assignment1_exercise3.Rmd

---
title: "Assignment template"
author: "James Bond, group 007"
date: "1 February 2033"
output: pdf_document
fontsize: 11pt
highlight: tango
---

## Imports
```{r}
library("ggpubr")
```

## 3a
```{r, fig.height=3.5}
data=read.table(file="dogs.txt",header=TRUE)
data

shapiro.test(data$isofluorane)
ggqqplot(data$isofluorane)
```

p-value < 0.05 so cannot assume data was taken from normal populations.

## 3b
```{r, fig.height=3.5}
res <- cor.test(data$isofluorane, data$halothane, 
                method = "pearson")
res
```
p-value > 0.05 so the colleration is not significant.

Permutation test is applicable because it doesn't assume normality and the sample size is small.

Isofluorane & halothane permutation test:
```{r, fig.height=3.5}
mystat=function(x,y) {mean(x-y)}
B=1000; tstar=numeric(B)
for (i in 1:B) {
  datastar=t(apply(cbind(data[,1],data[,2]),1,sample))
  tstar[i]=mystat(datastar[,1],datastar[,2]) }
myt=mystat(data[,1],data[,2])
myt
hist(tstar)
pl=sum(tstar<myt)/B
pr=sum(tstar>myt)/B
p=2*min(pl,pr)
p
```

p-value > 0.05 so no significant difference


## 3c

```{r, fig.height=3.5}
dataframe=data.frame(concentration=as.vector(as.matrix(data)),
                     variety=factor(rep(1:3,each=10)))

aov=lm(concentration~variety,data=dataframe)
anova(aov)
```

p-value < 0.05 so factor variety is significant. So yes, the type of drug has an effect on the concentration of plasma epinephrine.


```{r, fig.height=3.5}
summary(aov)
```
The estimated concentrations are 0.43 for isofluorane, 0.04 for halothane, and 0.42 for cyclopropane.


check normality again
```{r, fig.height=3.5}
par(mfrow=c(1,2)); qqnorm(residuals(aov))
plot(fitted(aov),residuals(aov))
```


## 3d
```{r, fig.height=3.5}
attach(dataframe); kruskal.test(concentration,variety)
```
p-value > 0.05 so factor variety is significant.

So no, the two tests don't arrive at the same conclusion. Probably because the population isn't normal and one-way ANOVA assumes normality while the Kruskal-Wallis test does not rely on the normality.


```{r, fig.height=3.5}

```