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T-Test Calculator

Perform an independent samples t-test (Welch's t-test for unequal variances) by entering the mean, standard deviation, and sample size of two groups. Determine if the groups are significantly different.

Group 1

Group 2

About this Calculator

Perform an independent samples t-test (Welch's t-test for unequal variances) by entering the mean, standard deviation, and sample size of two groups. Determine if the groups are significantly different.

Formula & Calculations

Formula

t = (x̄₁ − x̄₂) / √(s₁²/n₁ + s₂²/n₂); df = (s₁²/n₁ + s₂²/n₂)² / ((s₁²/n₁)²/(n₁−1) + (s₂²/n₂)²/(n₂−1))
Where:
  • x̄₁, x̄₂=Means of group 1 and group 2
  • s₁, s₂=Standard deviations of group 1 and group 2
  • n₁, n₂=Sample sizes of group 1 and group 2
  • t=T-statistic (measures the difference between groups in standard error units)
  • df=Degrees of freedom (Welch-Satterthwaite approximation)

Assumptions

  • Welch's t-test does not assume equal variances between the two groups.
  • Data in both groups should be approximately normally distributed.
  • Observations within each group are independent of each other.
  • For small sample sizes (n < 30 per group), normality assumptions become more important.

Calculation Examples

Example 1

Inputs:Group 1: Mean=75, SD=10, n=30; Group 2: Mean=80, SD=12, n=25
Result:t = −1.700, df = 49.3

t = (75−80) / √(100/30 + 144/25) = −5 / √(3.33 + 5.76) = −5/3.015 ≈ −1.66.

Example 2

Inputs:Group 1: Mean=100, SD=15, n=40; Group 2: Mean=110, SD=18, n=35
Result:t = −2.626, df = 68.7

The negative t-value indicates Group 1's mean is lower than Group 2's.

Frequently Asked Questions

What is the difference between Welch's t-test and Student's t-test?

Student's t-test assumes both groups have equal variances (homogeneity of variance) and uses a pooled variance estimate. Welch's t-test does not assume equal variances and uses separate variance estimates, making it more robust and generally preferred unless you are certain variances are equal.

How do I know if the t-test result is statistically significant?

Compare your calculated t-statistic to a critical value from the t-distribution table using your degrees of freedom and chosen significance level (e.g., α = 0.05, two-tailed). Alternatively, if the corresponding p-value is less than your significance level, the result is statistically significant.