# How to interpret results from non-parametric ANCOVA?

I 'm new to the CV and not very good at statistic:) I would much appreciate some help on a non parametric ANCOVA in R sm package. I do a pre post analysis on a set of pre/post variables of two groups (so group is a factor). The preand post variables are numeric values (measures) or ratios of numeric measures.

The sm.ancova output is simply a p-value and

• I do not really understand what the "models" are
• it does not say if there is an interaction factor:covariate.

How should I interpret the output of the sm.ancova function in R?

E.g. for var1 to var4, post as response, pre as co-variate, group as factor:

• var1 p-value: non significant for "equality model" and non significant for "parallel model",
• var2 p-value: significant for "equality model" and non significant for "parallel model",
• var3 p-value: non significant for "equality model" and significant for "parallel model",
• var4 p-value: significant for "equality model" and significant for "parallel model".

Edit: it seems that R sm package is about smoothing / "form of the relationship between y and a continuous covariate". Are there non-parametric alterniatives for ANCOVA when the distributional assumtions are not met? Some details: I compare 2 small gourps (group is a factor, categorical), y is post measure, and x is pre mesure (covariate). The question is if the effect of the treatement is the same on both groups.

• Of possible interest: Nonparametric equivalent of ANCOVA for continuous dependent variables. – chl Apr 4 '13 at 19:37
• Dear chl, yes I saw your answer to the other post before asking. And I must say that it helped me a bit but I still do not fully understand. (I also reporduced your example.) First, with my data, it does not make sense to run a parametric anova at first place, as you did, so I do not have a reference situation. Second, in your example, what do "equal model, p =0.0036" means? How to interpret it? Third, fANCOVA package is unfortunately even less documented than the sm. Many thanks! – akh Apr 4 '13 at 20:02
• @akh see my comment on the earlier post chi points to. I think it's essential to resolve that issue before asking anything else, or you're going to have a bad time. – Glen_b Apr 4 '13 at 23:55
• @Glen_b Thanks for your comment! You may be right because the title of sm is "Smoothing methods for nonparametric regression etc.". At the same time sm.ancova states that "This function allows a set of nonparametric regression curves to be compared, both graphically and formally in a hypothesis test." This is very confusing. The sm is based on the book by Bowman and Azzalini Applied Smoothing Techniques for Data Analysis: The Kernel Approach with S-Plus Illustrations’ but it is quite hard to find it. How can one find out if the sm package about first or second meaning of 'non-parametric'? – akh Apr 5 '13 at 0:19
• P.S. in my case, I refer to the first meaning, i.e. the distributional assumtions are not met. – akh Apr 5 '13 at 0:24