t-Score Calculator
Compute the one-sample t statistic from a value x, hypothesized or sample mean, sample SD s, and sample size n. Educational arithmetic only; no critical-value table.
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How to compute a one-sample t
- Enter the observed value x you want to locate relative to the reference mean.
- Enter the mean μ from the null hypothesis or known reference.
- Enter sample standard deviation s greater than 0, then sample size n of at least 1.
- Read t, the standard error s / √n, and the simpler (x − mean) / s row. The page does not look up a p-value. Nothing is uploaded.
One-sample t statistic
t = (x − μ) / (s / √n)
| Formula | t = (x − μ) / (s / √n) |
|---|---|
| Standard error | SE = s / √n |
| Also reports | (x − mean) / s without the √n factor |
| Defaults | x = 12, mean = 10, s = 4, n = 16 |
| Table lookup | None. No critical t or p-value. |
| Contrast with z | z divides by a known SD; t divides by SE from sample s |
What this t-score page returns
The one-sample t statistic measures how far x sits from a reference mean in units of the estimated standard error. This page computes that ratio, shows SE = s / √n, and also prints (x − mean) / s so you can see the effect of leaving out the sample-size root. It does not invert a Student-t table into a critical value or a two-sided p-value.
How t is computed
t = (x − μ) / (s / √n). s must be positive. n must be at least 1. With the defaults x = 12, mean = 10, s = 4, and n = 16, SE = 1 and t = 2. Degrees of freedom for a later table lookup would usually be n − 1, but this page never opens that table.
Standard error, z, and related interval jobs
Entities: sample mean, sample SD, standard error, one-sample t, and degrees of freedom (mentioned only as context). Scaling one observation by a known population SD is the z-score calculator. Building a normal mean interval with a chosen confidence percent is confidence interval. Computing s from a raw list first belongs on standard deviation.
Use cases
Methods homework that already states x-bar, μ0, s, and n and only asks for the t statistic. Checking that doubling n shrinks SE by √2. Not an automatic reject/fail decision for a lab report, and not a two-sample or paired t product.
t versus z on CZNull
z-score divides (x − mean) by a typed SD and ignores n. t-score divides by s / √n so larger samples produce larger |t| for the same raw gap. If your problem says the population SD is known, use z. If it says you estimated s from the sample, use t.
Limits
No critical-value table. No Welch or paired modes. No automatic normality check. Educational floating point in this tab. CZNull does not receive the numbers.