There are several methods for polling - some are scientific and some are not. An example of unscientific polling is a straw poll. This is a poll in which participation is voluntary. The reason straw polls are unscientific is that the polling organization has no control over who volunteers, so he or she knows nothing about the opinion of the overall population in relation to those being polled. On the other hand, random polls in which everyone being polled cooperates are scientific because they accurately reflect the opinions of the population being questioned. Most scientific polls are not purely random, but they can still be analyzed by using probability and statistics.
To get an idea of how random polling works, consider an example. Suppose 400 American adults are randomly chosen and asked whether they think the country is moving in the right direction and that 80 of them say yes. Since 80 is 20% of 400, we conclude that approximately 20% of all American adults think the country is moving in the right direction. How accurate is our estimate? To determine the reliability of this figure, we need to use some probability theory. Suppose 20% of all American adults really do think the country is moving in the right direction. Then if we sample 400 of them at random, we expect 80 of them to say they believe the country is moving in the right direction. This is like tossing a fair five-sided die (if you can imagine such a thing) 400 times and seeing how many times the number 1 turns up. The die will likely land on 1 close to 80 times, but probably not exactly 80 times. There is in fact a probability distribution, known as the binomial distribution, of how many times the number 1 shows up. There turns out to be a 68% chance that the actual number of times the die lands on 1 is within one standard deviation of the expected value of 80 and a 95% chance that the actual number is within two standard deviations of this
value. The standard deviation in this case can be calculated and turns out to be 8, meaning that there is a 68% chance that the number of times 1 turns up is between 72 and 88 (between 18% and 22%), and there is a 95% chance that the number of times 1 turns up is between 64 and 96 (between 16% and 24%). Since the die-tossing example is completely analogous to the random poll, we also conclude that there is a 95% chance that if we sample 400 American adults at random, between 16% and 24% of them will say they think the country is moving in the right direction.
In practice, however, as far as polling goes, things work the other way. For instance, we poll 400 American adults, determine the number of them who say they thing the country is moving in the right direction, and from this information draw a conclusion regarding the population as a whole. But the formula stays the same. Thus, for instance, if we poll 400 American adults at random and 80 (20%) of them say they believe the country is moving in the right direction, we conclude there is a 95% chance that the actual percentage of American adults who believe the country is moving in the right direction is between 16% and 24%. Another way of saying this is that we are 95% confident that the actual percentage of American adults who believe the country is moving in the right direction is within 4% of 20%. Thus we say that the margin of error (MOE) of our poll is 4%. It is standard to use a 95% confidence level in statistical surveys, though sometimes a 99% confidence level is used.