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What is a T-Test?

A t-test is a statistical test used to compare the means of two groups and determine if they are significantly different from each other. Developed by William Sealy Gosset in 1908 under the pseudonym "Student," the t-test is one of the most commonly used statistical tests in social science, psychology, medicine, and education research. It answers a simple question: is the difference between two group means likely due to a real effect, or just random chance?

Independent Samples T-Test

Use an independent samples t-test when comparing means from two different, unrelated groups. For example, comparing test scores between a treatment group and a control group, or comparing salary between male and female employees. This calculator uses Welch's t-test by default, which does not assume equal variances and is recommended by the American Psychological Association as the default approach.

Paired Samples T-Test

Use a paired samples t-test when comparing means from the same group at two different times (pre-test vs post-test) or when participants are matched on key variables. The paired t-test accounts for the correlation between measurements, making it more powerful than an independent samples test when the design allows it. Common examples include before/after intervention studies and within-subjects experimental designs.

When to Use a T-Test vs. Other Tests

Assumptions of the T-Test

Before interpreting your results, verify these assumptions are met:

Understanding Cohen's d Effect Size

While p-values tell you whether a difference is statistically significant, Cohen's d tells you how large the difference is in practical terms. This is critical because with large sample sizes, even tiny, meaningless differences can be "significant."

How to Report T-Test Results in APA Format

According to APA 7th edition guidelines, t-test results should include the t-statistic, degrees of freedom, p-value, effect size, and confidence interval. Here are templates you can use:

Note: Report t-values and degrees of freedom to two decimal places. Report p-values to three decimal places, except usep < .001 when the value is below .001. Always include an effect size measure.

Common Mistakes to Avoid

• Reporting p = .000: Statistical software sometimes displays p = .000, but you should report this as p < .001. A p-value is never exactly zero.
• Ignoring effect size: A statistically significant result with d = 0.1 may not be practically meaningful. Always report and interpret the effect size.
• Using a t-test for 3+ groups: If you have three or more groups, use ANOVA instead. Running multiple t-tests inflates your Type I error rate.
• Assuming equal variances: Unless you have strong reason to assume equal variances, use Welch's t-test (the default in StatMate).
• Confusing statistical significance with practical importance: A p < .05 result does not automatically mean the finding is important or clinically relevant.