Confidence Intervals and Levels

The confidence interval is the plus-or-minus figure commonly reported in newspaper, television, and web opinion poll results. For instance, if you use a confidence interval of 4 and 47% of your sample selects an answer, you can be confident that, had you asked the question of the entire relevant population, between 43% (47-4) and 51% (47+4) would have chosen that answer.

The confidence level indicates how sure you can be. It is expressed as a percentage and represents how often the true percentage of the population who would select an answer falls within the confidence interval. A 95% confidence level means you can be 95% certain; a 99% confidence level means you can be 99% certain. Most researchers aim for a 95% confidence level.

When combining the confidence level and the confidence interval, you can say that you are 95% confident that the true percentage of the population falls between 43% and 51%.

Factors that Affect Confidence Intervals

The confidence interval is influenced by the margin of error. Three factors determine the size of the confidence interval for a given confidence level: sample size, percentage of the sample choosing a particular answer, and population size.

Sample Size

The larger your sample, the more confident you can be that their answers truly reflect the population's views. This means that for a given confidence level, a larger sample size results in a smaller confidence interval. However, the relationship is not linear (i.e., doubling the sample size does not halve the confidence interval).

Percentage

Your accuracy also depends on the percentage of your sample that chooses a particular answer. If 99% of your sample says "Yes" and 1% says "No," the chance of error is minimal, regardless of sample size. Conversely, if the percentages are 51% and 49%, the chance of error is much higher. It is easier to be confident of extreme answers than of those that are near the midpoint.

When determining the required sample size for a certain level of accuracy, you should use the worst-case percentage (50%). This percentage should also be used if you want to determine a general level of accuracy for an existing sample. To calculate the confidence interval for a specific answer your sample provided, you can use the percentage selecting that answer to obtain a narrower interval.

Population Size

The size of the population your sample represents may vary, such as the number of people in a city you are studying or the number of people who buy new cars. Often, the exact population size may not be known, which is not a problem. Probability mathematics shows that the population size is irrelevant, unless the sample size exceeds a few percent of the total population under examination. Thus, a sample of 500 people is equally valid for examining the opinions of a state of 15,000,000 as it would be for a city of 100,000. Therefore, the sample calculator disregards the population size when it is "large" or unknown. Population size becomes a factor only when working with a relatively small and known group of people.

Note: The accuracy of confidence interval calculations relies on having a genuine random sample of the relevant population. If your sample is not truly random, the intervals cannot be relied upon. Non-random samples often result from flaws in the sampling procedure. An example of such a flaw is calling people on landlines only during the day, potentially missing almost everyone who works and cell phone users. 

Most information on this page was obtained from The Survey System

Del Siegle, Ph.D.
Neag School of Education – University of Connecticut
del.siegle@uconn.edu
www.delsiegle.com

updated on 3/07/2024