Entering the data and sorting them out:
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.obs9 <- c(570, 1063, 565,
565, 1080, 510,
583, 1043, 590,
528, 988, 526,
547, 1026, 538,
521, 1004, 532)
temp9 <- rep(c(800,825,850),6)
position9 <- c(rep(1,9), rep(2,9))
temp9fixed <- as.fixed(temp9)
temp9random <- as.random(temp9)
position9fixed <- as.fixed(position9)
position9random <- as.random(position9)model1 <- aov(obs9~temp9fixed*position9fixed)
gad(model1)## Analysis of Variance Table
##
## Response: obs9
## Df Sum Sq Mean Sq F value Pr(>F)
## temp9fixed 2 945342 472671 1056.117 3.25e-14 ***
## position9fixed 1 7160 7160 15.998 0.001762 **
## temp9fixed:position9fixed 2 818 409 0.914 0.427110
## Residual 12 5371 448
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1For a significance level of alpha = 0.05, both the fixed temperature and position show significant main effects with p-value < 0.05. No significant 2-way interaction observed.
fixed temperature p-value = 3.25e-14
fixed position p-value = 0.001762
2-way interaction p-value = 0.427110
model2 <- aov(obs9~temp9random*position9random)
gad(model2)## Analysis of Variance Table
##
## Response: obs9
## Df Sum Sq Mean Sq F value Pr(>F)
## temp9random 2 945342 472671 1155.518 0.0008647 ***
## position9random 1 7160 7160 17.504 0.0526583 .
## temp9random:position9random 2 818 409 0.914 0.4271101
## Residual 12 5371 448
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1For a significance level of alpha = 0.05, only temperature shows significant main effects with p-value < 0.05. No significant 2-way interaction observed.
fixed temperature p-value = 0.0008647
fixed position p-value = 0.0526583
2-way interaction p-value = 0.427110
model3 <- aov(obs9~position9fixed*temp9random)
gad(model3)## Analysis of Variance Table
##
## Response: obs9
## Df Sum Sq Mean Sq F value Pr(>F)
## position9fixed 1 7160 7160 17.504 0.05266 .
## temp9random 2 945342 472671 1056.117 3.25e-14 ***
## position9fixed:temp9random 2 818 409 0.914 0.42711
## Residual 12 5371 448
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1For a significance level of alpha = 0.05, only temperature shows significant main effects with p-value < 0.05. No significant 2-way interaction observed.
fixed temperature p-value = 3.25e-14
fixed position p-value = 0.05266
2-way interaction p-value = 0.42711
When both the main effects are considered fixed, both of them show significant p-value < 0.05. When both of them are considered random effects, only temperature shows significant main effect with p-value < 0.05. When temperature is considered random and position fixed, the same case of only significant temperature main effect persists. So, whether both the factors are fixed or both random, or only temperature random-It is always a significant main effect. Position becomes a significant main effect only if it is considered a fixed effect with a fixed temperature.
In a the cases, the two-way interaction is always insignificant with p-value > 0.05.
library(GAD)
obs9 <- c(570, 1063, 565,
565, 1080, 510,
583, 1043, 590,
528, 988, 526,
547, 1026, 538,
521, 1004, 532)
temp9 <- rep(c(800,825,850),6)
position9 <- c(rep(1,9), rep(2,9))
temp9fixed <- as.fixed(temp9)
temp9random <- as.random(temp9)
position9fixed <- as.fixed(position9)
position9random <- as.random(position9)
model1 <- aov(obs9~temp9fixed*position9fixed)
gad(model1)
model2 <- aov(obs9~temp9random*position9random)
gad(model2)
model3 <- aov(obs9~position9fixed*temp9random)
gad(model3)