Worksheet 3

library(tidyverse) library(dplyr) library(ggplot2) — 1) ! I imported “Exam Anxiety.dat” using file>import. — 2) Revision hours negatively correlate with anxiety levels independent - revise - quantitative. dependent - anxiety - ordinal. Anxiety levels positively correlate with exam scores. independent - anxiety - ordinal. dependent - exam - quantitative. Revision hours positively correlate with exam scores. independent - revise - quantitative. dependent - exam - quantitative. — (3 was skipped on the worksheet) 4)

ggplot (data = examData ) +
 geom_histogram (mapping = aes(x=Anxiety), binwidth=5) +
  labs(title = "Histogram Anxiety", x = "Anxiety as an EAQ Score", y = "Frequency")

ggplot(data = examData) +
  geom_density(mapping = aes(x=Anxiety)) +
  labs(title = "Density Curve Anxiety", x = "Anxiety as an EAQ Score", y = "Density")

ggplot (data = examData ) +
 geom_histogram (mapping = aes(x=Exam), binwidth=5) +
  labs(title = "Histogram Exam", x = "Exam Mark as an EAQ Score", y = "Frequency")

ggplot(data = examData) +
  geom_density(mapping = aes(x=Exam)) +
  labs(title = "Density Curve Exam", x = "Exam Mark as an EAQ Score", y = "Density")

ggplot (data = examData ) +
 geom_histogram (mapping = aes(x=Revise), binwidth=5) +
  labs(title = "Histogram Revise", x = "Number of Hours Revised", y = "Frequency")

ggplot(data = examData) +
  geom_density(mapping = aes(x=Revise)) +
  labs(title = "Density Curve Revise", x = "Number of Hours Revised", y = "Density")

Anxiety is skewed left, and Revise is skewed right. Exam is closer to being normally distributed. Even though anxiety has an overload of data ‘to the right’, we say it is skewed left. This is because the outliers from the larger set of data will pull it towards the other side.

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 ggplot(data = examData) +
  geom_point(mapping = aes(x = Revise, y = Exam)) +
  labs(title = "Scatterplot Revise and Exam", x = "Number of Hours Revised", y = "Exam Mark as a Percentage")

 ggplot(data = examData) +
  geom_point(mapping = aes(x = Anxiety, y = Exam)) +
  labs(title = "Scatterplot Anxiety and Exam", x = "Anxiety as an EAQ Score", y = "Exam Mark as a Percentage")

 ggplot(data = examData) +
   geom_point(mapping = aes(x = Revise, y = Exam, colour = Anxiety))+
     labs(title = "Scatterplot Revise and Exam with Anxiety shown by Colour", x = "Number of Hours Revised", y = "Exam Mark as a Percentage", colour = "Anxiety as an EAQ Score")

The first scatterplot has hours on the x axis, and exam marks on the y axis. Splitting the graph into four quadrants will make for an easier analysis. The two left quadrants have the bulk of points, meaning most students did not study for a comparatively long time. It seems the top two quadrants have slightly more points than the bottom quadrants, meaning most students passed, assuming a 50% is a pass. The bottom right quadrant has no points, meaning not one student studied for a long time only to fail. The quadrant with the highest concentration of dots seems to be either the top left or the bottom left. This means that most students did not study for a long time, and this equally resulted in passes and fails. The second scatterplot has hours on the x axis and exam marks on the y axis, keeping with the standard of the first plot. Again, I’ll split the graph into four quadrants. Similarly to the first graph, there is one quadrant with no points. In this graph, it is the bottom left, meaning no students had little anxiety and performed well. The majority of points are in the right two quadrants, meaning that most students were very anxious. The top left quadrant seems to be the most highly populated, telling me that most students who performed well were anxious. There are a few points in the left side, all of which are in the top left corner. This means that the students who were not anxious performed well, typically. The third scatterplot is handy because it combines two graphs into one understandable plot. The first two have fewer variables to interpret, so they can be easier interpreted as a whole. This last one however, has to be interpreted in chunks, by focussing on one variable or the interplay of two variables at a time. In getting more information on one graph, we sacrifice having an immediately understandable graphic.

ggplot(data = examData) +
  geom_boxplot(mapping = aes(x = Revise, y = Anxiety,)) +
  facet_wrap(~ Gender) +
  labs(title = "Boxplot Revise and Anxiety Gender Separated", xlab = "Number of Hours Revised", ylab = "Anxiety as an EAQ Score")

These two boxplots, on first glance, look very similar. The median anxiety level is slightly higher in men, but the difference is almost unnoticeable. The control box for men is larger towards the bottom, meaning men have the possibility to be or report to be less anxious than women. It seems women revised less than men, as the box is shifted to the left.

Bonus) I guess this isn’t the way it was intended to be done, but it works :)

     ggplot(data = examData) +
   geom_point(mapping = aes(x = Revise, y = Exam, colour = Anxiety<50))+
     labs(title = "Scatter plot Revise and Exam with Calm People Highlighted in Red", x = "Number of Hours Revised", y = "Exam Mark as a Percentage", colour = "Anxiety") +
    scale_colour_manual(labels=c("Anxiety Above 50", "Anxiety Below 50"), values=c("darkseagreen", "firebrick3"))

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