In my college statistics class, we learned MatLab and R using data from the Challenger to recreate why the engineers thought the o-ring might fail and raised the warning. I don't remember the specifics of all the stats, but it was fascinating and the data is publicly available.
I wonder what kind of effect that analysis would have on the launch decision. Here's how I would expect it to go:
Engineer: The logistic regression model shows there is a 99.96% chance of failure at 31deg
Manager: How good is the model?
Engineer: p=0.1157
Manager: So it's not statistically significant by our standards. In other words, it's not a very good model.
Engineer: Yeah, but still.
Manager: Well, what does the model say the temperature needs to be before we're more likely to have a successful launch than not?
Engineer: 64.8 degrees.
Manager: I can't defend pushing the schedule to the right that far based on a statistically insignificant model.
(It doesn't mean the manager was right, but I think it highlights hindsight bias. The model only seems good in hindsight because it aligns with the outcome we witnessed and not because it's a really good model. The managers at the time didn't have the benefit of hindsight.)
Here's a blog that shows some of the analysis (from google search): https://byuistats.github.io/Statistics-Notebook/Analyses/Log...