JF :: Brain Farts :: Archive of December, 2006

Archive of December, 2006

Only a Savings If Your Time Has No Value

December 29, 2006:

The last few weeks I've been shutting my bedroom door at night. It helps keep the moistened air from the humidifier in, which prevents me from waking up with a mouth that feels like the Sahara. On the downside, my room is effectively disconnected from the thermostat, so thanks to the double window my room tends to get a little chilly at night.

I bought some more of the plastic sheeting that I used back on Negley Street, which helped out quote a bit there. This place is different: There are no gaps in the walls leading directly to the outside world. Once I get the second window up I'll see if I notice any difference before I work on the living room with the balcony and the triple window next to my computer.

I don't feel any drafts coming in, just the slight convective flow of air that's being cooled by the glass. Not sure how that extra air-wall will help, but I guess it's worth a try.

Of course, by the time I get the rest of the plastic put up there's a good chance that winter will be over.

Notes For Myself: Statistical Significance

December 12, 2006:

For a client's web site I needed to calculate percentages and determine if the differences were statistically significant. In other words, if Group A answered yes 53% of the time and Group B answered 55% of the time, is that 2% difference likely to mean anything?

The first step is to compute the averages. That's easy enough.

Next come the standard deviations. Assuming the markup I'm about to write displays properly the calculation is:

σ² = _i=1Σⁿ (x - x_i)² / (n - 1)

In English, and accounting for the fact that HTML can't quite show what I want to*, that line says that to get the variance (the square of the standard deviation) you:

1. Find the difference between each measurement and the average
2. Square each of those differences
3. Add those all together
4. Divide what you get by one less than the total numebr of measurements

If you want the standard deviation you just take the square root of that whole mess.

OK, now we've got the variance of each group. Now we need to figure out the standard error. This is a measurement that lets us compare two groups of different sizes.

σ_A-B = √ (σ_A² / n_A) + (σ_B² / n_B)

For each group, divide the variance by the number of measurements. Add those to numbers together, then take the square root of the result. We now have the standard error (though I may not have written it out in "standard" stats format).

And now we're almost home. Our standard error is kind of like a standard deviation for both of the populations combined. Now, if we assume the normal bell curve, we have the following rough estimates about a sample:

• About two thirds of the group is within one σ
• About 95% is within 2σ
• About 99% is within 3σ

So let's find the difference between the two averages and see how many standard errors apart they are:

Z = |x_A - x_B| / σ_A-B

That one's easy enough. Now, those numbers (1σ = 66%, etc.) aren't quite accurate. The 95% figure is actually at 1.96σ. So if the two averages are more than 1.96 standard errors apart there's a 95% chance we're dealing with two different results. In statistician-speak, there's a probability (p) of 0.05 (5%) that they're not different. As Z goes up, the p of them being statistically insignificant goes down.

In most cases, the 95% chance is good enough, so if the two populations have a Z ≥ 1.96, we can say that the difference is statistically significant. And that means that you can say Group A is doing better (or worse) than Group B, or (if Z < 1.96) the two groups are basically the same.

The last (and only) stats course I took was in 1997. And just about every stats page I found online wanted me to read five chapters of material just to get the math. After a few days of searching I finally found the equations (and simple explanations) that let me write the VBScript code to do the math I wrote above.

Or, I could have paid attention in that stats class junior year.

* Yes, I could use MathML. There are only two problems with that. 80% of the world can't see it, and it requires about 5 megs of XML to write "2 + 2 = 4". I'll just stick with HTML and style sheets and let whoever's reading this figure out that the "i=1", "Σ" and "n" are all supposed to be vertically aligned.

Someone Probably Got Fired For That One...

December 04, 2006:

The internet connection at work went down Friday afternoon just before 4:00. It wasn't our fault; power-cycling the router showed the same thing: 2 T1 lines, both red.

After becoming increadingly annoyed at Verizon for not following up like they're supposed to during a reported outage, we finally got a promise to call the local Verizon center, find out what the hell was going on, and call us back. (Apparently the world will end if us plebes, or even the level-one call center techs, dare speak to the local office. After all, they're the ones who know what the hell's going on.)

When the call came about 45 minutes later, we had our answer: The worst case of backhoe fade I've ever heard of. Somewhere between Reston and Manassas, someone managed to damage the fiberoptic backbone of a large portion of the east coast's internet. At least an OC12, probably, maybe an OC48. But lots of people's connections went dark that afternoon.

Some construction guy definitely had himself a bad day.

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