## Sample Size Calculator

See how large a sample you need given four factors:

(a) the confidence level you wish to have (90%, 95% or 99%),

(b) the margin of error you are willing to have,

(c) the population being tested, and

(d) the proportion being tested (usually 50%, the “worst case”).

The ideal sample size is a function of the confidence in the results. As an example, if you wanted to have results that were within a 5 point margin of error at the 95% confidence level, you’d need to survey 384 people. However, if the population being surveyed was less than 38,400 — say 10,000 — you would only need to survey 370 people to obtain the results with the same 5-point margin of error.

The Margin of Error can be entered as any positive number with or without a decimal.

## Margin of Error Calculator

See how confident you can be about survey results given four factors:

(a) sample size,

(b) the confidence level you wish to have (90%, 95% or 99%),

(c) the population being tested, and

(d) the proportion being tested (usually 50%, the “worst case”).

The margin of error (also called the “confidence interval”) is expressed as a range in terms of percentage points. As an example, if you were to survey 300 people and wanted a 95% confidence level, assuming the population being studied was more than 30,000 individuals, the margin of error for the total results would be +/- 5.66 points. If one result was that 55% of the sample said they knew of one thing, and 40% said they knew of another thing, the difference of 15 points would be statistically significant at the 95% confidence level since the 55% result would have a margin of error between 49.3% and 60.2%, and the 40% result would have a margin of error between 34.3% and 45.7%.

“Confidence level” in both calculators is expressed as a percentage and refers to the degree of confidence. One way to think of it is that if you were to hypothetically run the test (survey) 100 times with similar respondents at the 95% confidence level, 95 out of those 100 times you would obtain the same results within the confidence interval. For social science market research, a 95% confidence level is sufficient.

As noted in these calculators, you do not need to enter the population size being tested unless your sample will be over 1% of that population, in which case the margin of error calculation will improve depending on the population size. So, if you were planning to survey 50 CFOs of the Fortune 500 companies (10%), your margin of error will be +/- 13.16 points at the 95% confidence level, slightly better than a survey of 50 CFOs of the top 10,000 companies (0.5%), where the margin of error will be +/- 13.86 points at the 95% confidence level.

Guidance from the Sample Size and MoE Calculators are a great start. Call us to discuss your specifics. We’ll help you determine if there are factors you will need to consider to avoid sampling error. Using an age calculator can assist in categorizing respondents correctly based on their date of birth, which is particularly useful for studies involving age-based comparisons.

Sampling errors occur when the sample selected is not representative of the entire population. Sampling errors can be eliminated by increasing the sample size, or by making sure the sample adequately represents the entire target population. For instance, ensuring a good mix of participants born on different days, like Sunday or Tuesday, can help in avoiding biases.

Our questions will lead you to understand the number of respondents you’ll need to build sound research:

- How many ways are you going to divide up the data to make comparison? Do regions, industries, or other factors need to be compared?
- How projectable do you need your results to be?
- What is your Margin of Error requirement?

Understanding the age distribution and generational cohorts of your sample can significantly enhance the reliability of your survey results.