The PLANTS2 data file gives data on four different species of plants grown in a

Question

The PLANTS2 data file gives data on four different species of plants grown in a laboratory. The species are Leucaena leucocephala, Acacia saligna, Prosopis juliflora, and Eucalyptus citriodora. The researchers who collected these data were interested in commercially growing these plants in parts of the country of Jordan where there is very little rainfall. To examine the effect of water, they varied the amount per day from 50 millimeters (mm) to 650 mm in 100 mm increments. There were four plants per species-by-water combination. There are two response variables. They are fresh biomass and dry biomass. High values for both of these variables are desirable.

Run a separate one-way analysis of variance for both response variables for each water level. If there is evidence that the species are not all the same, use a multiple comparisons procedure to determine which pairs of species are significantly different. In what way, if any, do the differences appear to vary by water level? Write a short summary of your conclusions.

http://www.webassign.net/mintrostat5/plants2.txt

Explanation / Answer

The complete R program for the problem is given below:

> tt <- read.csv("clipboard",sep=" ")
> head(tt)
obs species water fbiomass dbiomass
1   1       1     1   105.13    37.65
2   2       1     1   138.95    48.85
3   3       1     1    90.05    38.85
4   4       1     1   102.25    36.91
5   5       1     2   207.90    74.35
6   6       1     2   157.15    63.65
> tt$water <- as.factor(tt$water)
> tt$species <- as.factor(tt$species)
> fbiomass_aov <- aov(fbiomass~species+water,tt)
> dbiomass_aov <- aov(dbiomass~species+water,tt)
> summary(fbiomass_aov);summary(dbiomass_aov)
             Df Sum Sq Mean Sq F value Pr(>F)   
species       3 458295 152765   71.52 <2e-16 ***
water         6 491948   81991   38.38 <2e-16 ***
Residuals   102 217886    2136                  
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
             Df Sum Sq Mean Sq F value Pr(>F)   
species       3 50524   16841   65.77 <2e-16 ***
water         6 56624    9437   36.86 <2e-16 ***
Residuals   102 26117     256                  
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
> library(multcomp)
Loading required package: mvtnorm
Loading required package: survival
Loading required package: TH.data
Loading required package: MASS

Attaching package: ‘TH.data’

The following object is masked from ‘package:MASS’:

    geyser

Warning messages:
1: package ‘multcomp’ was built under R version 3.2.4
2: package ‘TH.data’ was built under R version 3.2.4
> f_species_mult <- glht(fbiomass_aov,linfct=mcp(species="Dunnett"),alternative="two.sided")
> f_species_mult

         General Linear Hypotheses

Multiple Comparisons of Means: Dunnett Contrasts

Linear Hypotheses:
           Estimate
2 - 1 == 0    48.92
3 - 1 == 0   -85.26
4 - 1 == 0 -109.72

> d_species_mult <- glht(dbiomass_aov,linfct=mcp(species="Dunnett"),alternative="two.sided")
> d_species_mult

         General Linear Hypotheses

Multiple Comparisons of Means: Dunnett Contrasts

Linear Hypotheses:
           Estimate
2 - 1 == 0   -3.694
3 - 1 == 0 -36.658
4 - 1 == 0 -49.777

> f_water_mult

         General Linear Hypotheses

Multiple Comparisons of Means: Dunnett Contrasts

Linear Hypotheses:
           Estimate
2 - 1 == 0    35.71
3 - 1 == 0    73.08
4 - 1 == 0   107.11
5 - 1 == 0   152.10
6 - 1 == 0   180.80
7 - 1 == 0   182.05

> d_water_mult <- glht(dbiomass_aov,linfct=mcp(water="Dunnett"),alternative="two.sided")
> d_water_mult

         General Linear Hypotheses

Multiple Comparisons of Means: Dunnett Contrasts

Linear Hypotheses:
           Estimate
2 - 1 == 0    14.89
3 - 1 == 0    26.76
4 - 1 == 0    40.68
5 - 1 == 0    51.78
6 - 1 == 0    64.61
7 - 1 == 0    61.13

If there is evidence that the species are not all the same, use a multiple comparisons procedure to determine which pairs of species are significantly different.

There is evidence that the species are not all the same since the p-value for species as well as water are signifcant. The multiple comparison procedure shows that difference for fresh biomass is largest between the group 4 and 1, while the same for dry biomass shows it is largest for the group 4 and 1.

In what way, if any, do the differences appear to vary by water level? Write a short summary of your conclusions.

The difference are significant for the water level too. It is clear from the water level multiple comparison test that higher water level gives higher yield of the biomass for both fresh and dry biomass.

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