Yep, the numbers I ran are already doing exactly what you suggest. Looking exclusively at the 10 lost packages and considering how likely it should be that 9 of

Yep, the numbers I ran are already doing exactly what you suggest. Looking exclusively at the 10 lost packages and considering how likely it should be that 9 of them would belong to one category, compared to our expectation (which is that they would be equally likely to have come from either category, coming from the fact that the same number of packages were shipped with Atheist labeling as without). The statistics is entirely identical to flipping a coin 10 times and asking the following questions: * Given that I saw 9 heads and 1 tail, how likely is it that the coin is a fair coin. This is the p-value which was about 0.0098 (less than 1% chance) * Given that we are only tossing 10 coins, how likely are we to have seen a statistically significant bias with the predicted bias in place. This is the statistical power, which was 74%. As you suggest in your other comment, the stats only point to a bias, the origin of the bias is left for people to decide. That said, the packages were sent in pairs, so subdividing the country into states and offices is irrelevant since a given states saw the same number of packages from each category as did each given office, the statistics are saying that on average (across the whole country) there is a bias. To ease your worries a little, this is not saying the USPS hates Atheist packages 9x more than non-Atheist packages, most of the packages were delivered successfully. All this is saying is that, for the ones that were lost, it is very likely that they were lost because of their labeling. This is the effect you would expect to see if 97.3% of USPS employees treated the packages identically and the other 2.7% have a strong bias. If we had more specifics about the delayed packages as well, we could get a more nuanced picture, I suspect we would find that 80+% of USPS employees are unbiased, some 10-15% might have some bias against Atheist labeling (would delay an Atheist labeled package), and 2-3% have a strong bias against Atheist labeling (would lose an Atheist labeled package). If I was at USPS, I would push to conduct an experiment to try to identify which offices were most likely to have some bias one way or another (not necessarily specifically about Atheism, one could test whatever they wanted presumably).