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<h1 class="title toc-ignore">Exercises</h1>
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<p> </p>
<div id="exercise-graphical-data-exploration-using-r"
class="section level2">
<h2>Exercise: Graphical data exploration using R</h2>
<p> </p>
<p>1. Start RStudio on your computer. If you haven’t already done so,
create a new RStudio Project (select File –> New Project on the main
menu). Create the Project in a new directory by selecting ‘New
Directory’ and then select ‘New Project’. Give the Project a suitable
name (‘pgr_stats’ maybe) in the ‘Directory name:’ box and choose where
you would like to create this Project directory by clicking on the
‘Browse’ button. Finally create the project by clicking on the ‘Create
Project’ button. This will be your main RStudio Project file and
directory which you will use throughout this course. See <a
href="https://intro2r.com/rsprojs.html#rsprojs">Section 1.6</a> of the
Introduction to R book for more information about RStudio Projects and
<a
href="https://alexd106.github.io/PGR-LM/howto.html#rstudio_proj-vid">here</a>
for a short video.</p>
<p>Now create a new R script inside this Project by selecting File –>
New File –> R Script from the main menu (or use the shortcut button).
Before you start writing any code save this script by selecting File
–> Save from the main menu. Call this script
‘graphical_data_exploration’ or something similar. Click on the ‘Files’
tab in the bottom right RStudio pane to see whether your file has been
saved in the correct location. Ok, at the top of almost every R script
(there are very few exceptions to this!) you should include some
metadata to help your collaborators (and the future you) know who wrote
the script, when it was written and what the script does (amongst other
things). Include this information at the top of your R script making
sure that you place a # at the beginning of every line to let R know
this is a comment. See <a
href="https://intro2r.com/proj-doc.html">Section 1.10</a> for a little
more detail.</p>
<p> </p>
<p>2. If you haven’t already, download the data file
<em>‘loyn.xlsx’</em> from the <strong><a
href="data.html"><i class="fa fa-download"></i> Data</a></strong> link
and save it to the <code>data</code> directory. Open this file in
Microsoft Excel (or even better use an open source equivalent - <a
href="https://www.libreoffice.org/download/download/">LibreOffice</a> is
a good free alternative) and save it as a tab delimited file type. Name
the file <em>‘loyn.txt’</em> and also save it to the <code>data</code>
directory.</p>
<p> </p>
<p>3. These data are from a study originally conducted by Loyn
(1987)<sup>1</sup> and subsequently re-analysed by Quinn and Keough
(2002)<sup>2</sup> and Zuur et al (2009)<sup>3</sup>. Note, I have had
to do some slight ‘tweaking’ of these data to improve usability for this
course. The aim of the study was to relate bird density in 67 forest
patches to a number of different environmental variables and management
practices. A summary of the variables is: <strong>ABUND</strong>:
Density of birds, continuous response variable; <strong>AREA</strong>:
Size of forest patch, continuous explanatory variable;
<strong>DIST</strong>: Distance to nearest patch, continuous
explanatory; <strong>LDIST</strong>: Distance to nearest larger patch,
continuous explanatory; <strong>ALT</strong>: Mean altitude of patch,
continuous explanatory; <strong>YR.ISOL</strong>: Year of isolation of
clearance, continuous explanatory; <strong>GRAZE</strong>: Index of
livestock grazing intensity, 5 level categorical explanatory 1= low
graze, 5 = high graze. Copy this information to your R script (make sure
you comment it out with a <code>#</code> - can you remember the keyboard
<a href="https://intro2r.com/proj_doc.html#proj_doc">shortcut</a>?) and
clearly highlight which variable is the response variable and which
variables are potential explanatory variables.</p>
<p> </p>
<p>4. Import your tab delimited file from Q2 (<em>‘loyn.txt’</em>) into
R using the <code>read.table()</code> function and assign it to an
object called <code>loyn</code> (checkout <a
href="https://intro2r.com/importing-data.html#import_fnc">Section
3.3.2</a> if you need a reminder). Use the <code>str()</code> function
to display the structure of the dataset and the <code>summary()</code>
function to summarise the dataset. Copy and paste the output of
<code>str()</code> and <code>Summary()</code> to your R code as a
record. Don’t forget to comment this code with a <code>#</code> at the
beginning of each line (use the keyboard to comment code blocks <a
href="https://intro2r.com/proj_doc.html#proj_doc">shortcut</a>?).</p>
<p>How many observations are in this dataset? How many variables does
the dataframe contain?</p>
<p>Are there any missing values (coded as <code>NA</code>) in any
variable?</p>
<p>How is the variable <code>GRAZE</code> coded? (as a number or a
string?). If you think this will cause a problem (hint: it will!),
create a new variable called <code>FGRAZE</code> <strong>in the
dataframe</strong> with <code>GRAZE</code> recoded as a factor. See <a
href="https://intro2r.com/data-types.html#data-types">here</a> to see
how to convert/coerce a numeric variable into a factor (TL;DR: use the
<code>as.factor()</code> or <code>factor()</code> function).</p>
<p> </p>
<p>5. Use the function <code>table()</code> (or <code>xtabs()</code>) to
determine how many observations were recorded for each
<code>FGRAZE</code> category (level). See <a
href="https://intro2r.com/summarising-data-frames.html">section 3.5</a>
of the Introduction to R book to remind yourself how to do this.</p>
<p> </p>
<p>6. Using the <code>tapply()</code> function what is the mean bird
abundance (<code>ABUND</code>) for each level of
<code>FGRAZE</code>?</p>
<p>Can you also determine the variance for each <code>FGRAZE</code>
level? Again see <a
href="https://intro2r.com/summarising-data-frames.html">section 3.5</a>
