Data from Jones and Forster (2014) provide an estimate of what we should expect for the difference (endogenous minus exogenous) between cuing effects (cued minus uncued), but specifically in the case of no stimulation (which we equate to beta/sham in the proposed new experiment). In order to extrapolate from these data to the new design for the purposes of estimating power, we have made the following assumptions /calculations:
The exogenous cuing effect (i.e., IOR) will be unaffected by alpha stimulation, but the endogenous cuing effect (i.e., facilitation of RTs) will be reduced to zero. Although not a conservative assumption, we consider this reasonable in combination with:
The size of the difference between endogenous and exogenous cueing effects (i.e. the 2x2 interaction) under sham/beta stimulation can be estimated as the lower bound of the 95% confidence interval estimated for this same RT difference from the Jones and Forster (2014) data – this yields a conservative anticipated effect of (at least) 76 ms.
The corresponding effect under alpha stimulation will be driven by only the (unaffected) exogenous cuing effect, estimated from Jones and Forster (2014) as 20 ms.
The difference between the values determined in steps 2 and 3 (~56 ms) equates to the anticipated 2x2x2 interaction. To derive a measure of Cohen’s D for this difference of differences between cuing effects, we must estimate the corresponding standard deviation. Here, we assume that under both alpha and beta/sham stimulation the SD of endogenous minus exogenous cuing effects will reflect that obtained without stimulation in Jones and Forster (2014). We then apply the variance sum law, with the conservative assumption of zero correlation between the difference scores that represent the 2x2 interaction in each half of the design (alpha vs. beta/sham).
By following these steps, we estimated a Cohen’s D (for the difference score best representing the anticipated 2x2x2 interaction) of 0.376. This yields N = 77 to achieve 90% power with alpha set to 0.05. Participants who do not meet the selection criteria or whose data is lost or damaged due to unforeseeable circumstances will not contribute to this sample size.
the text below comes from the corresponding OSF page
We used the software R and the package lavaan to conduct a power analysis using a Monte-Carlo simulation. We decided to base the power analysis on Hypothesis 4 because it has the highest requirements regarding sample size to achieve sufficient power. The population model was based on estimated model parameters from a previous data analysis in a German sample (N = 505) that was representative in terms of age and gender. The power for rejecting the H0 with regard to Hypothesis 4 for the 20-item version CAMSQ was estimated at 87% for N = 400. Given budget constraints, we did not aim for a larger sample.”