# What are statistical methods for comparing different brackets

I am not particularly familiar with statistics and am looking at methods for analysing numbers that have been broken into different "brackets" or "groups" for different entities.

Consider three companies.

• A announces that they have 10 factories generating between 10,000 and 20,000 widgets per year and 15 factories generating between 20,000 to 40,000

• B announces that they have 7 factories generating between 15,000 and 25,000 widgets and 5 factories generating between 25,000 and 35,000

• C announces they have 5 factories generating between 10,000 and 23,000 widgets and 14 between 23,000 and 40,000

To be clear all widget production is included in my simplified example above.

What statistical methods can be used (and do any exist) that would allow you to aggregate this data together and make generalised predictions (all companies have on average x factories that generate 15,000 widgets per year and y factories that generate 40,000)?

• It's a good question (+1), but I would urge caution: unless those companies are using some standard intervals for reporting their statistics, there may be substantial bias introduced by their choices of breakpoints. You're probably familiar with the myriad sports statistics flung about the media of the form "the team has won five of their last seven games--they're on a streak!" that exist because, of course, the team lost the eighth game back. Aggregation can be similarly jiggered to make data look better (or worse) than they really are. Statistical procedures won't cure that problem. – whuber May 2 '13 at 13:51
• @whuber totally agree with your point on bias. I edited the question to be clear that all data is included, so setting the break points in this example probably wouldn't be based on bias. – Robert Anton Reese May 2 '13 at 14:30
• You might be interested in Sheppard's corrections. For a recent exposition, see the first couple of pages of arxiv.org/pdf/1004.4989.pdf. – whuber May 2 '13 at 14:38