T-Test Calculator
Run a one sample, two sample or paired t-test with exact p-values, Welch correction, effect size, confidence interval and an explanation of what the result does and does not show.
Last reviewed by the Radiatus Cloud team
Need this done properly for your business?
Radiatus delivers secure cloud, DevOps & compliance engineering.
What a t-test compares
A t-test asks whether a difference in means is larger than the variability in the data can comfortably explain. The statistic is the difference divided by its standard error, so it grows when the difference grows, when the data is less variable, and when the sample is larger. All three matter equally, which is why a tiny difference becomes statistically significant in a large enough sample and a large one can fail to reach significance in a small sample.
The p-value answers a narrower question than people think
It gives the probability of seeing a difference at least this large if the null hypothesis were true. It is not the probability that the null hypothesis is true, not the probability the result is a fluke, and not a measure of how big or important the effect is. A p-value of 0.049 and one of 0.051 describe almost identical evidence, and the 0.05 threshold is a convention with no special mathematical status.
Effect size is the number that answers the practical question
Cohen's d expresses the difference in standard deviations, which is comparable across studies and scales. Reporting a significant result without it leaves out the part that matters: whether the difference is large enough to act on. A significant result with a d of 0.05 is a reliably detected effect too small to be worth anything, and that combination is common in large samples.
Related tools
- Percentage Calculator — Calculate percentages, percentage change, increase and decrease, and reverse percentages, with the working shown for each result.
- Statistical Calculator — Calculate mean, median, mode, standard deviation, and more.
- Probability Calculator — Calculate probabilities for single and combined events, including conditional probability and Bayes' theorem.
- Scientific Calculator — Perform advanced mathematical operations including trig, log, and exponents.
Frequently Asked Questions
What does the p-value mean?
The probability of observing a difference at least this large if there were genuinely no difference. It is not the probability that the null hypothesis is true, nor the probability the result is a fluke, and it says nothing about the size of the effect.
Should I use Welch or Student?
Welch, which does not assume the two groups have equal variances. That assumption is rarely justified, testing it first inflates the error rate, and Welch loses almost nothing when the variances do happen to be equal. It is the recommended default.
When do I use a paired test?
When each observation in one group is naturally matched with one in the other: the same subject before and after, the same server under two configurations, or matched pairs by design. Pairing removes the between subject variability and is substantially more powerful when it applies.
What is Cohen's d?
The difference in means divided by the pooled standard deviation, so it expresses the effect in standard deviations. Around 0.2 is conventionally small, 0.5 medium and 0.8 large, though these labels are rules of thumb rather than facts about any particular field.
Why report a confidence interval as well?
Because it shows the range of differences the data supports, which is what you need in order to decide whether the effect matters. A p-value only says whether zero is plausible, and a significant result can still be consistent with an effect too small to act on.
Privacy & Security
Everything runs in your browser; nothing is uploaded.
How to Use
Choose the test type, enter your sample figures and read the t statistic and p-value.
Disclaimer: This tool is provided "as is" without warranty of any kind. Results are for educational and utility purposes.
Related Tools
Percentage Calculator
MathCalculate percentages, percentage change, increase and decrease, and reverse percentages, with the working shown for each result.
Statistical Calculator
MathCalculate mean, median, mode, standard deviation, and more.
Probability Calculator
MathCalculate probabilities for single and combined events, including conditional probability and Bayes' theorem.