Create you own data.

In this WPA, we will practise plotting data. Often, before running an experiment, you will want to check your script is performing correctly by simulating data. Therefore, this week, we will start by simulating data for a fake Experiment. This fake Experiment will look at the effect of stress on memory performance. We will create 200 fake participants, half of whom conducted a memory test in a ‘high’ stress environment, while the other half completed it in a ‘low’ stress environment. We will also pretend that our researchers were also interested in any possible effect of either participant age or gender. The table shows the basic structure of the data we will generate.

Data

Variable	Description
id	Participant id number from 1 to 200
age	Participant age. All fake participants should be over 18
stress	Whether the participant completed the ‘low’ stress or ‘high’ stress task
gender	Participant gender
memory	Participant score on the memory task. All scores should be between 0 and 100

Either: Open your R project from last week and open a new R script and save it as wpa5.R in the R folder in your project directory. Or: Open a new R script and save it as wpa5.R in the R folder in your project directory. Copy, and run, the setwd code from your script last week to the current script.
We will use the code below to generate our fake data as a data.frame. All the functions we are using are those you should already be familiar with.

set.seed(100)
fakedf= data.frame(age= round(rnorm(n=200, mean=50, sd=18) ), 
                     stress= rep(1:2 , each=100),
                     gender= sample(x=c("female", "male"), size=200, replace=TRUE) )
fakedf$memory<- with(data=fakedf, exp= 55 + 15*stress - 0.7*age + rnorm(n=200, mean=5, sd=10) )
fakedf$stress[fakedf$stress==1]= "low"
fakedf$stress[fakedf$stress==2]= "high"

Look at the structure of the data frame using str().

Histograms

Several columns of our data (age, memory) have restrictions on acceptable data values that may not be met due to the way we generated our data. We could use logical indexing, or function like range or table to check for innappropriate values. Or we could use histogram to both check for incongruous scores, and visualise our data.

Create a histogram of age using hist.
The default title and axis labels R uses aren’t very informative. Add your own (e.g. “Histogram of Ages”, “Age”). Use the main and xlab arguments.
The histogram shows several values of age that are below 18. Replace these with values of 18 (hint: Use indexing like last week). Redo the histogram to check.
Create a histogram for memory scores. Remember to label the x-axis and change the title. If there are any scores below 0, or above 100, replace them.
When checking statistical assumption (e.g. normality, homoscedacity), we often need to look at the distribution of our Dependant Variable (in this case memory), at each level of our Independent Variable (stress). Create separate memory histograms for each level of stress (Hint: use indexing or subset). Give the histograms appropriate titles.
Plot the two histograms side by side, using either layout or par(mfrow). Remember to return the layout to the default afterwards.
Make the scale of the x-axis the same for both plots by using the breaks argument (you could also use xlim, but don’t). Change the bin widths for both histograms to 5 as well (also using breaks).
Use abline or segments to add the mean memory score to each histogram. You’ll need to calculate the mean for each level of stress first.
You can’t create a histogram for the stress or gender columns. What would be a better way to check these data?

Scatterplots

Create a scatterplot showing the relationship between age and memory score. Look back at the section where we generated our data. Does the figure look like you would expect?
If you haven’t already, add appropriate labels and titles to the figure. The arguments are the same as those used for the histogram (e.g. main, ylab, xlab).
Now, make the plot look a bit nicer! Try changing the point types (e.g.; pch = 16), point colors (e.g.; col = gray(.0, .5), col=rgb(0, 0, 1, 0.5), or col = "blue")

Bonus on Setting Colours

Rather than using the colour name (e.g. "blue") you can also set colours, with transparency, by using col= rgb(red, green, blue, alpha). By default rgb accepts values between 0 and 1 for each of the named colour arguments, and for the alpha argument, which sets the transparency (if you prefer to give the colour components as values between 0 and 255, you can set the optional maxColorValue argument to 255). For example if you wanted non-transparent red you would use col= rgb(1,0,0,1), while col= rgb(1, 1, 0.8) would produce a slightly transparent yellow. You can play around with rgb if you would like.

plot(x = 1:10,
     y = 1:10,
     xlab = NA,
     ylab = NA,
     main = "Colours using rgb",
     pch = 16,
     col = rgb(red=1, green=0, blue=1, alpha=.8) )  #Change these values to change the colours and transparency.

