I'm trying to establish whether certain soil types are associated with (statistically significant) higher rates of gas pipe failure.
I have a set of polygons representing different soil characteristics. Each soil association has an ID (not unique as the same soil characteristics could exist in many non-contiguous locations) and is also classified from 1-6 in terms of the shrink-swell potential and similar for corrosivity.
I also have a set of line features representing gas pipes, and a set of point features representing pipe repairs.
I've carried out a GIS intersect which I can aggregate to get the repair rate in repairs per kilometre for each soil class. I am also able to filter on pipe material and repair cause - Cast Iron and Spun Iron pipes tend to fail by fracturing, which is associated with high shrink-swell soils, and Ductile Iron and Steel pipes tend to corrode, which is associated with high corrosivity soils.
My initial approach was to plot a scatter graph with length along the x-axis and number of repairs along the y-axis, with the points each representing one soil class. By adding a trendline we could then say that soil classes with positive residuals were more leaky than we'd expect for the length of pipe in that class. This seemed to show that the corrosivity and shrink-swell classes were not useful as there were no big residuals, but when we used the individual soil IDs (closer to 100 different classes rather than just 6) there were some that stood out more.
I'm not sure how valid this approach is, as the trendline is only derived from relatively few soil classes, which could potentially have a high leverage potential.
I've also calculated Z-scores comparing the failure rate for each soil class with the overall failure rate in all soil classes. This seemed to show only a few soil types with p<0.05, all of which had very low pipe lengths. I then realised that the failure rates are not normally distributed, so the Z-scores were not valid. A log transform got them to look a bit more normal, but still right-skewed.
At this point I'm a bit out of my depth with the statistics side of it all!
My question is: am I approaching this in a sensible and valid way? Are there other approaches people with more stats skills would take for this kind of analysis? I've been reading up as much as I can on various statistical tests in the hope of finding some examples that match this situation, but most of them are written in terms of not knowing the population statistics and using samples - in this case I know the full population and I'm struggling to find examples that match what I'm trying to do.
Any help or suggestions appreciated!