No you're not seeing it from the management perspective. They've already selected their model and assumed that performance depends on the worker involved. There

No you're not seeing it from the management perspective. They've already selected their model and assumed that performance depends on the worker involved. There isn't any "they’re all performing the same within the margin of error" because that would violate a model assumption. It has a probability of ~0%, there isn't any point checking for it. You're working from a model where the performance could be the same and then doing the obvious statistical checks. Typically in the wild management have sufficient knowledge to do those checks if their model allowed for performance to be equal. But they don't have a model where that is a reasonable possibility so there is nothing to check. They're doing the correct statistics for the wrong model. And the model happens to be really stupid but that is managers for you. You can teach them all that theory and they still won't apply it. The problem isn't usually a gap in statistical knowledge. Take another look at how Deming framed his experiment - if you look closely he is imparting statistical knowledge but that isn't where the real focus is. He's actually attacking the idea that the workers have any influence on outcomes.