T-test calculator
One and two sample t-tests that lead with the difference between your groups, not with p — and Cohen’s d beside every result, because whether something is detectable and whether it matters are different questions. Nothing you type here leaves your browser — it is worked out on your own device, so there is nothing to send and nothing to log.
Before the number. A p-value is not the probability that your hypothesis is true. It is not the probability the result happened by chance. It is not a measure of how big or important the effect is. It is the probability of seeing data at least this extreme if there were no effect at all — and that is a narrower statement than almost everybody takes it for.
The difference comes first, and that is deliberate
Every other t-test calculator leads with p. This one leads with the difference between your groups, because that is the quantity you were actually asking about. The p-value is a statement about whether that difference could plausibly be nothing — useful, secondary, and not the answer.
Leading with p is how a page teaches exactly the misreading it then disclaims further down.
Welch by default, which is the other way round
Student’s t-test assumes the two groups have the same spread. Welch’s does not. That assumption is almost never checked, the correction costs essentially nothing when it happens to be true, and when it is false Student’s test is wrong in a direction nobody notices.
So Welch is the default here and Student’s is the option, which is the reverse of most calculators. Welch’s degrees of freedom usually come out fractional — 13.898 rather than 14 — and that is correct, not a rounding failure.
Cohen's d is beside every result, not on another page
A t-test that reports t and p but not the size of the difference tells you a result is detectable without telling you whether it matters. With enough data, a difference far too small to care about will produce any p-value you like.
Cohen’s d is the difference measured in standard deviations, so it does not change when you collect more data — it gets more precisely estimated. The conventional labels (0.2 small, 0.5 medium, 0.8 large) are Cohen’s own rough guide and were never meant as thresholds; this page reports them as conventions rather than as findings.
What the test assumes, and does not check
That your observations are independent, and that the means are roughly normally distributed — which for reasonable sample sizes follows from the data being roughly symmetric and not wildly outlier-ridden.
Nothing here checks either of those, because nothing can from the numbers alone. If your data are paired, or clustered, or the same people measured twice, this is the wrong test and it will still give you an answer.