One thing that annoys me a lot on the web is the extremely inefficient use of space on many (if not most) web pages. Why does the header always take up a third of the page? Or take a look at this:

That's a screen shot of my fantasy baseball league's live scoring page on a 21" monitor (1280x1040 resolution) where I've set the browser window size to 1024x768. The three things I really want to see on that page are: (1) The score of this week's match-up (5-4), (2) How each player is doing today (the section below the score) and (3) how this week's stats break down by category (which isn't even close to being on the page.. it's way below).

So the problem with this page is that we have about 9.5 inches of screen height to work with, and the score takes up almost 2 inches (it could easily take up 1/2 an inch), and the rest of the junk above the score takes up about 5 inches. The ad banner at the top is huge, but hey, it's supposed to generate money for the site, so I can accept that (and by accept I mean I block it with adblock of course, but it still takes up the space). The biggest problem is that the section between the top banner ad and the scoreboard takes up about 3.5 inches, which is more than a third of the page, yet conveys almost nothing. I'm quite aware that I'm on the Big Sky Baseball 2007 (listed twice for some reason) page, so maybe they could make that text a little smaller? There's also at least an inch of wasted white space in the "GameCenter" section. The links below "GameCenter" could be next to it instead of below for one thing.

Of course, this is only one of many web sites with similar problems, although this is about as bad as it gets.

I'm by no means web design expert, but I'm pretty sure I'm right about this. I even get annoyed by the space taken up by the header on my own website, UrbanDrinks.com, and it's only about an inch or so.

In my job at Sun as a quality engineer I have made several web-based applications to help analyze and report our manufacturing quality data. One common situation is where we have a number of units that tested during a time period and a number of them failed, and we want to know if the fail rate was worse than a threshold fail rate.

For example, we might have a threshold fail rate of 10% (in reality the thresholds we use are much, much lower, but this is easier for demonstration purposes) and tested 100 units, 12 of which failed. If we treat these 100 units as a sample out of a theoretical infinite population, are we at least 95% confident that population's fail rate is greater than or equal to 10%? To find out, we can use the binomial distribution class from the rubystats Ruby library (I ported this from the PHPMath project. It's available at RubyForge or you can install it with "gem install rubystats" on a system that already has RubyGems installed).

Once you have the rubystats gem installed, you can test our scenario rather easily. Below is a code sample that tests 10 scenarios against the 10% threshold (called bad_fail_rate in the code). This consists of finding the cumulative probability of observing f or more failures if the theoretical infinite population's true fail rate is 0.10. We use the cdf method (cumulative density function) to calculate the probability of observing (f-1) or fewer failures, then subtract that value from 1. If it's less than 0.05 (the alpha value for 95% confidence, i.e. 1 - 0.95 = 0.05), then the fail rate is significant.

require 'rubygems'
require 'rubystats'
require 'binomial_distribution'

tested = [100, 68, 67, 96, 46, 2, 13, 33, 88, 71]
failed = [12,  9,  12, 7,  7,  0, 6,  4,  5,  5]

bad_fail_rate = 0.10
alpha = 0.05

for i in 0..9
  t = tested[i]
  f = failed[i]
  bin = BinomialDistribution.new(t,bad_fail_rate)
  cdf = bin.cdf(f-1)
  pval = 1 - cdf
  pval = sprintf("%.3f",pval).to_f
  status = pval <= alpha ? "RED ALERT" : "OK"
  puts "Tested: #{t}\tFailed: #{f}\tpval: #{pval}\tStatus:#{status}"
end

Which outputs:

Tested: 100     Failed: 12      pval: 0.297     Status:OK
Tested: 68      Failed: 9       pval: 0.237     Status:OK
Tested: 67      Failed: 12      pval: 0.033     Status:RED ALERT
Tested: 96      Failed: 7       pval: 0.856     Status:OK
Tested: 46      Failed: 7       pval: 0.172     Status:OK
Tested: 2       Failed: 0       pval: 1.0       Status:OK
Tested: 13      Failed: 6       pval: 0.001     Status:RED ALERT
Tested: 33      Failed: 4       pval: 0.423     Status:OK
Tested: 88      Failed: 5       pval: 0.947     Status:OK
Tested: 71      Failed: 5       pval: 0.85      Status:OK

As you can see, the first scenario where 12 out of 100 failed is not statistically significant at 95% confidence.