rgraphanovaposthoctukey

How to perform Post Hoc test, Tukey in agricolae package?

I did this with

library(lsmeans)

and

library(multcomp)
lm(Chlorophyll ~ Treatment + Stage + Treatment:Stage, "")

but I'm interested how to perform a post-hoc test after TW ANOVA in R. In agricolae package?

structure( list(Treatment = structure(c(3L, 3L, 3L, 3L, 3L, 3L,
    3L, 3L, 3L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 
    1L, 1L, 1L, 1L, 1L), .Label = c("Control", "Nitrogen", "Salt"
    ), class = "factor"), Stage = structure(c(1L, 1L, 1L, 2L, 2L, 
    2L, 3L, 3L, 3L, 1L, 1L, 1L, 2L, 2L, 2L, 3L, 3L, 3L, 1L, 1L, 1L, 
    2L, 2L, 2L, 3L, 3L, 3L), .Label = c("Green", "Pink", "Red"), class = "factor"), 
   Chlorophyll = c(0.2, 0.3, 0.4, 0.5, 0.3, 0.2, 0.5, 0.6, 0.7, 
   0.4, 0.6, 0.9, 0.2, 0.3, 0.5, 0.4, 0.2, 0.3, 0.5, 0.6, 0.8, 
   0.5, 0.4, 0.6, 0.2, 0.3, 0.1)), .Names = c("Treatment", "Stage", 
   "Chlorophyll"), class = "data.frame", row.names = c(NA, -27L)
    )

After mean separation, How Can we plot the graphs for each stage with the group numbers/letters?

plot

Solution

  • I assume you want to group data according to Treatment, Stage and the interactions Treatment*Stage.

    1. Before performing pairwise ANOVAs, it's instructive to calculate the number of comparisons: Treatment and Stage each have 3 levels, so we have choose(length(levels(df$Treatment)), 2) = 3 and choose(length(levels(df$Stage)), 2) comparisons, respectively; for the interaction term we have to consider all possibe combinations between Treatment and Stage

      combn_interact <- apply(
    expand.grid(levels(df$Treatment), levels(df$Stage)), 
    1, 
    paste, collapse = ":");
combn_interact;
#[1] "Control:Green"  "Nitrogen:Green" "Salt:Green"     "Control:Pink"
#[5] "Nitrogen:Pink"  "Salt:Pink"      "Control:Red"    "Nitrogen:Red"
#[9] "Salt:Red"

      resulting in a total of choose(length(combn_interact), 2) = 36 comparisons. So the interaction term results in a large number of pairwise comparisons.

    2. We perform multiple pairwise ANOVA analyses

      model <- aov(Chlorophyll ~ Treatment + Stage + Treatment*Stage, data = df);

    3. We now perform a post-hoc test to account for multiple hypothesis testing using PostHocTest from the DescTools library. Different methods to correct p-values exist, here we use Tukey's Honest Significant Difference test

      library(DescTools);
PostHocTest(model, method = "hsd")

