# Correlation being muddied by outliers

I have a study in which I find a decent correlation: on a quadratic prediction plot between a binary outcome and a continuous x. However, there are a few observations that have numbers that are not unrealistic, but so much higher than the rest that they are being plotted in a category of their own in which of course the 95% CI is terrible as there is 1-2 observations above 0.035 in the x value. I suspect this may be the reason I am not getting significant p values like I would expect from this relationship.

Would it be incorrect to simply remove these observations? Is there a tool that corrects for these outliers?

CSV file: https://gofile.io/?c=tHrojc

Measurement 1 and 2 are measurements done that are correlated and I believe their ratio may be able to predict the outcome. The ratio is Measurement3.

• It depends on exactly where in the plot those outliers might fall, the reasons why they are outlying, and the objectives of your analysis. Please supply as much of that information as you can in your post.
– whuber
Commented Jan 11, 2020 at 13:56
• Thank you for clarifying, I have changed it to a CSV file.
– Paze
Commented Jan 11, 2020 at 14:08
• The outcome appears to have 40 outcome values of 1 and 11 values of 0. This has the effect of weighting the data towards 1. I made scatterplots of the data that do not appear to clearly distinguish outcome based solely on M1, M2, or their ratios. My conclusion is that this data - by itself - is insufficient to make either an explanatory or predictive model of outcome. Commented Jan 11, 2020 at 16:08
• Thank you for your insight, I have a problem understanding when and how many observations I need to have before applying what tests. How would you choose to relay this data and/or correlations in a paper, assuming it's all you had? Also I would love to see your scatterplots to see if mine are "correctly" made.
– Paze
Commented Jan 11, 2020 at 16:10
• Last question, I find it easy to do with continuous dependent variables, but difficult for binary variables, how do you prefer to plot a binary dependent variable to visualize the model?
– Paze
Commented Jan 11, 2020 at 16:26