8.2 Obtain estimates from a previous study
First we load and prepare the relative clause data for data analysis.
gg05e1 <- read.table("data/grodnergibsonE1crit.txt", header = TRUE)
gg05e1$so <- ifelse(gg05e1$condition == "objgap", 1 / 2, -1 / 2)
gg05e1$logrt <- log(gg05e1$rawRT)Next, fit the so-called maximal model. We will ignore the singularity warning as it won’t affect us in our simulations.
library(lme4)
m <- lmer(logrt ~ so +
(1 + so | subject) +
(1 + so | item),
data = gg05e1,
## "switch off" warnings:
control = lmerControl(calc.derivs = FALSE)
)## boundary (singular) fit: see help('isSingular')The model summary shows that we can reject the null hypothesis of no difference in relative clauses:
summary(m)$coefficients## Estimate Std. Error t value
## (Intercept) 5.883 0.05202 113.082
## so 0.124 0.04932 2.515Let’s focus on that effect for our power analysis. What is the prospective power of detecting this effect for a future study? Note that we never compute power for an existing study—that is called post-hoc power and is a pointless quantity to compute because once the p-value is known, the power is just a transformation of the p-value (Hoenig and Heisey 2001).
What we are doing below will look like post-hoc power because we are using existing data to compute power. However, what is crucially different in our approach is that (a) we remain unsure about the true effect, (b) we are making a statement about what the power properties would be if we ran the same study again, with new subjects, but in the same environment (lab, etc.). We are not making any claim about the power properties of the current experiment; that ship has already sailed, the data are already at hand! Once the data are analyzed, it’s too late to compute power for that particular data-set. A power analysis is only relevant for a design to be run in the future.