ANOVA power analysis - MCPower app

ANOVA builds its model from structured factor and covariate cards, not a typed formula. The panel has two sections — ANOVA factors and Covariates — each with its own Add button. Top to bottom:

1. Add factors

Click Add factor to create a factor card; factors are auto-named F1, F2, …. Each card's header contains:

  • An editable name input — rename the factor here.
  • A static factor kind badge (primary ANOVA factors are always factors).
  • A levels stepper — set the number of levels (minimum 2). Each non-reference level becomes one comparison, so a factor with k levels contributes k − 1 effect rows.
  • An Advanced (⚙) button — opens the Advanced dialog for that factor (see below).
  • A remove (trash) button.

Inside the card, effect rows list each comparison in order: the reference level appears first as disabled text, then one labelled effect row per non-reference level ([2], [3], …). Set the standardised effect size on each row — 0.20 / 0.50 / 0.80 (small / medium / large); prefer a value from prior evidence. See effect sizes and variable types.

Factor Advanced dialog

Click ⚙ on a factor card to open its Advanced dialog. Here you can:

  • Set level labels — rename the levels from their default index labels.
  • Set shares — the relative size of each level. Shares are weights: they don't need to sum to 100%, the app rescales them automatically. The optional Rescale shares to sum to 100% button just normalises the displayed numbers.
  • Choose the reference level — the level all others are compared against.
  • Sampled-shares toggle — simulate group proportions as random draws rather than fixed values.
Sparse levels

If any group's proportion times your sample size gives fewer than 5 observations, MCPower warns before simulating and excludes that factor at that N (its effects report power 0). The Diagnostics panel names the factor and the minimum N needed. Details: concepts/limitations#Sparse factor levels at small N.

2. Add covariates (optional)

Click Add covariate to create a covariate card; covariates are auto-named cov1, cov2, …. Unlike factor cards, the kind badge is switchable — choose continuous, binary, or factor. Set the standardised effect size in the card (continuous benchmarks: 0.10 / 0.25 / 0.40; binary or factor: 0.20 / 0.50 / 0.80). This is an ANCOVA design: the covariate is included as a predictor to adjust for. See variable types.

3. Robustness scenarios

The Robustness scenarios toggle in the status bar repeats every run under three perturbation sets — Optimistic (your exact settings, no perturbations), Realistic (moderate assumption violations), and Doomer (severe violations, a worst case) — so you get a range of power instead of one optimistic number. If even Doomer clears your target, the design is robust; if only Optimistic reaches it, increase the sample size. Each set's knobs are editable under Settings → Scenarios. See scenario analysis.

4. Optional settings

  • Tests & post-hoc corrections — pick the omnibus test and any pairwise comparisons between factor levels. Tukey is the standard all-pairwise post-hoc (Bonferroni, Holm also available); correcting controls false positives at the cost of power. multiple testing
  • Advanced — number of simulations (ANOVA defaults to 1,000), α (0.05), seed (2137), and the failed-simulation tolerance.