fro experimental design 2 topic factorial design Q.1 The percentage of hardwood

Question

fro experimental design 2 topic factorial design

Q.1 The percentage of hardwood concentration in raw pulp, the Vat pressure and the cooking time of the pulp are being investigated on the strength of pulp for their effects on the strength of paper. These levels of hardwood concentration, three levels of pressure, and two cooking times are selected. A factorial experiment with two replicates is conducted, and the following data are obtained king time 3.0 Hours king time 4.0 Hours Pressure Pressure Concentratio 650 400 196.6 197.7199.8 198.4 199.6 200.6 196.0 196.0 199.4 198.6 200.4 200.9 198.5 196.0198.4197.5 198.7 199.6 197.2 196.9 197.6 198.1 198.0 199.0 197.5 195.6197.4197.6 197.0 198.5 196.6 196.21 198.1 198.4 197.8 199.8 500 650 400 500 4 Analyze the data and draw conclusion. Use 0.05 level of significance Apply Tukey's test for significant effects

Explanation / Answer

For the given problem, we need to write the R code "The ANOVA for the factorial experiment is performed in the R statistical software."

> tt <- read.csv("clipboard",sep=" ")
> head(tt)
Hardwood Cooking Pressure Strength
1        2       3      400    196.6
2        2       3      400    196.0
3        2       3      500    197.7
4        2       3      500    196.0
5        2       3      600    199.8
6        2       3      600    199.4
> tt$Hardwood <- as.factor(tt$Hardwood)
> tt$Cooking <- as.factor(tt$Cooking)
> tt$Pressure <- as.factor(tt$Pressure)
> Strength_aov <- aov(Strength~.,tt)
> summary(Strength_aov)
            Df Sum Sq Mean Sq F value    Pr(>F)   
Hardwood     2 8.8472 4.4236 6.9143 0.003392 **
Cooking      1 21.7778 21.7778 34.0396 2.217e-06 ***
Pressure     2 20.3739 10.1869 15.9226 1.937e-05 ***
Residuals   30 19.1933 0.6398                     
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Each of the factors is significant.

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