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How to Determine Sample Size Discussion Forum "I was asked today to determine a sample size required for different conf idence intervals (80, 90, and 95 percent respectively) I have not found a way to accurately answer this question."
Pam Hunter A survey is a valuable assessment tool in which a sample is selected and information from the sample can then be generalized to a larger populati on. Surveying has been likened to taste-testing soup a few spoonfuls t ell what the whole pot tastes like. Just as the soup mus t be stirred in order for the few spoonfuls to represent the whole pot, when sampling a population, the group must be stirred before respondents are selected. It is critical that respondents be chosen randomly so tha t the survey results can be generalized to the whole population. How well the sample represents the population is gauged by two important statistics the survey's margin of error and confidence level. They tel l us how well the spoonfuls represent the entire pot. For example, a sur vey may have a margin of error of plus or minus 3 percent at a 95 percen t level of confidence. These terms simply mean that if the survey were c onducted 100 times, the data would be within a certain number of percent age points above or below the percentage reported in 95 of the 100 surve ys. In other words, Company X surveys customers and finds that 50 percent of the respondents say its customer service is "very good." The confidence level is cited as 95 percent plus or minus 3 percent. This information m eans that if the survey were conducted 100 times, the percentage who say service is "very good" will range between 47 and 53 percent most (95 pe rcent) of the time. Survey Sample Size Margin of Error Percent* 2,000 2 1,500 3 1,000 3 900 3 800 3 700 4 600 4 500 4 400 5 300 6 200 7 100 10 50 14 *Assumes a 95% level of confidence Sample Size and the Margin of Error Margin of error the plus or minus 3 percentage points in the above exam ple decreases as the sample size increases, but only to a point. A ver y small sample, such as 50 respondents, has about a 14 percent margin of error while a sample of 1,000 has a margin of error of 3 percent. The s ize of the population (the group being surveyed) does not matter. By doubling the sample to 2,000, the margin of error only decreases from plus or minus 3 percent to plus or m inus 2 percent. Although a 95 percent level of confidence is an industry standard, a 90 percent level may suffice in some instances. A 90 percen t level can be obtained with a smaller sample, which usually translates into a less expensive survey. To obtain a 3 percent margin of error at a 90 percent level of confidence requires a sample size of about 750. For a 95 percent level of confidence, the sample size would be about 1,000. Determining the margin of error at various levels of confidence is easy. Although the statistical calculation is relatively simple the most adv anced math involved is square root margin of error can most easily be determined using the chart below. A few web sites also calculate the sam ple size needed to obtain a specific margin of error. Thus, if the resea rcher can only tolerate a margin of error of 3 percent, the calculator w ill say what the sample size should be.
html which allows researchers to compare the s ample sizes needed with various levels of confidence similar to comparis on shopping. Calculating Margin of Error for Individual Questions Margins of error typically are calculated for surveys overall but also sh ould be calculated again when a subgroup of the sample is considered. So me surveys do not require every respondent to receive every question, an d sometimes only certain demographic groups are analyzed. If only those who say customer service is "bad" or "very bad" are asked a follow-up qu estion as to why, the margin of error for that follow-up question will i ncrease because the number of respondents is smaller than the overall su rvey sample. Similarly, if results from only female respondents are anal yzed, the margin of error will be higher, assuming females are a subgrou p of the population. Survey Data Is Imprecise Margin of error reveals the imprecision inherent in survey data. A researcher surveying custo mers every six months to understand whether customer service is improvin g may see the percentage of respondents who say it is "very good" go fro m 50 percent in one period to 47 percent in the next six-month period. B oth are accurate because they fall within the margin of error. On the other hand, if those percen tages go from 50 percent to 54 percent, the conclusion is that there is an increase in those who say service is "very good" albeit a small one. The Dark Side of Confidence Levels A 95 percent level of confidence means that 5 percent of the surveys will be off the wall with numbers that don't make much sense. Therefore, if 100 surveys are conducted using the same customer service question, five of them will provide results that are somewhat wacky. Normally research ers do not worry about this 5 percent because they are not repeating the same question over and over so the odds are that they will obtain resul ts among the 95 percent. However, if the same question is asked repeated ly such as a tracking study, then researchers should beware that unexpec ted numbers that seem way out of line may come up. For example, customer s are asked the same question about customer service every week over a p eriod of months, and "very good" is selected each time by 50 percent, th en 54 percent, 52 percent, 49 percent, 50 percent, and so on. If 20 perc ent surfaces in another period and a 48 percent follows in the next peri od, it is probably safe to assume the 20 percent is part of the "wacky" 5 percent, assuming proper methodology is followed. About the Author Pamela Hunter is director of the Center for Survey Research and Analysis at the University of Connecticut's Stamford campus. She has worked for t he Pew Research Center for the People and the Press and an international polling firm in Washington, DC Dr. Hunter has worked on projects rang ing from a presidential campaign to international studies on workplace i ssues to investigation of the market for genetic products. She has field ed surveys in many countries from India to the United Kingdom. She recei ved her PhD from the University of Connecticut specializing in survey research. As a graduate student, she worked for the Roper Center for Pub lic Opinion Analysis, the world's largest archive of public opinion data . The Roper Center is located at the University of Connecticut.
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