Statistical
Two-sample t-test formula (Welch's unequal-variance t-statistic)
Compare two independent group means (e.g., A/B order value or cycle time) using Welch's t-statistic (Mean1 - Mean2) / SQRT(Var1/sampleCountA + Var2/sampleCountB).
Compare independent means without assuming equal variances
Whereas a two-proportion Z-test compares binary conversion rates (%), a two-sample t-test compares continuous metrics like Average Order Value ($), session duration, or processing time across two independent groups.
Welch's t-test does not assume both groups share identical variance: t = (AVERAGE(A) - AVERAGE(B)) / SQRT(VAR.S(A)/COUNT(A) + VAR.S(B)/COUNT(B)).
| Statistic | Group A [111,117,123,129] | Group B [92,98,104,106] |
|---|---|---|
| Sample Mean | 120.00 | 100.00 (Diff = +20.00) |
| Sample Variance (VAR.S) | 60.00 (s^2/n = 15) | 40.00 (s^2/n = 10) |
| Combined SE & Welch t | SE = SQRT(15 + 10) = 5.00 | t = 20 / 5 = 4.0000 |
Welch's t-statistic and Welch-Satterthwaite degrees of freedom
Bind varianceTermA = VAR.S(A)/COUNT(A) and varianceTermB = VAR.S(B)/COUNT(B) inside LET to compute both t and approximate degrees of freedom cleanly.
=LET(varianceTermA, VAR.S(A2:A5)/COUNT(A2:A5), varianceTermB, VAR.S(B2:B5)/COUNT(B2:B5), ROUND((AVERAGE(A2:A5) - AVERAGE(B2:B5)) / SQRT(varianceTermA + varianceTermB), 4))Welch-Satterthwaite degrees of freedom
Approximates effective df = (varianceTermA + varianceTermB)^2 / (varianceTermA^2/(sampleCountA-1) + varianceTermB^2/(sampleCountB-1)).
=LET(sampleCountA, COUNT(A2:A5), sampleCountB, COUNT(B2:B5), varianceTermA, VAR.S(A2:A5)/sampleCountA, varianceTermB, VAR.S(B2:B5)/sampleCountB, ROUND((varianceTermA + varianceTermB)^2 / (varianceTermA^2/(sampleCountA-1) + varianceTermB^2/(sampleCountB-1)), 2))Inputs and interpretation
Use independent groups with at least two numeric observations each and positive combined variance. Small-sample inference requires approximately normal populations and attention to outliers. The t-statistic is not a p-value; select tails and significance level before testing, and use unrounded intermediate values for inference.
Try the example
Use the original values or change them to test your understanding.