---
title: "Comparison with G*Power"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{Comparison with G*Power}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

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

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

The balanced simulation and calculation-only functions accept
`gpower = TRUE` when results should follow G\*Power's noncentrality convention.
For within-subject designs, this corresponds to selecting G\*Power's
**as in Cohen (1988)** option.

## A typical 2 x 2 design

In a 2 x 2 mixed design, the default and G\*Power conventions usually give very
similar results. Here they differ by one participant per group:

```{r two-by-two}
default_2x2 <- power_n_calc(
  between = c(group = 2),
  within = c(time = 2),
  term = "group:time",
  target_pes = 0.08,
  power = 0.90
)

gpower_2x2 <- power_n_calc(
  between = c(group = 2),
  within = c(time = 2),
  term = "group:time",
  target_pes = 0.08,
  power = 0.90,
  gpower = TRUE
)

c(default = default_2x2$n_needed, gpower = gpower_2x2$n_needed)
```

Set `gpower = TRUE` in `power_n()`, `power_curve()`, `power_achieved()`, or
`power_sensitivity()` in the same way when running simulations.

## More than three within-subject levels

The conventions can diverge more noticeably for smaller samples and for terms
with more degrees of freedom, such as within-subject factors with more than
three levels. With four within-subject levels, the same inputs produce:

```{r four-levels}
default_4 <- power_n_calc(
  between = c(group = 2),
  within = c(time = 4),
  term = "group:time",
  target_pes = 0.08,
  power = 0.90
)

gpower_4 <- power_n_calc(
  between = c(group = 2),
  within = c(time = 4),
  term = "group:time",
  target_pes = 0.08,
  power = 0.90,
  gpower = TRUE
)

c(default = default_4$n_needed, gpower = gpower_4$n_needed)
```

In this case, use the package default, `gpower = FALSE`, so `target_pes`
continues to match the partial eta squared you supplied. Use `gpower = TRUE`
only when reproducing G\*Power's **as in Cohen (1988)** result is specifically
required.