How to use and interpret t-test results

# What is a T-test?

Explore t-tests: the statistical testing analysis that helps make data insights more reliable. Learn how to use t-tests for confident, data-driven decisions.

## T-tests definition

A t-test is a statistical analysis to establish whether the difference between two groups’ means is statistically significant.

For product teams, this means determining if the change they made to their product (such as a new feature or design) impacted user behavior or if the differences were due to random chance.

### What does a t-test calculate?

The t-test calculates the “t-statistic” or “t-value” based on the two groups' means, standard deviations, and sample sizes.

This t-value is then compared to the critical value—the point in the data where you’d reject the null hypothesis and say there is no significant difference—to decide whether the difference is significant.

### Why are t-tests important?

T-tests enable you to make data-driven decisions by quantifying the likelihood that there’s a significant difference between two groups rather than relying only on observational evidence, like metrics.

This information can guide your entire product’s lifecycle, including which features to release, new products to launch, and where to focus future development efforts.

## The role of t-tests in A/B testing

A/B testing compares two versions of something (e.g., website designs or marketing campaigns) to decide which performs better.

T-tests are crucial in A/B testing as they help you analyze the results and make statistically valid conclusions.

When you run an A/B test, you create two sample groups—one exposed to the original version (the control) and one exposed to the new or modified version (the variation). Each visitor’s behavior, such as clicks and purchases (i.e., conversions), is measured and recorded.

After the experiment, you’re left with two data sets representing each version’s performance.

Performing a t-test can help you determine if the observed differences are one of two things:

• Statistically significant, meaning the variation impacted user behavior and wasn’t just due to chance. Statistical significance validates that changing to the new version will likely improve results. Calculate statistical significance with our easy-to-use calculator.
• Not statistically significant, meaning normal fluctuations could have caused the difference. In this case, you don’t have enough evidence to say the variation is better than the original.

Without t-tests, you’d have no way to reliably assess whether one version outperformed the other or if the results occurred randomly.

## When to use a t-test?

In general, use a t-test when you:

• have one or two samples.
• want to compare the means of the samples.
• can assume data normality (it clusters in the middle and tapers off towards either extreme) or have sufficiently large sample sizes.

However, though they’re beneficial, t-tests aren’t the best fit for every scenario. Do not use a t-test when:

• you have more than two groups to compare.
• your data is not normally distributed (i.e., it doesn’t look like a bell or hill shape).
• you want to analyze relationships, not compare means.
• you’re interested in proportions, not means.
• you have a complex study design.

If a t-test isn’t ideal for your needs, explore and use a more appropriate statistical test instead. That might mean using an ANOVA to compare three or more groups, Mann-Whitney U for non-normal data, correlation, or chi-square and z-test for proportions.

## Types of t-tests

There are three main types of t-tests, each suited to different data scenarios and research questions.

### One-sample t-test

The one-sample t-test compares the mean of a single sample to a hypothesized population mean, testing if the sample could have come from that population.

Some common uses include:

• testing if a production batch meets a specified quality standard.
• checking if customer satisfaction ratings differ from an expected level.
• determining if sales figures match a projected target.

Running a one-sample t-test involves taking a sample and calculating its mean. Next, you state the hypothesized population mean to compare against. The one-sample t-test will determine if the difference between the two means is statistically significant.

### Two-sample t-test (independent samples)

This t-test analyzes the difference between the means of two independent sample groups. The groups are assumed to have no paired observations.

Example use cases include:

• Comparing conversion rates between two different landing pages.
• Testing if there’s a difference in ratings between two products.
• Analyzing if two groups of customers have different mean preferences (i.e., males and females).

To conduct a two-sample t-test, randomly divide the subjects into two independent groups, collect sample data, and calculate the average (mean) for each group. You’ll then run a two-sample t-test to compare the means of the two groups and determine if the difference is statistically significant.

### Paired/dependent t-test

Sometimes, your sample contains paired observations, meaning each observation in one sample corresponds to a data point in the other sample. In this case, you can use a paired/dependent t-test, which accounts for the non-independent nature of the samples.

Common applications include:

• Before-and-after tests, such as testing an educational program.
• Matched pairs study design, including for twins, spouses, and cases matched by age or gender.
• Testing if there is a change within the same subjects exposed to different conditions.

Collect the paired data with “before” and “after” observations and calculate the difference between the observations in each pair. The paired t-test then analyzes whether the mean of the difference is statistically significant.

## Which t-test to use?

Deciding which t-test to use depends on your study and data type. Think about what you’re measuring and map them to the characteristics of the t-test.

Generally, you use a one-sample t-test when checking against a target, a two-sample for separate unpaired groups, and a paired test for before and after measurements on the same subjects.

Here’s what that might look like in a real-world setting.

One-sample t-test:

• Testing if your website's average page load time meets the target of under two seconds.
• Checking if user ratings for a new app feature differ from the expected 4-star level.
• Determining if free trial signups match the projected number of 5,000 per month.

