CX 101 Archives – InMoment

There’s a lot that goes into creating statistically sound research, but few elements are as important as getting the right sample size. This is because the size of your sample can have a direct impact on your findings. If your chosen sample is too small, your results will likely be inconclusive. On the other hand, overly large samples can make minor differences appear statistically significant while also increasing the time and resource demands of collecting and cleaning the data.

Unfortunately, understanding the need for correct sample sizes and understanding how to select the right sample sizes are two different issues. For effective sample size determination, many researchers rely on the sample size formula.

Here, we’ll walk you through the sample size formula and how to apply it. But first, let’s take a look at what “sample size” means.

What Is a Sample Size?

Sample size is a term used in research and statistics that defines the total number of subjects, samples, or observations included in a survey or experiment.

For example, if you were to interview 50 travelers about their air-travel experience, then your sample size would be 50. Similarly, an experiment that makes daily observations regarding soil content over the space of one full year would have a sample size of 365. And if an online survey were to return 11,328 completed questionnaire forms, then that’s a sample size of 11,328. Simply put, the sample size is the number of samples you’re interacting with.

Sampling allows researchers to select a representative portion of an entire population; to expand on one of the examples provided above, an airline that chooses the right sample group can hopefully draw meaningful and accurate conclusions from interviewing 50 travelers, instead of having to interview every traveler who flies on a plane.

As previously addressed, sample size plays a key role in any statistical setting—from lab experiments to employee surveys—and is a vital factor in any research project.

What Is the Sample Size Formula?

The sample size formula is a calculation for determining what sample size is appropriate to ensure that the test has a specified power. To do this, we must first calculate the sample size for an infinite (or unknown) population, after which we will adjust our sample size to fit the required finite (or known) population.

Sample Size Formula: Infinite Population

S = Z² x P x (1 – P)M²

Adjusted Sample Size Formula: Finite Population

Adjusted sample size = (S)1 + (S – 1)Population

In these formulas, the variables are expressed as follows:

S = The sample size for an infinite population
Z = The Z-score (determined based on the confidence level)
P = The population proportion (assumed as 50%)
M = The margin of error (typically taken as 5%)

Applying the Sample Size Formula

The formulas presented above may be used to correctly determine viable sample sizes, but before that can be put to work, the values of the various variables need to be defined.

To correctly apply the formula, follow these steps:

Determine Your Key Values
The primary key value in this equation is the total population size within your target demographic. Where possible, be as accurate as you can in determining the population number—this will allow for greater statistical impact, particularly when dealing with a small population size. That said, larger populations may allow for some approximation (such as rounding to the nearest hundred or thousand).
Determine Your Margin for Error/Confidence Interval
Although you want your study to be as precise as possible, it will never be completely accurate. Understanding how much error can be allowed in the study is essential to correctly presenting your findings. This is called the margin for error and is usually represented as a percentage detailing how close the sample results should be to the true value. Smaller margins of error produce more accurate results, but also require larger sample sizes. The margin for error is typically expressed in results as a +/- followed by the percentage.
Set Your Confidence Level
Similar to the margin of error, the confidence level describes and measures how certain the study is about the accuracy of the sample’s representation of the total population. This is expressed as a percentage, with a higher percentage indicating greater confidence; most studies try to operate within the 95%–99% confidence range—less than that could cast doubt on the validity of the results.
Specify the Standard of Deviation
The standard of deviation details how much variation you can expect from the results of your study. Will the results be very similar, or are they likely to be spread out? Extreme answers where there is a high deviation are often more accurate. It’s generally accepted that a standard deviation of 50% will help ensure a large enough sample size to correctly represent the population within the margin for error and confidence level.
Determine Your Z-Score
Finally, the Z-score is a constant value showing the number of standard deviations between the average/mean of the population and any specific value. The Z-score corresponds directly to the confidence level, with the most common confidence levels corresponding to the following Z-scores:

Conclusion

Determining your sample size is the first step in any market research project. Whether you decide to use systematic sampling, simple random sampling, or are looking to alleviate voluntary response bias, you’ll need to identify your sample size before you can take those actions—and improve experiences!

Data runs the business world these days. It’s great to always use data to back everything from major business decisions to website tweaks. But data is only as good as the survey that pumped it out. If you put bad information into your survey, your data isn’t reliable to base your business decisions off of. How do you prevent this from happening? After all, you don’t want to have bad data at the helm of your decisions.

One way researchers try to ensure their information is great is to use random sampling, specifically systematic sampling. By adding the element of randomness, results are more representative of the population you’re trying to study. Handpicking participants gives you skewed data, but random sampling can give you a real look at your population. But there are a few different ways to go about sampling randomly. One way is to use systematic sampling. Read on to learn all about systematic sampling as a way to boost your survey methods.

What Is Systematic Sampling?

Systematic sampling is a type of probability sampling that uses a specific interval to select participants. Probability sampling is when every member of the population (the entire group you want to study) has an equal chance of being selected. It’s the foundation of good data collection. But with systematic sampling you choose a regular interval and select your participants that way.

Imagine you have a list of 100 people in your population, and you want to use systematic sampling to select your sample. You decide on an interval of five. The best way to use systematic sampling is then to choose a random place to start on your list. Maybe you start at the second name listed. From there, you would choose every fifth name to be a participant. That’s systematic sampling.

