Exploring non linear relationship between two variables

#1
I did a study measuring the relationship between metamemory and actual memory scores in a test. Basically what I find is that only those people who are good or bad in memory have a accurate metamemory. However, those in the middle of the distrution do not. I have analysed my results with simple correlations (weak but reliable correlation when all the sample is included) and dividing the sample in four groups according to their scores in the objective memory test. Is there any way to analyze the data in a different way?
 

Miner

TS Contributor
#2
What type of correlation? Pearson only works for linear relationships, and you already stated that it was not linear. Spearman's will work for monotonic relationships. Have you plotted the data to see whether it is monotonic? Can you attach such a plot?
 
#3
What type of correlation? Pearson only works for linear relationships, and you already stated that it was not linear. Spearman's will work for monotonic relationships. Have you plotted the data to see whether it is monotonic? Can you attach such a plot?
Hi Milner, thanks for your reply. I attach the plot
 

Attachments

Miner

TS Contributor
#4
What is your rationale for breaking this into quartiles? Given your plot, I would try both Pearson and Spearman across the entire range to see which is stronger. It is difficult to tell because this is very noisy data (see Andrew Gelman's kangaroo).
 

hlsmith

Less is more. Stay pure. Stay poor.
#6
Not really seeing non-linear. If it is non-linear, GAM, polynomials, or quantile regression is usually the way to go. But it dependents on what isn't non-linear and why.