Excuse me while I geek out

I had a meeting at work today where we discussed our audit testing approach. During this meeting, the senior on my engagement brought up Benford analysis. I had never heard of this before and it completely blew my mind when I saw it illustrated. Let me (wikipedia) explain:

Benford's law, also called the first-digit law, states that in lists of numbers from many real-life sources of data, the leading digit is 1 almost one-third of the time, and further, larger numbers occur as the leading digit with less and less frequency as they grow in magnitude, to the point that 9 is the leading digit less than one time in twenty.

This counter-intuitive result applies to a wide variety of figures from the natural world or of social significance - including electricity bills, street addresses, stock prices, population numbers, death rates, lengths of rivers, physical and mathematical constants, and processes described by power laws (which are very common in nature).

It is named after physicist Frank Benford, who stated it in 1938. However, it was earlier stated by Simon Newcomb, in 1881.

Did you get all that? Benford's law says that if you take any random sample of numbers and find the distribution of the leading digit, it should look like this:

While that's all well and good, it doesn't mean much until you see it. The manager on my team showed me the results from a previous Benford analysis that they had performed and the curve matched nearly perfectly. I thought that was just amazing, so I tried it myself. The first thing I tried was with some employee expense reporting data.

While it's not perfect, it still follows the general trend. I think the problem here is that people tend to round their expenses. If someone had an out of pocket expense of $29.88, they're probably just going to report it as $30. This was skewing my data, so I wanted to try something with little concious human interaction. This led me to a random data set online showing the number of faculty at various colleges in 1995.

As you can see, it's a much closer and smoother line than the expense reports, but it still isn't as close as the results I saw on our test at work. It's still pretty impressive though. I thought I'd try one final test, so I pulled some completely random census data from the state of Illinois. This provided me a really large population to sample from.

It's fairly spot on. It's crazy how it doesn't really matter where your numbers come from, it will (almost) always follow this same trend. I'm sure this has no bearing in your life, but it does in mine and I find it really interesting, so I thought I would share.

Would you pay $500,000 to vote in a midterm election?

That's the value of a 1918 Inverted Jenny, one of the rarest stamps in the world, which Broward County elections officials said was affixed to an envelope containing an absentee ballot.

I heard about this on Countdown with Keith Olbermann, but I'm too lazy to write my own post about it, so I just stole Digg's... but who knew that Montgomery Brewster voted in Broward County?

read more | digg story

NYC Marathon

Yesterday was the 2006 New York Marathon, so I walked over to first avenue to check out the runners. I got there after the "real" runners had already finished, but that actually turned out to be more entertaining. Pictured to the left are just some random people running. I felt the need to show a normal shot before highlighting the people that I found funny or interesting...

This one is my favorite. At first glance, it is just a normal group of runners. But wait, is that a guy dressed like ballerina? It sure is...

And this was a good one...running in a rhino suit

I saw a lot of people running with flags actually. One person was wearing a viking hat and a Swedish flag as a cape. Bonus points if you identify this flag...

It's super woman!

Just a shot of the crowd

I've got to give credit where credit is due. This is a big guy. If he made it 26 miles, he deserves to be recognized.

I actually saw more of this than I would have expected. The guy in the middlein on his cellphone. I saw people talking and even texting as they ran by...

This was fairly common as well. I guess people needed some way for their friends and family to spot them in the crowd.

I didn't catch them on film, but I also saw a guy running in a Spiderman costume, two guys dressed as the Blues Brothers, and a guy wearing a Ghost Busters costume - complete with backpack and gun.

This is where the title would go

Anyone who has watched TV, read a newspaper, walked down the street, or breathed during the last month is aware of the impending election. We've been bombarded with negative, attack ads and mudslinging over the past several weeks, so it was nice to come home, check my mail, and find a positive, helpful mailing from a state senator. Senator Liz Krueger (D) of New York's 26th district sent "The Harris Family or Current Resident" a "newcomer's guide to New York politics." It welcomed me to the district and provided some insight into New York state politics. It wasn't particularly helpful, but it was an entertaining read nonetheless. I was impressed with the publication until I looked at the front page. In the lower left-hand corner, Krueger included a screenshot of her blog. She obviously made the blog for the purpose of this mailing and didn't bother to even look at it before she mailed it out. She left all the filler in the template intact. I'm supposed to vote for this woman, but she can't even proof her own mailer. That's just embarrassing. Click here for a high resolution view.