library(GAD)## Warning: package 'GAD' was built under R version 4.2.2## Loading required package: matrixStats## Loading required package: R.methodsS3## R.methodsS3 v1.8.2 (2022-06-13 22:00:14 UTC) successfully loaded. See ?R.methodsS3 for help.Pos<- rep(c(rep(1,3), rep(2,3)),3)
Temp<-c(rep(1,6), rep(2,6), rep(3,6))
Obs_9<-c(570,565,583,528,547,521,1063,1080,1043,988,1026,1004,565,510,590,526,538,532)
Data_9<-data.frame(Pos,Temp,Obs_9)Assume that both Temperature and Position are fixed effects. Report p-values
Data_9$Pos<-as.fixed(Data_9$Pos)
Data_9$Temp<-as.fixed(Data_9$Temp)
model_9A<-aov(Obs_9~Pos*Temp, data = Data_9)
summary(model_9A)## Df Sum Sq Mean Sq F value Pr(>F)
## Pos 1 7160 7160 15.998 0.00176 **
## Temp 2 945342 472671 1056.117 3.25e-14 ***
## Pos:Temp 2 818 409 0.914 0.42711
## Residuals 12 5371 448
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Comment: P value for Position: 0.00176, P value for Temp : 3.25e-14 and for Interaction Position: Temp is 0.42711
Assume that both Temperature and Position are random effects. Report p-values
Data_9$Pos<-as.random(Data_9$Pos)
Data_9$Temp<-as.random(Data_9$Temp)
model_9B<-aov(Obs_9~Pos*Temp, data = Data_9)
summary(model_9B)## Df Sum Sq Mean Sq F value Pr(>F)
## Pos 1 7160 7160 15.998 0.00176 **
## Temp 2 945342 472671 1056.117 3.25e-14 ***
## Pos:Temp 2 818 409 0.914 0.42711
## Residuals 12 5371 448
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Comment: P value for Position: 0.00176, P value for Temp : 3.25e-14 and for Interaction Position: Temp is 0.42711
Assume the Position effect is fixed and the Temperature effect is random. Report p-values
Data_9$Pos<-as.fixed(Data_9$Pos)
Data_9$Temp<-as.random(Data_9$Temp)
model_9C<-aov(Obs_9~Pos*Temp, data = Data_9)
summary(model_9C)## Df Sum Sq Mean Sq F value Pr(>F)
## Pos 1 7160 7160 15.998 0.00176 **
## Temp 2 945342 472671 1056.117 3.25e-14 ***
## Pos:Temp 2 818 409 0.914 0.42711
## Residuals 12 5371 448
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Comment: P value for Position: 0.00176, P value for Temp : 3.25e-14 and for Interaction Position: Temp is 0.42711
Comment on similarities and/or differences between the p-values in parts a,b,c.
Comment: As per above analysis, we found that there is no effect of having Fixed or Random effect of Position or Temperature on model. all p values are same for all kind of trials.