I mentioned it over on the Anything and Everything board, but I'll mention it over here since I suspect not everyone looks at that board and it seems to fit in here. I don't know how many households Nielsen surveys each week for their ratings, but this week, my household is one of them.
I would have thought it would be more than 25,000 households nationally since this is the second time I've received a ratings diary (the first time was as a teenager back in the 1970s). I'd figured that after the first time, it probably wouldn't ever happen again. A little simple math shows that 25,000 households times 52 weeks a year over 40 years comes out to about 52 million households. I guess it wasn't as unlikely as I thought, but it's still probably 5 or 10 to 1 against it happening (as a rough guess). Maybe it was fewer households in the past. As for the accuracy of using 25,000 as a sample size, I'll point out that political polling uses far less, though they always say it's plus or minus 3 or 4 percent. I suspect the networks want better accuracy than that, thus a larger poll of 25,000 homes. It's a fairly costly process. Neilsen is paying us 5 dollars to fill out the survey, so that is $125,000 each week just for paying people to fill out surveys, let alone postage and reading and tallying the diaries. It probably costs at least $500,000 a week to conduct the weekly Nielsen ratings. That's not even factoring in the electronic boxes they use for the overnight ratings, so the cost is probably a lot higher than that. Anyway, we'll be helping TAR out against the Oscars this week, even though we won't be in the overnight ratings, just in the final ratings that comes out weeks after the fact.
Getting back to SuperTux's question, I couldn't explain it now, but the statistics courses I took in college showed me that you could get a good poll from a relatively small group of people if they were representative of the population as a whole. A lot of personal data about each of us has been collected through various means and I believe it's very possible to get a reasonably accurate and representative group of households each week. The other issue is whether people are going to be honest about what they watch. I suspect they aren't completely honest. I know the first time I filled a diary out, all my favorite shows got written in whether I actually watched them or not. This time I'm being honest since we don't watch all that much TV and I don't have nearly as many favorite shows as I did back then. Let's ignore whether or not we will really have 500 or so people in our living room when TAR or Survivor is on.
I expect the fraudulent entries probably tend to cancel out when thousands of people are involved and the networks are happy to have anything that appears to raise the overall viewer numbers.