A weighted mean (or weighted average) is like an ordinary mean, but the observations don't contribute equally - more emphasis is placed on some data values than others; they are weighted by a bigger or smaller amount than 1/n.

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Estimated Treatment Effect in the full sample is not between the estimates of the stratified samples?

I am estimating the relationship between students' math scores and using a supplemental math software. I've adjusted for some demographic variables in the model. In my first model, I use the full ...
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202 views

Better method to estimate gender gap: difference between medians or median gap by occupation?

I'm doing some analysis of Bureau of Labor Statistics data on wages earned by men and women, and I'm trying to determine which of the two methods I've used is the better estimate of the gender wage ...
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477 views

Negative weights in a moving average?

A number of well known moving averages, such as Spencer's 15 point MA, and Henderson moving averages have negative weights in the averages. What does this mean in a conceptual sense? What information ...
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3k views

Computing standard error in weighted mean estimation

Suppose that $w_1,w_2,\ldots,w_n$ and $x_1,x_2,...,x_n$ are each drawn i.i.d. from some distributions, with $w_i$ independent of $x_i$. The $w_i$ are strictly positive. You observe all the $w_i$, but ...
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1answer
265 views

Estimate the population variance from a set of means

I have a set of measurements which is partitioned into M partitions. However, I only have the partition sizes $N_i$ and the means $\bar{x}_i$ from each partition. Because all measurements are assumed ...
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296 views

Standard error for the sum of weighted means

I am looking at a two-stage process of diagnosis. Stage 1 is a screen that identifies people with the diagnosis with some error, Stage 2 is a detailed examination (a gold standard) In Stage 1, N ...
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34 views

How to symmetrically adjust data by removing certain value

Say I have a data set in the following format: {a:200, b: 100; c:400} The sum of a, b and c equals 700. Now, I have another value which is supposed to be the actual total say 500. How do I adjust ...
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2answers
604 views

Weighted mean of two 2D Gaussian random variables

I have two 2D Gaussian random variables. I'd like to find the weighted average of the two (based on their covariance matrix around the mean, meaning that the mean of the final Gaussian should be ...
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88 views

Weighting datapoints by uncertainty - asymmetric CIs

I have several estimates obtained using different softwares, these programs give me an estimate as well as a 95% confidence interval. However, these CIs are not symmetric around my point estimates, ...
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261 views

Averages of averages (of averages, of averages…)

Consider the following cell biology experiment. We are comparing $T$ different treatments of cultured cells. Each treatment $t$ is replicated in several (microtiter) wells, indexed by the variable ...
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1answer
470 views

Determining true mean from noisy observations

I have a large set of data points of the form (mean, stdev). I wish to reduce this to a single (better) mean, and a (hopefully) smaller standard deviation. Clearly I could simply compute $\frac{\sum ...
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1answer
185 views

How do I introduce features and their confidence values into classifiers

I would appreciate some advice on how best to weight or give more importance to a percentage with a larger denominator. Eg A. 1 out of 2 = 50% B. 5 out of 10 = 50% C. 500 out of 1000 = 50% Some of ...
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How do I calculate a weighted standard deviation? In Excel?

So, I have a data set of percentages like so: ...