# data directly from the assignment
Ammonium <- c(2,2,30,30,2,2,30,30,2,2,30,30,2,2,30,30)
StirRate <- c(100,100,100,100,150,150,150,150,100,100,100,100,150,150,150,150)
Temperature <- c(8,8,8,8,8,8,8,8,40,40,40,40,40,40,40,40)
Density <- c(14.68,15.18,15.12,17.48,7.54,6.66,12.46,12.62,
10.95,17.68,12.65,15.96,8.03,8.84,14.96,14.96)
df <- data.frame(Ammonium, StirRate, Temperature, Density)
df$Ammonium <- factor(df$Ammonium)
df$StirRate <- factor(df$StirRate)
df$Temperature <- factor(df$Temperature)
mod <- lm(Density ~ Ammonium * StirRate * Temperature, data = df)
anova(mod)## Analysis of Variance Table
##
## Response: Density
## Df Sum Sq Mean Sq F value Pr(>F)
## Ammonium 1 44.389 44.389 11.1803 0.010175 *
## StirRate 1 70.686 70.686 17.8037 0.002918 **
## Temperature 1 0.328 0.328 0.0826 0.781170
## Ammonium:StirRate 1 28.117 28.117 7.0817 0.028754 *
## Ammonium:Temperature 1 0.022 0.022 0.0055 0.942808
## StirRate:Temperature 1 10.128 10.128 2.5510 0.148890
## Ammonium:StirRate:Temperature 1 1.519 1.519 0.3826 0.553412
## Residuals 8 31.762 3.970
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1coef(mod)## (Intercept) Ammonium30
## 14.930 1.370
## StirRate150 Temperature40
## -7.830 -0.615
## Ammonium30:StirRate150 Ammonium30:Temperature40
## 4.070 -1.380
## StirRate150:Temperature40 Ammonium30:StirRate150:Temperature40
## 1.950 2.465At α = 0.05:
Ammonium, Stir Rate, and their interaction (A×B) are significant.
Temperature and other interactions are not significant.
The density of silver powder is mainly affected by ammonium concentration and stir rate, and their combined effect matters.
library(agricolae)
A <- c("Organic compost", "Chemical fertilizer")
B <- c("Once per day", "Twice per day")
C <- c("22°C", "28°C")
treatments <- c(
"A1B1C1","A2B1C1","A1B2C1","A2B2C1",
"A1B1C2","A2B1C2","A1B2C2","A2B2C2"
)
design <- design.rcbd(trt = treatments, r = 3, seed = 123, randomization = TRUE)
design$book## plots block treatments
## 1 101 1 A1B2C2
## 2 102 1 A1B1C1
## 3 103 1 A2B2C2
## 4 104 1 A2B2C1
## 5 105 1 A1B1C2
## 6 106 1 A2B1C1
## 7 107 1 A2B1C2
## 8 108 1 A1B2C1
## 9 201 2 A2B2C1
## 10 202 2 A2B1C1
## 11 203 2 A2B2C2
## 12 204 2 A1B1C2
## 13 205 2 A1B2C2
## 14 206 2 A1B1C1
## 15 207 2 A2B1C2
## 16 208 2 A1B2C1
## 17 301 3 A1B1C1
## 18 302 3 A1B1C2
## 19 303 3 A1B2C2
## 20 304 3 A2B1C1
## 21 305 3 A1B2C1
## 22 306 3 A2B2C2
## 23 307 3 A2B1C2
## 24 308 3 A2B2C1