Welch and Student T-Test Calculator for Independent Means
This t-test calculator offers Welch's test for unequal population variances and Student's pooled-variance test. It reports the mean difference, p-values and a 95% two-sided confidence interval using the selected method.
Further Information
A t-test is used when you're looking at a numerical variable — for example, height — and then comparing the averages of two separate populations or groups (e.g., males and females).
Requirements
- Two independent samples
- Data should be normally distributed
- The two samples should have the same variance; use Welch's t-test when that assumption is not appropriate
Null Hypothesis
H₀: μ₁ - μ₂ = 0, where μ₁ is the mean of first population and μ₂ the mean of the second.
As above, the null hypothesis tends to be that there is no difference between the means of the two populations; or, more formally, that the difference is zero (so, for example, that there is no difference between the average heights of two populations of males and females).
Pooled Student equation
t = (M₁ - M₂) / √[((SS₁ + SS₂) / (n₁ + n₂ - 2)) × (1/n₁ + 1/n₂)]
Where M₁ and M₂ are the sample means, SS₁ and SS₂ are the sum of squares, and n₁ and n₂ are the sample sizes.
Welch equation
t = (M₁ − M₂) / √(s₁²/n₁ + s₂²/n₂)
Welch uses the sample variances separately and Welch–Satterthwaite degrees of freedom, which need not be an integer. See the SciPy method documentation.
