# What type of statistical analysis would be best to use?

I'm awful at statistics so could really use some help regarding statistical analysis and which approach to use. Here is what I know -

1. I need to determine, based on stats I have been given, whether vocabulary learning is related to age.
2. I have 19 subjects data, around half of which are children and half of which are adults. Each data point represents the number of words said participant learnt in the week.
3. The results are non linear, although there is a monotonic relationship.

So basically the two variables are age and number of words learnt, can anyone help? :)

• The simplest solution would be to start with an OLS model with words learned as your dependent variable and age as your predictor. Since this is a linear specification it will have its flaws but it's a good starting point to get a feel for the data. – rbm Apr 24 '15 at 21:09
• What does your scatterplot of words learned against age show? – whuber Apr 24 '15 at 21:45
• It shows a non-linear relationship; although it is monotonic negatively. Hope that helps! – JakeP Apr 24 '15 at 22:32
• Sample size n = 19 is really low. but maybe you could use $age$ and $age^2$ as an explantory variable (predictor) in OLS model. – snoram Apr 25 '15 at 1:15
• You could use Spearman's correlation coefficient. It doesn't make a linearity assumption, but rather describes how good the data agrees with a "monotonic relationship". R's cor.test function calculates the corresponding statistics. – Roland Apr 27 '15 at 9:50