Calculating Confidence levels

Hi,

I haven't done maths for a while and have a task of creating some confidence levels in excel and displaying them on a graph (which is obviously easy).

So the data I have looks like this:

-32.78% (55-82 vs 48-140)
-7.28% (13-82 vs 12-140)
What this data means:

82 = total population for filter X
55 = total population for filter X, that are of a certain type
140 = total population for filter Y
48 = total population for filter Y, that are of a certain type

The next row is the same but of a different type.

Percentage is obviously the difference between the too filter populations.

The total population is 140 + 82.

Can someone help me get started on how to get the confidence levels for each type? Pretty stuck on how to get started.

Cheers,

Sam

Also the output is going to be a bar chart with the percentages, and the confidence levels to go over the top of that percentage bar.

Cheers,

Sam

There's not enough information to answer this question right now. Quite a bit more detail is needed. That is, you could say the first percentage has a confidence interval at 95% confidence of +/- x%, and I could construct a model where that's true with exactly your first post's data alone, for any choice of x.

First you need to define the probability distribution (decent writeup; not great) which your percentages come from. This would probably require figuring out the distribution for the filter population numbers and then seeing what the distribution of their quotient (or something) is. From there it would be a simple matter of numeric integration / iterative inverting to construct your confidence interval, unless the distribution is particularly nice in which case analytic formulas could be used.

It's actually unclear to me how you combine the filter population numbers to get your percentages. The "difference between the too [sic] filter populations" is 140 - 82 = 58 in the first case, which seems entirely unrelated to 32.78%. Various quotients also don't seem to make sense.


So, where does your uncertainty come from? Can you quantify it precisely? How confident are you that the filter population numbers are within 1 of the correct answer? 2? 3? 15? Essentially, you need to be able to answer this question to generate a confidence interval at the end.