Setting up
library(tidyverse) # open our beloved package
examData <- ____ #load the dataframe "examData.csv"
___(___) # how do look at the *structure* of the dataframe (it's not head()...)
The data we will be analyzing today is called examData. A psychologist was interested in the effects of exam stress on exam performance. So, they devised and validated a questionnaire to assess state anxiety relating to exams (called the Exam Anxiety Questionnaire, or EAQ). This scale produced a measure of anxiety scored out of 100. Anxiety was measured before an exam, and the percentage mark of each student on the exam was used to assess the exam performance.
Visualizing the data
Ok, let’s plot the two variables. We will want to plot it as a scatterplot, what is the appropriate geometry?
plotExam <- ggplot(__________)+
geom_?????()
plotExam
Calculating r
Let’s calculate the correlation between the two variables….this function just gives you Pearson’s r.
r <- cor(examData$x, examData$y) # what are our x and y? Replace them with the appropriate variable from the dataset
But remember you can always calculate Pearson’s r manually. Let’s try that. First, we need the covariance of the two variables. For that, we need:
- the covariance
Wait, how do we calculate the covariance?
n <- # the sample size -- in this case, the number of observations/rows...
meanExamScore <- ______ # the mean of the exam score variable
meanAnxietyScore <- _____ # the mean of the anxiety score variable
cov.byHand <- sum(______) # Now, we are ready to calculate the covariance. It's the summation of the product between the differences between each value of each variable and its mean, divided by n-1
cov.byFormula <- cov(____, ____) # this is the function for covariance, just to make sure our manual calculations are correct
- The maximum variance that the two variables could possibly have: s_x * s_y
max_variance <- ____
Now we are ready to calculate r!
r.byHand <- _____ # is the output the same as the one spit out by the function in l. 24?
…and, why not?, t!
Imagine that you want to have both r, and the corresponding t and p-value. Did you really think that R was gonna leave you to do it manually?
cor.test(x, y, alternative) #what are our x and y? what's our alternative hypothesis?
Although, you could calculate t manually… if you wanted.
How do we do that again? The denominator is hard to remember – it’s $\sqrt{\frac{1-r^2}{n-2}}$.
the square root of the division of 1-r^2 and n-2.
tCorr.byHand <- r.byHand/_______ #
And from there retrieve the p-value
pt() # we want the two-tailed p-value of our t; so, what do we do here?