An example of a limitation is using an opt-in online poll, such as one promoted on a website.

For most purposes, the non-working population cannot be assumed to accurately represent the entire (working and non-working) population. An example of such a flaw is to only call people during the day and miss almost everyone who works. Non-random samples usually result from some flaw or limitation in the sampling procedure. If your sample is not truly random, you cannot rely on the intervals. The confidence interval calculations assume you have a genuine random sample of the relevant population. Population size is only likely to be a factor when you work with a relatively small and known group of people ( e.g., the members of an association). For this reason, The Survey System ignores the population size when it is 'large' or unknown. This means that a sample of 500 people is equally useful in examining the opinions of a state of 15,000,000 as it would a city of 100,000. The mathematics of probability prove that the size of the population is irrelevant unless the size of the sample exceeds a few percent of the total population you are examining. Often you may not know the exact population size. How many people are there in the group your sample represents? This may be the number of people in a city you are studying, the number of people who buy new cars, etc. To determine the confidence interval for a specific answer your sample has given, you can use the percentage picking that answer and get a smaller interval. You should also use this percentage if you want to determine a general level of accuracy for a sample you already have. When determining the sample size needed for a given level of accuracy you must use the worst case percentage (50%). It is easier to be sure of extreme answers than of middle-of-the-road ones. However, if the percentages are 51% and 49% the chances of error are much greater. If 99% of your sample said 'Yes' and 1% said 'No,' the chances of error are remote, irrespective of sample size. Your accuracy also depends on the percentage of your sample that picks a particular answer. However, the relationship is not linear ( i.e., doubling the sample size does not halve the confidence interval). This indicates that for a given confidence level, the larger your sample size, the smaller your confidence interval. The larger your sample size, the more sure you can be that their answers truly reflect the population. There are three factors that determine the size of the confidence interval for a given confidence level: The wider the confidence interval you are willing to accept, the more certain you can be that the whole population answers would be within that range.įor example, if you asked a sample of 1000 people in a city which brand of cola they preferred, and 60% said Brand A, you can be very certain that between 40 and 80% of all the people in the city actually do prefer that brand, but you cannot be so sure that between 59 and 61% of the people in the city prefer the brand. When you put the confidence level and the confidence interval together, you can say that you are 95% sure that the true percentage of the population is between 43% and 51%.

Most researchers use the 95% confidence level. The 95% confidence level means you can be 95% certain the 99% confidence level means you can be 99% certain. It is expressed as a percentage and represents how often the true percentage of the population who would pick an answer lies within the confidence interval. The confidence level tells you how sure you can be. For example, if you use a confidence interval of 4 and 47% percent of your sample picks an answer you can be 'sure' that if you had asked the question of the entire relevant population between 43% (47-4) and 51% (47+4) would have picked that answer. The confidence interval (also called margin of error) is the plus-or-minus figure usually reported in newspaper or television opinion poll results. Sample Size Calculator Terms: Confidence Interval & Confidence Level

Calculating sample size xlstat