Description
1) (20 pts) This problem will not only give you practice creating visualizations, but requires you to
follow carefully a somewhat complicated specification of experimental data and use
visualization for problem solving. Recall the perception experiment from our first week. You
saw a sequence of slides each with four encoded values, marked A, B, C and D. You were
supposed to write down the values for B, C and D as a proportion of A. On each slide the
encodings (e.g. aligned bar, volume, etc.) changed, and each encoding was repeated. The data
file for this problem, PerceptionExperiment.csv, contains the results from 92 previous students.
(For those interested in experimental design, note that the order of the slides was changed for
different classes.)
Here is how the data are laid out in columns: each type of encoding is a Test, and each one got
displayed with two separate slides. The individual PowerPoint slides are called Displays. Each
individual Display of each Test, has a unique TestNumber. Each sample that you estimated a
value for was labelled B, C or D as its Trial. The Subjects are the students and the estimates they
made are the Responses. Each row has a copy of the TrueValue, i.e. the correct value that the
student should have entered (if the whole point weren’t how hard it is).
One way to help yourself understand this is to open the data up in RStudio (or Excel) and scroll
through the rows. If you watch how the variable values change as you scroll, you will see what
is happening. It is also helpful to use functions like select, unique, filter, group_by and
summarize to get intuition. For example, use select to pick Test and then pipe to unique to find
out how many encodings there were (group_by Test and then summarise accomplishes the
same). Try group_by with Test, Display, TestNumber piped to summarise and then arrange to
sort by TestNumber. See our earlier tidyverse tutorial for more information.
The Responses themselves are not very useful for initial visualizations because they will naturally
cluster around each True Value. The first thing you will need to do is to create a new column
that contains the amount of error. Define Error:
Error = Response – TrueValue
Explore the data for the following features and display them as clearly as possible using any
techniques that we have covered for displaying and comparing distributions. You may do this
either in R or Tableau, but be aware that R will give you more options for your visualization. In
either case, be thorough in looking at what methods are appropriate. Focus on the clarity of the
display, keeping in mind the criteria from the lectures on clarity and accuracy.
a. Were there any tests where people generally underestimated or overestimated the
data? Explain what field you can graph to test this, what graphical method reveals this
clearly. Analyze the results and explain in a short paragraph.
b. Use a univariate scatterplot or another technique that shows fine detail for a collection
of distributions. For each Test (don’t divide between Display 1 & 2 or Trial B, C and D)
plot the AbsoluteError (absolute value of Error). Then write a short paragraph of
analysis. How do the distributions of the data compare across the different methods
our perception test studied for encoding numerical data visually? Is there any
noticeable clumping of responses for any of the methods?
c. Compare the data for Displays 1 and 2 for subjects 56-73 (you will need to filter the data
in Tableau or R). Create a visualization that shows any differences in the response
patterns between the two. These subjects all saw the first set of Displays before the
second set. Is there any difference in the values for Displays 1 and 2? Did the
participants get better at judging after having done it once?
d. An erroneous stimulus was used for the first Display of “vertical distance, non-aligned”
for a small subset of the subjects. They manifest themselves as an anomalous sequence
of “1” Responses across Trial B, C and D. Look closely at the original raw scores and
identify the sequence of subjects (hint: they are contiguous). Visualize the raw scores in
a way that highlights these values and makes their anomalous nature clear. It should
make it clear not only that they are outliers but should show any features that
distinguish them from ordinary outliers. Some features that you might think about
exploiting: they are identical values across all three Trials, regardless of what the true
values for the Trial is; they are only for a small subset of subjects.
2) (20pts) Download the astronomical data for the Messier objects. These are objects that can be
seen in a dark sky with binoculars or a telescope that Charles Messier cataloged in France in the
18th century so that they wouldn’t be confused with comets. Some of these are clusters of stars
or great clouds of gas in our galaxy, some are galaxies that are much farther away. The dataset
contains a list of 100 deep sky objects along with their distances from the earth in light-years.
Graph this data in the following ways to explore the information provided about these
interesting objects.
For this dataset, you will have to pick suitable scales to make the data readable in your graphs.
You should not wind up with a majority of the points squashed down along the one axis. In
particular, for distances, the scale should show the “order-of-magnitude” of the distance in light
years (10, 100, 1000, etc.) clearly.
a. Start by trying to graph one or more properties of the objects against the Messier
Number. Remember, there is nothing ‘intrinsic’ about this number, it is just the order of
Messier’s list. Is there any property that exhibits a pattern with respect to the ordering
in his list?
b. Create a visualization that compares the distributions of the distances to the objects in
each Kind. Note that the Type variable is a very different category and is really a subcategory of Kind. Do not use that here. Sort the distribution displays in a way that
makes the relationship clear.
c. Create a scatter plot with the distance to the Messier objects plotted against their
Apparent Magnitude (it’s their visual magnitude, a measure of how bright they are in
the sky). Note that these values may be… backwards from what you would think. The
higher the number the fainter the object is in the sky. Try to incorporate that into your
visualization to make the relationship clear.
d. Augment the visualization in (c) by adjusting the size of the points in the scatter-plot
based on the angular Size of the objects in the sky. Evaluate how easy it is to analyze all
encoded aspects of the data from this graph and give a suggestion on how you might
modify the graph to display all this information more readably.
3) (15pts) Download and graph the Montana Population data set (different from the one we used
previously). Create visualizations using logarithmic scales, and intended for a technical
audience, that clearly demonstrate visually the answers to the following questions. Viewers
should be able to read the answers to these directly off the graph scales. Different logarithmic
scale techniques may be appropriate for each part. If you use a single graph to answer multiple
parts, make it clear that you are doing so.
a. How many times has the population doubled since 1890?
b. Has the percentage rate of change in the population increased or decreased over the
years? What years had the greatest increase in population %-wise?
c. What years was the population percentage increase greater than 15%?
4) (20 pts) We will look at data on air quality, captured from May to September in New York. This
is actually built into R, but not as a data frame. There is a copy on the D2L site.
a. Use a scatterplot to look at the relationship between Wind and Solar.R (solar radiation).
Show a fit line. Make sure to produce a clean visualization with emphasis on the trend.
This provides one view of the relationship.
For help doing this in R, see Tutorial 5. In Tableau, this is available from the Analysis tab.
It is one of the tabs along with Data for the panel on the far left (i.e. look at the top of
the panel from which you drag variables).
b. Use a plot that will show the distributions of Wind and Solar.R and allow you to compare
with fine detail.
c. Finally, show these distributions in context of the rest of the variables by using a
technique for comparing multiple distributions.
Note: you will need to transform the data in a particular way that we have studied. I it
showed in the Tableau tutorial and in an R tutorial. Hint – you need to collapse the
current variables into two: (1) stores the original variable name, and (2) stores the
corresponding original value.
d. For extra credit, compare Wind and Solar.R again with a QQ plot. What does this tell
you?
