GIFSQ Tools · Module 16 — Statistics, Experimental Design & Research · Tool 305 of 500
Compare two measurements made on the same samples — before and after, method A versus method B on the same batch — with the paired t-test (ISO 16269-1).
Try sample values — fills the form with the worked example below.
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t statistic
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p-value (two-sided)
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Degrees of freedom
Equation: Differences d = second − first. t = d̄ ÷ (s_d ÷ √n), df = n − 1. Two-sided p = 2 × P(T ≥ |t|). 95% CI for the mean difference: d̄ ± t(0.975, df) × s_d ÷ √n.
Method: Student’s paired t-test per ISO 16269-1: the test is a one-sample t-test on the differences. The p-value is computed from the t distribution itself (incomplete beta function).
Assumptions: the pairs are matched (same sample, same unit) and the differences are approximately normally distributed; the two lists must be in the same order and the same length.
Limitations: pairing that is not real (unmatched samples) makes the test invalid — use the independent t-test instead. A single outlying pair can dominate the result.
Rounding: t to 4 decimal places; p to 4 decimal places; mean difference 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: Student’s paired t-test per ISO 16269-1: the test is a one-sample t-test on the differences. The p-value is computed from the t distribution itself (incomplete beta function).
Assumptions: the pairs are matched (same sample, same unit) and the differences are approximately normally distributed; the two lists must be in the same order and the same length.
Limitations: pairing that is not real (unmatched samples) makes the test invalid — use the independent t-test instead. A single outlying pair can dominate the result.
Rounding: t to 4 decimal places; p to 4 decimal places; mean difference 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: Before 10, 12, 14, 16 and after 12, 13, 16, 19: differences 2, 1, 2, 3, mean difference 2.00, t = 4.8990, df = 3, p = 0.0163 — significant at α = 0.05.
Enter values above to see results.
Always check the pairs line up: the first value in each list must belong to the same sample. Tool 305 of 500 — GIFSQ
