Hey all -

I'm deep into my thesis, and have only realized now that I don't know nearly enough statistics.

I have two sets of data which, when plotted on the same scatter graph, show two negative trends. When the trend-lines are drawn, one lies above the other. I'd like to be able to prove that this difference is statistically significant.

Doing some research, I've found that this is basically an ANCOVA analysis. However, ANCOVA appears to only work for parallel lines, which mine aren't.

Is there a similar analysis that can be performed on NON-parallel lines?

Thanks!

A chi square test might be appropriate to compare both sets: see http://www.georgetown.edu/faculty/ballc/webtools/web_chi_tut.html

I think the devil is in the details when trying to fit a particular statistical method to real data. For example: I assume you have several types of shoeware, 2 sexes of shoe wearers, several points in time. Is there something else being measured, such as shoe comfort or running speed? Or is the issue the type of shoeware chosen by the person?

Hi Sam,
I think I may be a little confused, as you mentioned time as a dependent variable. I think you may be fixing time on each algorithm and your dependent metric measures quality of solution. And your independent variable is complexity. To confound the issue, there are several other variables floating around even when complexity is fixed, such as starting values, the problems used, and time allotted. Since both algorithms probably converge to “the” solution over enough time, the limits you set are important. I assume you are running the algorithm on several problems of a fixed complexity and taking an average. (Pray for normality.)
Other issues you may face is how close to continuous are your dependent and independent variables; if they are too coarse you are going to have to move to non-parametric techniques. Ditto if the distribution of the quality of solution metric is not fairly normal over a fixed problem complexity.
I do think CS folks spend a great deal of time with how to construct reasonable metrics so that they can actually apply statistical techniques. The techniques themselves are well documented in biology and psychology; they have been dealing with this kind of data situation since day one. And I found several courses on the web about research methods in these two areas.
But before jumping into the quagmire of super-stats, notice that the power of the picture and some simple stats may work fine. For instance, I think an ANOVA test of some sort will address precisely the issue of whether your slopes are different (assuming that a linear model is a good fit for the two data sets). Or you could do a linear regression on the paired differences of the two sets (across complexity or even across problems and average over complexity) and do a goodness of fit on this model. Assuming a fairly good fit, the line tells most of the story for you. And then you could focus on a few select complexity levels for a more in-depth analysis.
I have seen researchers outside of the life sciences sometimes back off larger scale experiments because of the statistics barrier. But remember, half of the confusion is the fuzziness. Ignore the fuzz :-)