5.1.3a: The Additive Model
- Page ID
- 33638
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- Obtain the ANOVA table with interaction.
- Obtain the ANOVA table without interaction.
- Obtain estimators and CIs for means for each treatment level.
- Obtain Tukey’s multiple comparisons CIs and grouping.
1. Load the glucose in blood serum data by using the following commands:
setwd("~/path-to-folder/")
glucose_data <- read.table("glucose_data.txt",header=T)
attach(glucose_data)
2. Obtain the ANOVA table with interaction by using the following commands:
anova<-aov(glucose ~ factor(method) + factor(doping) + factor(method)*factor(doping),data=glucose_data) summary(anova) Df Sum Sq Mean Sq F value Pr(>F) factor(method) 1 264 264 98.347 3.92e-07 *** factor(doping) 2 57026 28513 10632.526 < 2e-16 *** factor(method):factor(doping) 2 14 7 2.577 0.117 Residuals 12 32 3 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Here we can see that the interaction term is not significant, and we can drop it from the model. Also, notice that I have defined method and doping as factors since they have numeric values.
3. Obtain the ANOVA table without interaction by using the following commands:
anova1<-aov(glucose ~ factor(method) + factor(doping),data=glucose_data) summary(anova1) Df Sum Sq Mean Sq F value Pr(>F) factor(method) 1 264 264 80.27 3.58e-07 *** factor(doping) 2 57026 28513 8677.63 < 2e-16 *** Residuals 14 46 3 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
The Error SS is now 46.001, which is the sum of the interaction SS and the error SS of the model with the interaction. The df values were also added the same way.
4. Obtain estimators and CIs for means for each treatment level by using the following commands:
library(lsmeans) lsmeans(anova1,"method") method lsmean SE df lower.CL upper.CL 1 123 0.604 14 122 125 2 116 0.604 14 114 117 Results are averaged over the levels of: doping Confidence level used: 0.95 lsmeans(anova1,"doping") doping lsmean SE df lower.CL upper.CL 1 43.7 0.74 14 42.1 45.3 2 136.8 0.74 14 135.2 138.4 3 178.3 0.74 14 176.7 179.9 Results are averaged over the levels of: method Confidence level used: 0.95
5. Obtain Tukey’s multiple comparisons CIs and grouping by using the following commands:
tukey_multiple_comparisons<-TukeyHSD(anova1,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 = glucose ~ factor(method) + factor(doping), data = glucose_data) $`factor(method)` diff lwr upr p adj 1-2 7.655556 5.822828 9.488283 4e-07 $`factor(doping)` diff lwr upr p adj 2-1 93.10000 90.36089 95.83911 0 3-1 134.61667 131.87755 137.35578 0 3-2 41.51667 38.77755 44.25578 0 tukey_grouping<-multcompLetters4(anova1,tukey_multiple_comparisons) print(tukey_grouping) $`factor(method)` 1 2 "a" "b" $`factor(doping)` 3 2 1 "a" "b" "c" detach(glucose_data)