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I have two variables which are measured on a Likert scale. I ran the Spearman correlation test to test the relationship between them and they have a negative correlation coefficient (-0.729 with a p-value < 1.2e-12). I am pretty new to plotting with R and my question is, is there any way I can plot the relationship between the two variables? I am having difficulties with what kind of plot can depict the relationship since they are discrete.

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One idea is to do a jittered scatterplot.

I simulated 100 Likert scores x from 1 to 7, and roughly positively associated Likert scores y. They are summarized and tabulated below.

summary(x)
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
   1.00    3.00    5.00    4.48    6.00    7.00 
table(x)
x
 1  2  3  4  5  6  7 
 5  8 13 22 24 16 12 

summary(y)
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
   1.00    3.00    4.00    3.94    5.00    7.00 
table(y)
y
 1  2  3  4  5  6  7 
 9 11 19 23 19 14  5 

cor(x, y, meth="s")
[1] 0.9044931

A standard scatterplot shows locations of the 100 $(x,y)$ pairs, but there is a lot of over-plotting and we can't get an idea how many individuals are represented by each point.

plot(x, y)

enter image description here

By jittering (adding a small amount of random noise to) each score, I can see how many individuals correspond to each location.

xj = x + runif(100, -.2,.2)
yj = y + runif(100, -.2,.2)
plot(xj, yj, pch=20)
 abline(v=1:7, col="green2")
 abline(h=1:7, col="green2")

enter image description here

Here I have jittered by $\pm 0.2$ or less. One can choose the amount of jittering---depending on the sample size and the strength of the association---to seek the best graphical effect. If you have a very large sample size, then you may want to use small dots for individual subjects, by using parameter pch-"." in plot,

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