Gene lab based simple statistics question

[Tloh]

Pretty basic math question, but I really haven't taken Statistics since the AP in HS.

The basics are... There are several thousand things (genes) that are measured and have a numeric value. Each of these numeric values has an associated error with it. There are six trials for EACH of those (thousands) of genes with the error also. What I am trying to do is to find the average value and the associated error for each of the genes separately.

The average value, I'm thinking just simple arithmetic mean, but I'm at a loss for how to approach the error.

 

[wywong]

The basics are... There are several thousand things (genes) that are measured and have a numeric value. Each of these numeric values has an associated error with it. There are six trials for EACH of those (thousands) of genes with the error also. What I am trying to do is to find the average value and the associated error for each of the genes separately.

First you need to identify if the associated errors of the 6 measurements of a gene are random or systematic. If they are random (e.g. round off error), they tend to cancel each other out, and the average error should be 1/sqrt(6) (or about 0.408) of each error (I assume them equal). If they are systematic (caused by common factors that affect the measurements in the same sense, such as a poorly calibrated instrument), they don't cancel each other and the average error is the same as the individual errors. If the associated error is a combination of both random and systematic errors, the average error should be somewhere in-between. To be precise, you need to separate both types of errors, apply averaging to the systematic part, and then combine them (adding the sum of squares and then take the square root).

The above is based on what I learned at HS some 30 years ago, so maybe other experts can provide a better answer.

 

[Rasine]

i believe the error can be equivable to the standard deviation and if that is not true you can find that out by using the error.

but the average s.d is the square of the sum of the s.d.

even if you don't have s.d., which is very unlikely in real world situations, you can use standard error. the above will give you a pretty good estimate.