diff --git a/03_anova/powersim-anova.R b/03_anova/powersim-anova.R
index 7f4ef02..215aa01 100644
--- a/03_anova/powersim-anova.R
+++ b/03_anova/powersim-anova.R
@@ -63,7 +63,7 @@ dat <- data.frame(
   A = factor(rep(1:2, each = n/2), labels = c("low", "high")),
   B = factor(rep(rep(1:2, each = n/4), 2), labels = c("low", "high"))
 )
-X <- model.matrix(~ A*B, dat)
+X <- model.matrix(~ A * B, dat)
 unique(X)
 beta <- c(mu = 30, a2 = 30, b2 = 5, ab22 = 12)
 means <- X %*% beta
@@ -86,7 +86,7 @@ boxplot(t(out))
 
 pval <- replicate(2000, {
   y <- means + rnorm(n, sd = 10)
-  m <- aov(y ~ A*B, dat)
+  m <- aov(y ~ A * B, dat)
   summary(m)[[1]]$"Pr(>F)"[3]      # test of interaction
 })
 mean(pval < 0.05)
diff --git a/05_mixed1/powersim-lmm.R b/05_mixed1/powersim-lmm.R
index fee09f4..362244e 100644
--- a/05_mixed1/powersim-lmm.R
+++ b/05_mixed1/powersim-lmm.R
@@ -5,8 +5,8 @@
 #' bibliography: ../lit.bib
 #' ---
 
-library(lattice)
-library(lme4)
+library("lattice")
+library("lme4")
 
 #' # Reanalysis