Statistics & Data Analysis

T-Test Calculator

Generate instant statistical T-Scores and specific Degrees of Freedom (df) bounds. Supports both One-Sample and Independent Two-Sample (Welch's Unequal Variance) data testing.

Fast One-Sample vs Population testing
Robust Welch's Two-Sample test for differing variances
Generates complete Standard Error math proofs
T-Test Calculator
Calculate the statistical T-value and degrees of freedom to determine if the means of your datasets differ significantly from each other or from the population.

The Mathematics of the T-Score

When researchers claim a study is "statistically significant," they are frequently referring to the results of a T-Test. In simple terms, a T-Test breaks down your data to analyze the signal-to-noise ratio: it compares the variance between your groups against the variance inside your groups.

The One-Sample T-Test Formula

If you want to know if the 30 students in your local chess club have a higher IQ than the national global average, you use the One-Sample equation:

t = (x̄ - μ) / (s / √n)
  • Numerator (x̄ - μ): The difference between your Local Sample Mean and the large Population Mean.
  • Denominator (s / √n): The Standard Error. It is your sample's Standard Deviation divided by the square root of your sample size. It quantifies the 'spread' of your data points.

Welch's Two-Sample Formula

When comparing two unlinked, separate groups (like comparing Plant Type A to Plant Type B height), assuming both groups share the exact same standard deviation variance is scientifically risky. Welch's T-Test handles unequal variances directly:

t = (x̄₁ - x̄₂) / √(s₁²/n₁ + s₂²/n₂)
(Note: The complex Welch-Satterthwaite equation is required to find the exact Degrees of Freedom for this formula, which this calculator handles natively behind the scenes).

Frequently Asked Questions

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T-Test Calculator - Find T-Value & Degrees of Freedom