One key question faced by Gallup statisticians: how many interviews does it take to provide an adequate cross-section of Americans? The answer is, not many -- that is, if the respondents to be interviewed are selected entirely at random, giving every adult American an equal probability of falling into the sample. The current US adult population in the continental United States is 187 million. The typical sample size for a Gallup poll which is designed to represent this general population is 1,000 national adults.
The actual number of people which need to be interviewed for a given sample is to some degree less important than the soundness of the fundamental equal probability of selection principle. In other words - although this is something many people find hard to believe - if respondents are not selected randomly, we could have a poll with a million people and still be significantly less likely to represent the views of all Americans than a much smaller sample of just 1,000 people - if that sample is selected randomly.
To be sure, there is some gain in sampling accuracy which comes from increasing sample sizes. Common sense - and sampling theory - tell us that a sample of 1,000 people probably is going to be more accurate than a sample of 20. Surprisingly, however, once the survey sample gets to a size of 500, 600, 700 or more, there are fewer and fewer accuracy gains which come from increasing the sample size. Gallup and other major organizations use sample sizes of between 1,000 and 1,500 because they provide a solid balance of accuracy against the increased economic cost of larger and larger samples. If Gallup were to - quite expensively - use a sample of 4,000 randomly selected adults each time it did its poll, the increase in accuracy over and beyond a well-done sample of 1,000 would be minimal, and generally speaking, would not justify the increase in cost.
Statisticians over the years have developed quite specific ways of measuring the accuracy of samples - so long as the fundamental principle of equal probability of selection is adhered to when the sample is drawn.
For example, with a sample size of 1,000 national adults, (derived using careful random selection procedures), the results are highly likely to be accurate within a margin of error of plus or minus three percentage points. Thus, if we find in a given poll that President Clinton's approval rating is 50%, the margin of error indicates that the true rating is very likely to be between 53% and 47%. It is very unlikely to be higher or lower than that.
To be more specific, the laws of probability say that if we were to conduct the same survey 100 times, asking people in each survey to rate the job Bill Clinton is doing as president, in 95 out of those 100 polls, we would find his rating to be between 47% and 53%. In only five of those surveys would we expect his rating to be higher or lower than that due to chance error.
As discussed above, if we increase the sample size to 2,000 rather than 1,000 for a Gallup poll, we would find that the results would be accurate within plus or minus 2% of the underlying population value, a gain of 1% in terms of accuracy, but with a 100% increase in the cost of conducting the survey. These are the cost value decisions which Gallup and other survey organizations make when they decide on sample sizes for their surveys.
