The answer I gave you is that the only data I've seen brings the government sector and the private sector together. I haven't seen a study that breaks the private sector out in the way you're asking. When the public is generally made aware by union leaders that they secure higher wages, I believe the skew in that data is a result of the public sector compensation levels in this country.
I was just on a job site in Saskatoon, where the employer was having difficulty finding enough people. I had just been with some people who had been dealing with a union hall in Toronto, where 50% of the people on the union hiring hall list were out of work.
In this country, from a taxpayer outrage point of view, you get extra ability to earn EI because you can be on the union's hiring hall list. So we have hiring hall people all over this nation earning EI, while we have jobs wanting in Saskatchewan and Alberta, the have provinces that are funding the have-not provinces like Ontario and Quebec. This is a problem in the EI system that is screwing up the labour market, in the same way we are screwing up by not making sure that there is full competition by, from my point of view, having more engaged, more satisfied, more driven union-free workers, but who are barred from doing unionized work.