---
title: "Exploration 3.3"
output: word_document
---
  
```{r}
#install.packages("lattice")
```

```{r setup, include=FALSE}
knitr::opts_knit$set(global.par = TRUE)
knitr::opts_chunk$set(fig.width=4, fig.height=2.67) 
load(url("http://www.isi-stats.com/isi2/ISI.RData"))
```

**Load the hurricanesA dataset, e.g.,**
```{r}
hurricanesA= read.delim("http://www.isi-stats.com/isi2/data/hurricanesA.txt", stringsAsFactors=T)
head(hurricanesA)
```

**9) Interaction plot**
```{r}
with(hurricanesA, interaction.plot(HurrGender, Participant, Rating))
```

**Describe the nature of the interaction shown in this graph. Do you think it will be statistically significant?**


**10) ANOVA table**
```{r}
with(hurricanesA, summary(aov(Rating ~ HurrGender*Participant)))
```
**11) Is the interaction statistically significant?**


**Load the hurricanesB dataset, e.g.,**
```{r}
hurricanesB= read.delim("http://www.isi-stats.com/isi2/data/hurricanesB.txt", stringsAsFactors=T)
head(hurricanesB)
#ParticipantID is numeric, change to a factor
hurricanesB$ParticipantID = as.factor(hurricanesB$ParticipantID)
```

```{r}
library(lattice)
with(hurricanesB, histogram(~Rating | HurricaneGender))
with(hurricanesB, histogram(~Rating | HurricaneAge))
with(hurricanesB, interaction.plot(HurricaneGender, HurricaneAge, Rating))

```

**14) Based on your numerical and graphical summaries, is there much evidence of a gender effect? Is there an age effect? An interaction? Describe the nature of the interaction that is present.**



```{r}
with(hurricanesB, summary(aov(Rating ~HurricaneGender*HurricaneAge + as.factor(ParticipantID))))

```

**15)How much variation in ratings of hurricanes is explained by this model?**

**16) Reproduce the ANOVA table. For each of the degrees of freedom provided, explain where it comes from/why it is what it is.**


**17) Examine the residual plots for this model. Do you consider the validity conditions for the theory-based $F$-tests to be met? Include supporting evidence for your conclusions.**


**18) State the null and alternative hypotheses for the interaction. What do you conclude? Is this consistent with your interaction plot?**



**Because the interaction is not statistically significant, we will summarize the main effects.Rerun the analysis without including the interaction.**

```{r}
with(hurricanesB, summary(aov(Rating ~HurricaneGender +HurricaneAge + as.factor(ParticipantID))))
```
**19) State the null and alternative hypotheses for the hurricane gender effect. What do you conclude?**


```{r}
model1=lm(Rating ~HurricaneGender +HurricaneAge + as.factor(ParticipantID), data=hurricanesB)
#default in R is indicator coding
lower = confint(model1)[[2]]
upper=confint(model1)[[350]]
```
A 95% confidence interval for male - female: (`r lower`, `r upper`)