Does Familiarity breed Contempt?

Thanks to my new job, I have at my disposal piles of data on different radio stations around the country and their listeners' opinions of their songs. Each week, a station sends us 30 - 40 short song hooks, and we set up a survey where people play the hooks, then rate the song. They tell us first whether they're familiar with that song, then how much they like it, and finally whether or not they're sick of it.

Here's some graphs of the data from four different stations who've completed surveys in the last few weeks. In these graphs, each dot represents a particular song, "familiarity" represents the proportion of respondents familiar with the song, and "contempt" represents the proportion of those familiar who said they were sick of hearing it.

I've also included the regression formula, R-squared, and R values on each of these graphs. See, in a linear regression formula, the number in front of the x is the important one: it tells us whether the correlation is positive or negative. The R value tells us how strong the correlation is: when R is close to 0, the relationship is weak; when R is closer to +1 or -1, the relationship is strong. (To be technical, the R value tells you the proportion of the variation in your data that can be explained by the linear relationship rather than random error. The more variation you can explain, the better your model!) The y-intercept is important for positioning the line, but otherwise useless for analysis. It's just telling you the projected contemptibility of a theoretical song with 0% familiarity, which doesn't mean anything. Don't take y-intercepts too seriously in regression analysis. They're just out to confuse you.

Gingers, Genes, and the Binomial Function

Happy Birthday, Ansley! For your birthday, I'm going to answer your question! Ansley asks: "I would like to know how probable it is that my soulless kind (aka redheads) are actually going to die out in the current century."

Would you like to help Ansley stave off the extinction of her people?

What Women Want

Quickie little post, reporting some findings from work.

Should I play the lottery?

It's easy to assume that those who buy lottery tickets have no understanding of mathematics, or at least no understanding of probability. These idiots are just letting the allure of a giant jackpot overpower their understanding of the odds. Why would anyone buy a ticket if they knew their chances of winning were infinitesimal?

Well, as it turns out, the gut instinct that motivates lottery players-- "Sure, I have almost no chance of winning, but if I do win, I could be a millionaire!"-- has a little mathematical support. One of the most useful formulas for everyday decision-making is the Expected Value Formula, pictured below:


In English, the idea is that the expected value of any random variable X (for example, the amount of money you might win from the lottery) can be calculated by multiplying each possible value of X (you win $5, you win $10, you win $100...) by that possibility's respective probability (there's a 10% chance of winning $5, a 3% chance of winning $10, a 1% chance of winning $100...) and add all those products together. Even if the chance of winning the jackpot is small, a big enough jackpot can outweigh the cost of participation.

Obviously, it's a little complicated to explain in the abstract, so let's use a simple example.