This is a bit of a simple question I would suspect for many users here, but for someone like me who has never covered this in my statistics classes, this is posing a bit of a problem. I want to convert forecasted scores with a regular error bar into rankings with error bars.
For example, the following individuals are to be ranked.
A [Forecasted Score: 1000, Standard deviation: 25]
B [Forecasted Score: 940, Standard deviation: 35]
C [Forecasted Score: 950, Standard Deviation: 10]
D [Forecasted Score: 910, Standard deviation: 40]
The ranking without any way of expressing how uncertain you are would be the following.
Is this done using simply by rifling through all the combinations? As in, if I chose 2 standard deviations, A could be ranked 1, 2, or 3 while B could be ranked 1, 2, 3, or 4?
This stuff was never covered in my statistics classes, and the statistics books I have handy do not cover this. Any help would be greatly appreciated.
I thought I would give a bit of background of what I am trying to do here. Suppose you are in a bar with your best friends and you are discussing a subject which can be ranked. Sports teams is popular but it can be decided clearly on the basis of who is winning and who is not. But judging songs? You're judging and ranking art. Taking a firm position on rankings might be helpful in saying that you have a ranking, but it doesn't help if someone else can make another convincing argument based on the same criteria why someone should be ranked over someone else. Sometimes it is just more helpful to describe the ranks it can have more than it does have.
This is the problem we are tackling here.