# Correlation between two percentages

I'm trying to describe the behavior of a scatter plot I have. I'm looking at the results of a game that occurs in rounds where one player is voted out each round. I'm trying to find a correlation between how many rounds Player A (who wins a particular advantage in the first round of each game) ultimately survives and how many people voted for the person Player A wanted out in the first round. There are 22 iterations of this game total, and each iteration has one data point because there is only one Player A per game. However, each iteration of this game has a different number of rounds, and a different number of people voting in the first round.

Ex: Game 1 - 10 rounds, 12 people voting in first round
Game 2 - 12 rounds, 13 people voting in first round

So to get around this, I converted both variables into percentages (i.e., the percentage of rounds Player A survived vs. the percentage of people who voted for the person Player A wanted out). I ended up with a plot like this: There are two distinct clusters that appeared, and the fact that there appears to be a negative correlation (r = ~0.349) in the top-right red cluster would be an interesting trend to note. However, I've done some reading on here that states that finding the pearson's r between two percentages is a bad statistical practice, even when the percentages are not compositional. My question has two parts -- 1) Would it be fair to say that there is a negative correlation in the red cluster? 2) Does anyone have suggestions for how to better perform this analysis if finding the correlation between the percentages is incorrect?

-ve correlation in red cluster appears to be an artefact. Linear correlation analysis doesn't seem to reflect the complex relationships in that cluster, especially the hard limit at 100% for both variables.

The two clusters seems correct, seems there's some threshold effect at 50%.

The non-100% points seem to have a positive correlation.

The small cluster on top around (60, 100) seems related. Could be some specific effect. If these points are removed, the rest of the points seem to have clear positive correlation.

• Thank you so much for the reply! So when you say that linear correlation analysis doesn't reflect the complexity of the relationships in that cluster, are you saying that it might be a curved relationship? Or does the fact that many points are hitting the 100% limit in both directions disqualify that too? Jun 12, 2020 at 14:15
• No simple parametric curve for the red points as a whole. However if the points at (60,100) and the two points at (100,50) are excluded, you can see a positive correlation. You can exclude all 100% points for consistency and the positive correlation stays. Jun 12, 2020 at 14:50
• Can you post a link where it says "finding the pearson's r between two percentages is a bad statistical practice"?
– rnso
Sep 2, 2020 at 2:05
• Since your data is likely to be non-parametric, it may be best to use Spearman's correlation rather than Pearson's.
– rnso
Sep 2, 2020 at 10:53