---
title: "Extra R: CA2"
subtitle: "H2 Statistics for Marine Science"
author: "Name"
date: today
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# Extra: CA2

## Overview 

Coverage: L11-L19, P4-P6

This is a document to **supplement** the document for CA1. Keep in mind that CA2 covers **all** lectures and practicals. Please work through `CA1_extra_R.qmd` again as well.

Note that there are often many possible paths to the correct solution.

## Air quality

The `airquality` dataset is available in R upon start-up, and gives daily values of mean ozone, solar radiation, mean wind speed, and max temperature at LaGuardia Airport in New York City (`?airquality`).

Assume we do not know the population parameters, but wish to estimate the probability of observing our sample mean under the hypothesis that $\mu = 11 mph$. What is the T statistic?

```{r}

```


Under this hypothesized $\mu$, what is the probability of collecting a sample with a mean further from $\mu$ than in this dataset?

```{r}

```


## Iris

The `iris` dataset is available in R upon start-up.

**Research question:** What is the difference in mean sepal area among *Iris setosa*, *I. versicolor*, and *I. virginica*?

What type of variables are the response and predictor variables?

>

What analysis is appropriate for this question?

>

For this question, is `Species` a fixed effect or a random effect?

>


### Calculate Sepal.Area

Create a new column in the data.frame `iris` called `Sepal.Area`.

```{r}

```


Create a histogram of Sepal.Area, showing the distribution for each species using the same limits for the x-axis.

Option 1. ggplot:

```{r}

```


Option 2. Base R:

```{r}

```


### Perform the analysis

Perform the analysis and assess the assumptions.

```{r}

```


What assumptions of this ANOVA can you evaluate with these plots? Do they appear reasonable?

>

What is the null hypothesis?

>

What is the probability of the observed difference in group means if the null hypothesis were true?

```{r}

```


### Follow up analysis

What are the means and 95% confidence intervals for each species?

```{r}

```


What is the best interpretation of these 95% confidence intervals?

>

What are the effect sizes and 95% confidence intervals? That is, which species are meaningfully different from one another and how confident are we in those differences?

```{r}

```


## Iris (reprise)

**Research question:** For the species *I. virginica*, what is the effect of sepal width on petal width?

What type of variables are the response and predictor variables?

>

What analysis is appropriate for this question?

>

### Create the appropriate data.frame

Create a new dataframe containing all columns in `iris`, but only rows where the species is `virginica`.

```{r}

```


Create a scatterplot of the relationship, with the predictor variable on the x-axis and the response variable on the y-axis.

Option 1. ggplot:

```{r}

```


Option 2. Base R:

```{r}

```


### Perform the analysis

Perform the analysis and check the assumptions.

```{r}

```


What assumptions of this linear regression can you evaluate with these plots? Do they appear reasonable?

>


What is the null hypothesis?

>

What would the null hypothesis look like on the scatter plot above?

>

What is the probability of the observed change in petal width per unit increase in sepal width if the null hypothesis were true?

```{r}

```


### Follow up analysis

To three significant figures, what is the best estimate of the change in petal width per unit increase in sepal width, and what are the 95% confidence intervals?

```{r}

```

Create a scatter plot of the relationship and add the best fit line from the linear regression with 95% confidence intervals.

```{r}

```



## NMDS, PCA

You will not be asked to produce any R code relating to Practical 6, so I am not including extra R practice here. You should nevertheless be familiar with the concepts, confident in the steps involved, and comfortable interpreting the output.