Background

Some time ago at work, I had the occasion to move offices. There were a number of reasons for this. However, the reason is not particularly germane. Here, we are concerned with a much more important issue: the new route to the breakroom.

There are now two paths to the breakroom. The choice is agonizing. Do I want to go left or right? The routes seem almost the same length. There are no coworkers whose presence necessitate one particular route.

Obviously I need to add some empiricism to my life and determine the shortest route as laziness reigns supreme. (Some would euphemize laziness as optimization or efficiency.) (Perhaps I could even persuade my manager of this?)

My solution: count steps going left and going right, compute a two-tail null test (Student’s T-test) on them to see if they represent different means and report the result.

Data

Long Tangent

So, this was not so simple. Not for me was to get out my trusty HP calculator and do the necessary math. I couldn’t even choose to write some simple code. Instead, I decided that would install a nice statistics package and do simple statistics with style.

So, I embarked on a long painful journey:

1. I set up ASDF and ASDF-install. (Yes, I must do statistics in LISP. The packet lithps when drunk.) Take-away: the ASDF-install tutorial was very helpful but didn’t really address the whole gpg integration issue. And restarts in OpenMCL are confusing for the neophyte.

2. I installed cl-mathstats. This is a package that appears under the hood to be a bit of Frankenstein: lots of pieces from different places. And the docs don’t actually help me very much but then perhaps I am simply silly. (In a perfect world, I would offer some patches against TINAA that have a different CSS aesthetic.)

At last, I was ready to do some statistics in style:

( import 'cl-mathstats:mean )
( import 'cl-mathstats:variance )
( import 'cl-mathstats:data-length )
( import 'cl-mathstats:students-t-significance )

( defun left-or-right ( right-v left-v ) 
	"uses statistical tools from cl-mathstats to do
	with style what I should have done with a pencil:
	perform a two-tail null hypothesis test comparing
	right-v and left-v.

	returns the probability that the normally distributed
	populations from which samples right-v, left-v are
	drawn have different means."
	( let
		(( sv  ( /  
			( abs ( -  (mean right-v ) ( mean left-v )))
			( sqrt  ( + 
				( / ( variance right-v  ) ( length right-v ))
				( / ( variance left-v ) ( length left-v ))))))
		( dof 
			( + ( length right-v )  ( length left-v ) -2 )))
			
			( students-t-significance sv dof :both )))

( left-or-right  '(   67 66 65 64  ) '(   80 76 77 79 ) )

Result

Ah ha! To a 0.9999 significance level, going right and left differ! Wow. So much effort to save 12 whole steps by going right, albeit at least three times a day. I am so efficient. I have optimized my life further. Soon, I will only travel under rainbows and wear a woven bamboo hat.