The two-sample t-test takes two lists of numbers, works out the mean and variance of each, and tells you whether the gap between them is big enough to be interesting or small enough to be noise. Paste comma-separated values into both boxes, press Calculate, and you get means, variances, a t-statistic, degrees of freedom, a p-value and a plain sentence about the 0.05 level.
It is for the lab report or the stats assignment where you have two sets of five measurements and need the arithmetic done without opening a package. Two samples, independent of each other, each with at least two values.
The inputs are deliberately dumb: numbers separated by commas, nothing else. No columns to format, no header row, and the reset button clears both boxes so you can paste the next pair straight in.
Perform a two-sample t-test. Enter two sets of comma-separated data values to compare their means.
How the numbers are worked out
Each sample gets a mean, the average of its values, and a variance, which is the average squared distance from that mean using n minus 1 on the bottom so it matches the usual sample variance. The standard error is the square root of variance one over n one plus variance two over n two, and the t-statistic is the difference between the two means divided by that. Degrees of freedom is n one plus n two minus two, so two samples of five give 8.
The p-value comes from the t-distribution with those degrees of freedom, doubled for a two-sided test, and the last line compares it against 0.05. Under 0.05 the tool says the difference is statistically significant, at or above it the tool says it is not. That sentence is the one people quote, and it is only as good as the number above it.
Two runs with real numbers
Take the example in the fields: sample one is 23, 25, 28, 22, 30 and sample two is 18, 20, 22, 19, 21, five values each. The first has a mean of 25.6000 and a variance of 11.3000, the second a mean of 20.0000 and a variance of 2.5000. The standard error works out to 1.6613, so t is 5.6 divided by 1.6613, which is 3.3708 with 8 degrees of freedom.
That is the case worth being careful about. The page prints a p-value of 0.0515 and reports the difference as not significant at 0.05, while a statistics package given the same two samples returns about 0.0098, which is significant. Same means, same t, different verdict. The t-statistic, the means and the variances are computed the standard way; the p-value comes from a quick series expansion that drifts, sometimes a long way, so read it as a flag rather than a result.
Here is one where both agree. Sample one is 64, 70, 66, 72, 68 and sample two is 78, 74, 80, 76, 82. Means are 68 and 78, both variances are 10, the standard error is exactly 2, so t is -10 over 2, which is -5.0000 with 8 degrees of freedom. The page prints p = 0.0025 and calls the difference significant, and that conclusion holds under any proper test.
What this tool does not do
- The degrees of freedom assume two samples of equal standing while the standard error keeps the two variances separate. When spreads are very different and the sample sizes differ too, check the result elsewhere before quoting it.
- Paired data is not handled. Two lists of the same length measured on the same people are still treated as independent groups, which throws away the pairing.
- If every value in a sample is identical the variance is zero, and if both are flat you get a standard error of zero and an error message instead of a t-statistic, even when the two flat lines sit at different heights.
- Two values per sample is the minimum the fields accept, and a test on two numbers tells you almost nothing. Five is a floor worth keeping to.
- No graph, no confidence interval and no effect size. A p-value on its own never tells you how big the difference is, only whether noise could plausibly explain it.
Other tools
- Task Priority Matrix – when the stats homework is one of six things competing for tonight
- Text Case Converter – clean up the label on the dataset before it goes into the report
- TOEFL to IELTS – the other conversion you may be running alongside this one
Frequently asked questions
When should I use a t-test?
When you have two independent groups and a numeric measurement from each, and you want to know whether the difference between the means is bigger than the noise inside them. If the same subjects were measured twice, that is a paired test instead, which this tool does not do.
What does the p-value mean?
The probability of seeing a gap this large if there were really no difference between the groups. Small means the gap is hard to explain as luck. The number the page prints is an approximation, so confirm anything that decides your grade against a calculator or a stats package.
What is the 0.05 line about?
It is the conventional cutoff, not a law of nature. Anything below it gets called statistically significant and anything above does not. At 0.05 you are accepting a one in twenty chance of calling a difference real when it is not, which is why a result sitting just above the line deserves a second look rather than a shrug.
Can I paste in decimals or negatives?
Yes. Values are split on commas, trimmed and parsed as numbers, so 3.5, -2 and 17.75 all work. Anything that does not parse as a number stops the run with a message telling you to separate the values with commas.