power_analysis.Rmd

---
title: "Power analysis"
output: html_notebook
---

```{r}
library(tidyverse)
library(WebPower)
```

### Minimum effect size detectable with full sample

```{r}
wp.correlation(n = 640, r = NULL, power = .8, alpha = 0.0125, p = 4)

```
### Minimum effect size detectable with a partial sample (25% missing)

```{r}
wp.correlation(n = 480, r = NULL, power = .8, alpha = 0.0125, p = 4)
```
In both cases, a small effect size is detectable (r 0.13 - 0.15)

### Power curve

```{r}
get_power <- function(eff_size){

  wp_obj <- wp.correlation(n = seq(440, 640, 20), r = eff_size, power = NULL, alpha = 0.0125, p = 4)

  bind_cols(n = wp_obj$n, power = wp_obj$power)
}

power_df <-
tibble(r = seq(0.1, 0.2, 0.01)) %>% 
  mutate(power = map(r, get_power)) %>% 
  unnest(power) %>% 
  mutate(power_dicht = case_when(power >= 0.8 ~ "> 80%",
                                 power >= 0.7 & power < 0.8 ~ "> 70%",
                                 TRUE ~ "< 70%"))
  
power_df %>% 
  ggplot(aes(x = r, y = n, fill = power)) +
  geom_tile() +
  geom_tile(data = power_df %>% filter(power >= 0.8),
            color = "midnightblue") +
  geom_tile(data = power_df %>% filter(power >= 0.7 & power < 0.8),
            color = "gray") +
  labs(x = "Pearson's (partial) r", y = "Sample size", fill = "Power\n",
       title = "Power curve for detecting Pearon's r with four confounders",
       subtitle = "Blue outlines indicate points with 80% power, gray with 70% power") +
  scale_x_continuous(limits = c(.09, .21),
                     expand = c(0, 0),
                     breaks = seq(.1, .2, by = 0.02)
                     ) +
  scale_y_continuous(limits = c(420, 660),
                     expand = c(0, 0),
                     breaks = seq(440, 640, by = 40)) +
  scale_fill_continuous(breaks = seq(0.2, 1, 0.2),
                        limits = c(0.2, 1),
                        labels = scales::percent) +
  theme_light() +
  theme(panel.grid = element_blank(),
        aspect.ratio = .75,
        panel.border = element_blank())

ggsave("plots/power_analysis.png", scale = 2)
```