One-Sample t-Test
One-Sample t-Test with explicit assumptions and reproducible inputs.
Formula
- Use the units shown beside each field.
- Results update automatically whenever you change an input.
- Displayed values use up to four decimal places, or scientific notation for very small or large numbers. Calculations use standard floating-point arithmetic; exact integer and fraction tools identify their own precision rules.
- Independent observations; normal population or adequate approximation. Sample SD must be positive. Direction must be chosen before examining results. Numerical results are approximate. Extremely small probabilities can underflow to zero. No personal, clinical or financial decision rule is inferred.
Example Calculation
- Sample mean: 52
- Sample SD: 10
- Sample size: 25
- Null mean: 50
- Alternative: Two-sided
Mean52, SD10, n25 against μ₀=50 give t=1 with 24 degrees of freedom.
Method references
Frequently asked questions
How do I use this calculator?
Enter sample mean, sample sd, sample size, null mean, alternative. The result updates automatically. Use Reset to restore the example values.
What method does it use?
t=(sample mean−null mean)/(s/√n); df=n−1.. Independent observations; normal population or adequate approximation. Sample SD must be positive. Direction must be chosen before examining results. Numerical results are approximate. Extremely small probabilities can underflow to zero. No personal, clinical or financial decision rule is inferred.
Why might a rounded result differ?
The calculation keeps full numeric precision internally, then rounds the displayed result. Rounding intermediate steps by hand can produce a slightly different answer.
Are my inputs saved online?
No. This calculator processes your inputs in your browser. A recently used list stores only calculator names on this device, not your entered values.
Check the assumptions and units before using this result. Read about calculation methods.