I got an email from the senior member of a rival research group about a published paper. He had several detailed questions, clearly pasted in from a Word document complete with sub-items (a, b, c, d) and bold font for the item titles. I had a sinking feeling in my stomach because he asked straight out whether one of the numbers was correct because it seemed high to him, and I remembered why it might not be correct.
I spent over four hours going back over my paper, pulled up all the programming again, and discovered the mistake that I had suspected. That one number was too high by one because of a programming oversight. No other numbers were off and it doesn't change the primary or even secondary results of the paper because I'm interested in differences, and even after being corrected, my number would still seem "high" so qualitatively my results are the same.
It made me nervous to admit the mistake to a rival especially when I'm on the job market so being scrutinized. I also felt weird sending him exact details in writing because I know that they have enough people in their group that if they wanted to, they could replicate my paper quickly and perhaps discover errors that I hadn't seen. I'll submit a correction to that one number to the journal once I'm done with the job market, but the correction will have no practical effect on anyone's future work and could have a negative impact on me.
Most of the questions were just details about definitions, and so I wrote up my answers to all the questions and dallied over sending it. Then I realized the phone exists. Thank you, Alexander Graham Bell!
I called him up and answered all his questions. For the one answer where I am off by one, I told him how I defined the quantity, a bit different than most, and then gave an argument for why the answer should be "high" since it really is high both as published and once corrected.
He said, "Oh!" like he hadn't thought of my answer why it was plausible. He agreed that it made sense, and he seemed sincerely satisfied by that answer. And his qualitative understanding will be exactly the same if he finds out it is really x-1 instead of x.
And then I got to find out about their group's newest research, and I even gave him a tip that I think could really help them.
Beyond the lesson about the phone being oh so useful, it's really nice to realize that no matter how quantitative you get, people think qualitatively. Someone is short, average height, or tall, and even if their height is off by a few inches they probably wouldn't change categories. Likewise, my answer was "high", and qualitatively it didn't make a difference whether it was n or n-1.