Well I'm not working for the school system, so I can't help you there.
There is no doubt that unions, unfortunately, save the jobs of people who should be fired. I see it time and time again just where I work. But, on the other side of the coin...you could lose/keep your job through your relationship, good/bad, with your bosses in a non-union shop.
If you belong to the YMCA you know going in that you have to pay dues. You can either pay them, or not sign up. Same with a job.
I do find it quite startling that only 5 states do not have collective bargaining for educators, and they are all the worst scoring schools in the country:
Those states and their ranking on ACT/SAT scores:
South Carolina 50th
North Carolina 49th
Georgia 48th
Texas 47th
Virginia 44th
Wisconsin is 2nd
Ah.. interesting conclusion, but there are so many factors that you need to look at. Here is one from the US bureau of statistics:
Ranking of African American Population by state:
15. Wisconsin 6.2%
33. Texas 12.0%
39. Florida 16.1%
44. North Carolina 21.6%
46. South Carolina 28.2%
48. Georgia 30.2%
These are all people - the rates may even skew higher if looking at children 18 and younger (since minorities are growing faster than white population).
These ranks seem to match the ranks you've shown above (at least directionally).
It may be possible, just possible that there are other factors involved in school success than just the fact that collective bargaining is at play here.
I'm sure there are other factors involved too - such as average household income per state, and also how big and strong the private school system is in each state.
But to think collective bargaining is the reason schools are strong in WI is just wrong. In fact, I'll be willing to be that IL is not ranked ahead of WI in outcomes based on the study you showed - even though the average teacher salary is much higher in IL than WI. Of course, IL has a much higher minority population, which makes it much harder to show success as teachers.
First law of statistical analysis - you need to hold all other variables constant before making inferences off the data like this.
And in this case, it may be impossible to hold all the variables constant (I just showed one variable, of likely many, that have a positive correlation to the data you showed).
I could show you higher average SAT scores in the private schools in WI than public schools. I could also show you that private school teachers make 50% less than their public school counterparts, based on the same education/experience. So, I'd make the argument that public teachers are way overpaid based on this data. You, of course, would counter that private schools have admission standards, and as such, draw a "better" student. Of course, you'd be right in that assumption.
But, the bottom line, based on the crude analysis you supplied above, is that it does nothing to support your argument on collective bargaining. At least not with the data/analysis you've presented. Nothing has been been provided that would indicate that collective bargaining is the factor with the highest correlation to student achieve. It MAY be one of the factors, and it just as easily could NOT be one of the factors.