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T Score Calculator

Calculate T-Statistic with Step-by-Step Derivation

Sample Mean (x̄)
Population Mean (μ)
Sample Std (s)
Sample Size (n)

T Score Formula

t = (x̄ - μ) / (s / √n)
DF = n - 1 (degrees of freedom)
Where: x̄=sample mean, μ=pop mean, s=sample std, n=sample size

T-score is used for hypothesis testing when population standard deviation is unknown or sample size is small.

Sample size must be at least 2. Sample standard deviation must be positive.

What is T Score?

The t-score (t-statistic) is a statistical measure used in hypothesis testing when the population standard deviation is unknown and/or the sample size is small.

T-Distribution

Similar to normal but with fatter tails for small samples

Degrees of Freedom

DF = n-1, affects the shape of t-distribution

Standard Error

s/√n, measures uncertainty in sample mean

vs Z-Score

Use t when σ unknown, z when σ known

💡 Example: x̄=85, μ=80, s=12, n=25. t=(85-80)/(12/5)=5/2.4=2.083. DF=24.

Applications

Hypothesis Testing Confidence Intervals Small Samples Statistics Research

Frequently Asked Questions

What is t-score?
T-score (t-statistic) measures how many standard errors the sample mean is from the population mean. t = (x̄ - μ) / (s/√n). Used when population σ is unknown.
Difference between t-score and z-score?
Z-score uses population σ, t-score uses sample s. T-distribution has fatter tails, especially with small n. Use t when n<30 or σ unknown.
What are degrees of freedom?
DF = n - 1 for one-sample t-test. DF determines the shape of t-distribution. Larger DF makes t-distribution closer to normal.
When to use t-score?
Use t-score for small samples (n<30), when population standard deviation is unknown, or when sampling from non-normal distributions with large n.

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