T-Test Calculator

One-Sample T-TestTwo-Sample T-Test

Sample Data (comma or space separated)

Hypothesized Mean (μ₀)

Significance Level (α)0.10 (90% confidence)0.05 (95% confidence)0.01 (99% confidence)

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What is a T-Test?

A t-test is a statistical test used to compare means. It helps determine whether there’s a significant difference between group means or between a sample mean and a known value.

Types of T-Tests

One-Sample T-Test

Compares a sample mean to a known or hypothesized population mean.

Use when: Testing if your sample differs significantly from a standard or expected value.

Two-Sample T-Test (Independent)

Compares the means of two independent groups.

Use when: Comparing two separate groups (e.g., treatment vs. control).

Paired T-Test

Compares means from the same group at different times or under different conditions.

Use when: Comparing before/after measurements on the same subjects.

T-Test Formulas

One-Sample T-Test

t = (x̄ - μ₀) / (s / √n)

Two-Sample T-Test (Welch’s)

t = (x̄₁ - x̄₂) / √(s₁²/n₁ + s₂²/n₂)

Understanding the Results

• T-statistic: Measures the size of the difference relative to variation
• Degrees of freedom: Related to sample size(s)
• P-value: Probability of observing results if null hypothesis is true
• Significance: If p-value < α (e.g., 0.05), the result is statistically significant

Assumptions of T-Tests

1. Data is approximately normally distributed
2. Random sampling from the population
3. Independence of observations
4. For two-sample: Similar variances (unless using Welch’s t-test)

Related Tools

• Z-Score Calculator - Standardize values
• Mean Calculator - Calculate sample means
• Standard Deviation Calculator - Calculate standard deviations