I have an existing study. What is my power?
Source:vignettes/from-existing-find-power.Rmd
from-existing-find-power.RmdSuppose we have a published study with a design similar to the one we are planning. We know the standard error and sample size from that study, we know how many respondents we can recruit, and we have a specific treatment effect in mind. We want to find the power—the probability that the study will produce a statistically significant result if the true effect equals our assumed value.
from_existing() piped into find_power()
answers this question.
Example
Ahler and Sood (2018) find that correcting respondents’ misperceptions of their out-party reduces affective polarization. In their experiment, respondents first report their perceptions of the percent of out-party members with certain demographic attributes, then receive the correct information. Compared to a control group, the treatment group evaluated supporters of the out-party more favorably on a 101-point feeling thermometer. Ahler and Sood estimate a treatment effect of 6.4 points with a standard error of 1.8, a 95% confidence interval of [3, 10], and a sample of 268 per condition.
Suppose we plan to run a similar experiment on a CES module with 1,000 respondents (500 per condition). The lower bound of Ahler and Sood’s 95% confidence interval is 3 points. We use this as our assumed effect, tau = 3.
library(powerrules)
from_existing(se_existing = 1.8, n_existing = 268) |>
find_power(n_planned = 500, tau = 3)#> -- Power Analysis ------------------------------------------------------
#> Design: balanced, between-subjects
#> Source: existing study
#> CI level: 90% (size-0.05 test of directional hypothesis)
#>
#> Inputs:
#> SE (existing) = 1.8
#> n (existing) = 268 per condition
#> n (planned) = 500 per condition (1,000 total)
#> tau = 3
#>
#> Predicted SE = sqrt(268 / 500) * 1.8 = 1.32 [Rule 7]
#> tau / SE = 3 / 1.32 = 2.28
#> Power = 1 - pnorm(1.64 - 2.28) = 74% [Rule 2]
#>
#> -- Manuscript sentence (edit as needed) --------------------------------
#> For a balanced, between-subjects design with 500 respondents per
#> condition (1,000 total) replicating an existing study with a standard
#> error of 1.8 (268 per condition), the predicted standard error is
#> 1.32. Using a one-sided test at the 0.05 level, the experiment has 74%
#> power to detect a treatment effect of 3 units.The output scales the existing SE to the planned sample size (Rule 7), then computes power for the assumed effect (Rule 2). With 500 per condition, the study has 74% power to detect a treatment effect of 3 points. This falls below the conventional 80% threshold.
What makes an existing study “close enough”?
The existing study and planned study should share the same design (balanced, between-subjects), a similar population, and the same or a similar outcome measure (Rainey 2026). The existing study can differ in sample size and treatment—the rule adjusts for sample size and the researcher supplies the assumed effect separately.
Interaction designs
For 2×2 factorial designs, from_existing() accepts
interaction = TRUE. The SE computation is unchanged—the
existing SE already encodes the design—but the output reports totals as
N = 4n and labels the design as a 2×2 factorial. See
vignette("interactions") for worked examples.