q3

library(GAD)

## Loading required package: matrixStats

## Loading required package: R.methodsS3

## R.methodsS3 v1.8.1 (2020-08-26 16:20:06 UTC) successfully loaded. See ?R.methodsS3 for help.

response <- c(570,1063,565,
              565,1080,510,
              583,1043,590,
              528,988,526,
              547,1026,538,
              521,1004,532)
temp <- rep(seq(1,3),6)
pos <- c(rep(1,9),rep(2,9))
pos

##  [1] 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2

data.frame(temp,pos,response)

##    temp pos response
## 1     1   1      570
## 2     2   1     1063
## 3     3   1      565
## 4     1   1      565
## 5     2   1     1080
## 6     3   1      510
## 7     1   1      583
## 8     2   1     1043
## 9     3   1      590
## 10    1   2      528
## 11    2   2      988
## 12    3   2      526
## 13    1   2      547
## 14    2   2     1026
## 15    3   2      538
## 16    1   2      521
## 17    2   2     1004
## 18    3   2      532

temp <- as.fixed(temp)
pos <- as.fixed(pos)
exp <- aov(response~temp+pos+temp*pos)
GAD::gad(exp)

## Analysis of Variance Table
## 
## Response: response
##          Df Sum Sq Mean Sq  F value   Pr(>F)    
## temp      2 945342  472671 1056.117 3.25e-14 ***
## pos       1   7160    7160   15.998 0.001762 ** 
## temp:pos  2    818     409    0.914 0.427110    
## Residual 12   5371     448                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

# 2-a
# p-value of temp 3.25e-14
# p-value of pos 0.001762
# p-value of interaction 0.427110

temp <- as.random(temp)
pos <- as.random(pos)
exp <- aov(response~temp+pos+temp*pos)
GAD::gad(exp)

## Analysis of Variance Table
## 
## Response: response
##          Df Sum Sq Mean Sq  F value    Pr(>F)    
## temp      2 945342  472671 1155.518 0.0008647 ***
## pos       1   7160    7160   17.504 0.0526583 .  
## temp:pos  2    818     409    0.914 0.4271101    
## Residual 12   5371     448                       
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

# 2-b
# p-value of temp 0.0008647
# p-value of pos 0.0526583
# p-value of interaction 0.427110

temp <- as.random(temp)
pos <- as.fixed(pos)
exp <- aov(response~temp+pos+temp*pos)
GAD::gad(exp)

## Analysis of Variance Table
## 
## Response: response
##          Df Sum Sq Mean Sq  F value   Pr(>F)    
## temp      2 945342  472671 1056.117 3.25e-14 ***
## pos       1   7160    7160   17.504  0.05266 .  
## temp:pos  2    818     409    0.914  0.42711    
## Residual 12   5371     448                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

# 2-c
# p-value of temp 3.25e-14
# p-value of pos 0.05266
# p-value of interaction 0.42711

# 2-d
# The interaction p-values has not changed in any case,  
# By comparing a and b parts, p-values of both temp and postion(factors) has changed.
# By comparing b and c parts, p-values of temp has changed