The key features of systematic sampling are that it’s probability based and that there’s a specific number interval used to select your sample.

Types of Systematic Sampling

The basics of systematic sampling are the same, but there are a few ways you can perform a systematic sample. Here are three types of systematic sampling and how each one works.

Systematic Random Sampling

Systematic random sampling is the classic way to use systematic sampling. It works exactly as described earlier: a particular interval is used to randomly select participants. But how do researchers choose effective intervals? Most use their population size and figure out how many they want in a sample. For example, if you have 100 people in your population, and you know you want to survey 20 of them, you know your interval will be 5.

Circular Systematic Sampling

Circular systematic sampling is most useful if you know you want to sample your entire population, but you still want the element of randomness in your sampling methods. Circular systematic sampling works the same as classic systematic sampling at first. But instead of stopping selection after you reach the end of the population list, you start again and keep selecting using your numeric interval until you’ve sampled everyone in your population.

For example, let’s return to our list of 100 people. You choose the interval of 5 for your sampling and randomly select starting on the fourth name. You sample every fourth name until you reach the end of the list. But instead of stopping there, circular systematic sampling has you keep sampling every fourth name until you’ve gone through the whole list. It’s a great way to continue to select randomly while sampling your whole population. Circular systematic sampling isn’t a great choice if you have a very large population, and you really only need a small sample and a way to whittle the list down.

Linear Systematic Sampling

Linear systematic sampling is another variation, but it’s different from circular sampling. Linear systematic sampling doesn’t repeat and continue until the whole population is sampled. Instead, linear sampling uses a form of skip logic to select. Skip logic is something you might use to send participants in a survey to a different spot in the survey based on their answers. The researcher uses skip logic to select where to start on the survey and the interval to use. If you think of the list of 100 population members, here you would use skip logic to determine where the sampling starts and who is chosen, and it doesn’t repeat at the end.

When Is Systematic Sampling Used?

When do researchers choose to use systematic sampling? Systematic sampling provides a unique way to use random sampling without having to have a lot of details on your population or on a tight budget or timeline. These are some of the scenarios when systematic sampling is commonly used:

Budget or timing restrictions: If you have an upcoming deadline or a small budget for sampling, systematic sampling is simple to implement and quick for picking a sample under a time crunch. You can very quickly number a population list and randomly select an interval and starting point and choose participants quickly. This same process also requires few resources, and you don’t have to know much about your population to get started with systematic sampling.
Simple outcomes: Systematic sampling is a simple way to choose a sample, so it’s best when used when the outcomes are simple. A complicated survey isn’t the place for a simple systematic sample.
Absence of data patterns: Systematic sampling is used when the data aren’t arranged or have an obvious pattern or opportunity for data manipulation. That could lead to problems. But without that, systematic sampling is a great choice.

Advantages and Disadvantages of Systematic Sampling

As with most things in sampling, there are advantages and disadvantages to using systematic sampling. There are times when it’s particularly valuable to use systematic sampling, and there are weak points with the method that are important to watch for and mitigate as much as possible.

Advantages:

There are some of the major advantages of systematic sampling:

Simple to understand: Not every method of sampling randomly is easy for researchers to understand—especially not with an extensive background in statistics. Systematic sampling is easy to grasp and easy to get started with.
Easy to implement: Nothing’s worse than having extremely difficult sampling requirements to grapple with that take forever to actually get started. Systematic sampling avoids that. Instead, it’s easy to get started with quickly.
Organized method of sampling: Organization with your data is key to making analysis simple and doable down the road. Systematic sampling is exactly what it sounds like: systematic. And systematic is organized and can help you keep track of what’s going on.
Low risk for bias or contamination when done well: Data contamination and bias can leave you with bad results and bad data to base your decisions off of. Systematic sampling can be a way to combat that. So long as the population list can be ordered randomly, there’s a low risk for bias or data contamination when you use this sampling method.

Disadvantages:

There are also a few disadvantages that researchers have to plan for and make sure to avoid when using systematic sampling:

Risk of bias: While there’s a low risk of bias, there’s still a risk that has to be managed. The list of population members must be ordered randomly, or there’s sampling bias. That’s easy when you have a list of names and can order that randomly but could be complicated for other populations.
Risk of data manipulation: When you use systematic sampling, you’re setting up a system to use. There’s a risk that researchers might set up a system to intentionally give them the results they want, introducing a world of problems into their data.
Requires population size: The other risks can be controlled for, but this disadvantage is an inherent one. To effectively use systematic sampling, you have to be able to number your population. That means you have to know your population size exactly before you can sample. It might be easy when you’re sampling the employees at your company, but it might be more difficult when you have a potentially massive population that you aren’t sure what it entails.

The Bottom Line

Overall, systematic sampling is a form of probability sampling and can be incredibly valuable on a tight timeline or budget with simple populations. The key is to make sure you’re using the right sampling method for your surveys. InMoment has special CX software that’s designed to help you make the most of your surveys—from sampling methods to analysis. Schedule a demo to see how InMoment can help you optimize the results from your CX surveys.