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BTW, I just checked out a sample size calculator. For a 95 percent confidence level with a +- 5% confidence interval, and a population of 400 million, guess what your sample size needs to be.

384.

Now this calculation for a survey is a little different from what the researchers are doing here, but it illustrates my point. You can do a lot with small sample sizes if the differences between groups are large.

That's if they're only trying to estimate a grand rate. To make state-by-state estimates they need this number *per state*.

BTW, I just checked out a sample size calculator. For a 95 percent confidence level with a +- 5% confidence interval, and a population of 400 million, guess what your sample size needs to be.

384.

Now this calculation for a survey is a little different from what the researchers are doing here, but it illustrates my point. You can do a lot with small sample sizes if the differences between groups are large.

One of the consequences of the law of large numbers is that the sample result is independent of the population size if the population is large compared to the sample size.

Your opinion was known to be wrong some 400 years ago.

You can see the results of this in the following calculator.

http://www.surveysystem.com/sscalc.htm

1. the same size is small.. probably too small to make the claims they did.

Probably? So you don't actually know, but instead are just going to rely on the old saw of "Well they didn't ask me! I don't know anyone they asked! Those muckity muck scientists aren't so smart!"

The population of the UK is approximately 60,943,912. Assuming your draws (i.e. choosing who to ask and who answered) are uniformly random, and independent and identically distributed (i.e. the answers of any one person does not effect the answers of anyone else, nor who you ask) the size of your sample for being 95% sure (i.e. your "confidence level") that your results are within 4 percentage points (i.e. the "confidence interval" (i.e. the +- number seen at the bottom of polls)), then you need to a mere 600 random individuals. If you want to be 99% sure that number of file sharers are within 4 percentage points of you counted, then you need to ask 1,040.

Assuming the sample is unbiased, asking 1,176 individuals from a population of 60,943,912 with a confidence level of 95% in your 11.6% result gives you an error bar (i.e. confidence interval) of 1.83%. Going up to 99%, your error bar increases to 2.41%.

2. they altered the numbers on an estimate of how many people fileshare on the assumption that the number was under-reported

This is known as controlling for sampling bias. Not only is it an long established and mathematically proven method, but to not control for sampling bias is sign of shoddy work. Work so shoddy, that you would fail an undergrad statistics course.

3. conflict of interest... it's like the tobacco industry sponsoring studies claiming that smoking doesn't have anything to do with lung cancer... there is significant reason to believe that the study carries significant bias in favor of their conclusion and must at the least be repeated by other sources.

Same can be said about your unsupported allegations of bias, especially given your lack understanding of long established statistical sampling techniques.

N. real statistics researchers know that this study has numerable crippling flaws and should not be held as gospel by anyone. Even a first year stats student can see it. The reason this story is important is that it may influence governmental policy and it's flawed... That's danger

At least the irony of you making this statement isn't lost on one of us.

In short. Go to school and take a stats class.

According to this 5000 respondent survey the failure rate is 54.2%, but the article points out that over 30 million consoles have been sold. I would place little confidence in the 5000 person survey.

Actually, with a population of 30 million, you can be 99% confident of the result with a confidence interval of +-2% with a sample size of 4,160. Check these numbers here. This means you know with 99% confidence that the actual population failure rate is between 52.2% and 56.2%.
Sample sizes don't need to be as large as most people think to produce statistically significant results. Of course, that calculation assumes a random sample from the population, whereas this was sampled only from readers of Game Informer. I could see an argument that the numbers are skewed by selection bias, but the sample size is large enough.

I'm pretty sure you'd need a RANDOM sample for that to be true. As in pollsters randomly called phone numbers, found 5,000 xbox owners, and then obtained failure rates.

www.applerocksmssucks.com/xboxbadyesorno.htm is probably not a "random" distribution.

According to this 5000 respondent survey the failure rate is 54.2%, but the article points out that over 30 million consoles have been sold. I would place little confidence in the 5000 person survey.

Actually, with a population of 30 million, you can be 99% confident of the result with a confidence interval of +-2% with a sample size of 4,160. Check these numbers here. This means you know with 99% confidence that the actual population failure rate is between 52.2% and 56.2%. Sample sizes don't need to be as large as most people think to produce statistically significant results. Of course, that calculation assumes a random sample from the population, whereas this was sampled only from readers of Game Informer. I could see an argument that the numbers are skewed by selection bias, but the sample size is large enough.

Sigh... It's not just you--vast swathes of other people, certainly the majority of the Western world, are ignorant of basic statistical concepts, just like you (no disrespect!). A sample size of 500 is almost certainly big enough for this kind of study.

For any given sample-extrapolation experiment, you can calculate a "conservative" sample size that will be "big enough" to meet your criteria for confidence level, confidence interval, etc. I just Googled this guy up, if you want to play around with some values, to see how big of a sample you need if you want to extrapolate to a population of 300,000,000:

  * http://www.surveysystem.com/sample-size-formula.htm

(PROTIP: It's smaller than you think.)

Wikipedia has an explanation of what/how/why, but I'll warn you ahead of time, unless you already took a stats class and just need a refresher, you won't understand (no disrespect!):

  * http://en.wikipedia.org/wiki/Sample_size#Estimating_proportions

For those too lazy to FTFL (no disrespect!), it takes somewhere around 1,000-2,000 sample members, if you want to get a 95% confidence level and a confidence interval of 5%, given a p/q split of ~ .5/.5. So assuming these researchers did their math correctly when they formally stated the results of their significance tests.

(NOTE: I'm NOT saying the study is valid--that's a whole 'nother Oprah. I'm just making a general statement about how big of a sample size a study needs to obtain a certain amount of probabalistic reliability.)

As long as the sample is representative, the margin of error there is only about +/- 3.5%. (Sample Size Calculator)

Most national polls use sample sizes of 1000 or less, chosen from a population of 300 million. The whole point of polling is that you don't need to talk to a huge percentage of the population in order to be confident in your results.

If you don't trust my equations, you have them here and on the same site you can find a javascript sample size calculator which you can test the values with.

If you don't trust my equations, you have them here and on the same site you can find a javascript sample size calculator which you can test the values with.

2,000 is a RIDICULOUSLY small sample size to extrapolate the views of 60+ million people from.

Check out this Sample Size Calculator.

In a nutshell, for 150,000,000 you need a sample of about a 1000 people to get a representative result.

Maybe you can use the sample size calculator linked here to find the sample popluation required. With a large population that calculator suggests 384 people as a suitibla sample size to aim for a 95/5 accuracy. A sample size of 20 people is highly unlikely to give a 5% margin. Think about it, if you swap any one person in there for any one person outside the group you have immediately skewed your results by over 5%. The reason for large samples is to avoid these problems. It would seem that you are the one who needs to read a statistics book or two because if you for a second believe that a sample of 20 can represent accurately a large population you obviously have not had any exposure to statistics, or if you have it has been way over your head.