How Large Of A Sample Size Is Required

How To Make up one's mind Sample Size: Summate Using This Formula

By Indeed Editorial Team

September 28, 2021

When conducting a report or survey, choosing the right sample size can have a huge impact on your results. In order to ensure your results are accurate and indicative of the total population, you'll want to cull a percentage of the population that will accurately reflect the perspectives, preferences and feelings of the whole. In this article, we explicate what a sample is, explore why sample size is important, list the steps for calculating the necessary sample size and provide some valuable tips to help you throughout the procedure.

Charts and graphs

What is a sample?

Samples are a pct of a population that serves every bit a representation for the whole. Samples are imperative in statistics when conducting a survey or experiment considering, when chosen wisely, they accurately draw the overall preferences or feelings of a larger group of people.

For instance, let's say y'all desire to accept a survey to explore the brand preferences of cat owners when choosing and purchasing cat food. It would be extremely fourth dimension-consuming and expensive to survey every cat owner in the country. Instead, you lot would accept a sample that would consist of several thousand true cat owners. Additionally, if you effectively choose your sample, it will still provide a good representation of all cat owners and the brands of true cat food they prefer.

Related: 5 Basic Statistics Tools and How To Choose the Right One

Why is sample size important?

As we mentioned before, samples tin can offering information that permit statisticians to make inferences most the whole population. It is through the information gathered from a sample that surveyors can estimate things virtually a population. Determining sample size is one of the more challenging aspects of statistics and is dependent on a variety of factors, including the size of the original population.

The more robust the sample size, the more statistically significant the data that is gathered from it. In other words, a larger sample population means that there is a decreased likelihood that the data is a result of a coincidence, making it more accurate and reliable. Though statistical significance is oft a positive consequence, it's non always a necessity. Even when a sample size is unable to give an accurate representation of a general population, it tin can still provide valuable information.

An example of this is when a company takes customer feedback surveys. Regardless of whether you have obtained a statistically pregnant sample size, the perspectives and thoughts gathered from your customers volition requite you valuable feedback that you can so use to improve your business. On the other hand, political polls must exist diligent when selecting an advisable sample size in order to accurately stand for the entire population.

Related: Analytical Skills: Definitions and Examples

How to calculate sample size

Follow these steps to summate the sample size needed for your survey or experiment:

1. Determine the total population size

First, yous need to determine the total number of your target demographic. For case, if your goal is to get together data about fathers living in Florida, your population size would need to be the total number of fathers that are currently residing in Florida. Information technology's okay if you are uncertain about the exact number. Many surveyors simply approximate the total population between several educated guesses.

2. Decide on a margin of mistake

As well known every bit a confidence interval, the margin of mistake determines how much room for error you are willing to permit. In other words, how much of a difference you volition allow between your sample mean and the mean of the total population.

3. Choose a confidence level

Your confidence level indicates how bodacious you are that the actual mean will fall within your chosen margin of error. Most surveyors choose confidence levels that are 90%, 95% or 99% confident. Your specified confidence level then corresponds with a Z-score, or constant value, that is necessary for the sample size equation. Hither are the Z-scores for those 3 near mutual conviction levels:

xc% = one.645

95% = 1.96

99% = 2.576

four. Pick a standard of deviation

Next, y'all will need to determine your standard of deviation, or the level of variance you're expecting in the information gathered. If you have even so to administer the survey, choosing 0.five is typically a safety pick that will ensure a large enough sample size.

5. Complete the calculation

Finally, you can apply these values to calculate the sample size that you lot will need. You can do this past using a formula or by finding a sample size calculator online. In society to calculate the sample size yourself, y'all will need to use this equation:

Sample size formula

Related: How To Calculate a Z-score

Tips

Here are a few tips that could prove beneficial when attempting to decide and calculate the necessary sample size:

If the population is small-scale plenty, you could consider conducting a census. This, of course, volition depend on how small the population is, what kind of time you have and your available budget.
Someone has probable conducted a survey similar to yours before so it could be useful to search bookish databases to discover a similar study and utilize the same sample size. However, beware: you lot will be relying on their calculations, which could exist incorrect.
Depending on the size of your population and the type of study you're conducting, you may be able to find a tabular array that outlines the necessary sample sizes.
As we mentioned earlier, y'all could always employ an online sample size calculator instead of completing the calculations yourself. These are often free and relatively easy to use.

Related: What Is Standard Deviation? How It Works and Other FAQs