Description

Saket Choudhary (USCID: 2170058637) (skchoudh@usc.edu)
Chapter 13: 12
data <- read.csv(‘case1301.csv’) data$Cover <- data$Cover/100
data$Cover <- log(data$Cover/(1-data$Cover)) grandmean <- mean(data$Cover)
agg <- aggregate(Cover ~ Treat, data, mean) agg
## Treat Cover
## 1 CONTROL 0.1804836
## 2 f -0.3136515 ## 3 fF -0.8214197 ## 4 L -1.7119924 ## 5 Lf -2.0043847 ## 6 LfF -2.7246679
agg1 <- aggregate(Cover ~ Treat + Block, data, mean) agg1
## Treat Block Cover
## 1 CONTROL B1 -1.51180059
## 2 f B1 -1.62171030 ## 3 fF B1 -2.04909167 ## 4 L B1 -3.17805383 ## 5 Lf B1 -3.21026883 ## 6 LfF B1 -4.24347007 ## 7 CONTROL B2 -0.94235279
## 8 f B2 -1.30770463 ## 9 fF B2 -1.96591282 ## 10 L B2 -2.51451819 ## 11 Lf B2 -3.11381700 ## 12 LfF B2 -3.21026883 ## 13 CONTROL B3 1.11226627
## 14 f B3 0.22200404 ## 15 fF B3 -0.12058103 ## 16 L B3 -0.31084411 ## 17 Lf B3 -1.55687711 ## 18 LfF B3 -2.53258512 ## 19 CONTROL B4 2.84798715
## 20 f B4 1.83818418 ## 21 fF B4 0.63823686 ## 22 L B4 -0.80683089 ## 23 Lf B4 -0.52153713
## 24 LfF B4 -1.92617786
## 25 CONTROL B5 -0.27157495
## 26 f B5 -0.68573964
## 27 fF B5 -0.68437097
## 28 L B5 -1.39946308
## 29 Lf B5 -2.62903695
## 30 LfF B5 -2.84798715
## 31 CONTROL B6 0.71069284
## 32 f B6 -0.18363476
## 33 fF B6 -0.40616081
## 34 L B6 -1.22917369
## 35 Lf B6 -0.66390985
## 36 LfF B6 -1.89142592
## 37 CONTROL B7 -0.78507724
## 38 f B7 -0.08085342
## 39 fF B7 -0.73537410
## 40 L B7 -2.59694117
## 41 Lf B7 -2.58524200
## 42 LfF B7 -2.37986447
## 43 CONTROL B8 0.28372826
## 44 f B8 -0.68975734
## 45 fF B8 -1.24810310
## 46 L B8 -1.66011416
## 47 Lf B8 -1.75438883
## 48 LfF B8 -2.76556416
Part (a)
means <- agg$Cover variance <- var(means) variance
## [1] 1.212415
16*variance ## [1] 19.39864
which is what is in Display 13.11
Part (b)
#block.averages <- c(-2.64, -2.18, -.53, .34, -1.42, -.61, -1.53, -1.31) agg2 <- aggregate(Cover ~ Block, agg1, mean) variance.block.averages <- var(agg2$Cover) agg2
## Block Cover
## 1 B1 -2.6357325
## 2 B2 -2.1757624 ## 3 B3 -0.5311028 ## 4 B4 0.3449771 ## 5 B5 -1.4196955 ## 6 B6 -0.6106020 ## 7 B7 -1.5272254
## 8 B8 -1.3056999

## [1] 10.89123
which is same as what is in Display 13.11 Part (c)
cell48.variance <- var(agg1$Cover) 2*cell48.variance
## [1] 4.009835
which is same as model mean square in Display 13.10 Part (d)
fit <- aov(Cover ~ Treat + Block + Block*Treat, data=data)
s <- summary(fit) s
## Df Sum Sq Mean Sq F value Pr(>F)
## Treat 5 96.99 19.399 64.055 <2e-16 ***
## Block 7 76.24 10.891 35.963 <2e-16 ***
## Treat:Block 35 15.23 0.435 1.437 0.121
## Residuals 48 14.54 0.303
## —
## Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ‘ 1
block.ss <- 76.2386 treatment.ss <- 96.9932 interaction.ss <- 15.2304 between.ss <- 188.4622
between.ss – (block.ss+treatment.ss)
## [1] 15.2304
which is the same as interaction.ss(interaction sum of squares)