I was wondering whether these 2 variables are correlated. According to the analysis, the correlation is 0.89, which is expected, as they are items of the same scale. But I'm having trouble with interpreting this scatter plot.
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1$\begingroup$ I recommend you consider the marginal and joint distributions of these variables more closely. $\endgroup$– GalenCommented Oct 29, 2021 at 2:04
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2$\begingroup$ Is there a way to plot the point size according to how many points are on top of each other? $\endgroup$– DaveCommented Oct 29, 2021 at 2:10
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1$\begingroup$ Use the point size or showing points as bins reflecting the number of points sharing the same coordinates, or use jittering. $\endgroup$– ttnphnsCommented Oct 29, 2021 at 3:51
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1 Answer
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As @Dave and @ttnphns point out in the comments, the plot does not really communicate anything because nothing on the graph indicates the number of points sharing the same coordinates (i.e., $[x,y]$ or [Hoax1,Hoax2] pairs). For example, your graph communicates that of the $5^2=25$ possible coordinates (assuming your data is interval data), 21 contain an equal number of observations, resulting in a Pearson's correlation of 0.28 (see R code below for verification).
df <- data.frame(
Hoax1 = c(rep(5,5), rep(4,5), rep(3,5), rep(2,3), rep(1,3)),
Hoax2 = c(rep(seq(1,5,1),3), rep(seq(1,3,1),2))
)
cor(df[,1], df[,2])
Finally, the fact Hoax1 and Hoax2 are on the same scale has nothing to do with what your expected correlation should be as Pearson's correlation is standardized. For more information see the correlation wiki.
Also, because you are a SPSS user I recommend you check out Andy Field's intro to statistics book (Field, 2013).
References
Field, A. (2013). Discovering statistics using IBM SPSS statistics. sage.
answered Feb 14 at 3:39