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data("InsectSprays")
summary(InsectSprays)## count spray
## Min. : 0.00 A:12
## 1st Qu.: 3.00 B:12
## Median : 7.00 C:12
## Mean : 9.50 D:12
## 3rd Qu.:14.25 E:12
## Max. :26.00 F:12anova1 <- aov(count ~ spray, data = InsectSprays)
summary(anova1)## Df Sum Sq Mean Sq F value Pr(>F)
## spray 5 2669 533.8 34.7 <2e-16 ***
## Residuals 66 1015 15.4
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1anova2 <- aov(sqrt(count) ~ spray, data = InsectSprays)
summary(anova2)## Df Sum Sq Mean Sq F value Pr(>F)
## spray 5 88.44 17.688 44.8 <2e-16 ***
## Residuals 66 26.06 0.395
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1library(agricolae)## Warning: package 'agricolae' was built under R version 4.1.2out <- LSD.test(anova1,"spray", p.adj="bonferroni")
out## $statistics
## MSerror Df Mean CV t.value MSD
## 15.38131 66 9.5 41.28318 3.045792 4.876648
##
## $parameters
## test p.ajusted name.t ntr alpha
## Fisher-LSD bonferroni spray 6 0.05
##
## $means
## count std r LCL UCL Min Max Q25 Q50 Q75
## A 14.500000 4.719399 12 12.2395786 16.760421 7 23 11.50 14.0 17.75
## B 15.333333 4.271115 12 13.0729119 17.593755 7 21 12.50 16.5 17.50
## C 2.083333 1.975225 12 -0.1770881 4.343755 0 7 1.00 1.5 3.00
## D 4.916667 2.503028 12 2.6562453 7.177088 2 12 3.75 5.0 5.00
## E 3.500000 1.732051 12 1.2395786 5.760421 1 6 2.75 3.0 5.00
## F 16.666667 6.213378 12 14.4062453 18.927088 9 26 12.50 15.0 22.50
##
## $comparison
## NULL
##
## $groups
## count groups
## F 16.666667 a
## B 15.333333 a
## A 14.500000 a
## D 4.916667 b
## E 3.500000 b
## C 2.083333 b
##
## attr(,"class")
## [1] "group"out1 <- LSD.test(anova2,"spray", p.adj="bonferroni")
out1## $statistics
## MSerror Df Mean CV t.value MSD
## 0.3948178 66 2.812433 22.3417 3.045792 0.7813094
##
## $parameters
## test p.ajusted name.t ntr alpha
## Fisher-LSD bonferroni spray 6 0.05
##
## $means
## sqrt(count) std r LCL UCL Min Max Q25
## A 3.760678 0.6243234 12 3.3985262 4.122831 2.645751 4.795832 3.388646
## B 3.876631 0.5768841 12 3.5144792 4.238784 2.645751 4.582576 3.533320
## C 1.244857 0.7630074 12 0.8827045 1.607009 0.000000 2.645751 1.000000
## D 2.164354 0.5033405 12 1.8022017 2.526506 1.414214 3.464102 1.933013
## E 1.809461 0.4963695 12 1.4473089 2.171613 1.000000 2.449490 1.652591
## F 4.018617 0.7512773 12 3.6564650 4.380769 3.000000 5.099020 3.533320
## Q50 Q75
## A 3.741657 4.210363
## B 4.061553 4.182054
## C 1.207107 1.732051
## D 2.236068 2.236068
## E 1.732051 2.236068
## F 3.872983 4.742557
##
## $comparison
## NULL
##
## $groups
## sqrt(count) groups
## F 4.018617 a
## B 3.876631 a
## A 3.760678 a
## D 2.164354 b
## E 1.809461 bc
## C 1.244857 c
##
## attr(,"class")
## [1] "group"#Question5
data1 <- read.table("quetion5.txt", header = T)
data1## Hum Temp Resp
## 1 Humidity_1 Temperature_1 35
## 2 Humidity_1 Temperature_1 25
## 3 Humidity_1 Temperature_1 26
## 4 Humidity_1 Temperature_2 35
## 5 Humidity_1 Temperature_2 31
## 6 Humidity_1 Temperature_2 37
## 7 Humidity_2 Temperature_1 28
## 8 Humidity_2 Temperature_1 22
## 9 Humidity_2 Temperature_1 21
## 10 Humidity_2 Temperature_2 23
## 11 Humidity_2 Temperature_2 19
## 12 Humidity_2 Temperature_2 18str(data1)## 'data.frame': 12 obs. of 3 variables:
## $ Hum : chr "Humidity_1" "Humidity_1" "Humidity_1" "Humidity_1" ...
## $ Temp: chr "Temperature_1" "Temperature_1" "Temperature_1" "Temperature_2" ...
## $ Resp: int 35 25 26 35 31 37 28 22 21 23 ...aov.out = aov(Resp ~ Hum + Temp + Hum:Temp, data=data1)
summary(aov.out)## Df Sum Sq Mean Sq F value Pr(>F)
## Hum 1 280.33 280.33 18.383 0.00266 **
## Temp 1 3.00 3.00 0.197 0.66913
## Hum:Temp 1 65.33 65.33 4.284 0.07225 .
## Residuals 8 122.00 15.25
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1LSD_Test<- LSD.test(aov.out, c("Hum", "Temp"))
LSD_Test #Difference in mean length## $statistics
## MSerror Df Mean CV t.value LSD
## 15.25 8 26.66667 14.64422 2.306004 7.352743
##
## $parameters
## test p.ajusted name.t ntr alpha
## Fisher-LSD none Hum:Temp 4 0.05
##
## $means
## Resp std r LCL UCL Min Max Q25 Q50
## Humidity_1:Temperature_1 28.66667 5.507571 3 23.46749 33.86584 25 35 25.5 26
## Humidity_1:Temperature_2 34.33333 3.055050 3 29.13416 39.53251 31 37 33.0 35
## Humidity_2:Temperature_1 23.66667 3.785939 3 18.46749 28.86584 21 28 21.5 22
## Humidity_2:Temperature_2 20.00000 2.645751 3 14.80083 25.19917 18 23 18.5 19
## Q75
## Humidity_1:Temperature_1 30.5
## Humidity_1:Temperature_2 36.0
## Humidity_2:Temperature_1 25.0
## Humidity_2:Temperature_2 21.0
##
## $comparison
## NULL
##
## $groups
## Resp groups
## Humidity_1:Temperature_2 34.33333 a
## Humidity_1:Temperature_1 28.66667 ab
## Humidity_2:Temperature_1 23.66667 bc
## Humidity_2:Temperature_2 20.00000 c
##
## attr(,"class")
## [1] "group"