TukeyHSD()无法处理重复测量ANOVA的aovlist结果。作为替代方法，您可以使用lme4::lmer()拟合等效混合效应模型，然后使用multcomp::glht()进行事后检验。

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)

混合效应模型的ANOVA表与重复测量ANOVA结果的比较表明，两种方法在处理treat变量的方式方面是等效的：

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