T Test Calculator
Calculate two-sample t-test statistics and determine significance.
Pooled SD = sqrt(((n₁−1)*SD₁^2 + (n₂−1)*SD₂^2) / (n₁+n₂−2))\nStandard Error = Pooled SD * sqrt(1/n₁ + 1/n₂)\nT-Statistic = (Mean₁ − Mean₂) / SE\nDegrees of Freedom = n₁ + n₂ − 2
Example:\nGroup 1: mean=100, SD=15, n=30\nGroup 2: mean=105, SD=12, n=30\nalpha=0.05\n\nPooled SD ≈ 13.58\nSE ≈ 3.51\nT-Stat = (100−105) / 3.51 ≈ −1.42\ndf = 58\nCritical = +/-1.96\nResult: Not significant (|-1.42| < 1.96)
What is a t-test?
A statistical test to determine if two sample means are significantly different. Used when population standard deviation is unknown.
When should I use a t-test?
Use when comparing two groups (e.g., treatment vs control) with continuous data and unknown population variance.
What is the null hypothesis?
The assumption that there is no difference between the groups. T-test determines if you can reject this assumption.
What does significance level mean?
alpha is the probability of rejecting the null hypothesis when it is true (Type I error). Common: 0.05 (5% risk).
What if sample sizes are unequal?
This calculator handles unequal sample sizes using pooled standard deviation. Results are still valid.
🔗 Related Calculators
📐 Formula
Pooled SD = sqrt(((n₁−1)*SD₁^2 + (n₂−1)*SD₂^2) / (n₁+n₂−2))\nStandard Error = Pooled SD * sqrt(1/n₁ + 1/n₂)\nT-Statistic = (Mean₁ − Mean₂) / SE\nDegrees of Freedom = n₁ + n₂ − 2
📝 Example Calculation
Example:\nGroup 1: mean=100, SD=15, n=30\nGroup 2: mean=105, SD=12, n=30\nalpha=0.05\n\nPooled SD ≈ 13.58\nSE ≈ 3.51\nT-Stat = (100−105) / 3.51 ≈ −1.42\ndf = 58\nCritical = +/-1.96\nResult: Not significant (|-1.42| < 1.96)
❓ Frequently Asked Questions
What is a t-test?▼
A statistical test to determine if two sample means are significantly different. Used when population standard deviation is unknown.
When should I use a t-test?▼
Use when comparing two groups (e.g., treatment vs control) with continuous data and unknown population variance.
What is the null hypothesis?▼
The assumption that there is no difference between the groups. T-test determines if you can reject this assumption.
What does significance level mean?▼
alpha is the probability of rejecting the null hypothesis when it is true (Type I error). Common: 0.05 (5% risk).
What if sample sizes are unequal?▼
This calculator handles unequal sample sizes using pooled standard deviation. Results are still valid.