Goto Lab:

Lab 1

Due Tues 7 Sept in class

This lab focuses on graphical summaries for one and two variables. The things you'll do here will be very useful for the remainder of the course.

Start up Splus
The main dataset we'll be focusing on here is in the file fish.asc. Here's a brief description of the dataset:

A study was recently conducted in the Wacamaw and Lumber Rivers to investigate mercury levels in tissues of large mouth bass. At several stations along each river, a group of fish were caught, weighed, and measured. In addition a filet from each fish caught was sent to the lab so that the tissue concentration of mercury could be determined for each fish. Each fish caught corresponds to a single row of the file. In order, the recorded information for each fish is

river station length in cm weight in grams mercury concentration in parts per million
We're going to make some plots. So tell Splus to use 4 plots per page:
```
> par(mfrow=c(2,2))
```
Make a histogram of conc; this can be done with the command:
```
> hist(fish$conc)
```
The label is a bit ugly; you can specify your labels by specifying labels and the title in the histogram call
```
> hist(fish$conc,xlab="concentration ppm",ylab="count",
       main="mercury concentrations")
```
The mercury concentrations are skewed to the right (as you'd expect). A log transformation may help spread out the data better. Create the log concentrations using
```
> fish$logconc_log(fish$conc,base=10)
```
To see what the dataframe fish now looks like type:
```
> fish
```
fish now has an additional column. Make a histogram of the log concentrations:
```
> hist(fish$logconc,xlab="log concentration ppm",ylab="count",
       main="log mercury concentrations")
```
Let's investigate how mercury concentration varies with station and river. We'll focus on the new variable logconc. Let's first look at logconc by river. One thing to try is to plot the data values against the two river locations. First make the variable rivernum; then plot it
```
> rivernum_ifelse(fish$river=="wacamaw",1,2)
> plot(rivernum,fish$logconc,ylab="log concentration ppm",xlab="river",
       main="concentration by river")
```
Check out the function ifelse(); it can be very useful. To get more info on the function, type
```
> ?ifelse
```

This plot isn't so hot. Boxplots may give a better picture:

> boxplot(split(fish$logconc,fish$river),
  ylab="log concentration ppm",xlab="river",
  main="concentration by river")

Now let's look at logconc by station -- a plot and a boxplot:

> plot(fish$station,fish$logconc,ylab="log concentration ppm",
       xlab="station", main="concentration by station")
> boxplot(split(fish$logconc,fish$station),
          ylab="log concentration ppm",xlab="station",
          main="concentration by station")

Let's investigate the relationship between length and weight of the fish. Plot length vs. weight:
```
> plot(fish$length,fish$weight,xlab="length in cm",
       ylab="length in gm", main="fish size")
```
The plot nearly follows a quadratic: y = x^2 (does this make sense?).
Some points seem to be away from the point cloud. Let's identify the stations from which these fish were taken using the identify() function:
```
> par(mfrow=c(1,1)) # make the plot bigger
> plot(fish$length,fish$weight,xlab="length in cm",
       ylab="length in gm", main="fish size")
> identify(fish$length,fish$weight,fish$station)
```
Now click on the plot the points you want to identify using the left mouse button. When you are thru, click the right button. Note the fish from station 2 all seem to be away from the rest of the observations.
We can make this same plot using station number as the plotting sympol. This can be done a couple of ways. We'll use text after making the initial plot. Make the plot of length by weight but specify type="n". This will tell Splus not to make any marks inside the plotting region.
```
> par(mfrow=c(2,2))
> plot(fish$length,fish$weight,xlab="length in cm",type="n",
       ylab="length in gm", main="fish size by station")
```
Next use text to fill in the plotting symbols. text() only adds points to the existing plot. Type ?text to find out more about the text() function.
```
> text(fish$length,fish$weight,fish$station)
```
Finally, a simple way to get a good overview of your data is to use the pairs scatterplot matrix. This plots each pair of variable against each other. To do this, enter the command:
```
> pairs(fish)
```
You may only want to focus on a subset of the variables in the dataframe fish. This can be done by controling the index of fish. The command below gives pairwise scatterplots for the variables length, weight and logconc - the 3rd, 4th and 6th columns of the dataframe:
```
> pairs(fish[,c(3,4,6)])
```

Assignment:

Turn in the following plots. Print them out 4 plots to a page. The scatterplot matrix plot should be printed on a single page. All plots should have thoughtful axis labels and a title.

histogram of mercury concentrations.
histogram of the log of the mercury concentrations.
side by side boxplots of log concentration for the two rivers.
side by side boxplots of log concentration for the each station.
plot of length by height with outlying points identified with their station number.
plot of length by height using station number as plotting symbol.
plot of weight by log conc using different plotting symbols for the two rivers.
plot of length by log conc using different plotting symbols for the two rivers.
scatterplot matrix of length, weight and log concentration.

You should only have to turn in 3 pages - the first two with 4 plots on each, and one with the 3 by 3 scatterplot matrix. Good luck!