GIFSQ Tools · Module 16 — Statistics, Experimental Design & Research · Tool 320 of 500
Build a results table from group means, standard deviations and sample sizes: the weighted grand mean, the pooled standard deviation, and a clean table ready to copy into a report.
Try sample values — fills the form with the worked example below.
Saved on this device only.
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Grand mean
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Pooled SD
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Total N
Equation: Grand mean = Σ(nᵢ × x̄ᵢ) ÷ Σnᵢ. Pooled SD = √(Σ(nᵢ − 1)sᵢ² ÷ (Σnᵢ − k)). Group standard error SEᵢ = sᵢ ÷ √nᵢ.
Method: Weighted-mean and pooled-variance combination (standard textbook method; the pooled SD is the same quantity used in the equal-variance t-test and one-way ANOVA).
Assumptions: the groups estimate the same underlying quantity with a common variance; the pooled SD is only meaningful when the group SDs are similar.
Limitations: the builder combines summaries — it cannot recover information lost in the summaries, and it does not test whether the groups differ (use Tool 306 for that).
Rounding: grand mean and pooled SD to 2 decimal places; standard errors 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: Weighted-mean and pooled-variance combination (standard textbook method; the pooled SD is the same quantity used in the equal-variance t-test and one-way ANOVA).
Assumptions: the groups estimate the same underlying quantity with a common variance; the pooled SD is only meaningful when the group SDs are similar.
Limitations: the builder combines summaries — it cannot recover information lost in the summaries, and it does not test whether the groups differ (use Tool 306 for that).
Rounding: grand mean and pooled SD to 2 decimal places; standard errors 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: Groups with means 10, 12, 14, SDs 2, 2, 2 and n = 5 each: grand mean 12.00, pooled SD 2.00, total N = 15.
Enter values above to see results.
Saved on this device only — the table stays in this browser until you clear it. Tool 320 of 500 — GIFSQ