Two-sample independent t-test:

• Comparing conversion rates between your existing checkout flow and a redesigned version.
• Analyzing the difference in engagement times between mobile and desktop users.
• Testing if users from two acquisition channels, such as Facebook vs Google ads, have different retention rates.

Paired/dependent t-test:

• Evaluating if individual users experience faster task completion times before and after a UI update.
• Determining if the same set of users consumes more or less data before and after a new data compression feature.
• Seeing if there’s a change in individual customer satisfaction scores before and after a pricing range.

In A/B testing, a two-sample t-test is ideal because it requires two independent, randomly assigned groups.

## How to use a t-test

Running a t-test is a straightforward process with a few essential steps. Though you can do these manually, most analysts use statistical software to run t-tests with a few inputs and lines of code.

Whatever route you choose, understanding the key stages is crucial.

### State your hypotheses

Establish a null and alternative hypothesis about the differences you want to test.

The null hypothesis proposes there is no statistically significant difference between the means. The alternative is the opposite—that there is a considerable difference.

### Pick a test type

Based on your study's design and data type, decide if you need a one-sample, two-sample, or paired t-test.

### Check the test assumptions

Most t-tests assume your data is approximately normally distributed (a bell shape), especially for small sample sizes. You may want to test this assumption. Some types of tests also require variances to be equal between groups.

### Calculate the test statistic

This core stage involves calculating a t-value or t-statistic based on factors like the mean differences, standard deviations, and sample sizes using the appropriate t-test formula.

### Find the p-value

Compare the calculated t-value against a critical value from the t-distribution to get a p-value. Your p-value is the probability of an extreme result if the null hypothesis is true. A lower value makes it harder to trust the null hypothesis.

### Make your conclusion

Now, it’s time for the final judgment. If your p-value is below your predetermined significance level (e.g., 0.05), reject your null hypothesis because there’s sufficient evidence that your noted differences are statistically significant.

However, if your p-value exceeds the significance level, fail to reject the null because the opposite is true—the difference is not statistically significant based on your sample evidence.

## Interpreting and applying the results

After running a t-test, it’s vital to correctly interpret your results and translate them into actionable insights for optimizing your product.

For example, if you ran an A/B test between two landing page designs and found a p-value of 0.02, you can conclude that the difference in conversion rates is genuine and not due to chance.

### Consider the effect size

Statistical significance alone doesn’t tell the whole story. The effect size, indicating the magnitude of the difference, is also important.

Common effect size measures like Cohen’s d can be used to determine whether the difference between the groups is small, medium, or large in practical terms.

A tiny p-value but a small effect may not justify a major product change, especially if implementation is costly or disruptive.

### Make optimization decisions

For A/B tests and experiments, a statistically significant difference with a meaningful effect size is a green light to permanently implement the winning product variation.

If you’re testing user flows, UI changes, pricing plans, etc., you can use the superior-performing version to optimize the user experience and other metrics.

Failed tests pinpoint areas that don’t require changes, enabling you to prioritize other optimizations.

### Practice ongoing testing and monitoring

Don’t treat a single t-test result as your only source of truth. Instead, continue validating by repeating the test and carrying out other tests over time.

When you make changes based on tests, closely monitor key metrics to ensure continuous improvement and quickly find and fix unintended consequences.

Testing is an iterative process of forming hypotheses, running tests, applying insights, and generating new test ideas. The best practice is to engrain it in your product development process and make it something your team does regularly.

## T-test best practices

Using a t-test is relatively simple. However, there are a few things to keep in mind to ensure valid and reliable results, including:

• verifying your data meets the required assumptions
• setting an appropriate significance level, such as 0.05 or 0.01
• using large enough sample sizes
• ensuring groups are randomly sampled or assigned
• considering using data transformations if the data is heavily skewed or has outliers
• reporting confidence intervals
• validating with other tests
• examining and reporting effect sizes
• using analysis tools properly
• combining t-tests with qualitative insights, past research, and business knowledge

Following these best practices will help increase the real-world usefulness of your t-test results. The goal is to run tests that enable you to make product changes that positively affect your users and overall bottom line.

## Run reliable t-tests with Amplitude

Amplitude Experiment provides tools to rigorously analyze your experiment data—including t-test capabilities. Establish if the results you saw during product tests are statistically significant and use the insights to help guide your development.

Easily run t-tests, including one-sample, two-sample, and paired. Simply select the required inputs, like your metrics, user segments, time ranges, and any grouping you want to test. Amplitude will then automatically calculate the relevant t-statistics, degrees of freedom, and p-value.

Beyond the statistical output, Amplitude enables you to visualize significance levels on charts, making it easy to see which differences between variations are meaningful.

Combining statistical testing and product data in one platform helps streamline experiments. Conduct and analyze your A/B tests, feature launches, and other experiments to make better, data-driven product decisions.

Implement changes with confidence. Get started with Amplitude today.