T-test Explorer
Change an average. Move a curve. See what the evidence says.
Load your sample data
Paste numbers for each group, or upload a CSV and choose a column. Each group needs at least two observations and some variation. Files stay in your browser.
The default question follows your group labels and test direction. You can edit it for your example; clear it to restore the automatic question.
1. Compare the data distributions
Illustrative normal curves using your sample averages and sample standard deviations.
Curve width represents the spread of individual values, not uncertainty in the average. Sample averages alone do not determine a t-test.
2. Locate the t-statistic
The null hypothesis says the two population means are equal.
What is a t-test testing?
A t-test asks whether the difference between two averages is large relative to the variation in the data, or whether ordinary sampling variation could plausibly explain it.
The probability part: If the populations really had the same average, how likely would random sampling be to produce a result at least this extreme in the direction(s) being tested? That probability is the p-value.
For example, p = 0.03 means results at least this extreme would occur about 3% of the time under the equal-average assumption. It does not mean there is a 3% chance that the population averages are equal. A statistically significant difference can still be too small to matter in practice.
What is this demonstrating?
This is an independent-samples Welch t-test calculated from summary statistics. It allows the groups to have different standard deviations and sample sizes. In sample-statistics mode, the upper curves are normal illustrations, not actual observations or a normality check. In data-loading mode, the histograms show the observations themselves; a t-test does not require each histogram to form a perfect bell curve. Strong skew and outliers can affect reliability, especially for small samples.
The t-statistic is the difference in sample means divided by its standard error. Moving the means farther apart increases |t|. Increasing variability lowers |t|. Increasing sample size generally raises |t| for the same means and standard deviations.
The p-value is the probability, under the null model, of a t-statistic at least as extreme in the direction(s) selected. It is not the probability that the null hypothesis is true. Failing to reject the null does not establish equal means.
A two-tailed test needs only one comparison group: it considers differences in either direction. If you add another comparison, each test is shown separately; these p-values are not adjusted for multiple comparisons. For repeated measurements of the same subjects, select Paired samples above.