Confidence Intervals of ratios Watch

bramp
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#1
Report Thread starter 11 years ago
#1
Hello,
I'm a PhD student and I'm a little embarrassed to be asking for Maths help on here, but there is something I couldn't find out by googling, so I figured I'll ask here.

I have been running two sets of experiments, the first is a base line, and the second is hopefully an improvement on the first. I repeat each experiment many times and get a set of values, for example:

first = ( 2, 3, 3, 2, 4, 2 ) mean = 2.67, stddev = 0.82, 95% interval = +/- 0.65
second = (4, 5, 6, 5, 4, 5 ) mean = 4.83, stddev = 0.75, 95% interval = +/- 0.6

Now I can work out a 95% confidence interval for both sets of values, but what I've been writing in my report is that the second experiment produces values 1.81 (4.83/2.67) higher (and better) than the first experiment. However I do not know what the confidence intervals would be on this value.

I had thought I could divide the intervals together for example the first min value divided by the second's min value. But I have a feeling this isn't right.

Hopefully this has explained my problem, and that someone is able to help.
Thanks
Andrew
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bramp
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#2
Report Thread starter 11 years ago
#2
Sorry I'm not sure I'm following you thirdrate. What are a, b and n?

Are you saying that
the Probability that R = a/b is the same as the Probability of X = n, times the probability of Y = n * a/b ?

So that will give me a distribution, and then from the distribution I can work out the +/- 5% around the mean? It would help a lot of you could show me how this works on the values I actually gave.

One thing I should note. The values I've given are not the real values for my experiment, and just some I made up. However I plan to work out the ratio for both discrete and continuous data.

thanks
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bramp
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Report Thread starter 11 years ago
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Ok, now I understand your first post. Thanks for taking the time to show me with my data.

I'm sorry to be a pain but I don't see how this relates to the confidence intervals. Is it that basically now that I know all the possible ratios from my samples, thus I can work out the confidence interval on those values?

thanks
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bramp
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#4
Report Thread starter 11 years ago
#4
Thanks for all the help, but I have now found the solution here:
http://www.graphpad.com/quickcalcs/ErrorProp1.cfm
http://graphpad.com/FAQ/images/Ci%20of%20quotient.pdf

What I needed to use was the Fieller method to work out the confidence intervals.

thanks
Andrew
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