About One-Sample T-Test Calculator
This one-sample t-test calculator checks whether the mean of your sample differs from a hypothesised population mean, using the t distribution with n minus 1 degrees of freedom. It is free, needs no sign-up and runs in your browser, so nothing you enter is uploaded.
Paste your data or type the sample mean, standard deviation and size, then type the value to compare with (μ0). The page returns the t statistic, the p-value for a two-tailed, right-tailed or left-tailed test, the confidence interval for the mean and Cohen’s d.
Typical questions: is the average fill of a bottle different from the label, is a class average different from a national average, did a process hit its target mean. The curve shows where your t statistic lands against the rejection region.
How to use One-Sample T-Test Calculator
- Choose the test: one-sample, paired or two-sample.
- Choose raw data or summary statistics. For raw data, paste each list; for paired data, keep the two lists in the same order and the same length.
- For a one-sample test type the hypothesised mean. For two samples pick Welch or Student.
- Pick the alternative hypothesis (two-tailed, right or left) and the significance level.
- Read the t statistic, p-value, interval and Cohen's d, then open the working to see every formula.
Features
- One-sample, paired and independent two-sample t-tests.
- Welch (unequal variances) and Student (pooled) two-sample tests, compared side by side with a recommendation.
- Raw data or summary statistics (mean, standard deviation, n).
- Cohen's d with a size label, plus the standard error and a confidence interval.
- Left, right or two-tailed tests, with the critical value for your significance level.
- A bell curve with the rejection region shaded and the t statistic marked.
- Step-by-step KaTeX working and a plain-English conclusion.
One-sample t-test
The statistic is the distance from the hypothesised mean in standard errors.
t = (x̄ − μ0) / (s / √n), df = n − 1
d = (x̄ − μ0) / sWorked examples
Ten measurements 24.1, 26.3, 22.8, 25.0, 27.2, 23.9, 25.6, 24.4, 26.8, 23.5 against μ0 = 25 gives mean 24.96, t = -0.08575, df = 9, p = 0.934
NIST ZARR13: n = 195, mean 9.26146, SD 0.022789, μ0 = 5 gives t = 2611.262, df = 194, critical values ±1.9723
The NIST/SEMATECH e-Handbook, section 1.3.5.2, reports T = 2611.284.
Privacy: how it works
- The test is calculated by code in your own browser tab. Your data is not sent to Ulkaa or to any other server.
- There is no account and nothing is stored. Closing the tab clears what you entered.
Tips
- Use the paired test when the same people or items are measured twice. Using the two-sample test on paired data throws away the pairing and usually loses power.
- Decide one-tailed or two-tailed before you see the data. A two-tailed test is the safe default.
- Report the effect size and the interval with the p-value. A tiny p-value with a negligible Cohen's d is statistically significant but may not matter in practice.
- If your lists have different lengths, that is fine for the two-sample test, but the paired test needs equal lengths.
Frequently asked questions
Is it really free?
Yes. There is no price, no trial and no credit card. Ulkaa Tool does the work with your own device, so there is no server bill to pass on to you.
Do I need an account?
No. There is no sign-up and no login. Open the page and use it. An Ulkaa account is not needed for anything on this tool.
Does it run in my browser?
Yes. Your data are processed by code running in your browser tab, on your own device.
Is my data uploaded?
No. Your data are never sent to Ulkaa or to anyone else. You can check this yourself by watching the Network tab in your browser developer tools while you use the tool.
When do I use a one-sample t-test?
When you have one group of measurements and want to know whether its population mean differs from a specific number, and you do not know the population standard deviation.
What if I know the population standard deviation?
Then a z-test is appropriate. For large samples the two give nearly the same answer. The confidence interval calculator on this site has a known-sigma option.
More T-Test Calculator pages
- T-Test CalculatorRun a one-sample, paired or two-sample t-test from raw data or summary statistics, with Cohen's d, the p-value and the working.
- Paired T-Test CalculatorPaste two matched lists and get the paired t statistic, p-value and working.
- Two-Sample T-Test CalculatorCompare the means of two independent groups with the classic pooled Student t-test.
- Welch's T-Test CalculatorCompare two means without assuming equal variances, with Welch-Satterthwaite degrees of freedom.
- Cohen's d CalculatorGet Cohen's d for two groups from summary statistics, with the matching t-test and a size label.