Stats 101

Everyday, we see new poll numbers telling us everything from GWB's job approval (mid to high 30's, depending on who is polling), support for the Iraq war (30's), belief in intelligent design / creationism, i.e., that humans were created exactly how the bible described it 10,000 years ago (high 40's - low 50's), to UFOs (high 40's). We remember the 2004 presidential election exit polls showing John Kerry ahead by as much a 5 points in Ohio, but still within the margin of error of +/- 11 points.

There are some who doubt the accuracy of polling numbers; afterall, how could a tiny fraction represent all 100 million of us? A good poll result is predicated on only one thing: a good sample. Your sample should be randomly selected and representative of the entire population, so if you want to poll for extraterrestial inclination, you wouldn't want to select your respondents from a Star Trek Convention.

Another key is your sample size n:

I'm not going into the entire formula, as you can easily find the definition of each variable. I'm just going to point out the denominator Ε which represents the margin of error. The smaller the margin of error, the higher the required sample size n is going to be.

Two of the measures of a good population distribution are kurtosis and skewness.

Skewness is a measure of symmetry, or more precisely, the lack of symmetry. A distribution, or data set, is symmetric if it looks the same to the left and right of the center point. Kurtosis is a measure of whether the data are peaked or flat relative to a normal distribution. That is, data sets with high kurtosis tend to have a distinct peak near the mean, decline rather rapidly, and have heavy tails. Data sets with low kurtosis tend to have a flat top near the mean rather than a sharp peak. A uniform distribution would be the extreme case.

Without knowing the mathematical proof, you can look at the formulas and conclude that the bigger the sample size, the more normally distributed it is:

where the denominator (N-1) = sample size

I really don't know the point of this post, probably to release my inner geek. But I do admit I like looking at formulas: they paint a thousand words and take you to wonderful places in your head. Weird. And speaking of a thousand words... I hope Her Hotness, Delia Gallagher's talk yesterday was a smashing success. If you have pictures, please send them to me.