Deriving error bars for a quantity derived from the division of two means

Joined
Mar 28, 2015
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Hi Everyone,

So I have 5 measurements, two for one group and three for another, so each group are averaged and have an error bar (I'm using SD as the error - should I use SE or CI instead?). However, I want to present the fold-change in a graph, and I'd like to show the correct error bars too.
To avoid confusing analogies I'll just give you my raw data and ask how to derive the error bars for my graph.
My quantity is number of cells and my two averages are "young" and "old".

Young. Sample 1: 2,352,511. Sample 2: 2,150,219. SD of these two numbers: 143,042. Mean: 2,251,365.
Old: Sample 1: 899,599. Sample 2: 1,259,732. Sample 3: 1,267,710. SD: 210,263. Mean: 1,142,347.

What I am doing to present this data is then to divide old by young to show the fold change = (1,142,347/2,251,365) = 0.507
Then I find the percentage change by deducting 1 and multiplying by 100 and this is the data I present on a bar graph.
(0.507 - 1)*100 = -49%.

Could anyone help me get my error bars onto the fold-change or percentage change graph bar?
Many, many thanks for any help.

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