T-Test Calculator
Calculate t-statistics, p-values, and determine statistical significance for one-sample, independent, and paired t-tests
t = (x̄ - μ₀) / (s / √n)
Basic T-Test Formula
Group 1
Group 2
Format: before,after pairs separated by semicolons
Quick Examples
t-Statistic
Significance Scale
t-Statistic
Degrees of Freedom
p-Value
Critical Value
±
Effect Size (Cohen's d)
Confidence Interval
[, ]
Interpretation
✅ Reject the null hypothesis. The p-value () is less than your significance level (α = ).
❌ Fail to reject the null hypothesis. The p-value () is greater than or equal to your significance level (α = ).
The absolute t-statistic (|t| = ) exceeds the critical value ().
The absolute t-statistic (|t| = ) does not exceed the critical value ().
Critical Values Reference (Two-Tailed)
| df | α = 0.10 | α = 0.05 | α = 0.01 |
|---|---|---|---|
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About T-Test Calculator
What is a T-Test?
T-tests are statistical hypothesis tests used to compare means and determine if there is a statistically significant difference between groups or between a sample and a population.
Types of T-Tests
1. One-Sample T-Test
Compares a sample mean to a known or hypothesized population mean.
Formula: t = (x̄ - μ) / (s / √n)
Use when: You want to test if your sample differs from a known value.
2. Independent Samples T-Test (Two-Sample)
Compares the means of two independent groups.
Formula (Welch's): t = (x̄₁ - x̄₂) / √(s₁²/n₁ + s₂²/n₂)
Use when: Comparing two separate groups (e.g., treatment vs. control).
3. Paired Samples T-Test
Compares two related measurements from the same group.
Formula: t = d̄ / (sᵈ / √n)
Use when: You have before/after measurements or matched pairs.
Key Concepts
| Term | Description |
|---|---|
| t-statistic | Measures how many standard errors the sample mean is from the hypothesized mean |
| Degrees of Freedom (df) | n-1 for one-sample/paired, complex formula for independent |
| p-value | Probability of getting results at least as extreme, assuming null hypothesis is true |
| Significance Level (α) | Threshold for rejecting null hypothesis (usually 0.05) |
Interpretation Guidelines
- p < 0.01: Highly significant - very strong evidence against null hypothesis
- p < 0.05: Significant - sufficient evidence to reject null hypothesis
- p < 0.10: Marginally significant - weak evidence
- p ≥ 0.10: Not significant - insufficient evidence to reject null hypothesis
Assumptions
- Normality: Data should be approximately normally distributed
- Independence: Observations should be independent (except for paired test)
- Equal Variances: For pooled t-test (Welch's t-test relaxes this assumption)
Note: This calculator uses Welch's t-test for independent samples, which doesn't assume equal variances.