Will AMOs Ever Be Bigger Than One Point?

Question
Will Kentucky schools ever have AMOs (annual measurable objectives) that ask them to improve by more than a single point per year?

Short Answer
Under Kentucky's current accountability system, AMOs greater than 1.0 are effectively impossible.

More Detailed Answer
It is mathematically possible for Kentucky AMOs to be bigger than 1.0, but scores would have to change so dramatically that it is simply not a meaningful possibility.

For example, if the top half of elementary schools all raised their scores by 10 points and the bottom half all dropped their scores by 5 points, that would allow AMOs of 1.1 points.

A change like that, with elementary scores changing radically in both directions so that the strong and weak are pulled much further apart, is hugely improbable. Effectively, it's impossible.

Middle and high schools would need even more improbable-to-impossible changes, with even bigger growth in the difference between the upper and lower results.

Technical Answer 
(To Avoid Statistical Details, Skip the Fine Print Below)
In Kentucky, our AMOs are based on standard deviations. A standard deviation is a way of saying how results spread out around the mean.  If results all clump together close to the mean, the standard deviation is small. If they spread out a lot, the standard deviation is large.

Under changes voted on by the Kentucky Board of Education earlier this month, future AMOs will ask most schools to improve their next-generation learner scores by one-third of a standard deviation in five years, meaning one-fifteenth of a standard deviation a year.

That formula means a standard deviation of 15.8 or higher will be needed to allow a 1.1 AMO.

A web-based standard deviation calculator allowed some experiments about what scores would yield that 15.8.

Entering the 2014 next-generation learner results for our 720 elementary schools yielded a 9.2 standard deviation.  One-fifteenth of that would be about 0.6. With a result like that, the new minimum AMO of 1.0 will apply.

A next step was adding 5 points to the top 365 scores, subtracting 5 points from the bottom 355, and entering those results in the calculator.  That change was not big enough to yield a 15.8 standard deviation. 

Moving each group 6 points did not work either.

10 up and 5 down worked.

10 up and 4 down did not, showing 10 and 5 to be one of the smallest elementary changes yielding 15.8 as the standard deviation and 1.1 as an AMO.

For middle and high schools, the 2014 standard deviations were smaller than at the elementary level, so it would take even bigger changes to get to a 15.8 standard deviation and a 1.1 AMO for most schools.

Why did the experiments try scenarios with some schools moving up and others down?  Because, again, standard deviations get larger when results get further apart. Bigger AMOs can only happen when the distance between the top and bottom results gets larger.  

Bottom Line
Under Kentucky's current accountability system, AMOs greater than 1.0 are effectively impossible.  The scale of change that would be required just isn't going to happen.

--Posted by Susan Perkins Weston