#  Posthoc multiple comparisons of means : Tukey HSD
#    95% family-wise confidence level
#
#$Treatment
#                        diff     lwr.ci    upr.ci   pval
#Nitrogen-Control -0.02222222 -0.1939346 0.1494902 0.9418
#Salt-Control     -0.03333333 -0.2050457 0.1383791 0.8744
#Salt-Nitrogen    -0.01111111 -0.1828235 0.1606013 0.9851
#
#$Stage
#                  diff     lwr.ci     upr.ci   pval
#Pink-Green -0.13333333 -0.3050457 0.03837906 0.1455
#Red-Green  -0.15555556 -0.3272679 0.01615684 0.0797 .
#Red-Pink   -0.02222222 -0.1939346 0.14949017 0.9418
#
#$`Treatment:Stage`
#                                      diff      lwr.ci      upr.ci   pval
#Nitrogen:Green-Control:Green  0.000000e+00 -0.40832017  0.40832017 1.0000
#Salt:Green-Control:Green     -3.333333e-01 -0.74165350  0.07498684 0.1643
#Control:Pink-Control:Green   -1.333333e-01 -0.54165350  0.27498684 0.9586
#Nitrogen:Pink-Control:Green  -3.000000e-01 -0.70832017  0.10832017 0.2624
#Salt:Pink-Control:Green      -3.000000e-01 -0.70832017  0.10832017 0.2624
#Control:Red-Control:Green    -4.333333e-01 -0.84165350 -0.02501316 0.0327 *
#Nitrogen:Red-Control:Green   -3.333333e-01 -0.74165350  0.07498684 0.1643
#Salt:Red-Control:Green       -3.333333e-02 -0.44165350  0.37498684 1.0000
#Salt:Green-Nitrogen:Green    -3.333333e-01 -0.74165350  0.07498684 0.1643
#Control:Pink-Nitrogen:Green  -1.333333e-01 -0.54165350  0.27498684 0.9586
#Nitrogen:Pink-Nitrogen:Green -3.000000e-01 -0.70832017  0.10832017 0.2624
#Salt:Pink-Nitrogen:Green     -3.000000e-01 -0.70832017  0.10832017 0.2624
#Control:Red-Nitrogen:Green   -4.333333e-01 -0.84165350 -0.02501316 0.0327 *
#Nitrogen:Red-Nitrogen:Green  -3.333333e-01 -0.74165350  0.07498684 0.1643
#Salt:Red-Nitrogen:Green      -3.333333e-02 -0.44165350  0.37498684 1.0000
#Control:Pink-Salt:Green       2.000000e-01 -0.20832017  0.60832017 0.7303
#Nitrogen:Pink-Salt:Green      3.333333e-02 -0.37498684  0.44165350 1.0000
#Salt:Pink-Salt:Green          3.333333e-02 -0.37498684  0.44165350 1.0000
#Control:Red-Salt:Green       -1.000000e-01 -0.50832017  0.30832017 0.9927
#Nitrogen:Red-Salt:Green       3.885781e-16 -0.40832017  0.40832017 1.0000
#Salt:Red-Salt:Green           3.000000e-01 -0.10832017  0.70832017 0.2624
#Nitrogen:Pink-Control:Pink   -1.666667e-01 -0.57498684  0.24165350 0.8718
#Salt:Pink-Control:Pink       -1.666667e-01 -0.57498684  0.24165350 0.8718
#Control:Red-Control:Pink     -3.000000e-01 -0.70832017  0.10832017 0.2624
#Nitrogen:Red-Control:Pink    -2.000000e-01 -0.60832017  0.20832017 0.7303
#Salt:Red-Control:Pink         1.000000e-01 -0.30832017  0.50832017 0.9927
#Salt:Pink-Nitrogen:Pink      -5.551115e-17 -0.40832017  0.40832017 1.0000
#Control:Red-Nitrogen:Pink    -1.333333e-01 -0.54165350  0.27498684 0.9586
#Nitrogen:Red-Nitrogen:Pink   -3.333333e-02 -0.44165350  0.37498684 1.0000
#Salt:Red-Nitrogen:Pink        2.666667e-01 -0.14165350  0.67498684 0.3967
#Control:Red-Salt:Pink        -1.333333e-01 -0.54165350  0.27498684 0.9586
#Nitrogen:Red-Salt:Pink       -3.333333e-02 -0.44165350  0.37498684 1.0000
#Salt:Red-Salt:Pink            2.666667e-01 -0.14165350  0.67498684 0.3967
#Nitrogen:Red-Control:Red      1.000000e-01 -0.30832017  0.50832017 0.9927
#Salt:Red-Control:Red          4.000000e-01 -0.00832017  0.80832017 0.0574 .
#Salt:Red-Nitrogen:Red         3.000000e-01 -0.10832017  0.70832017 0.2624
#
#---
#Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

    4. Plotting distributions of values in every group requires pulling out observations for every relevant group of our 3 Treatment, 3 Stage and 36 Treatment*Stage comparisons. For example, for the 3 Treatment comparisons, you can do 

      df %>%
    ggplot(aes(x = Treatment, y = Chlorophyll)) +
    geom_boxplot() +
    geom_jitter(width = 0.2)

      enter image description here

      Consistent with results from the post-hoc test, there are no statistically significant changes in the mean between any of the three distributions.

      The other plots are as straightforward, and I'll leave that up to you.

    Sample data

    df <- structure( list(Treatment = structure(c(3L, 3L, 3L, 3L, 3L, 3L,
    3L, 3L, 3L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L,
    1L, 1L, 1L, 1L, 1L), .Label = c("Control", "Nitrogen", "Salt"
    ), class = "factor"), Stage = structure(c(1L, 1L, 1L, 2L, 2L,
    2L, 3L, 3L, 3L, 1L, 1L, 1L, 2L, 2L, 2L, 3L, 3L, 3L, 1L, 1L, 1L,
    2L, 2L, 2L, 3L, 3L, 3L), .Label = c("Green", "Pink", "Red"), class = "factor"),
   Chlorophyll = c(0.2, 0.3, 0.4, 0.5, 0.3, 0.2, 0.5, 0.6, 0.7,
   0.4, 0.6, 0.9, 0.2, 0.3, 0.5, 0.4, 0.2, 0.3, 0.5, 0.6, 0.8,
   0.5, 0.4, 0.6, 0.2, 0.3, 0.1)), .Names = c("Treatment", "Stage",
   "Chlorophyll"), class = "data.frame", row.names = c(NA, -27L)
    )