How does standard deviation change with mathematical operations on the mean?

marinebioloj

New Member
Hi everyone,

while this question is not homework, I found it to basic to be put in the "research" category.
I am comparing nutrient uptake rates of algae under different conditions and have taken samples with three replicates after different times (but also from different beakers each time, so I guess they are independent?). To get the rate for a specific timeframe I have to substract the previous mean from each mean, then divide the result to get to the uptake per hour.

In short: Substract, divide, and sometimes also multiply means with standard deviations from and with each other or single numbers.

I am doing all of this in excel and so far my resulting SDs are not right, since I just tried to puzzle together formulas with the limited knowldge I have. There seems to be no concise guide for this online. Unfortunately, I do not understand a page long essay with a dozen sum signs and other operators, so I hope someone here can help me.

marinebioloj

New Member
Hi again,

is the question not good or thought too easy to solve?
For me it is not, unfortunately, but very important for my results.

JesperHP

TS Contributor
I am comparing nutrient uptake rates of algae under different conditions and have taken samples with three replicates after different times (but also from different beakers each time, so I guess they are independent?). To get the rate for a specific timeframe I have to substract the previous mean from each mean, then divide the result to get to the uptake per hour.
I do not fully understand youre calculations nor the statistical assumptions you are making from the above the description hence a general answer. One approach would be to use the delta method another would be to simulate and or bootstrap.

marinebioloj

New Member
Thank you for the quick reply!
I thought it might be important to know where the data came from, in case it made a difference in the formula I have to use. Maybe I wrote a bit confusing, so I added an excerpt from one of my data sets. The rest can be ignored for now. I do not know the methods you mentioned (or not those names at least) but I will look them up as well.