5.2 ANOVA TABLE

dat <- read.csv("https://raw.githubusercontent.com/maryadepoju98/DesignExperiment/main/question5_2.csv")
dat
##            Source DF       SS       MS        F     P
## 1               A  1   0.0002  0.00020 0.000100 0.992
## 2               B  3 180.3780 60.12600 3.029690 0.093
## 3 Interaction(AB)  3   8.4790  2.82633 0.142416 0.932
## 4           Error  8 158.7970 19.84560       NA    NA
## 5           Total 15 347.6530       NA       NA    NA

Handwritten Calculations for Anova Table

please see the image for calculations

There are 2 replications. Factor B has 4 levels. By looking at the p values, and setting \(\alpha = 0.05\) we conclude that there is no significance between Factor A and B (interaction). However, Factor B is of significance.

5.9 Feed Rate and Drill Speed

Hypothesis

Factor A: Drill Speed

\(H_o: \alpha_i = 0 \;\; \forall \; i\)
\(H_a: \alpha_i \neq 0\) for some \(i\)

Factor B: Feed Rate

\(H_o: \beta_i = 0 \;\; \forall \; i\)
\(H_a: \beta_i \neq 0\) for some \(i\)

Factor AB Interaction between Drill Speed and Feed Rate

\(H_o: \alpha \beta_{ij} = 0 \;\; \forall \; i\)
\(H_a: \alpha \beta_{ij} \neq 0\) for some \(i\)

dat2 <-read.csv("https://raw.githubusercontent.com/maryadepoju98/DesignExperiment/main/question5_9")
dat2$drillSpeed<-as.factor(dat2$drillSpeed)
dat2$feedRate<-as.factor(dat2$feedRate)
model2<-lm(dat2$data~dat2$drillSpeed*dat2$feedRate)
interaction.plot(dat2$feedRate,dat2$drillSpeed,dat2$data, xlab = "Feed Rate", ylab = "Data")

anova(model2)
## Analysis of Variance Table
## 
## Response: dat2$data
##                               Df   Sum Sq  Mean Sq F value    Pr(>F)    
## dat2$drillSpeed                1 0.148225 0.148225 57.0096 6.605e-05 ***
## dat2$feedRate                  3 0.092500 0.030833 11.8590  0.002582 ** 
## dat2$drillSpeed:dat2$feedRate  3 0.041875 0.013958  5.3686  0.025567 *  
## Residuals                      8 0.020800 0.002600                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

At \(\alpha = 0.05\) We claim that factor A, factor B and the interaction are significant. We also reject the null hypothesis of all three test.