Interesting story. I sympathize with you. Seems to me that when you use actual numbers, they should mean what numbers mean -- otherwise, what's the point of using them in the first place? So yes, 99.5% means 5 errors in 1000 rows, etc.
I'll just make 55% of the rows doubly accurate. The other 45% of the rows... well, we just won't talk about those.
> When you use actual numbers, they should mean what numbers mean
That's what I thought, but percentages seem to be thought-terminating cliches for most people. I generally use ratios when presenting information to most people as a result, but I really thought my manager and I were on the same page. This issue certainly wouldn't have happened if I had described our error as "1-in-200" from the start.
I report directly to the director of the organization now though, and in addition to being much more pragmatic about necessary trade-offs, he is pretty hands-off. I think a hands-off style to management goes a long way to reducing communications errors. Each conversation becomes much more important when you aren't having them just for the sake of having them, so everyone seems to pay attention more.
I hope your manager took at least some responsibility for the miscommunication, because I can't figure out how you could have been clearer. Pointing out the cost of getting to true 99.99% accuracy should have been enough -- particularly when the prediction was borne out.
Nobody understands percentages. This isn't just something that happens to people with normal average intelligence. It happens to lawyers in adversarial situations; it happens to doctors and nurses talking about test results; it happens to bosses.
If you ever find yourself using a percentage you're often better off switching to normal numbers. "1 in 10,000"; "50 out of 100"; "9,999 out of 10,000". This is especially true if you're communicating changes. "Risk rises from 1 in 10,000 to 2 in 10,000", rather than "100% increase in risk".
Just tell her you're giving it 110% effort :-)