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.

Inaugural Post

Hey, everybody! I've got a new statistics blog, and this is the first of hopefully many (but probably few) fascinating (but probably not) posts about the mysteries of statistics!

I know it's a bad plan to poison the well against myself right from the start, but I feel it prudent to point out that I only have a bachelor's degree in statistics, and I don't consider myself a mathematical genius by any means. My investigations will be therefore somewhat straightforward, pedestrian, and probably won't uncover any truly amazing relationships or startling results-- I'm no Nate Silver, just a curious soul with a graphing calculator and a standard normal table.

 What I need from you, my friendly reader(s?), are ideas for posts! Are there any questions you want answered, that might be answerable with the power of statistics? If you can point me toward where I might find some data, I'll happily scurry off to analyze it for you and get you an answer! Not necessarily a nice answer, and not necessarily a correct answer, but an answer nonetheless.

 Currently, these are the ideas I'm working on:

 - Should I play the NC Education Lottery? I can use the expected value formula to find out! We'll examine what kinds of lottery playing give you the best chances of winning the most money-- or, more likely, how to play the lottery so that you don't lose money (spoiler alert: the secret is to not play the lottery).

 - Exactly how weird is it to be gay? If I can get my hands on the percentage breakdown of the Kinsey gray scale data, I should be able to fit human sexuality to a (totally oversimplified) numeric scale and apply an appropriate probability distribution. It might turn out that colloquially "deviant" behavior actually falls nicely within +/- one standard deviation of the mean!

 - When listening to music on the radio, does familiarity breed contempt? Do fans of different kinds of music get tired of songs at different speeds? (Preliminary analysis suggests that country fans never get tired of anything, ever.) I've just got a new job working for a market research firm testing new music for radio stations, so I've got loads of fun data for this one! I'll just have to scrub it of any identifying characteristics so as to preserve client confidentiality.

 Send me ideas, and I'll try to keep your interest!