Sample size terms : confidence interval & confidence level

Before determining how many people you need to interview in order to get results that reflect the target population as precisely as needed, there are two terms that you need to know.  These are: confidence interval and confidence level.

The confidence interval (also called margin of error) is the plus-or-minus figure usually reported in newspaper or television opinion poll results. For example, if you use a confidence interval of 3 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 44% (47-3) and 50% (47+3) would have picked that answer.

 

Market Research Hub - Sample Sizes

The table above indicates the margin of error you can expect according to the sample size you select.

The ideal sample size is 1000.

The confidence level tells you how sure you can be. 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 95% confidence level means you can be 95% certain; the 99% confidence level means you can be 99% certain. Most researchers use the 95% confidence level.

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 44% and 50%. 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.

Factors that affect confidence intervals

There are three factors that determine the size of the confidence interval for a given confidence level:

Sample size

Percentage

Population size

Sample Size

The larger your sample size, the more sure you can be that their answers truly reflect the population. This indicates that for a given confidence level, the larger your sample size, the smaller your 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 picks a particular answer. If 99% of your sample said "Yes" and 1% said "No," the chances of error are remote, irrespective of sample size. However, if the percentages are 51% and 49% the chances of error are much greater. It is easier to be sure of extreme answers than of middle-of-the-road ones.

When determining the sample size needed for a given level of accuracy we use the worst case percentage (50%).

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. Often you may not know the exact population size. This is not a problem. 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. 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. For this reason, Market Research Hub ignores the population size when it is "large" or unknown. 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).

The confidence interval calculations assume you have a genuine random sample of the relevant population. If your sample is not truly random, you cannot rely on the intervals. Non-random samples usually result from some flaw or limitation in the sampling procedure. An example of such a flaw is to only call people during the day and miss almost everyone who works. For most purposes, the non-working population cannot be assumed to accurately represent the entire (working and non-working) population.

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