Combining two standard errors

Hi all, I have some summary statistics from a data set that look something like this:

Category------Color---------Avg Growth-------Std Error
Flowers--------All Colors-------2.9--------------0.8

What I would love to do is calculate/estimate the average growth and standard error of the combined set of Red and Yellow flowers. Ideally, I'd have access to the underlying dataset so I could calculate these measures directly, but I don't have access to the raw data.

Is there a way I can estimate the combined Avg Growth and Std Error of the Red and Yellow flowers?

Any advice is appreciated.

Thank you!
Hi, unfortunately no. I do know the two sample are about the same size though.

Since standard error is supposed to decrease as n size increases, I can't just try to average the std errors or use sqrt of sum of squares. That would leave me with an overall std error roughly similar in size to the original individual.

My tentative plan is to estimate the overall std error this way: (avg of Red and Yellow std error) / (sq root of 2)

To try to mimic the decrease in std error as n size increases. I plugged in 2 in the denominator because the n size doubled. It's a swag, but that's my reasoning anyway.


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What exactly is your goal. Why do you want the combined se. And what do you think it would represent?
Thanks so much for helping me think this through.

I have a much larger set of data than the example I used above. Most categories have about the same n sizes but I don't have access to the actual numbers.

I was hoping to use the standard error to index the avg growth to normalize for the n size ( avg growth / std error = index )

The index is necessary (I think) because a couple of the categories need to be consolidated, which will make their n sizes much larger than the others. So I'm trying to figure out how to estimate the effect of that grouping on the standard error.