Iris: ANOVA, Tukey HSD, and Compact Letter Display

Question

Do the three Iris species differ in sepal length, and which pairs differ from each other?

Data

data(iris)
summary(iris$Sepal.Length)

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  4.300   5.100   5.800   5.843   6.400   7.900 

table(iris$Species)

    setosa versicolor  virginica 
        50         50         50 

One-way ANOVA

fit <- aov(Sepal.Length ~ Species, data = iris)
summary(fit)

             Df Sum Sq Mean Sq F value Pr(>F)    
Species       2  63.21  31.606   119.3 <2e-16 ***
Residuals   147  38.96   0.265                   
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

The species factor is highly significant — at least one species mean differs from the others. ANOVA does not tell us which pairs differ; for that we use Tukey’s HSD post-hoc test.

Tukey HSD

tuk <- TukeyHSD(fit)
tuk

  Tukey multiple comparisons of means
    95% family-wise confidence level

Fit: aov(formula = Sepal.Length ~ Species, data = iris)

$Species
                      diff       lwr       upr p adj
versicolor-setosa    0.930 0.6862273 1.1737727     0
virginica-setosa     1.582 1.3382273 1.8257727     0
virginica-versicolor 0.652 0.4082273 0.8957727     0

Compact letter display

Means that share a letter are not significantly different at \(\alpha = 0.05\).

library(multcompView)

cld <- multcompLetters4(fit, tuk)
cld_letters <- cld$Species$Letters
cld_df <- data.frame(
  Species = names(cld_letters),
  cld     = unname(cld_letters)
)
cld_df

     Species cld
1  virginica   a
2 versicolor   b
3     setosa   c

Plot with letters

library(ggplot2)

y_label_pos <- max(iris$Sepal.Length) + 0.4

ggplot(iris, aes(Species, Sepal.Length, fill = Species)) +
  geom_boxplot(alpha = 0.7, outlier.shape = 1) +
  geom_text(
    data = cld_df,
    aes(x = Species, y = y_label_pos, label = cld),
    inherit.aes = FALSE, size = 6, fontface = "bold"
  ) +
  labs(
    y = "Sepal length (cm)",
    x = NULL
  ) +
  theme_minimal(base_size = 12) +
  theme(legend.position = "none")

Figure 1: Sepal length by Iris species. Means sharing a letter are not significantly different (Tukey HSD, α = 0.05).

Session info

sessionInfo()

R version 4.5.2 (2025-10-31)
Platform: aarch64-apple-darwin20
Running under: macOS Tahoe 26.3.1

Matrix products: default
BLAS:   /System/Library/Frameworks/Accelerate.framework/Versions/A/Frameworks/vecLib.framework/Versions/A/libBLAS.dylib 
LAPACK: /Library/Frameworks/R.framework/Versions/4.5-arm64/Resources/lib/libRlapack.dylib;  LAPACK version 3.12.1

locale:
[1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8

time zone: America/New_York
tzcode source: internal

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
[1] ggplot2_4.0.1       multcompView_0.1-10

loaded via a namespace (and not attached):
 [1] vctrs_0.6.5        cli_3.6.5          knitr_1.51         rlang_1.1.6       
 [5] xfun_0.55          otel_0.2.0         generics_0.1.4     S7_0.2.1          
 [9] jsonlite_2.0.0     labeling_0.4.3     glue_1.8.0         htmltools_0.5.9   
[13] scales_1.4.0       rmarkdown_2.30     grid_4.5.2         tibble_3.3.0      
[17] evaluate_1.0.5     fastmap_1.2.0      yaml_2.3.12        lifecycle_1.0.4   
[21] compiler_4.5.2     dplyr_1.1.4        RColorBrewer_1.1-3 pkgconfig_2.0.3   
[25] htmlwidgets_1.6.4  farver_2.1.2       digest_0.6.39      R6_2.6.1          
[29] tidyselect_1.2.1   dichromat_2.0-0.1  pillar_1.11.1      magrittr_2.0.4    
[33] withr_3.0.2        tools_4.5.2        gtable_0.3.6