In the fast-paced world of online experimentation, understanding statistical testing is more important than ever.

Whether you're tweaking a website design or launching a new feature, making sense of the data can be a game-changer.

But statistical jargon can feel overwhelming. What's the difference between a t-test and a z-test? Why does it matter? Don't worry—we're here to break it down in a way that's easy to grasp.

Related reading: T-test fundamentals: Building blocks of experiment analysis.

The importance of statistical testing in online experiments

Statistical tests provide an objective method to evaluate changes in based on data. They help us distinguish real effects from random variations in user behavior. By defining null and alternative hypotheses, we set clear expectations for analyzing experimental results.

Hypothesis testing is at the heart of this process. It involves two hypotheses: the null hypothesis (H0), which assumes no effect or difference, and the alternative hypothesis (H1), which suggests there's something new happening. For example, if we're testing a new teaching method, H0 states there's no improvement, while H1 claims there's an enhancement.

In digital product A/B testing, choosing between a z-test and a t-test can get tricky. While z-tests are used when the population mean and variance are known, —especially when dealing with smaller sample sizes or unknown variances. Even if we think we know the population variance, t-tests can account for changes in user demographics over time.

is also crucial to ensure our experimental outcomes are accurate. Interaction effects are like a form of hypothesis testing where the null hypothesis assumes no interaction between experiments. A low p-value tells us there's an interaction, so we need careful statistical analysis—like using the Chi-squared test—to catch these.

Understanding t-tests: application and assumptions

T-tests are the go-to choice when sample sizes are small or population variance is unknown. They're essential for drawing conclusions from experiments with limited data. T-tests assume that data follows a normal distribution, observations are independent, and variances between groups are equal.

Different types of t-tests fit various experimental designs:

• One-sample t-test: compares a sample mean to a known value.

• Two-sample t-test: compares means of two independent groups.

• Paired t-test: compares means within the same group at different times.

In , t-tests are often preferred over z-tests—even when we think we know the population variance. The dynamic nature of user behavior and potential shifts in demographics make t-tests a safer choice. They absorb variability and account for assumptions that might not hold over time.

In practice, many practitioners favor t-tests no matter the sample size. Even though traditional teachings suggest using z-tests for larger samples (n > 30), the simplicity and robustness of t-tests make them a popular pick.

Understanding z-tests: application and assumptions

Z-tests are handy for large samples (n ≥ 30) when the population variance is known. They assume a normal distribution and rely on the Central Limit Theorem to justify the sample size.

There are three main types of z-tests:

• One-sample z-test: compares a sample mean to a population mean.

• Two-sample z-test: compares the means of two samples.

• Proportion z-test: compares sample proportions to a population proportion.

These tests can be applied to various metrics in online experimentation, like conversion rates. But here's the catch—the assumptions about population variance and the ever-changing nature of user behavior can make , even when variance seems known.

When running online experiments, it's essential to consider how data collection might vary. While z-tests are suitable for binary experiments like conversion rates, underlying assumptions about the population may not hold up with changes in user demographics.

Choosing between t-test and z-test for online experiments

So how do we choose between a t-test and a z-test? It boils down to their assumptions and applications. T-tests are great for small samples or when the population variance is unknown. Z-tests are used for large samples with known variance. But in the fast-moving world of digital products, user behavior and variance can be unpredictable.

Even if we're tracking variance, it's safer to use a t-test to account for potential changes in our user base or environment—as . The t-test absorbs this variability, making it a reliable choice for online experiments.

Picking the right test is crucial for getting valid results. As a general rule, . Aligning your test choice with your data's characteristics ensures your experimental findings are accurate and reliable.

At Statsig, we understand how critical accurate statistical testing is for your online experiments. That's why we provide the tools and insights to help you make the right decisions.

Closing thoughts

Understanding the nuances between t-tests and z-tests can make or break the insights you gain from online experiments. By choosing the right test, you ensure that your conclusions are valid and actionable. If you're keen to dive deeper, check out the resources linked throughout this blog.

At Statsig, we're here to help you navigate these statistical waters. Hope you found this useful!