GIFSQ Tools · Module 16 — Statistics, Experimental Design & Research · Tool 306 of 500
Test whether three or more independent groups have the same mean — the standard comparison for multi-batch or multi-treatment laboratory data (Fisher ANOVA, ISO 16269-1).
Try sample values — fills the form with the worked example below.
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F statistic
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p-value
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Eta-squared (η²)
Equation: F = MSB ÷ MSW, where MSB = SSB ÷ (k − 1) and MSW = SSW ÷ (N − k). SSB = Σ nᵢ(x̄ᵢ − x̄)², SSW = Σ Σ (x − x̄ᵢ)². η² = SSB ÷ SST.
Method: Fisher one-way ANOVA per ISO 16269-1. The p-value is computed from the F distribution itself (incomplete beta function), not read from a table. η² is the share of total variation explained by the grouping.
Assumptions: the groups are independent random samples from approximately normal populations with equal variances; the test compares means, not medians.
Limitations: a significant F only says at least one mean differs — it does not say which pair; follow up with a post-hoc test (for example Tukey HSD). Unequal variances or strong skew distort the F test.
Rounding: F to 4 decimal places; p to 4 decimal places; η² to 4 decimal places; intermediates unrounded.
This is a calculation aid, not a laboratory report — confirm against your accredited method before citing a value.
Method: Fisher one-way ANOVA per ISO 16269-1. The p-value is computed from the F distribution itself (incomplete beta function), not read from a table. η² is the share of total variation explained by the grouping.
Assumptions: the groups are independent random samples from approximately normal populations with equal variances; the test compares means, not medians.
Limitations: a significant F only says at least one mean differs — it does not say which pair; follow up with a post-hoc test (for example Tukey HSD). Unequal variances or strong skew distort the F test.
Rounding: F to 4 decimal places; p to 4 decimal places; η² to 4 decimal places; intermediates unrounded.
This is a calculation aid, not a laboratory report — confirm against your accredited method before citing a value.
Worked example: Groups (6,8,4,5,3,4), (8,12,9,11,6,8), (13,9,11,8,7,12): F = 9.2647, df 2 and 15, p = 0.0024, η² = 0.5526 — significant at α = 0.05.
Enter values above to see results.
With only two groups, the one-way ANOVA gives the same p as the equal-variance t-test. Tool 306 of 500 — GIFSQ
