- [taskus study - Google Docs](https://docs.google.com/document/d/1L3XR7T8cNQ5S2u2UFVaW95uEEr1m0gctfQZTCKOu_VY/edit)
- factors
- repetition: old/new headlines (30/30; 60 in total) (within)
- rating: accuracy/interest (between)
- veracity: true/false headlines (30/30) (within)
- outcome: truth/accuracy ratings
# power analysis
```r
# repetition effect
r
gt; rep_d <- c(0.33, 0.74, 0.590, 0.36)
rep_d_avg <- mean(rep_d)
rep_d_avg
[1] 0.505
rgt; # brashier 2020 cognition
# interaction effect for studies 1, 2, 3, 4
interact_d <- c(0.459, 0.905, 0.629, 0.505, 0.459)
interact_d_avg <- mean(interact_d)
interact_d_avg
[1] 0.5914
```
- repetition-rating interaction: d = 0.4, f = 0.2
- within-between design
- [[Brashier 2020 an initial accuracy focus prevents illusory truth]]
- study 1: Critically, we found an interaction between initial rating and repetition, F(1, 101) = 5.70, p = .019, η p2= 0.05.
- study 2: Overall, participants with an initial accuracy focus (initial truth ratings) (M = 0.49) made fewer “true” judgments than those in the standard (initial interest ratings) condition (M = 0.56), F(1, 97) = 4.02, p = .048, η p2= 0.04.
- study 3: Finally, they were less vulnerable to fluency (repeated M = 3.26, new M = 3.20) than participants in the standard condition (repeated M = 3.60, new M = 3.35) were, F(1,66) = 4.03, p = .049, η p2= 0.06.
gpower
![[Pasted image 20220128225918.png]]
```r
The design is set as
Model formula: y ~ REP * RATING + Error(subject/RATING)
Sample size per cell n = 80
```
```r
library(Superpower)
design_result <- ANOVA_design(design = "2b*2w",
label_list = c("RATING", "acc", "interest",
"REP", "new", "old"),
n = 80,
mu = c(0.48, 0.49, 0.50, 0.61),
sd = 0.22,
r = 0.5)
design_result
ANOVA_power(design_result, alpha_level = 0.05, nsims = 1000, verbose = TRUE)
ANOVA_exact(design_result, alpha_level = 0.05, verbose = TRUE)
f1 <- plot_power(design_result, max_n = 250, desired_power = 95)
f1
> f1
$anova_n
variable label n achieved_power desired_power
1 RATING Desired Power Achieved 194 95.04810 95
2 REP Desired Power Achieved 89 95.14165 95
3 RATING:REP Desired Power Achieved 127 95.03574 95
```
![[Pasted image 20220128233729.png]]
We have two between-subjects conditions (interest/accuracy), so we need 2x the number for 95% power.
---
If we have 200 participants in total (that’s what taskus say they’ll aim for), we should be able to detect all three effects in the model with at least 75% power (~75% for between-subject rating effect; >90% for the other two effects).
---
```
> d <- f * 2
> d
[1] 0.5897678
```