position<-c(rep(1,9),rep(2,9))
t<-c(800,825,850)
temp<-rep(t,6)
obs<-c(570,1063,565,565,1080,510,583,1043,590,528,988,526,547,1026,538,521,1004,532)
dat<-data.frame(position,temp,obs)
library(GAD)## Warning: package 'GAD' was built under R version 4.1.3## Loading required package: matrixStats## Warning: package 'matrixStats' was built under R version 4.1.3## Loading required package: R.methodsS3## Warning: package 'R.methodsS3' was built under R version 4.1.3## R.methodsS3 v1.8.2 (2022-06-13 22:00:14 UTC) successfully loaded. See ?R.methodsS3 for help.Question 1
position<-as.fixed(position)
temp<-as.fixed(temp)
model<-aov(obs~position*temp+position+temp)
GAD::gad(model)## Analysis of Variance Table
##
## Response: obs
## Df Sum Sq Mean Sq F value Pr(>F)
## position 1 7160 7160 15.998 0.001762 **
## temp 2 945342 472671 1056.117 3.25e-14 ***
## position:temp 2 818 409 0.914 0.427110
## Residual 12 5371 448
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1The p-value for position is 0.001762 (highly significant at 0.05)
The p-value for temp is 3.25e-14 (highly significant at 0.05)
The p-value for position and temp (0.427110) insignificant at 0.05
Question 2
position<-as.random(position)
temp<-as.random(temp)
model2<-aov(obs~position*temp+position+temp)
GAD::gad(model2)## Analysis of Variance Table
##
## Response: obs
## Df Sum Sq Mean Sq F value Pr(>F)
## position 1 7160 7160 17.504 0.0526583 .
## temp 2 945342 472671 1155.518 0.0008647 ***
## position:temp 2 818 409 0.914 0.4271101
## Residual 12 5371 448
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1The p-value for position is 0.0526583(significant at 0.05)
The p-value for temp is 0.0008647 (highly significant at 0.05)
The p-value for position and temp (0.4271101) insignificant at 0.05
Question 3
position<-as.fixed(position)
temp<-as.random(temp)
model3<-aov(obs~position*temp+position+temp)
GAD::gad(model3)## Analysis of Variance Table
##
## Response: obs
## Df Sum Sq Mean Sq F value Pr(>F)
## position 1 7160 7160 17.504 0.05266 .
## temp 2 945342 472671 1056.117 3.25e-14 ***
## position:temp 2 818 409 0.914 0.42711
## Residual 12 5371 448
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1The p-value for position is 0.05266 (significant at 0.05)
The p-value for temp is 3.25e-14 (highly significant at 0.05)
The p-value for position and temp (0.42711 ) insignificant at 0.05
#Question 4
#P-values (position, temperature, position:temperature) are nearly significant the same levels for question A,B and C