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I am a science student, however unfortunately a complete newbie in math and statistics. I am measuring soil respiration for my master thesis project and have a certain amount of carbon respired that I have measured over 30 day period. I plotted the respired carbon as a function of time in days and it looks similar to this:

Each data point is a sum of the measured value at a certain day plus value of the previous measurement at a certain day (time). Now, I know how to calculate and report error bars for a basic data, but these are sums of values (cumulative values), so I am wondering how to estimate standard error or deviation for this type of data. How would I calculate and report error bars for my data in this situation?

P.S. This graph is just an example, not my actual data, but it is essentially the same.

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From basic properties of variance:

$\text{Var}(X_1+X_2) = \text{Var}(X_1)+\text{Var}(X_2)+2\text{Cov}(X_1,X_2)$ and the $k-$variable case can be obtained recursively from that.

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You can just calculate the basic data from the cumulative data.

$f_n$ = $F_n$ - $F_{n-1}$

Where $f_n$ denotes the basic data and $F_n$ is the cumulative value

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  • $\begingroup$ Thanks, but I have both a cumulative and basic data sets given. I probably did not make myself clear. What I am looking for is a way to calculate standard deviation or standard error for the cumulative data set. $\endgroup$
    – iirisa
    Commented Jun 30, 2016 at 11:19

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