A process engineer wants to determine if a newer more costly gold alloy designed
ID: 3246573 • Letter: A
Question
A process engineer wants to determine if a newer more costly gold alloy designed computer chip is more efficient than the present (silicon) one being used. He wants to obtain an effective output voltage at both high and low temperatures, when tested at high and low signal strength. He hypothesizes that high signal strength will result in higher voltage output; lower temperature will result in higher output; and the gold alloy(newer) will result in higher output than the silicon material. He hopes that the main and interactions effects with the expensive gold will be minimal. The data that follows was gathered in testing of all combinations. What recommendation would you make?
Signal
Material
Temperature
Output Voltage
Low
Silicon
Low
7
High
Silicon
Low
16
Low
Gold
Low
8
High
Gold
Low
18
Low
Silicon
High
14
High
Silicon
High
10
Low
Gold
High
11
High
Gold
High
12
Signal
Material
Temperature
Output Voltage
Low
Silicon
Low
7
High
Silicon
Low
16
Low
Gold
Low
8
High
Gold
Low
18
Low
Silicon
High
14
High
Silicon
High
10
Low
Gold
High
11
High
Gold
High
12
Explanation / Answer
This is an ANOVA model, where we want to see the effect of three factors, Signal, Material and Temperature individually on the output voltage. Engineer's thinks that each of three factors has a significnt effect on voltage. So, we conduct a three factor ANOVA with two way interaction effect (because, as there is one one observtaion for each of the cell, so three way interaction can't be estimated). Following is the code to do it in R.
First to input the data in R:
signal<-rep(c("Low","High"), 4)
signal
material<-rep(c(rep("Silicon",2),rep("Gold",2)), 2)
material
temp<-rep(c("Low","High"),each=4)
temp
voltage<-c(7,16,8,18,14,10,11,12)
data<-data.frame(signal, material, temp, voltage)
data
Output:
> signal<-rep(c("Low","High"), 4)
> signal
[1] "Low" "High" "Low" "High" "Low" "High" "Low" "High"
> material<-rep(c(rep("Silicon",2),rep("Gold",2)), 2)
> material
[1] "Silicon" "Silicon" "Gold" "Gold" "Silicon" "Silicon" "Gold" "Gold"
> temp<-rep(c("Low","High"),each=4)
> temp
[1] "Low" "Low" "Low" "Low" "High" "High" "High" "High"
> voltage<-c(7,16,8,18,14,10,11,12)
> data<-data.frame(signal, material, temp, voltage)
> data
signal material temp voltage
1 Low Silicon Low 7
2 High Silicon Low 16
3 Low Gold Low 8
4 High Gold Low 18
5 Low Silicon High 14
6 High Silicon High 10
7 Low Gold High 11
8 High Gold High 12
>
Then following is the code to conduct the ANOVA in R:
Code:
anova<-aov(voltage~signal+material+temp+signal:material+material:temp+signal:temp,data=data)
summary(anova)
Output:
> anova<-aov(voltage~signal+material+temp+signal:material+material:temp+signal:temp,data=data)
> summary(anova)
Df Sum Sq Mean Sq F value Pr(>F)
signal 1 32.0 32.0 16.00 0.156
material 1 0.5 0.5 0.25 0.705
temp 1 0.5 0.5 0.25 0.705
signal:material 1 4.5 4.5 2.25 0.374
material:temp 1 2.0 2.0 1.00 0.500
signal:temp 1 60.5 60.5 30.25 0.114
Residuals 1 2.0 2.0
As we see that, all the p-values are greater than 0.05- the level of significance. So, we conclude that, there is no significant evidence to claim that, high signal strength will result in higher voltage output; lower temperature will result in higher output; and the gold alloy(newer) will result in higher output than the silicon material.
So, engineer's hypothesis is wrong. There is no effect of signal, material or temperature on Output Voltage.
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