of the Introduction to R book to remind yourself how to do this.</p>
<p> </p>
<p>7. Now onto some plotting action. Plot a Cleveland dotchart (<a
href="https://intro2r.com/simple-base-r-plots.html#dotcharts">Section
4.2.4</a>) of each <strong>numeric</strong> variable separately to
assess whether there are any outliers (unusually large or small values)
in the response variable (<code>ABUND</code>) or any of the continuous
explanatory variables (see Q3).</p>
<p>If you feel in the mood, output these plots to an external PDF file
in an <code>output</code> directory within your RStudio project (don’t
forget to create the directory first if required). If you would like to
include all of the plots on a single ‘page’ (technically a device) then
you can split your page into two rows and three columns using
<code>par(mfrow = c(2,3))</code> before you run your plot code for each
plot. Make a note of which variables contain outliers.</p>
<p> </p>
<p>8. If you do spot any unusual observations have a think about what
you want to do with them (NOTE: do <strong>not</strong> just remove them
without justification!). If you’re unsure, please speak to an instructor
to discuss your options during the practical session. Perhaps you should
apply a data transformation to see if this reduces the magnitude of any
outlier. The best thing to do here is to play around with different
transformations (i.e. <code>log10</code>, <code>sqrt</code>) to see
which transformation does what you want it to do. When applying a data
transformation to a variable, it’s best practice to create a new
variable <strong>in your dataframe</strong> to contain your transformed
variable rather than overwrite your original data.</p>
<p>After you have applied these data transformations make sure you
re-plot your dotcharts with any transformed variable to double check
whether the transformation is doing something sensible. Hint: a
log<sub>10</sub> transformation might help reduce the magnitude of the
outliers for some of the variables.</p>
<p> </p>
<p>9. Next, check if there is any potential collinearity between any of
the <strong>explanatory variables</strong>. Remember, collinearity is
<em>strong</em> relationships between your explanatory variables. Plot
these variables using the <code>pairs()</code> function (<a
href="https://intro2r.com/simple-base-r-plots.html#pairs-plots">Section
4.2.5</a>).</p>
<p>You will need to extract your explanatory variables from the
<code>loyn</code> dataframe (using <code>[]</code>) either before you
use the <code>pairs()</code> function or whilst using it (don’t forget
to plot the transformed versions of any variables from Q8).</p>
<p>Optionally, include the correlation coefficient between variables in
the upper panel of the pairs plot (see <a
href="https://intro2r.com/simple-base-r-plots.html#pairs-plots">section
4.2.5</a> of the introduction to R book for details) to help you decide
whether collinearity is an issue.</p>
<p> </p>
<p>10. Now that we’ve checked for collinearity let’s assess whether
there are any clear relationships between the response variable
(<code>ABUND</code>) and individual explanatory variables. Use
appropriate plotting functions (<code>plot()</code>,
<code>boxplot()</code>, <code>pairs()</code> etc) to visualise these
relationships.</p>
<p>Don’t forget, if you have applied a data transformation to any of
your variables (Q8) you will need to plot these transformed variables
instead of the original variables.</p>
<p>Also, don’t forget, you can split your plotting device up to allow
you to plot multiple graphs (<a
href="https://intro2r.com/mult_graphs.html#mult_graphs">Section 4.4</a>)
or again use a function like <code>pairs()</code> to create a
multi-panel plot. Output these plots to the <code>output</code>
directory as PDFs. Add some comments in your R code to summarise your
findings.</p>
<p> </p>
<p>11. One of the main aims of this study was to determine whether
management practices such as grazing intensity (<code>GRAZE</code>) and
size of the forest (<code>AREA</code>) affected the abundance of birds
(<code>ABUND</code>). One hypothesis was that the size of the forest
affected the number of birds, but this was dependent on the intensity of
the grazing regime (in other words, there is an interaction between
<code>AREA</code> and <code>GRAZE</code> - don’t worry if you haven’t
heard of an interaction term, we will go through this later on in the
course).</p>
<p>Use an appropriate plotting function to explore these data for such
an interaction (perhaps a <code>coplot()</code> or <code>xyplot()</code>
in <a
href="https://intro2r.com/simple-base-r-plots.html#coplots">Section
4.2.6</a> might be helpful?).</p>
<p>Again, don’t forget, if you have applied a data transformation to
your <code>AREA</code> variable you need to use the transformed variable
in this plot <strong>not</strong> the original <code>AREA</code>
variable. Likewise, as we’ve converted the <code>GRAZE</code> variable
into a factor type variable we should use our new factor
<code>FGRAZE</code> (or whatever you have called it).</p>
<p>Save this plot as a PDF to your <code>output</code> directory and add
some comments to your R code to describe any patterns you observe.</p>
<p> </p>
<p> </p>
<p><sup>1</sup> Loyn, R. (1987). Effects of patch area and habitat on
bird abundances, species numbers and tree health in fragmented Victoria
forests. Nature conservation: the role of remnants of native vegetation.
65-77.</p>
<p><sup>2</sup> Quinn, G. P., and Michael J. Keough. 2002. Experimental
design and data analysis for biologists. Cambridge, UK: Cambridge
University Press.</p>
<p><sup>3</sup> Zuur, A.F., Ieno, E.N. and Elphick, C.S. (2010), A
protocol for data exploration to avoid common statistical problems.
Methods in Ecology and Evolution, 1: 3-14. <a
href="doi:10.1111/j.2041-210X.2009.00001.x"
class="uri">doi:10.1111/j.2041-210X.2009.00001.x</a></p>
<p> </p>
<p>End of Graphical data exploration using R Exercise</p>
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