The margin of error formula is the square root of p(1-p) / n multiplied by 1.96. The symbol "p" is the estimate of the percentage of respondents answering a particular question, "n" is the total number of respondents, while 1.96 is called standard deviation, representing the "standard" level of a survey's precision, a 95 percent confidence level. The confidence level of 95 percent means that the answers to the survey are expected to contain the true value at least 95 times out of 100.
A good sample size is the one giving at least a 5 percent margin of error. This would mean that we must change the formula, placing the value of our desired margin of error and try to find the sample size variable. For this purpose, we must move the standard deviation to the other side of the equation (dividing the margin of error) and find the product of both sides factors of 2. This will remove the square root and allow us to find the sample size variable.
Before a mail survey is conducted, researchers must determine the number of people they have to send the survey to, taking the response rate into consideration. The response rate can be estimated based on previous experience of conducting surveys with the same recipients. For example, if the estimated response rate is 65 percent and the sample size we need for a 3 percent margin of error is 250, then we need to send the survey to 385 people.
Since surveys are conducted with only a fraction of the total population, the sample may not be representative of the public opinion. For example, before a mayoral election in a city of 6,000 residents, 100 people were asked about their intentions, with 60 willing to vote for candidate A and 40 for Candidate B. However, the majority of the public could be supporting candidate B, even if, simply by luck, we happened to question mostly supporters of candidate A. Some sampling errors can be eliminated if survey takers are careful not to confine samples to people of a specific area, income or marital status.