T-Test Calculator: One, Two, & Paired Samples

Perform statistical t-tests to compare means. Our tool handles one-sample, two independent samples, and paired data tests, giving you p-values and confidence intervals to support your conclusions.

T-Test Calculator

Perform one-sample, independent, or paired t-tests

Test Type

Variance Assumption

Confidence Level

Group 1 Data

Group 2 Data

About T-Tests

One-sample: Compares a sample mean to a known value.

Independent: Compares means from two independent groups. Use Welch's t-test when variances are unequal.

Paired: Compares means from the same subjects at two time points or under two conditions.

How the T-Test Calculator Works

Select your test type: one-sample (compare mean to a known value), two-sample independent (compare means from two groups), or paired (compare before/after measurements on same subjects). Enter your data or summary statistics accordingly.

For one-sample tests, enter your data values and the hypothesized mean. For two-sample tests, enter data for both groups or their summary statistics (mean, SD, n). For paired tests, enter the paired differences or both sets of measurements.

The calculator computes the t-statistic, degrees of freedom, and p-value. It also provides the confidence interval for the mean difference. Results indicate whether the observed difference is statistically significant at common alpha levels.

When You'd Actually Use This

One-sample: Quality specification testing

Test if product weight differs from the target 500g. Determine if your manufacturing process is centered correctly on the specification.

Two-sample: Treatment comparison

Compare blood pressure reduction between drug and placebo groups. Assess if the treatment produces significantly different outcomes than control.

Paired: Pre-post intervention analysis

Measure employee productivity before and after training. Paired test accounts for individual differences, focusing on change within each person.

Two-sample: A/B testing analysis

Compare average order value between website versions. Test if the new design leads to higher spending per transaction.

Paired: Method comparison studies

Compare two measurement techniques on the same samples. Determine if a new faster method gives equivalent results to the gold standard.

One-sample: Survey benchmark comparison

Test if your customer satisfaction score differs from industry average of 7.5. See if you're performing above or below the benchmark.

What to Know Before Using

T-tests assume normal distribution.Data should be approximately normally distributed, especially for small samples. T-tests are robust to mild violations with larger samples.

Two-sample tests have variance assumptions.Equal variance (pooled) or unequal variance (Welch's) options available. Use Welch's when group variances differ substantially.

Paired tests are more powerful.When you can pair observations, use paired t-test. It removes between-subject variability, making it easier to detect true differences.

One-tailed vs two-tailed matters.Two-tailed tests detect any difference. One-tailed tests only detect difference in specified direction. Choose before seeing data.

Pro tip: Always check for outliers before running t-tests. A single extreme value can dramatically affect the mean and inflate variance, leading to misleading results.

Common Questions

When should I use Welch's t-test?

Use Welch's when group variances are unequal or sample sizes differ greatly. It's safer and nearly as powerful as pooled when variances are equal.

What's the minimum sample size?

Technically 2 per group, but that's not useful. Aim for at least 15-20 per group for reasonable power. More is better for detecting small effects.

How do I check normality?

Use histograms, Q-Q plots, or Shapiro-Wilk test. For n > 30, the Central Limit Theorem makes normality less critical for the mean.

What if my data isn't normal?

Try data transformation (log, square root) or use non-parametric alternatives: Wilcoxon signed-rank (paired) or Mann-Whitney U (two-sample).

What does the confidence interval tell me?

The CI shows the range of plausible values for the true mean difference. If it excludes 0, the difference is statistically significant.

Can I use this for more than two groups?

No, use ANOVA for three or more groups. Multiple t-tests inflate Type I error rate. ANOVA controls the overall error rate.

What's Cohen's d?

Cohen's d is the standardized effect size: mean difference divided by pooled SD. Values: 0.2 small, 0.5 medium, 0.8 large effect.

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T-Test Calculator: One, Two, & Paired Samples