T-Test Calculator
T-Statistic
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Degrees of Freedom
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P-Value (two-tailed, approx)
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Significance
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Understanding the T-Test
The Student's t-test determines whether there is a statistically significant difference between means. A one-sample t-test compares a sample mean to a hypothesized population mean. A two-sample t-test compares the means of two independent groups. This calculator uses Welch's t-test for two-sample comparisons, which does not assume equal variances.
The t-statistic measures how many standard errors the sample mean is from the hypothesized or comparison mean. Larger absolute t-values indicate stronger evidence against the null hypothesis. The p-value represents the probability of observing results as extreme as yours if the null hypothesis were true.
A p-value below 0.05 is traditionally considered statistically significant, meaning there is less than a 5% chance the observed difference is due to random variation alone. However, statistical significance does not necessarily mean practical significance — a very large sample can make trivially small differences statistically significant.
Frequently Asked Questions
What is the difference between one-sample and two-sample t-tests?
A one-sample t-test compares your sample mean to a known or hypothesized value. A two-sample t-test compares the means of two separate groups to determine if they are significantly different from each other.
What does the p-value mean?
The p-value is the probability of getting results as extreme as observed, assuming the null hypothesis is true. A small p-value (< 0.05) suggests the observed difference is unlikely due to chance alone.
When should I use a t-test vs z-test?
Use a t-test when the population standard deviation is unknown and must be estimated from the sample (most real-world situations). Use a z-test only when the population standard deviation is known and the sample is large.
What are the assumptions of a t-test?
The data should be approximately normally distributed (less important for large samples due to the Central Limit Theorem), observations should be independent, and the data should be measured on an interval or ratio scale.