Prep

game<- c(
1,
2
,3
,4
,5
,6
,7
,8
,9
,10
,11
,12
,13
,14
,15)
game <- as.factor(game)

Basic <-
c(21,
20,
25,
22,
21,
22,
22,
24,
24,
23,
21,
25,
23,
24,
24)

Conehead<-c(
28
,28
,25
,29
,29
,27
,30
,29
,29
,29
,30
,26
,26
,26
,28)

Buckethead<- c(
23,
23,
23,
21,
21,
22,
20,
22,
22,
22,
19,
19,
21,
18,
18)

zoombies <- data.frame(Basic,Conehead,Buckethead)
szoombies <- stack(zoombies)

Boxplots

boxplot(zoombies$Basic,zoombies$Conehead,zoombies$Buckethead,names = c("Basic","Conehead","Buckethead"))

As seen from the boxplots it seems that there is a diffrence in the means, but the data appears to show equal varience and the boxes seem to be normally distributed.

ANOVA test

szoombies <- stack(zoombies)        
model <- aov(values~ind, data = szoombies)
summary(model)
##             Df Sum Sq Mean Sq F value   Pr(>F)    
## ind          2  396.4  198.20    73.8 1.79e-14 ***
## Residuals   42  112.8    2.69                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

From an ANOVA test there is defintly a diffrence in the means with a p-value close to zero.

Null hypothesis is that there is no diffrence of means in the types of zombies that appear, Alt Hypthesis is that there is a diffrence in the means.

TukeyHSD

library(car)
## Warning: package 'car' was built under R version 4.1.3
## Loading required package: carData
## Warning: package 'carData' was built under R version 4.1.3
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.
TukeyHSD(model)
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = values ~ ind, data = szoombies)
## 
## $ind
##                     diff       lwr        upr     p adj
## Conehead-Basic       5.2  3.746165  6.6538348 0.0000000
## Buckethead-Basic    -1.8 -3.253835 -0.3461652 0.0120723
## Buckethead-Conehead -7.0 -8.453835 -5.5461652 0.0000000

From Tukeys HSD all of the pairs differ significantly. It seems that buckethead is the rarest type of zombie. while conhead is most common.

Equality of Variences and Normality

qqnorm(zoombies$Basic)

qqnorm(zoombies$Buckethead)

qqnorm(zoombies$Conehead)

boxplot(zoombies$Basic,zoombies$Conehead,zoombies$Buckethead,names = c("Basic","Conehead","Buckethead"))

From the normal probabliltiy plots, it can be observed that the distribution of each zombie type is fairly normal for the given sample sizes.

From the boxplots it can be seen that there little difference of for each type.