T-Test Calculator
Calculate t-statistics, p-values, and critical values for statistical hypothesis testing. Supports one-sample, two-sample independent (Student's and Welch's), and paired t-tests with step-by-step calculations.
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T-Test Calculator - Student's t-Test & Welch's t-Test
Perform t-tests to compare means and make statistical inferences. Calculate t-statistics, p-values, degrees of freedom, and critical values for one-sample, two-sample independent, and paired t-tests. Includes Welch's t-test for unequal variances with complete step-by-step calculations.
What is the T-Test?
The t-test is a statistical hypothesis test used to determine if there is a significant difference between means. Developed by William Sealy Gosset under the pseudonym 'Student', it's used when sample sizes are small and population standard deviation is unknown. The test produces a t-statistic that follows the t-distribution, allowing us to calculate the probability (p-value) of observing our results if the null hypothesis is true.
One-Sample T-Test Formula
t = (x̄ - μ₀) / (s / √n)How to Perform a T-Test
T-Test Applications
Medical Research
Compare treatment effects, test drug efficacy, analyze patient outcomes before and after interventions using paired t-tests.
Quality Control
Verify if manufacturing processes produce items within specification limits using one-sample t-tests against target values.
A/B Testing
Compare conversion rates, user engagement, or revenue between control and treatment groups in marketing experiments.
Educational Assessment
Compare test scores between teaching methods, evaluate program effectiveness, analyze student performance differences.
Frequently Asked Questions
Use a t-test when the population standard deviation is unknown and you're estimating it from sample data, which is most real-world situations. Use a z-test only when you know the true population standard deviation or have very large samples (n > 100). The t-test is more conservative and appropriate for smaller samples.