The Better Business Bureau (BBB) is an institution in the United States that collects self-reported data on thousands of American businesses and charities - data which can be found here. For each BBB-accredited charity (and many non-BBB accredited ones as well who choose to give most data), you can find some important information like their assets, liabilities, income, as well as how they allocate their funds between programs, fundraising and administration.
We can define efficiency as the amount of funds spent on programs divided by the total income for a charity. Then we can plot efficiency versus charity size (by net assets). Are larger charities more efficient?
The answer is a clear no: there is no correlation between charity efficiency and size. More specifically, if we look at just the largest assets (ie. those with net assets between 100M and 1B), we again see no correlation.
Perhaps our initial efficiency definition wasn't the best measure of efficiency - after all, money spent for further fundraising may still be useful. So, we can redefine "efficiency" as non-administrative spending, or: 1 - administrative spending/total income. We now plot non-administrative spending against size:
Again we see no correlation between another measure of efficiency and size. But we also see another important result: virtually every large charity spends less than 20% on administration costs. Said otherwise, for every dollar you give to one of these charities, $0.80 is going to your cause (in some way). That's comforting.
Regressing efficiency (both funds spent on programs or non-administrative spending) on other readily available data like state, tax-exempt status or size of staff all yield no correlations. In other words, none of these variables explain the efficiency of charities. In even more words - we require more detailed data: variables that are significantly correlated with some measure of efficiency.
Perhaps in a follow-up analysis - here, at least, a negative result is still a result.
Code and .csv's can be found at bit.ly/1qdlRRB