Statistics & Probability

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One-Sample t-Statistic Calculator.

Calculate a one-sample t statistic from summary statistics.

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01

Set your values

Results update as you type.

tStatistic: 2

tStatistic

2.000000
degreesOfFreedom: 24

degreesOfFreedom

24.000000
standardError: 2

standardError

2.000000

Contract: t = (x̄ − μ₀)/(s/√n), with an entered sample SD and n ≥ 2. No p-value or tail decision is inferred.

Results update automatically as you type.

Use Cases

Hypothesis Testing in Research

Use the t-statistic to test whether a sample mean differs from a known population mean, common in psychology, biology, and social sciences.

Example: Test if a new teaching method's average test score differs from the school's historical average.

Quality Control in Manufacturing

Determine if a sample of product measurements deviates from the target specification, helping maintain process consistency.

Example: Check if the average diameter of produced bolts matches the specified 10 mm.

Frequently Asked Questions

What is a one-sample t-statistic?
It measures how many standard errors the sample mean is from the hypothesized mean. It's used to test if the sample mean differs significantly from a known or assumed population mean.
How do I calculate the t-statistic?
Subtract the hypothesized mean from the sample mean, then divide by the standard error (sample SD divided by the square root of sample size). This calculator does that for you.
What does the t-statistic tell me?
A larger absolute t-value indicates a greater difference between the sample mean and hypothesized mean relative to variability. Compare it to a critical t-value to assess significance.

Tips & Common Mistakes

Tips

  • Ensure your sample is randomly selected and independent to meet t-test assumptions.
  • Use the sample standard deviation (s), not the population standard deviation (σ), for this calculator.
  • Sample size (n) must be a positive integer; larger samples give more reliable t-statistics.
  • Remember that the t-statistic alone doesn't prove significance—consider degrees of freedom and critical values.

Common Mistakes to Avoid

  • Using the population standard deviation instead of the sample standard deviation.
  • Entering the sample size as the degrees of freedom (n-1) instead of the actual sample size.
  • Confusing the hypothesized mean with the sample mean, leading to a zero t-statistic.

Last updated: August 13, 2026