How to Use the T-Test Calculator

Enter your data values separated by spaces, commas, or newlines. Choose the appropriate test type based on your research design and set the significance level (alpha).

Types of T-Tests

One-Sample T-Test

Tests whether a sample mean differs from a hypothesized population mean:

H₀: μ = μ₀ (sample mean equals hypothesized mean)
H₁: μ ≠ μ₀ (two-tailed) or μ < μ₀ / μ > μ₀ (one-tailed)
Example: Testing if average test scores differ from 75

Two-Sample (Independent) T-Test

Compares means of two independent groups:

Student's t-test: Assumes equal variances
Welch's t-test: Does not assume equal variances (recommended)
Example: Comparing treatment vs. control group

Paired T-Test

Compares two related measurements on the same subjects:

Before/After studies: Same subjects measured twice
Matched pairs: Subjects paired on relevant characteristics
Example: Blood pressure before and after treatment

Interpreting Results

t-Statistic: Measures how many standard errors the sample mean is from H₀
p-Value: Probability of observing results as extreme under H₀
Significant if: p-value < α (reject null hypothesis)
Not significant if: p-value ≥ α (fail to reject null hypothesis)

Choosing the Right Test

One sample vs. known value: Use one-sample t-test
Two independent groups: Use two-sample t-test
Same subjects, two conditions: Use paired t-test
Large samples (n > 30): T-test approximates z-test

Assumptions

Normality: Data should be approximately normally distributed
Independence: Observations should be independent (except paired)
Equal variances: For Student's t-test (use Welch's if uncertain)
Random sampling: Data should come from random samples

Common Applications

Medical research (drug effectiveness)
Psychology experiments (treatment effects)
Quality control (process comparisons)
Education research (teaching methods)
A/B testing (conversion rates)

Formula Reference

One-sample: t = (x̄ - μ₀) / (s/√n)

Two-sample (pooled): t = (x̄₁ - x̄₂) / √(sp² × (1/n₁ + 1/n₂))

Paired: t = d̄ / (sd/√n)