# Correlation with one variable missing half of its values

Let´s say I want to run a correlation between "eye spherical defect" and height and I want to use only individuals with myopia, whose "spherical defect" goes from 0 to -20 or so. Whereas the sphericity of eyes may be a normally distributed variable with a mean of 0, if I use only myopic individuals I would be using a sample containing only half the values (i.e. from 0 to -20) of the normal distribution of that variable. My question: How can I run a correlation using such a variable? Would I be able to use parametric tests for this? (e.g. Pearson's $r$)

• The last line is contentious. I don't see that any kind of skewness means ipso facto that you should rule out using Pearson correlation and jump to Spearman correlation. You should naturally always plot your data and think about whether Pearson correlation is a good idea, but symmetry of marginal distribution isn't an essential. If $x$ is 1,2,4,7,11 and $y$ is twice that, then Pearson correlation is fine, and many less trivial examples, including those with real data, have the same flavour. Commented Mar 2, 2015 at 16:54