powersim_workshop_2026/04_ancova/exercises-ancova2.md

Exercise: Analysis and power simulation for baseline/follow-up measurements

MASS anorexia data

Data preparation

data(anorexia, package = "MASS")
dat <-
  subset(anorexia, Treat != "Cont") |>  # exclude control group
  droplevels()                          # drop empty factor levels
lbs2kg <- 0.4535924
dat$Prewt  <- lbs2kg * dat$Prewt        # to kg
dat$Postwt <- lbs2kg * dat$Postwt
lattice::xyplot(Postwt ~ Prewt, dat, groups = Treat,
                type = c("g", "r", "p"), auto.key = TRUE)

1. Analyze the original data:

   • In R, see ?MASS::anorexia
   • Estimate the average treatment effect (ATE) for FT relative to CBT.
   • What is the 95% CI for the ATE?
   • What are the pre- and post-weight means for the two groups?
   • What are the baseline-adjusted means for the two groups?

2. Run a power simulation for a replication study:

   • Draw plausible pre-weights.
   • Specify the minimum relevant effect.
   • Set the remaining parameters to plausible values.
   • What is the sample size required for the test to detect the effect with 80% power?
   • How robust is the power simulation when you repeat it with a new set of pre-weights? Try it!
   • Recover the parameters of the ANCOVA model.

3. Create a renderable R script or an R Markdown file that includes

   • a header with title, author, date
   • at least one section head line
   • the homework questions and your answers
   • the R code, output, and plots (if any)

   Render the R or Rmd file to HTML.