T-Score Calculator

t = (x̄ − μ₀) / (s/√n) — for testing a sample mean against a hypothesized population mean.

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How to use this calculator

  • Enter sample mean, hypothesized population mean, sample SD, and sample size.
  • Read the t-statistic and compare to a t-table at the right df.

About this calculator

t-score is to t-distribution what z-score is to normal — but t accounts for the additional uncertainty when σ is estimated from a small sample. Use t when σ is unknown and sample size is < 30; use z for large samples or known σ.

Frequently asked

When do I use t vs z?+
Use t when σ is unknown (estimated from sample) and n < 30. For large n, t and z converge — both work.
What is df (degrees of freedom)?+
For a one-sample t-test, df = n − 1. For two-sample tests, the formula is more complex (Welch's correction).
How do I get a p-value from t?+
Look up |t| in a t-table at the right df, or use the p-value calculator with t and df.
Is |t| > 2 always significant?+
For df ≥ 25 and two-tailed α = 0.05, the critical value is ~2.06. So roughly yes, but exact thresholds depend on df.
What's the standard error?+
SE = s/√n. It estimates how much the sample mean would vary across resamples.

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