t-Test Calculator

Run a t-Test directly in your browser. Choose between a one-sample t-test, two-sample (independent) t-test, or paired t-test, then enter your sample mean(s), standard deviation(s), sample size(s), and significance level. You get back the t-statistic, degrees of freedom, p-value, and a clear reject/fail-to-reject decision for your null hypothesis.

Select the type of t-test based on your study design.

For one-sample: your sample mean. For two-sample/paired: Group 1 mean or mean of differences.

Standard deviation of Group 1 (or of differences for paired test).

Number of observations in Group 1 (or total pairs for paired test).

The population mean under H₀. For two-sample tests this is typically 0 (no difference).

Required for two-sample t-test only.

Required for two-sample t-test only.

Required for two-sample t-test only.

Use Welch's if you cannot assume equal population variances.

Results

t-Statistic

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Degrees of Freedom

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p-Value

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Critical Value (tα)

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Conclusion

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Cohen's d (Effect Size)

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Standard Error (SE)

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t-Statistic vs Critical Value

Frequently Asked Questions

What is a t-test?

A t-test is a statistical hypothesis test used to compare means and determine whether they differ significantly. It calculates a t-statistic from your sample data and compares it to a critical value from the t-distribution to decide whether to reject the null hypothesis. It is especially useful for small samples (typically n < 30).

What is the difference between a one-sample, two-sample, and paired t-test?

A one-sample t-test compares a single sample mean to a known or hypothesized population mean. A two-sample (independent) t-test compares the means of two separate, unrelated groups. A paired t-test compares means from the same group measured at two different times or under two conditions, using the differences between pairs.

When should I use Welch's t-test instead of the pooled t-test?

Use Welch's t-test (unequal variances) when you cannot reasonably assume that the two populations have equal variances — which is often the case in practice. The pooled t-test assumes equal variances (homoscedasticity). Welch's test is generally the safer default for two-sample comparisons.

What does the p-value mean in a t-test?

The p-value is the probability of observing a t-statistic as extreme as the one calculated (or more extreme) if the null hypothesis is true. A small p-value (typically less than your chosen α, e.g. 0.05) indicates strong evidence against the null hypothesis, leading you to reject it.

What are the assumptions of a t-test?

The main assumptions are: (1) the data are continuous and approximately normally distributed (or the sample size is large enough for the Central Limit Theorem to apply), (2) observations are independent, and (3) for the pooled two-sample t-test, the two groups have equal population variances. Violations of normality become less critical as sample size increases.

How do I interpret the t-statistic?

The t-statistic measures how many standard errors the sample mean (or difference of means) is away from the hypothesized value. A larger absolute t-statistic means a greater difference relative to variability. If |t| exceeds the critical value for your chosen α and degrees of freedom, you reject the null hypothesis.

What is Cohen's d and why does it matter?

Cohen's d is a measure of effect size — it tells you the practical magnitude of the difference between means, independent of sample size. Values around 0.2 are considered small, 0.5 medium, and 0.8 or above large. A statistically significant result (small p-value) doesn't necessarily mean a practically important difference, so reporting Cohen's d alongside the p-value gives a more complete picture.

What does 'degrees of freedom' mean in a t-test?

Degrees of freedom (df) reflect the amount of independent information available to estimate variability. For a one-sample test, df = n − 1. For a pooled two-sample test, df = n₁ + n₂ − 2. Welch's test uses an approximated (Satterthwaite) df that may be non-integer. Higher df generally means the t-distribution is closer to a normal distribution.

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