GIFSQ Tools · Module 16 — Statistics, Experimental Design & Research · Tool 303 of 500
Test whether the mean of one set of laboratory results differs from a target or specification value, using Student’s 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: t = (x̄ − μ₀) ÷ (s ÷ √n), df = n − 1. Two-sided p = 2 × P(T ≥ |t|). 95% CI for the mean: x̄ ± t(0.975, df) × s ÷ √n.
Method: Student’s one-sample t-test per ISO 16269-1. The p-value is computed from the t distribution itself (incomplete beta function), not read from a table.
Assumptions: the sample is a random sample from an approximately normally distributed population; the test is robust to mild departures from normality when n is moderate.
Limitations: with very small n the test has little power; a non-significant result does not prove the mean equals μ₀. Outliers distort both the mean and the SD.
Rounding: t to 4 decimal places; p to 4 decimal places (shown as < 0.0001 when smaller); intermediates unrounded.
This is a calculation aid, not a laboratory report — confirm against your accredited method before citing a value.
Method: Student’s one-sample t-test per ISO 16269-1. The p-value is computed from the t distribution itself (incomplete beta function), not read from a table.
Assumptions: the sample is a random sample from an approximately normally distributed population; the test is robust to mild departures from normality when n is moderate.
Limitations: with very small n the test has little power; a non-significant result does not prove the mean equals μ₀. Outliers distort both the mean and the SD.
Rounding: t to 4 decimal places; p to 4 decimal places (shown as < 0.0001 when smaller); intermediates unrounded.
This is a calculation aid, not a laboratory report — confirm against your accredited method before citing a value.
Worked example: Values 6, 7, 8, 9, 10 against μ₀ = 5: mean 8.00, SD 1.58, t = 4.2426, df = 4, p = 0.0132 — significant at α = 0.05.
Enter values above to see results.
Report the mean, SD, t, df and p together — a p-value alone says nothing about the size of the difference. Tool 303 of 500 — GIFSQ
