# Calculating the Right Survey Sample Size

Calculating the right sample size is crucial to gaining accurate information! In fact, your survey’s confidence level and margin of error almost solely depends on the number of responses you received. That’s why FluidSurveys designed its very own Survey Sample Size Calculator. But before you check it out, I wanted to give you a quick look at how your sample size can affect your results.

### Explaining Confidence Levels and Margin of Errors

The first thing to understand is the difference between confidence levels and margins of error. Simply put, a confidence level describes how sure you can be that your results are accurate, whereas the margin of error shows the range the survey results would fall between if our confidence level held true. A standard survey will usually have a confidence level of 95% and margin of error of 5%.

Here is an example of a confidence level and margin of error at work. Let’s say we own a magazine with 1000 subscribers and we want to measure their satisfaction. After plugging in our information in the Survey Sample Size Calculator, we know that a sample size of 278 people gives us a confidence level of 95% with a margin of error of 5%. Our 95% confidence level states that 19 out of 20 times we conduct this survey our results would land within our margin of error. Our 5% margin of error says that if we surveyed all 1000 subscribers, the results could differ with a score of minus 5% or plus 5% from its original score.

For the purpose of this example, let’s say we asked our respondents to rate their satisfaction with our magazine on a scale from 0-10 and it resulted in a final average score of 8.6. With our allotted margin of error and confidence level we can be 95% certain that if we surveyed all 1000 subscribers that our average score would be between 8.1-9.1.

### What Happens When Your Sample Size is too Low?

Now that we know how both margins of error and confidence levels affect the accuracy of results, let’s take a look at what happens when the sample size changes. The lower your sample size, the higher your margin of error and lower your confidence level. This means that your data is becoming less reliable.

If we continue with our example and decide to lower our number of responses to 158, we’ll see a significant drop in our confidence level. Now our level of confidence has lowered to 90%, with a margin of error of 6%. So with the same satisfaction score of 8.6, we’d now only have a 9 in 10 chance of our results falling between a score of 8.0-9.2 if we surveyed all 1000 subscribers.

### What if Your Sample Size is too High?

Theoretically speaking a sample size can never be too high. Unfortunately, it is sometimes much more expensive to incentivize or convince your target audience to take part. This could be expensive, and from a statistical perspective, ultimately frivolous. In some surveys, a high confidence level and low margin of error are easier to achieve based on the availability and size of your target audience. But most surveys, especially those involving the general public, a high number of responses can be difficult to achieve.

For these reasons, there exists the standard confidence level of 95% with a margin of error of either 5% or 2.5%. In the end, attempting to go beyond this level of accuracy could be unrealistic and ultimately a less beneficial priority than focusing on making sure your respondents are valid for your survey and are giving truthful responses.

### How does the Calculator Work?

So you’re probably wondering how to figure out how the Calculator determines what your sample size should be. Well, all you need is your desired confidence level and margin of error, as well as the number of people that make up your total population size. After plugging these three numbers into the Survey Sample Size Calculator, it conducts two survey sample size formulas for you and comes up with the appropriate number of responses. But just so you know the math behind it, here are the formulas used to calculate sample size:

Sample Size = (Distribution of 50%) / ((Margin of Error% / Confidence Level Score)Squared)

• Finite Population Correction:

True Sample = (Sample Size X Population) / (Sample Size + Population – 1)

• Two things that may need explanation are the confidence level score and the distribution. The confidence level score is the standard deviation value that goes along with your confidence level. In the case of a confidence level of 95%, the confidence level score would equal 1.96. Distribution, on the other hand, reflects how skewed the respondents are on a topic. In the survey world it is almost always safest to stick with a 50% distribution, which is the most conservative.

Now that we cleared that out of the way, I know you’re as excited as I am to do this formula by hand for our example above. So let’s do it! To crosscheck my work, plug in our magazine company’s three values into our survey sample size calculator. Remember, we have a population of 1000, and a desired confidence level of 95% and margin of error of 5%:

Sample Size = 0.25 / ((0.02551…)Squared)

Sample Size = 0.25 / 0.00065077…

Sample Size = 384.16…

• True Sample = 384.16 x 1000 / 384.16… + 1000 – 1

True Sample = 384160.3024… /1383.1603

When we round our True Sample Size up to the nearest whole person, we get our value of 278 people. Therefore, in order to have a 95% confidence level with a 5% margin of error in our results, we would need to survey at least 278 of our 1000 subscribers.

### Check Out Our Survey Sample Size Calculator Right Now!

Like we mentioned earlier, you don’t need to go through this whole formula yourself. Simply click here or go through the FluidSurveys website’s resources to enter our Survey Sample Size Calculator. You’ll be able to determine your desired sample size in a matter of seconds!

Ready to get started, but don’t have a FluidSurveys account? Go ahead and set up your own account by visiting our pricing page!