5.1.3: Two-Factor Factorial - Greenhouse Example (R)
- Page ID
- 33636
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)- Load the greenhouse data.
- Produce a boxplot to plot the differences in heights for each species organized by fertilizer.
- Produce a “means plot” (interval plot) to view the differences in heights for each species organized by fertilizer.
- Obtain the ANOVA table with interaction.
- Obtain Tukey’s multiple comparisons CIs, grouping, and plot.
1. Load the greenhouse data by using the following commands:
setwd("~/path-to-folder/")
greenhouse_2way_data <-read.table("greenhouse_2way_data.txt",header=T)
attach(greenhouse_2way_data)
2. Produce the Boxplot by using the following commands:
library("ggpubr")
boxplot(height ~ species*fertilizer, data = greenhouse_2way_data,
xlab = "Species", ylab = "Plant Height",
main="Distribution of Plant Height by Species",
frame = TRUE)
3. Produce the means plot (interval plot) by using the following commands:
library("gplots")
plotmeans(height ~ interaction(species,fertilizer), data = greenhouse_2way_data,connect=FALSE,n.label=FALSE,
xlab = "Fertilizer*species", ylab = "Plant Height",
main="Means Plot with 95% CI")
4. Obtain the ANOVA table with interaction by using the following commands:
anova<-aov(height~fertilizer+species+fertilizer*species,greenhouse_2way_data)
summary(anova)
# Df Sum Sq Mean Sq F value Pr(>F)
# fertilizer 3 745.4 248.48 73.10 2.77e-16 ***
# species 1 236.7 236.74 69.64 2.71e-10 ***
# fertilizer:species 3 50.6 16.86 4.96 0.00508 **
# Residuals 40 136.0 3.40
# ---
# Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
5. Obtain Tukey multiple comparisons of means with 95% family-wise confidence level by using the following commands:
library(multcomp) library(multcompView) tukey_multiple_comparisons<-TukeyHSD(anova,conf.level=0.95,ordered=TRUE) tukey_multiple_comparisons Tukey multiple comparisons of means 95% family-wise confidence level factor levels have been ordered Fit: aov(formula = height ~ fertilizer + species + fertilizer * species, data = greenhouse_2way_data) $fertilizer diff lwr upr p adj f2-control 5.608333 3.5908095 7.625857 0.0000000 f1-control 7.758333 5.7408095 9.775857 0.0000000 f3-control 10.783333 8.7658095 12.800857 0.0000000 f1-f2 2.150000 0.1324762 4.167524 0.0328745 f3-f2 5.175000 3.1574762 7.192524 0.0000002 f3-f1 3.025000 1.0074762 5.042524 0.0013828 $species diff lwr upr p adj SppB-SppA 4.441667 3.365986 5.517348 0 $`fertilizer:species` diff lwr upr p adj control:SppB-control:SppA 2.700000 -0.7025601 6.102560 0.2100548 f2:SppA-control:SppA 4.866667 1.4641065 8.269227 0.0010962 f1:SppA-control:SppA 7.600000 4.1974399 11.002560 0.0000003 f3:SppA-control:SppA 8.200000 4.7974399 11.602560 0.0000001 f2:SppB-control:SppA 9.050000 5.6474399 12.452560 0.0000000 f1:SppB-control:SppA 10.616667 7.2141065 14.019227 0.0000000 f3:SppB-control:SppA 16.066667 12.6641065 19.469227 0.0000000 f2:SppA-control:SppB 2.166667 -1.2358935 5.569227 0.4721837 f1:SppA-control:SppB 4.900000 1.4974399 8.302560 0.0009970 f3:SppA-control:SppB 5.500000 2.0974399 8.902560 0.0001745 f2:SppB-control:SppB 6.350000 2.9474399 9.752560 0.0000138 f1:SppB-control:SppB 7.916667 4.5141065 11.319227 0.0000001 f3:SppB-control:SppB 13.366667 9.9641065 16.769227 0.0000000 f1:SppA-f2:SppA 2.733333 -0.6692268 6.135893 0.1979193 f3:SppA-f2:SppA 3.333333 -0.0692268 6.735893 0.0584747 f2:SppB-f2:SppA 4.183333 0.7807732 7.585893 0.0072041 f1:SppB-f2:SppA 5.750000 2.3474399 9.152560 0.0000832 f3:SppB-f2:SppA 11.200000 7.7974399 14.602560 0.0000000 f3:SppA-f1:SppA 0.600000 -2.8025601 4.002560 0.9991227 f2:SppB-f1:SppA 1.450000 -1.9525601 4.852560 0.8685338 f1:SppB-f1:SppA 3.016667 -0.3858935 6.419227 0.1150225 f3:SppB-f1:SppA 8.466667 5.0641065 11.869227 0.0000000 f2:SppB-f3:SppA 0.850000 -2.5525601 4.252560 0.9922487 f1:SppB-f3:SppA 2.416667 -0.9858935 5.819227 0.3344595 f3:SppB-f3:SppA 7.866667 4.4641065 11.269227 0.0000001 f1:SppB-f2:SppB 1.566667 -1.8358935 4.969227 0.8173904 f3:SppB-f2:SppB 7.016667 3.6141065 10.419227 0.0000019 f3:SppB-f1:SppB 5.450000 2.0474399 8.852560 0.0002022
We can see the mean differences for fertilizer combinations, for the two species and for all fertilizer*species combinations. By using the confidence intervals or the p-values we can conclude which of these combinations are significant or not.
6. Obtain Tukey grouping by using the following commands:
tukey_grouping<-multcompLetters4(anova,tukey_multiple_comparisons) print(tukey_grouping) $fertilizer f3 f1 f2 control "a" "b" "c" "d" $species SppB SppA "a" "b" $`fertilizer:species` f3:SppB f1:SppB f2:SppB f3:SppA f1:SppA f2:SppA control:SppB control:SppA "a" "b" "b" "bc" "bc" "cd" "de" "e"
7. Obtain a plot of differences in mean response for fertilizer*species combinations by using the following commands:
par(mar=c(4.1,13,4.1,2.1)) plot(tukey_multiple_comparisons,las=2) detach(greenhouse_2way_data)
