I would like to do Tukey HSD post hoc tests for a repeated measure ANOVA. The entered formula "TukeyHSD" returns me an error. I can't find the answer in the forum. Can I ask for help?
"treat" is repeated measures factor, "vo2" is dependent variable.
Below is a script that is producing this error:
my_data <- data.frame(
stringsAsFactors = FALSE,
id = c(1L,2L,3L,4L, 5L,1L,2L,3L,4L,5L,1L,2L,3L,4L,5L,1L,2L,3L,4L,5L),
treat = c("o","o","o","o","o","j","j","j","j","j","z","z","z","z","z","w","w","w","w","w"),
vo2 = c("47.48","42.74","45.23","51.65","49.11","51.00","43.82","49.88","54.61","52.20","51.31",
"47.56","50.69","54.88","55.01","51.89","46.10","50.98","53.62","52.77"))
summary(rm_result <- aov(vo2~factor(treat)+Error(factor(id)), data = my_data))
TukeyHSD(rm_result, "treat", ordered = TRUE)
TukeyHSD() can't work with the aovlist result of a repeated measures ANOVA. As an alternative, you can fit an equivalent mixed effects model with e.g. lme4::lmer() and do the post-hoc tests with multcomp::glht().
my_data$vo2 <- as.numeric(my_data$vo2)
my_data$treat <- factor(my_data$treat)
m <- lme4::lmer(vo2 ~ treat + (1|id), data = my_data)
summary(multcomp::glht(m, linfct=mcp(treat="Tukey")))
# Simultaneous Tests for General Linear Hypotheses
#
# Multiple Comparisons of Means: Tukey Contrasts
#
#
# Fit: lmer(formula = vo2 ~ treat + (1 | id), data = my_data)
#
# Linear Hypotheses:
# Estimate Std. Error z value Pr(>|z|)
# o - j == 0 -3.060 0.583 -5.248 <0.001 ***
# w - j == 0 0.770 0.583 1.321 0.5497
# z - j == 0 1.588 0.583 2.724 0.0327 *
# w - o == 0 3.830 0.583 6.569 <0.001 ***
# z - o == 0 4.648 0.583 7.972 <0.001 ***
# z - w == 0 0.818 0.583 1.403 0.4974
# ---
# Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
# (Adjusted p values reported -- single-step method)
Comparison of the mixed effects model's ANOVA table with your repeated measures ANOVA results shows that both approaches are equivalent in how they treat the treat variable:
anova(m)
# Analysis of Variance Table
# npar Sum Sq Mean Sq F value
# treat 3 61.775 20.592 24.23
summary(rm_result)
# Error: factor(id)
# Df Sum Sq Mean Sq F value Pr(>F)
# Residuals 4 175.9 43.98
#
# Error: Within
# Df Sum Sq Mean Sq F value Pr(>F)
# factor(treat) 3 61.78 20.59 24.23 2.22e-05 ***
# Residuals 12 10.20 0.85
# ---
# Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1