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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Will the mean of a set of means always be the same as the mean obtained from the entire set of raw data?

If I have calculated the mean for 4 data sets (which do have different sample sizes), can I then obtain an "overall mean" by calculating the "mean of the means"? If yes, will this "mean of the means" ...
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34 views

Do I need to use weighted means with the Wilcoxon signed rank test?

I have 22 patients. They have been measured pre and post treatment. There are 3 measurements per patient before treatment (pre baseline), and four measurements after treatment (post baseline). There ...
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84 views

How did they do this analysis? (weighted proportions)

I've read with interest the report by Ayanian et al "Racial and Ethnic Disparities among Enrollees in Medicare Advantage Plans" [1]. They have estimated adjusted proportions of individuals that ...
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69 views

Computation of the entropy of marginals?

I have implemented this paper: Efficient graph-based semi-supervised learning of structured tagging models In the last sentence of the section 4.2, the authors have mentioned another possible way of ...
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1answer
62 views

Obtain adjusted means - Weight? Standardize? Use LSmeans?

I'm attempting to compare means from one year to another (and between groups at the same time point) by calculating adjusted values. I'm not sure what method to use. I've thought about the following: ...
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48 views

Mean of an interval censored random variable

It is likely that I am incorrect terminology here, but I am trying to compute a "mean" of an interval censored random variable. Here is an example where: 1. a random sample from the standard normal ...
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1answer
31 views

Representing a subset of observation using weights

I have $n$ observations for $m$ variables that are sorted by time, e.g. observation $1$ is the oldest, whereas observation $n$ is the newest. I represent this data as an $n\times m$-dimensional matrix ...
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43 views

with two EWMA means of different window sizes, can we estimate any other means? slopes? jumps?

EWMA is defined as follows(1, 2, 3, 4, 5): $$ \mu_{N} = \frac {1}{N} \Sigma_{i=1}^{N}x_i $$ $$ =\frac {1}{N} \Sigma_{i=1}^{N-1}x_i + \frac{1}{N}x_{N} $$ $$ =\frac {N-1}{N} \frac{1}{N-1} ...
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155 views

Aggregating Standard Errors for Predicted Probability Estimates

I obtain predicted values from a logistic regression for a certain outcome (e.g., mortality) at the hospital level – the data is at the patient level – and need to compute the average across ...
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155 views

Exponentially Weighing Moving Average (EWMA) for weekly data

I'm aware that the typical EWMA approach is applied over larger time periods (say for Volatility, where lambda = 94% and all weights add up to 100% for stock returns data from last 5 years). ...
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128 views

Weighted variance of the weighted variance in frequency transition matrix?

Assume I have a $m\times n$ Transition Matrix $A$ with $m$ different observations and $n$ represents a discrete state space. Each column counts the frequency that state $j\in [1...n]$ was visited from ...
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158 views

Inverse-variance weighting

I'm writing a Bachelor Thesis in engineering an a small part of it has two deal with assigning weights to independent measurements. This is from the thesis: I am pretty sure that what equations ...
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1answer
33 views

Estimating costs with extreme values

I am trying to estimate health care costs and I was wondering what the standard practice is for extreme values? By extreme values I mean I have a large portion of my costs being zero and a small ...
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73 views

Weighting on tables

I have a question about terminology. Suppose I have data categorized by three factors A, B, and C, with cell means $\bar{y}_{ijk}$ and cell frequencies $n_{ijk}$, where $i$, $j$, and $k$ index A, B, ...
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33 views

Appropriate weighting for averages

What is the appropriate (or the advantages of disadvantages for each) measure for weighting mortality rates across countries: total population or total number of deaths? For example, if you have ...
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234 views

Calculating and comparing weighted means with changing number of daily values

I have daily data where the number of values changes with each day. I would like to calculate the weighted mean of this data, where days with more values are weighted higher than days with less. ...
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1answer
371 views

Compare Log-Normal Distributions

I am looking at distributions for the fuel consumption of vehicles in the US and I have two sets of data: Data Set 1 - This is a dataset for the fuel consumption of all vehicles made available for ...
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1answer
415 views

Estimating an overall summary statistic (mean) for a value reported by ten published studies

Background I am writing a systematic review and meta-analysis of the association of exposure to X with the outcome Y. I have identified ten studies that report on this subject. This will be a ...
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1answer
114 views

How to compare subjects with different weights?

I have a collection of products that could be rated as good or bad. Every product has a grade, that is the sum of "good" votes minus the sum of "bad" votes. These products are also split into two ...
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31 views

Computationally cheap estimation of the mode from 2D samples

I say 'mode' in the title – perhaps there's something more appropriate I can find. Here's my problem: A person is in a $100\mathrm m$ by $500\mathrm m$ space. I have about 100 samples randomly ...
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3answers
128 views

How to calculate the weighted mean?

For example assume I have three observations as given in matrix A $A = \left[ \begin{array}{ccc} 1 & 0 & 1 \\ 1 & 1 & 0 \\ 0 & 1 & 1 \\ \end{array} \right]$ each row vector ...
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1answer
270 views

Weighted average of measurements with unequal errors

Suppose I have the numbers below. Consider them as results of some measurement. ...
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1answer
775 views

Standard deviations and confidence intervals (weighted) running average

My question is related to this one. I am calculating averages, actually as many as I have samples because I calculate a running average, and for equal weighting I know how to calculate the $95\%$ CI, ...
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296 views

Weighted Standard Deviation vs. Weighted Regression Standard Error

This is an R question. I have $n$ observations of the variable $y$, with each observation, $i$, weighted by $w(i)$. Each $w(i)$ weight falls between zero and 1, with the sum of the weights, ...
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37 views

Aggregating based on inverse probability weight

I have a data set that includes life quality indices for many cities. I want to aggregate the indices to the metropolitan level. Since some cities in each metro area are missing, the data set provides ...
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50 views

How do I determine the appropriate “weight” of a point in fantasy basketball?

