There are issues with this sort of analysis and if possible a hierarchical analysis should be conducted.

[EDIT: Further information]

The important thing to check to begin with is your units of measurement. In your first example do you get satisfaction scores from the people who call? Do you get scores from all of them or just a sample?

In the first example it is also worth considering the time series aspect of the problem - would low satisfaction in month $i$ lead to efforts to improve waiting times in month $i+1$? Would there be a lag effect such that consumers could carry over dissatisfaction from previous months?

In the second example there may not actually be a problem in identifying the correlation but it will not tell you much about the causal relationship, eg does improving average employee satisfaction in a department reduce turnover in that department or is it somehow the other way around?

• It's great that you've provided a seminal reference but it would be better if you could flesh out your answer as well. Also, I fixed your link so that it would redirect to the paper outside your institution. The former link was a dead end for anyone else. – John Mar 18 '15 at 18:58
• Sorry it was a quick answer on my phone while cooking dinner. If you want to post a more comprehensive answer I'm more than happy or I'll try to flesh this out later tonight. – tristan Mar 18 '15 at 19:01