---
title: "Power for unbalanced designs"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{Power for unbalanced designs}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r, include = FALSE}
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)
```

```{r setup, message=FALSE}
library(anovapowersim)
```

`power_unbalanced()` is experimental and available only in the development
version of `anovapowersim`. Use it when the exact allocation, population means,
and standard deviations are already known. It simulates one fixed design; it
does not search over sample sizes or return calculated power.

## Define the cells

Define every cell with `cell_design()`. Factor values identify the cell, `n`
is the number of subjects in its between-subject group, and `m` is its
population mean. Name repeated-measures factors in `within`; all remaining
factors are between-subject factors. The common population SD is specified
separately with `unbalanced_covariance()`.

For repeated-measures designs, the same `n` must appear on every within-subject
row belonging to a given between-subject group.

```{r unbalanced-design, eval=FALSE}
unbalanced_design <- cell_design(
  group = "control",   time = "pre",  n = 22, m = 10.0,
  group = "control",   time = "post", n = 22, m = 11.0,
  group = "treatment", time = "pre",  n = 31, m = 10.1,
  group = "treatment", time = "post", n = 31, m = 12.4,
  within = "time"
)
```

The means define the complete effect pattern, including main effects and
interactions. A single marginal SD is shared across groups and within-subject
cells, preventing unequal cell sizes from being combined with unequal
variances in the classical ANOVA test.

Every factor must have at least two observed levels, and every factor-level
combination must be defined exactly once. If cells are missing,
`cell_design()` reports which ones. Supply `default_n` and `default_m`
together to fill missing cells automatically:

```{r unbalanced-default-fill, eval=FALSE}
cell_design(
  group = "control",   time = "pre",  n = 22, m = 10.0,
  group = "control",   time = "post", n = 22, m = 11.0,
  group = "treatment", time = "pre",  n = 31, m = 10.1,
  within = "time",
  default_n = 31, default_m = 12.4
)
```

## Define within-subject correlations

Use `unbalanced_covariance()` to define the common SD and, for repeated
measures, the correlation structure. `power_unbalanced()` constructs one
covariance matrix and uses it for every between-subject group.

If `covariance` is omitted, `power_unbalanced()` warns that it is using the
common `sd = 1` and, for repeated measures, correlation `0.5` for every pair.
Calling `unbalanced_covariance()` without `sd` likewise warns that `sd = 1` is
being used. When only some correlations are named, a separate warning reports
the number of undefined pairs: `default_correlation` applies only to those
undefined pairs and does not alter explicitly supplied correlations. For a
purely between-subject design, correlations do not apply and the warning
mentions only the common SD.

With one within-subject factor, pair names use its levels, such as
`"pre:post"`.

```{r unbalanced-power, eval=FALSE}
power_unbalanced(
  design = unbalanced_design,
  term = "group:time",
  covariance = unbalanced_covariance(
    sd = 2,
    default_correlation = 0.5,
    correlations = c("pre:post" = 0.7)
  ),
  n_sims = 5000,
  parallel = TRUE,
  seed = 123
)
```

## Interpret the result

The result reports simulated power, the common SD, partial eta squared from a
deterministic reference dataset matching the design assumptions, and the mean,
median, and 95% interval of partial eta squared across successful simulations.
These effect-size summaries describe the exact allocation, means, shared
variance, correlations, tested term, and sums-of-squares type supplied by the
user.

## Multiple within-subject factors

Name every repeated-measures factor in `cell_design()` and join their level
combinations with underscores in correlation-pair names:

```{r unbalanced-multi-within, eval=FALSE}
multi_within_design <- cell_design(
  group = "A", time = "pre",  cond = "control", n = 10, m = 0.0,
  group = "A", time = "pre",  cond = "treat",   n = 10, m = 0.5,
  group = "A", time = "post", cond = "control", n = 10, m = 0.2,
  group = "A", time = "post", cond = "treat",   n = 10, m = 1.0,
  group = "B", time = "pre",  cond = "control", n = 15, m = 0.0,
  group = "B", time = "pre",  cond = "treat",   n = 15, m = 0.6,
  group = "B", time = "post", cond = "control", n = 15, m = 0.3,
  group = "B", time = "post", cond = "treat",   n = 15, m = 1.4,
  within = c("time", "cond")
)

power_unbalanced(
  design = multi_within_design,
  term = "group:time:cond",
  covariance = unbalanced_covariance(
    correlations = c("pre_control:post_control" = 0.6)
  ),
  n_sims = 5000,
  seed = 123
)
```