# How do I calculate the (total) uncertainty - I am looking for the correct way to do it (Nov/14/2008 )

Hi

I am looking for the one and definite answer on uncertainty.
I am still a bit confused about it. I've read some information about it, and still wonder, what is the right way to calculate uncertainty in Biology.

I am just gonna use a random example, a common biology experiment like:

"The effect of temperature on enzyme activity".

I use different temperatures and conduct 3 trials for each temperature.
I collect the gas volume to investigate the effect; and I know the gas syringe has an uncertainty of 0.1 (lets say).

So I would have the following raw data:

---------------- Volume of gas (+/- 0.1)
Temperature - Trial 1 - Trial 2 - Trial 3
1 -------------- result 1 - result 2 - result 3 -> average
2 -------------- result 4 - result 5 - result 6 -> average
3 -------------- result 7 - result 8 - result 9 -> average

My first question is, if I calculate the average gas volume for each temperature, what is the right way to calculate the (average) uncertainty? I have read that the standard deviation is used - is that the correct way to do it or is a percentage uncertainty better? In the case of percentage uncertainty, how can I calculate the average percentage uncertainty? I know that for individual values the formula is: (Uncertainty of equipment/measurement) / (measurement value) * 100 - should I add up the individuals percentage uncertainties (e.g. for result 1-3) to get the total percentage uncertainty for each average?

I just assume now, that I calculated the average gas volume for every temperature and also the uncertainty for every average.
My second question now is, how do I combine the 3 average uncertainties into one total uncertainty? (I guess it also depends on whether I use standard deviation or percentage uncertainty?)

Since I want to indicate the uncertainty at the top of the table, next to "Volume of gas" I can't have 3 different uncertanties for every average. I need some kind of total uncertainty. Can I just calculate the average from the 3 average uncertainties or is there another way? What is the common and correct way to do this?

My desired table would look the following:

---------------- Volume of gas (+/- total uncertainty)
Temperature - Average
1 -------------- average 1
2 -------------- average 2
3 -------------- average 3

Thanks a lot!

-toulouse-

No one has an idea how to do it? A link to a website, which explains it would also help...

-toulouse-

It has been a long long time since I have done this sort of stuff, but I am pretty sure that the error in this experiment will be an average of the error at each measurement (i.e. +/-0.1 in this case). However, the significance of this error will depend on how large the volume measurement error is compared to the experimental error. For example, if the 0.1 you talked about is actually 10% of the total volume, then it probably plays a significant part, but if the 0.1 is only 0.1% is that significant compared to the variation in your results?

Anyway, Google is your friend: typing experimental error calculation into Google gave me any links, of which I found the second most useful.

-bob1-