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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How to relate raw scores on five-point Likert to three conceptual categories?

My thesis is on employee productivity and I had a questionnaire which consists of a five-point Likert scale (5-strongly agree, 4-agree, 3-agree, 2-disagree, and 1-strongly disagree). On the other ...
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279 views

How do I calculate the ranking of some galleries based on the rankings of the artists represented by them?

The mean is not good in this case, because there are galleries that have an artist with a high rank and several other artists with way lower ranks. I'm thinking about doing a weighted mean, but I ...
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277 views

Weighted harmonic mean vs weighted geometric mean [duplicate]

Possible Duplicate: Weighted geometric mean vs Weighted mean I searched for the differences between WHM and WGM. When to use each of them? when not?
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Weighted geometric mean vs weighted mean

I have a set of data, each element has a weight. I need to estimate the mean of this data. I found that there are two ways: A weighted geometric mean and a weighted mean. When should I use each of ...
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108 views

Error on weighted mean

I have some measured datapoints. Each of the points has attached an error, depending on how precise the measurement was done. Now I'm using the squared weighted mean with the inverse of the errors as ...
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Hypothesis test for difference between domain means with weighted data

I have a large dataset that is weighted due to: probability proportional to size sampling, & disproportionate stratification. I would like to compare the means for two different domains ...
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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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212 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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539 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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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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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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303 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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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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639 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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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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281 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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599 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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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: ...