For those who know something about statistics,

I'm wondering how to analyze a prediction interval encompassing other prediction intervals. To provide some background, I'm not talking about confidence intervals (they are often confused). I'm computing a 95% one-sided prediction upper-limit for a set of data. The definition I'm familiar with for a prediction upper-limit is that we can predict that a future test would be less than the upper-limit 95% of the time. Without assuming anything about the data distribution, the maximum of 19 instances will give me a 95% upper limit. This is because 19 data points create 20 bins, and so a future test (#20) has a probability of 1/20 or 5% of landing within each bin. The last bin is everything higher than the maximum value of the 19 repetitions, and so there is a 5% chance the future test will be higher than this value, and a 95% chance it will be lower.

So that's all fine and dandy, but now I have two levels of prediction limits, and the best way I can illustrate this is with a simple example. Suppose I want to analyze the performance on my computer, and there is inherent randomness in how I test this, so I create a 95% prediction upper-limit using 19 tests to know a future test has a 95% chance of falling below that value for my computer. But there are many different types and brands of computers, and if I want to know about the performance of computers in general, I test 18 more computers (19 total) of different types and brands. So now each computer has its own 95% prediction upper-limit specific to itself, and the maximum of all 19 upper-limits provides an upper-limit for computers in general.

My question is this: Do I have a 95% prediction limit for all computers? Because each one has an individual 95% limit, is it actually a 90.25% limit (.95 * .95)? Or possibly a 99.7% limit (since there are 19*19 total data points)?




Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.