The objective evidence shows an increase in rear-end crashes but a reduction in injury and fatal crashes, offering a net overall benefit.

Council et al., 2005 -- https://www.fhwa.dot.gov/publications/research/safety/05048/...

There's a regression to the mean issue at work.

Sometimes an intersection simply has bad luck, draws more accidents than anything about it would cause. Put a camera there, you'll see an "improvement".

This states that there are many variables they were not able to control for, such as the yellow light timing, as I previously mentioned. Warning signs were another major factor. There doesn't appear to be enough investigation into the protected left issue.

This is pretty damning, in my opinion. AKA we did some cheap analysis on a small dataset, without confidence or effect size, and just agree with the people running the programs.

"The intent of the multivariate regression analysis was to confirm the direction of the effect, not to establish effects with statistical significance or to assess the size of the effect. To undertake analyses for these purer purposes would have required a substantially larger database, much more precision in the estimate of economic effect at each site, and more accurate specification and measurement of the independent variables. For the purposes of this current investigation, it suffices that both the univariate and multivariate analyses are reasonably in accord with the perceptions that are commonly held by those involved in red-light-camera programs."