I am working with collision data and want to run a few tests. I thought a chi-square was what I wanted, but it doesn't let me say what I want to. Then I thought a z-test of two proportions was what I wanted, but I realized I'm violating the major assumption of independence.
DV: Injury severity of collision (either fatal/severe or non-fatal/severe). IV: Road classification that collision occurred on (principal, primary, major, collector, secondary and local).
I want to be able to determine:
Is the distribution of crash severity the same for all road classifications? I would conduct six chi-square test of homogeneity, where each record would take on six new dummy variables for each road class—the collision was either on a primary road (=TRUE) or not on a primary road (=FALSE); on a major road (=TRUE) or not on a major road (=FALSE); etc. The results are below:
Is there a significant difference between the proportion of collisions that were fatal/severe and the proportion of collisions that were non-fatal/severe? This is where I messed up, forgetting that these two are not independent (the more fatal collisions, the fewer non-fatal collisions). Still my incorrect results are below. However, what I want to be able to say with statistical confidence is, "Collisions are between X and X% more likely to be fatal when they occur on Y-type of roads than other types of roads."
Does anyone have any advice on how to choose the right test to say what I want? Any other comments on what would be a better test? Or follow-up tests?