Hi all,(adsbygoogle = window.adsbygoogle || []).push({});

It's been a while since I have asked a question here, but statistics has never been my forte. I have the feeling that although I know the definitions I do not completely grasp the concept of confidence intervals. Unfortunately I do need to come up with something sensible here.

The situation is that I'm performingnexperiments, and for each experiment I'm measuringmvalues. Step 1 is, for every quantity, to calculate the average over all experiments and provide a 95% confidence interval. So far so good: I have some nice code that will give me a two-sided student t-value which I can use to construct the confidence interval.

Now the tricky bit, for me, is that I also need to take a weighted average of these averages. The question is how to calculate a statistically sensible confidence interval on this average.

So to summarize with symbols: I havenmquantities ##q_{ij}## (##i = 1, \cdots, n##; ##j = 1, \cdots m##). I have calculated ##\bar{x}_j = \frac{1}{n} \sum_{i = 1}^n q_{ij}## with the corresponding 95% CI ##[\bar{x}_j - \Delta x_j, \bar{x}_j + \Delta x_j]##.

Now I wish to calculate the weighted average ##\mu = \sum_{j = 1}^m w_j \bar{x}_j## (if you want, you may assume the w_{j}sum to 1) and would like to know how I can construct the CI for this, either from the ##\Delta x_j## or from ##q_{ij}## directly.

If they were standard deviations I would expect something like ##\sigma^2 = \frac{1}{n} \sum_{j = 1}^m \Delta x_j^2## but I don't think it works that way for confidence intervals.

[edit]Let's also assume independence where needed, I will worry about that after I get an initial idea.[/edit]

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# 95% Confidence of weighted average

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