Confidence Size
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How to calculate the sample size to use in a market research carried out via an online survey
In this article, we discuss how to calculate the minimum size of a sample that will be used to calculate a proportion within a given population. Important decisions are often made based on the proportions obtained through an internet survey. For example, if the proportion of participants who have an interest for a new product or service is high enough, investments will be made to bring it to market.
A proportion is the number of individuals within a population that share a certain characteristic from a set of possible characteristics. Proportions are generally calculated as percentages. For example, the proportion of individuals who are willing to pay for a new product or service.
It is often impossible to calculate the exact proportion of individuals that form a population. The population as whole might contain thousands, even hundreds of thousands of individuals. In such a case, we need to calculate the proportion within a sample of the population. The proportion within the sample be an adequate substitute for the proportion within the whole population.
The size of the sample used to study a proportion within a population is a critical factor to obtain reliable results about the proportion in the whole population. The reliability of the data is never absolute, but is located within an interval of confidence. The smaller the interval must be, or the lower the error rate must be, the larger the sample size must be in order to get an accurate reflection of the proportion within the population as a whole.
The following formula is used to calculate the size of the required sample
n = (z)2 p ( 1 – p ) / d2
or when p = 1/2 (0.5)
n = (z)2 / 4d2
n = sample size
z = level of confidence according to the standard normal distribution (for a level of confidence of 95%, z = 1.96, for a level of confidence of 99%, z = 2.575)
p = estimated proportion of the population that presents the characteristic (when unknown we use p = 0.5)
d = tolerated margin of error (for example we want to know the real proportion within 5%)
Examples
1) To calculate a proportion with a 95% level of confidence and a margin of error of 5% we obtain
n = (1.96)2 / 4(0.05)2 = 384.16
2) To calculate a proportion with a 95% level of confidence and a margin of error of 7% we obtain
n = (1.96)2 / 4(0.07)2 = 196
3) To calculate a proportion with a 99% level of confidence and a margin of error of 2% we obtain
n = (2.575)2 / 4(0.02)2 = 3218.75
Conclusion
In order to conduct a reliable market research analysis using an online survey, it is preferable to conduct the internet survey with at least 400 participants. If your budget is more limited, the survey can be conducted with 200 participants, but the results will be less accurate. You can use the Interceptum market research platform to create and deploy online surveys. Interceptum offers advanced analysis capabilities.
About the Author
Thomas Legault is the president of Acquiro Systems, Inc. a graphics design, web site development, and custom software development company.
How to calculate sample size in statistical analysis for confidence level of 95%?
If you are measuring something, then,
n = [Zα/2(σ/E)]² where Zα/2 = 1.96, from the standard normal table for α/2 = 0.025. σ is an estimate of your population standard deviation. E is your allowed margin of error as a decimal fraction.
If you are counting something (for example --defectives), then,
n = [Zα/2/E]²p(1-p) where p is an estimate of the fraction non-conforming to some specification (defectives). If you cannot estimate this value, then use worse case, p = 0.50.
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