Module 9 · Lesson 12 of 22
ANOVA laboratory
Learning objectives
- Run a one-way ANOVA calculation in a free spreadsheet.
- Interpret F, degrees of freedom and p-value with practical follow-up.
- Recognise when to use planned contrasts or non-parametric tests.
Core idea
ANOVA partitions total variation into between-group and within-group components; F = MS_between / MS_within. A significant omnibus F does not identify which pairs differ.
Spreadsheet lab
- Group means: =AVERAGEIF(group, "A", value).
- SSB = Σ n_i (x̄_i − x̄)²; SSW = Σ (x_ij − x̄_i)².
- df_between = k−1; df_within = N−k.
- F = (SSB/df_between)/(SSW/df_within); p = =F.DIST.RT(F, df1, df2).
- Follow with planned contrasts; adjust for multiplicity if unplanned.
Garment-factory example
Seam strength across four needle types (n=15 each) gives F(3,56) = 6.4, p < 0.001. Post-hoc pairwise comparison shows needle B underperforms A and C; D is comparable to A.
Method
- Plot group distributions first.
- Compute means, SSB, SSW, F, p.
- Check residual normality and equal variance; use Welch or Kruskal-Wallis if violated.
Common mistakes
- Concluding which group is best from the omnibus F alone.
- Running many unplanned pairwise t-tests without adjustment.
Knowledge check
Pick one answer per question. Explanations appear after you submit.
1. In one-way ANOVA with k groups and N observations, df for the F test are:
2. Which function converts an F statistic to a right-tail p-value?
Author: Sanjeewa Dehiwalage · Last reviewed: 2026-07-21