Now let’s add a regression line to the plot from Question 15. Adding a regression line is easy. First, create a linear model object created with lm(). Then add the model to the plot with abline():

# JUST COPY, PASTE, AND RUN!

# Create a regression model
model <- lm(memory ~ age, 
            data = fakedf)

# Rerun your plot.

# Add the model to the plot!
abline(model,
       lwd = 2, 
       col = "red")

Lets now create a new scatterplot of age against memory, but with the two stress conditions plotted in different colours. This will give us an idea of whether the relationship between age and memory interacts with stress. First copy and modify the code for the previous scatterplot, so that it only shows participants in the low stress condition (use indexing). Make sure the points are slightly transparent.
Now use the points function to add the values for those in the high stress condition. Make sure the colour is different. You could also use separate point types (pch). Do you notice anything wrong with the figure?
Because you didn’t specify the axis lengths (xlim, ylim), R set them automatically to accommodate the total range of values in the plot. However, as we only use the low stress data when calling the plot function, this is based only on the memory and age ranges for the low stress participants. Use xlim and ylim to set the axis lengths yourself, so that they include all data.
Finally add grid lines with grid() (Hint: Just evaluate grid() after your plot!). Now that you have the completed plot, compare the relationship between age, stress and memory in the figure, to the code you used to generate the dataset.

Barplot

Create a barplot of mean memory score by stress condition. You’ll need to use the means you calculated in Question 11.
Now we’ll create a new barplot which includes both gender and stress. In order to create a stacked barplot with the barplot() function, we first need to create a matrix of values. Run the following code to calculate a matrix of mean memory scores as a function of stress and gender with aggregate() and cbind():

# JUST COPY, PASTE, AND RUN!

# Create a matrix of group means
mem.means <- aggregate(memory ~ stress + gender,
                      FUN = mean, 
                      data = fakedf)

mem.means.mtx <- cbind(mem.means[1:2, 3], mem.means[3:4, 3])
colnames(mem.means.mtx) <- c("Female", "Male")
rownames(mem.means.mtx) <- c("High", "Low")

Now create a barplot by entering the correct arguments in the following code

# FIX THE CODE BY REPLACING ZZZ WITH THE CORRECT ARGUMENTS

barplot(height = mem.means.mtx,
        beside = TRUE, 
        legend.text = TRUE, 
        ylab = "ZZZ",
        xlab = "ZZZ",
        ylim = c(ZZZ, ZZZ))

CHECKPOINT!

If you got this far you’re doing great!

Error Bars on plots

In exercise 22-24 you have created plots of the mean scores for different groupings of our participants. In general it is very bad practice to plot only the means of your groups without giving an indication of the spread of your individual participants around these means. This is because your reader can only interpret the difference between means if they are aware of the scaling and spread of the responses. For instance the 2 Figures below have the same group means (shown by the bars) but very different standard errors of the means (shown by the error bars). Would you draw different conclusions from the 2 figures?

There are many ways to show spread in your data. You could use a barplot with error bars (see above), use plots that show distributions of your data or individual data points in addition to the means (see pirateplot in the textbook or the vioplot package), or use different summary plots, like boxpots. Here we will go through the steps to add error bars to the plot you created in exercise 22. This is not covered in the textbook. For simplicity we will plot standard deviations in our error bars. To do this we first need to calculate the standard deviation of memory scores for each stress level. Save these standard deviations as sd.memory.