For fantasy basketball, I want to quantify a player's output based on his Points, Rebounds, Assists, Steals, 3s, and Blocks production. Let's pretend that over the course of an imaginary basketball ...
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1answer
908 views

Degrees of freedom for a weighted average

And yet another for the long list of degrees-of-freedom questions! Given an i.i.d. sample $x_1,..., x_n$ from an arbitrary real-valued distribution with expectation $\mu$, the sample mean can be ...
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1answer
1k views

Using the eigenvalues from PCA in k-nearest-neighbours

I'm quite new to this StackExchange, only been a lurker till now, but my StackOverflow fellows have said you'd be the best people to ask about this. Anyway, enough introduction. I'm using the ...
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1answer
159 views

Comparing two lists to measure for similarity

The problem I am trying to solve is finding the probability that two people are the same by cross-referencing the associates of the two people. For example, if person A is associated with the ...
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83 views

How to bootstrap confidence of a weighted measure?

I have a large data set of 20M observations with 20+ measures for each observation (people). Additionally I have a set of weights that reflect the racial population where each person lives. For ...
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3answers
2k views

Weighted standard deviation of average

For two groups (a and b) with unequal numbers of observations (n=10 and n=30), I have given their means and sd. Calculating the weighted mean is pretty straight forward. But how can I derive the sd of ...
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1answer
154 views

Standard error of a weighted mean when observations are not independent

I have a situation where I have a bunch of noisy observations with known (and normal) sampling error and a non-trivial co-variance structure between the observations. In an uncorrelated setting, I'd ...
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1answer
57 views

Estimate the parameters of an ellipse in the presence of large outliers

I have a number of points $x_1,\ldots,x_m\in\mathbb{R}^n$ with weights $w_1,\ldots,w_m$ between 0 and 1. There is an ellipse which contains a very high concentration of points with weights close to ...
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3k views

How to compute weighted means and SDs?

I want to calculate volume weighted average price and standard deviation for the following dataset: ...
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290 views

Confusion regarding weighted average

This is a pretty simple question and I'm wondering how to go about finding a solution. I have the following data. ...
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1answer
183 views

Given weighted mean and raw data, derive weights to minimize error

Imagine I have a set of data from an experiment: Observed Measurement 1: 5 Observed Measurement 2: 6 Observed Measurement 3: 7 Observed Measurement 4: 8 Observed Measurement 5: 9 I have a target ...
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1answer
10k views

Weighted Variance, one more time

Unbiased weighted variance was already addressed here and elsewhere but there still seems to be a surprising amount of confusion. There appears to be a consensus toward the formula presented in the ...
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136 views

Best fit of weighted mean?

The title might be somewhat misleading. I am trying to solve the following optimization problem and do not find any clues. Can any one help? I have a sequence of $n$ observation $s_i$. Each ...
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1answer
307 views

Is there a more elegent solution for exponentially weighted-mean in R? [closed]

OK so I have a working code to do what I want but I am new to R and feel like my solution is very clunky and there is likely a more efficient way to get the same result. I have a set of data that ...
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1answer
156 views

Computing lowess mean value

I am trying to reimplement the lowess algorithm in java. I read the matlab page explaining lowess with the following steps: Compute the regression weights for each data point in the span. A ...
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1answer
375 views

How does a Daniell kernel differ from a two sided average?

As far as I can understand, the Daniell kernel, is simply $K(j/M)=\frac{1}{2M+1}1(|j|\leq M)$. Namely, this is a two sided average. Why do people call this an untruncated kernel and differentiate ...
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169 views

Always get confused by “probabilities and weighted probabilities” type of questions as cant differentiate between two

Urn 1 contains 5 white balls and 7 black balls. Urn 2 contains 3 whites and 12 black. A fair coin is flipped; if it is Heads, a ball is drawn from Urn 1, and if it is Tails, a ball is drawn from Urn ...
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3k views

Bias correction in weighted variance

For unweighted variance $$\text{Var}(X):=\frac{1}{n}\sum_i(x_i - \mu)^2$$ there exists the bias corrected sample variance, when the mean was estimated from the same data: ...
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1answer
841 views

Optimize Weights used in a Weighted Average

I want to calculate a weighted average, mostly for illustration purposes. However, I have an outcome variable that is Y/N and would like to optimize the weights relative to this outcome. What are ...
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1answer
222 views

Voting system that uses confidence for each voter

Let's say, we have simple "yes/no" question that we want to know answer to. And there are N people "voting" for correct answer. Every voter has a history - list of 1's and 0's, showing whether they ...
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1answer
8k views

A simpler way to calculate Exponentially Weighted Moving Average?

Proposed Method: Given a time series $x_i$, I want to compute a weighted moving average with an averaging window of $N$ points, where the weightings favour more recent values over older values. In ...
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1answer
525 views

Handling missing attributes when using weighted average

I was trying this optimization where I have some predictors and I want to predict the real value using weighted average of the predictors. What I am trying to do is given the predictors' prediction ...
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1answer
591 views

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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499 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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1answer
413 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?