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I am unsure how to interpret the second of two scatterplots I created.

The first scatterplot shows a slight negative correlation between the variables (n=14, population not sample). This interpretation is reinforced by the Pearson r.I also calculated a Spearman rho. The first scatterplot is below. The dashed line is a linear trend and both the Pearson r and Spearman's rho are listed on the chart.

enter image description here

On a whim, I also created a scatterplot of the rank of the two variables for each observation. This second scatterplot shows two clusters with each cluster having a moderate positive correlation. This scatterplot is below. enter image description here

Is this second scatterplot meaningful? If so, how should I interpret it?

Note: I am already aware of issues related to the small number of observations. I am only interested in whether the scatter plot of variable rank has any meaning.

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It means what you probably think it means: It's a scatter plot of the ranks.

Both plots (but especially the second) show that the data seem to be in two groups, with positive relationships in each group and a negative relationship between the groups. This is a definite warning sign about interpreting either correlation coefficient because both of them are about linear relationships and the relationship here doesn't look linear.

I don't know what "uncompensated care" and "FAP richness" are, but I think you should think about the data set and why it might be in two groups.

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  • $\begingroup$ Thank you! As an aside, FAP richness is a measure of a hospitals financial assistance program (i.e. charity care program). The higher the score the more "generous" the program. Uncompensated care is the sum of charity care and bad debt as a percentage of gross revenue. Our state is small and the number of hospitals (points) examined is the total number of hospitals in the state. $\endgroup$
    – Eric
    Dec 2, 2019 at 13:50

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