Atheists identified as America’s most distrusted minority

I guessing that if the same question were asked about non-religious people, they would have a higher degree of acceptance. People just don't understand the meaning of "atheist".

It has to do with how they are depicted on the media. What people mostly see are the in-your-face angry atheists. The people who simply don't have any religious beliefs are ignored, so people don't identify them as atheists. It seems that most of the militant ones left Britain, and headed this way.

I'll have to agree with Zhimbo here.Sampling is based on the mathematics of probability. A sample size of 2000, if I recall correctly, gives a result within a 3% confidence interval. In looking at the results, you have to recognize that their accuracy is limited to the confidence interval. This is usually stated when such sampling is presented. The sampling methodology is usually also published, and is thus subject to critical analysis. The mathematics is based on random sampling, not on representative sampling. It is important that the sampling be reasonably random, but it need not be fully representative.Getting an adequately random sample can be tricky. There is actually a body of research on that problem.Using a sample size of, say, 10 million would actually make the problem far harder. It is difficult to use that large a sample without introducing a lot of systematic bias.These sampling methods gain credibility from the fact that they are repeatable. Some other group will likely carry out a similar experiment, and that will either support the results or provide a basis for challenging them. If much larger samples were used, you would actually lose this benefit of repeatability, for the cost of repeating would be prohibitive.

This is a bogus issue. The researchers are sampling the population, not the geography. To the extent that they use geographic methods, they have to take into account local population densities so that there will be a random selection from the population. This is a known and well studied problem. There is published research in the area. Here is a link to a professional organization in the discipline. It is sensitive to social trends - a sampling method that works today might not work next year. If the sampling is done reasonably well, then 2,000 is sufficient. If it is done poorly, a larger sample size won't solve the problems of poor sampling. Overall, the experience pubic opinion survey organizations to rather well. Amateurs are more prone to poor experimental design.Poor sampling is only one of the problems. The wording of the questions asked can be important. Poorly chosen wording can result in misunderstood questions or can stimulate emotional responses. This is a harder problem than the sampling problem. Using a larger sample size does nothing to avoid this problem. Incidently, a survey about attitudes toward atheism may be particularly sensitive to problems associated with how the questions are worded. Elections are not public opinion surveys. In an election, you are expecting the voters to make some sort of committment to support the legislature that they elect. I think there is some evidence to support this. However, the national census does provide basic data that can be used in polling - local population densities, for example. Polling works best when you have clear issues. That is, you know what you are looking for and just need the opinion data. As far as I know, Kinsey and associates were looking for more basic data, such as would be required before you could even design a statistical experiment.

What you are missing, is that it is harder to do the sampling "reasonably well" with a sample size of 4000, than it is with a sample size of 2000. No. But it doesn't claim to give information about all humans. It only claims to give an estimate of the mean (as taken over all humans). Sure. In fact increasing the sample size makes it more difficult to do the sampling "reasonably well." As others have pointed out, elections are not public opinion surveys, for various reasons.The accuracy of a public opinion survey depends on the honesty and the disinterest of those conducting the survey. There is much at stake in an election, such that it would be impossible to guarantee this degree of honesty and detachment. It's hard enough keeping elections honest. Also elections are sometime won or lost on a margin smaller than the error margin of a public opinion survey. When used to survey public opinion, that's my impression. I admit that I don't have hard data to back it up.Keep in mind that the surveying of public opinion is a secondary issue in the census. The primary issue is finding the geographical distributions, such as needed for electoral redistribution and for implementing various other public policies.