Big thanks to Mark for clarifying what he meant by "data".

Data gathering on the scale suggested (hundreds of desktops over several
weeks) can be a pretty big undertaking if taken seriously.

My comments to Mark's questions:

Question 1: "Where does the average mouse rest? I.e., when it's not
being used."

Data gathering methods:
1A: Ask people where the mouse usually rests within a 3X3 screen grid.
1B: Observe users doing everyday tasks, and make note of the mouse location.
1C: Create and install a piece of software that collects statistical data over 
a period of days or weeks.

Caveats:
What does "not being used" mean? Does it mean the mouse is in the hand but not 
actively doing anything productive, or does it also include situations where 
the user has let go of the mouse? My opinion is that 5 seconds with the mouse 
motionless but in hand is much more relevant than 5 minutes where the user has 
let go of the mouse while reading an article.
Are we only interested in the habits of existing Ubuntu users? Or are we also 
interested in Windows users? And Mac users? Should we collect data separately 
for each group to see if there are statistically relevant differences?

Question 2. "Are there accidental clicks on the close button in the new
location?"

Data gathering methods:
2A: Ask people how often they have clicked on the close button when they did 
not mean to.
2B: Observe users doing everyday tasks, and make note of the mistakes they make.

Caveats:
The fact that a users click the wrong button (e.g. close instead of maximize) 
might not automatically be attributable to the placement. Maybe they would have 
made the mistake even with the right side button placement? What we really are 
interested in is are there more or less accidents now than before. So gathering 
the same type of data from a control group (with the regular button placement) 
might be useful to create a baseline to measure against.

Question 3. "Does it take longer to click it in the new location, once
one is moving with intent in the right direction?"

Data gathering methods:
2A: Ask people if they feel the use of window buttons takes longer or shorter 
now than before.
2B: Ask people if the use of window buttons feels more natural and intuitive 
now than before.
2C: Observe users doing everyday tasks before the switch, measuring the time of 
critical operations. Then do the switch. Then make them do the same type of 
tasks, and measure the time of the same operations. Then compare to see if 
certain operations have become slower or quicker.
2D: Create and install a piece of software to measure mouse activity and gather 
statistical data from the seconds immediately preceding a button operation. 
(Did the mouse change course or did it go straight? How fast did it move? How 
far from the target button did the speed start to decelerate? How quickly after 
deceleration did the click occur?)

Caveats:
Data gathering should start before doing the switch, in order to collect 
control data. What we are interested in is the difference before/after, for 
each individual test subject.

If we want to gain scientific information about these things we need to be 
specific about what specifically we are measuring and why exactly that is 
relevant to our research. This is even more important if several groups of 
people gather data from around the world, and we want to be able to merge the 
data sets later.
http://en.wikipedia.org/wiki/Operationalization

My 2 cents...

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[Master] Window Control buttons: position/order/alignment
https://bugs.launchpad.net/bugs/532633
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