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What Is the Difference Between a T-Test and a Z-Test?

By September 29, 2021October 6th, 2021No Comments

Statistics are vital for understanding consumer insights and learning about informational data that could help steer future business decisions. Using statistical tests and their subsequent data can bring awareness to organizational ideas and possibly be used to shape the foundation and structural processes of a business.

That’s the overall vision of using statistical tests, but when you break it down to the bare bones of, say, comparing a t-test vs. z-test in your research, which do you use? Receiving raw numbers without any knowledge of how to use the data isn’t helpful. Therefore, using the right statistical test is vital.

If a data scientist is using a t-test or z-test in their research, that means the person is taking part in hypothesis testing. If you’re looking to better understand the kind of hypothesis testing you are taking part in by asking yourself how to perform a test that searches for statistical significance and even what type of test you should be using — for instance, inquiring about the difference between a t-test and a z-test — you’ve come to the right place in KnowledgeHound.

What Is a T-Test?

So, what is a t-test? Like a z-test, a t-test falls underneath the umbrella of comparison, or parametric, tests. But if you’re asking, specifically, what a t-test is, at the crux of it, a t-test compares the means — or averages — of exactly two groups.

If you’re not a researcher, you’ve probably taken part in a t-test and not even known it. For instance, imagine a scenario of being at the grocery store and you’re standing in front of the cheese section. You’re deciding what to get and looking at a group of mozzarella cheeses that are all different prices and a group of cheddar cheeses that are all different prices. If you’ve ever taken the averages of the mozz and the averages of the cheddar to decide which cheese to buy, you’ve, in a very simplistic way, performed a t-test. And if you have conducted research on hypothesis testing, you more than likely have used a t-test in your statistical research gathering and data analysis.

Regardless of the type of t-test used in research — one-sample, two-sample (also known as independent), or paired; one-tailed or two-tailed — a t-test will always look at the averages of two groups.

By conducting a t-test, the researcher assumes that the data is independent, (nearly) normally distributed, and the predictor variable is categorical while the outcome variable is quantitative. It’s important to remember that with a t-test, the sample size (also known as the population range) is small as it’s equal to or less than 30.

It’s also vital to keep in mind that if a researcher wants the validity of the t-test to be passed, then they must ensure that, even if it’s small, the sample size needs to be large enough to reflect the true distribution of the population being studied.

What Is a Z-Test?

A z-test, like a t-test, is a form of hypothesis testing. Where a t-test looks at two sets of data that are different from each other — with no standard deviation or variance — a z-test views the averages of data sets that are different from each other but have the standard deviation or variance given.

In its simplest form, a z-test will test the mean or average of a distribution. A data analyst or researcher will know right away if they’re working with data that has a normal distribution if there happens to be a bell curve shape when the data is inputted and placed in a graph.

A researcher performing a z-test will keep in mind that the test is being done while taking a null hypothesis. This means that the researcher performing the z-test takes the stance that there is no statistical significance or relationship between variables.

One more note to point out for what is a z-test is that in terms of delineated sample size, unlike a t-test which is used for small population testing, a z-test is used for large, defined populations of 30 or more subjects.

Comparing a T-Test vs. Z-Test

Now that you understand what a t-test is and what a z-test is, you can probably assume what our next question is: what is the difference between a t-test and a z-test?

For all intents and purposes, when looking at a t-test vs. z-test, they are very comparable. Because the differences between a z-test and t-test are so similar, it’s critical to import, organize, and tag research data into easily digestible and distinguishable insights. All of which is possible and easy with a survey data analysis experience like KnowledgeHound. By doing this, and whether it’s a t-test or z-test, both researchers and non-researchers can transform and analyze survey data.

Therefore, an important aspect in the differences between a t-test and a z-test is remembering the sample size for each type of test. As mentioned, a t-test is primarily used for research with limited sample sizes whereas a z-test is deployed for hypothesis testing that requires researchers to look at a population size that’s larger than 30.

When it comes to t-test vs. z-test, a researcher or non-researcher will have to look at a few specifics in what they want out of the data and its subsequent analysis. The following table should help out in your comparison between the two types of tests and how a t-test and z-test are differentiated from each other.

Whether you use a t-test, z-test, or a different statistical method to interpret data, KnowledgeHound makes raw survey data accessible to brands and their stakeholders. Take control of your survey data with KnowledgeHound’s intuitive analysis experience and take a step towards better data analysis and visualization.