Basic stats question.

QuantumTurk

So, I apparently did not pay enough attention in my physics labs, and am now suffering in the real world for it.

I have average expression data for proteins we will call A, B and C. Each of these averages, sensibly has a related standard deviation.

I am relating expression of A to B, A to C and so on via a simple ratio, such as A/B=(RATIO#) and using the resulting number.

My question is, what is the new standard deviation/ error bars on RATIO#? I don't know how to phrase it into google, and I honestly did not take stats beyond the most basic level, so I am terrified of doing something mathematically invalid.

I can clarify further if need be, but the problem really is as simple as stated above.

Thanks in advance for all explanations!

romanqwerty

Are A and B dependent on eachother or independent?

The rule when multiplying or dividing is that the relative standard deviations (sd(A)/A) add together to make the relative standard deviation of the product(or quotient). For independent variables this means that:

sd(R)/R=sd(A)/A + sd(B)/B

where R is your ratio and sd(A) means standard deviation of A.

For dependent errors you have to perform the addition in quadrature resulting in:

(sd(R)/R)^2=(sd(A)/A)^2 + (sd(B)/B)^2

Gdiguy

The second one you describe is what I've commonly seen (quick google searching gives an example derivation here http://www.nap.edu/openbook.php?record_id=54&page=284 , where the covariance terms drop to zero if they're independent)... I don't think I've seen it without the square terms, and I can't figure out a mathematical reason why they'd drop out (admittedly I'm a little tired)

QuantumTurk

romanqwerty wrote:

Are A and B dependent on eachother or independent?

The rule when multiplying or dividing is that the relative standard deviations (sd(A)/A) add together to make the relative standard deviation of the product(or quotient). For independent variables this means that:

sd(R)/R=sd(A)/A + sd(B)/B

where R is your ratio and sd(A) means standard deviation of A.

For dependent errors you have to perform the addition in quadrature resulting in:

(sd(R)/R)^2=(sd(A)/A)^2 + (sd(B)/B)^2

First of all thanks for the answer! So I think I should treat them as independant, as their expression is not known to be influenced by the other. This could of course be wrong, but we wouldnt know, so this seems safest. Now my charts have error bars, but I admit I am puzzled as to why (and no offense but IF) that is valid. If you could reccomend any references or similar I'd appreciate it before I run this past my PI. Thanks again!

romanqwerty

I don't actually remember where in a physics degree I learned it. But a quick skimming of this (http://www.physics.unc.edu/~deardorf/uncertainty/UNCguide.html) is consistent with everything i've learned about this.

Gdiguy

QuantumTurk wrote:

romanqwerty wrote:

Are A and B dependent on eachother or independent?

The rule when multiplying or dividing is that the relative standard deviations (sd(A)/A) add together to make the relative standard deviation of the product(or quotient). For independent variables this means that:

sd(R)/R=sd(A)/A + sd(B)/B

where R is your ratio and sd(A) means standard deviation of A.

For dependent errors you have to perform the addition in quadrature resulting in:

(sd(R)/R)^2=(sd(A)/A)^2 + (sd(B)/B)^2

First of all thanks for the answer! So I think I should treat them as independant, as their expression is not known to be influenced by the other. This could of course be wrong, but we wouldnt know, so this seems safest. Now my charts have error bars, but I admit I am puzzled as to why (and no offense but IF) that is valid. If you could reccomend any references or similar I'd appreciate it before I run this past my PI. Thanks again!

If you have pubmed access, the second equation is identical to what people use for calculating stdevs of normalized qPCR values (and there's some amount of derivation in the paper/supplement - equations 10 & 14):
http://www.biomedcentral.com/1471-2105/8/131