The easiest way to add error bars to a barplot (or to a scatterplot or line plot), is to use the segments plotting function. segments lets you add multiple lines to a plot by specifying the start and endpoints of each line. This is done by passing four vectors (or matrices) to segments using the argument names x0, x1, y0 and y1. x0 and y0 provide the x and y coordinates for the startpoint of each line, with the first item of x0 and y0 the startpoint of the first line, the second item the startpoint of the second line etc. Similarly x1 and y1 provide the endpoints of each line.

For our error bars we want each line to be vertical, meaning that x0 and x1 should contain the same values (i.e. same x-axis position). Further x0 and x1 should match the placement of the bars in our barplot. To find the placement of our bars on the x-axis, we can store and access this information by storing our plot as variable. Check that bars is a vector containing the x-placement of our two bars.

bars<-barplot(mean.memory[,2], 
              names.arg=mean.memory[,1], 
              ylab="Mean Memory Score", 
              xlab="Stress Level",
              ylim=c(0, 70))

Now that we have the x-placement of our error bars, we just need the y-placement. The bottom of each error bar y0 should just be the height of each bar in our plot, minus the standard deviation for that group. Similarly the top of each error bar should be the height plus the the standard deviation. We have already calculated both the heights of each bar (the means) and the standard deviations, so you should be able to fill in the following code.

# FIX THE CODE BY REPLACING ZZZ  WITH THE CORRECT ARGUMENTS

segments(x0=ZZZ, 
         x1=ZZZ, 
         y0=ZZZ, 
         y1=ZZZ,
         lwd=2)

28a. OPTIONAL: If you have time you could also add error bars to your clustered bar plot (exercise 23/24) using the same method.

2 variable histogram

Go back to the memory score histograms you created. Rather than creating two separate histograms of memory scores for the two stress conditions, we can create overlapping histograms, using the add=T argument. Modify the following code.

# FIX THE CODE BY REPLACING ZZZ WITH THE CORRECT ARGUMENTS

# low stress memory scores
hist(x = ZZZ, 
     col = transparent("red", .5),
     border = "white", 
     xlab = "ZZZ", 
     main = "ZZZ")

# high stress memory scores
hist(x = ZZZ, 
     col = transparent("blue", .5),
     border = "white", 
     add = TRUE)

legend(x = 1,
       y = 15, 
       legend = c("ZZZ", "ZZZ"), 
       col = c("red", "blue"), 
       pch = c(15, 15), 
       bty = "n")

Scatterplot with separate reference lines

Go back to the scatterplot separated by colour. The reference line is for both groups together. Instead create separate reference lines for each group. You’ll need to run two abline commands, one for each group.
You should also add a legend to the plot. Modify the following code:

legend(x = ZZZ,
       y = ZZZ,
       legend = c("ZZZ", "ZZZ"), 
       pch = c(ZZZ, ZZZ), 
       col = c("ZZZ", "ZZZ"),
       bty = "n")

Bonus Exercise: You pick the plot

For the following exercises, make a plot that you think represents the data best. We are going to use the movies dataframe from the yarrr package. We installed the yarrr package in Week 1, so you should be able to load it using library(yarrr). If you don’t have it installed, use the install.packages function.

The movies dataframe in the yarrr package contains data about the top 5000 grossing movies of all time. You can learn more about the data using the help menu ?movies

Create a plot that shows the relationship between a movie’s release year and its running time. Customise it and make it look nice!
Create a plot that shows the relationship between a movie’s budget and its revenue. Customise it and make it look nice!
Create a plot that shows the relationship between genre and time. Customise it and make it look nice! (Hint: You may notice that many of the times are equal to 0, try creating the plot after excluding these values using subset.)

Submit!

Save and email your ‘.R’ file wpa_5_LastFirst.R to me at ashleyjames.luckman@unibas.ch. Put the subject as WPA5-23496-02.

WPA #5 – Plotting- Chapters 11 & 12