GIFSQ Tools · Module 16 — Statistics, Experimental Design & Research · Tool 304 of 500
Compare the means of two independent groups — two batches, two methods, two suppliers — with Welch’s t-test, which does not assume equal variances (ISO 16269-1).
Try sample values — fills the form with the worked example below.
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t statistic (Welch)
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p-value (two-sided)
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Degrees of freedom
Equation: t = (x̄₁ − x̄₂) ÷ √(s₁² ÷ n₁ + s₂² ÷ n₂). Welch df = (s₁² ÷ n₁ + s₂² ÷ n₂)² ÷ [(s₁² ÷ n₁)² ÷ (n₁ − 1) + (s₂² ÷ n₂)² ÷ (n₂ − 1)]. Two-sided p = 2 × P(T ≥ |t|).
Method: Welch’s two-sample t-test per ISO 16269-1. The p-value is computed from the t distribution itself (incomplete beta function). Welch’s version is used because it stays valid when the two variances differ.
Assumptions: the two groups are independent random samples from approximately normal populations; pairing (same sample measured twice) needs the paired t-test instead.
Limitations: with very small n the test has little power; unequal variances with very unequal n can still mislead. A significant p does not measure how large the difference is — report the difference in means too.
Rounding: t to 4 decimal places; p to 4 decimal places; df to 2 decimal places; intermediates unrounded.
This is a calculation aid, not a laboratory report — confirm against your accredited method before citing a value.
Method: Welch’s two-sample t-test per ISO 16269-1. The p-value is computed from the t distribution itself (incomplete beta function). Welch’s version is used because it stays valid when the two variances differ.
Assumptions: the two groups are independent random samples from approximately normal populations; pairing (same sample measured twice) needs the paired t-test instead.
Limitations: with very small n the test has little power; unequal variances with very unequal n can still mislead. A significant p does not measure how large the difference is — report the difference in means too.
Rounding: t to 4 decimal places; p to 4 decimal places; df to 2 decimal places; intermediates unrounded.
This is a calculation aid, not a laboratory report — confirm against your accredited method before citing a value.
Worked example: Group A 1, 2, 3, 4, 5 and Group B 2, 3, 4, 5, 6: means 3.00 and 4.00, t = −1.0000, df = 8.00, p = 0.3466 — not significant at α = 0.05.
Enter values above to see results.
If the same samples were measured by both methods, use the paired t-test (Tool 305) instead. Tool 304 of 500 — GIFSQ
