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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13 views

Optimal weight for weighted average

I have some data points for which I do not have individual errors. My goal is to calculate the weighted average and I am looking for the "optimal weights" that can be used. I was thinking about the ...
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7 views

Comparing weighted means of unequal subsets of values

If I have a range of data on a grid with associated weights, what is a correct method of calculating a weighted mean of values that fall within one cell, so they may be compared with the weighted ...
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1answer
37 views

Is precision-based (i.e. inverse-variance) weighting integral to meta-analysis?

Is precision-based weighting central to meta-analysis? Borenstein et al. (2009) write that for meta-analysis to be possible all that is necessary is that: Studies report a point estimate which can ...
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2answers
83 views

What is the correct method for “standardising” scores -1 to +1 (ideally in R)?

I have a dataset 3,270 rows long of news stories DOWNLOAD HERE from Mega. For each story I have calculated a basic sentiment score for the title, description and body texts (which is just a simple ...
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38 views

Alternate weighting schemes for random effects meta-analysis: missing standard deviations

I am working on a random effects meta-analysis covering a number of studies which do not report standard deviations; all studies do report sample size. I do not believe it is possible to approximate ...
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1answer
23 views

Deriving mean of percentages from clustered data

I am getting into a roadblock about how to analyse this data set. I hope folks here will be able to give me some hints and suggestions. Here is an example of the data: I'm using sugar as the ...
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1answer
22 views

Standard Error for Weighted Values

I want to calculate the standard error for an experimental measurement. The data is stored as a 2D image which is circularly symmetric about a center point. To reduce the data we radially integrate ...
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28 views

Ranking based on weight for multiple variables and objectives

First of all, I know very little about statistics. I need help ranking a set of multiple solutions (about 138 solutions) based on three objectives. I work on the architectural design field, I analyzed ...
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13 views
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32 views

Estimate the population variance from a set of weighted means

Proviso: I do not have a lot of experience with statistical theory, so please forgive my occasionally poor choice of notation.$$\\$$ My problem is as follows: I have a set of measurements $X_i, ...
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29 views

Averaging standard deviations of unequal weight?

I'm sorry if the title is unclear, but I'm not sure of the appropriate way to phrase this question. I'm in med school (and sadly not as versed in statistics as I ought to be), and I am trying to use ...
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1answer
10 views

I get a different result when I try and calculate the mean-variance formula of risky and riskless asset [closed]

I'm having trouble seeing how the expected return of a two asset portfolio, where the weight of the risk-free asset is positive, but the weight of the risky asset is negative, results in the final ...
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1answer
158 views

Model averaging predictions from lmer models [closed]

I am trying to model average predictions (not betas) and estimate confidence intervals from linear mixed models run with lme4::lmer. I have experimented with functions in the MuMIn and AICcmodavg ...
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29 views

Construct confidence interval for price per area, from weighted average price for quantity, and weighted average quantity per area

I have function for obtaining the weighted mean for price per quantity, where $p$ is price, and $w$ is the weight, for some product $i$. $$\bar p_a = \sum p_{i} w_{i}$$ and a quantity per area, ...
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2answers
40 views

How should I determine an average from a set of averages

I have a set of lines. I measure their length each 5 times, and then take the mean of their lengths (as I measure them). I also take the standard deviation. I want to know the 'average' line length. ...
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40 views

Averaging Rank Sum Weights and Rank Order Centroid

I have calculated Weights of fourteen items using Rank Order Centroid, Rank Sum Method. ...
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56 views

Standard Error for Relative Frequency Distribution

I have a weighted distribution with weights $w_i$, such that: $$\sum_i{{w_i}}=1$$ I know that the mean is defined by: $$\sum_i{{w_i}{x_i}}=\mu$$ And that the unbiased variance is defined as: ...
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37 views

what is name outlier detection method

I want to find the name of method for outlier detection. this method calculate standard deviation and mean of data set. sample that is not in (mean-sd mean+sd) is an outlier.
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80 views

Borda Count (Weighted Sum) vs Weighted Mean

I recently ran a survey where I gave users 36 options and had them rank their top 10 from most important to least important. I've taken the results and assigned each position a weight (i.e. ranked ...
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103 views

Identification of Difference in Weighted Mean and its Standard Error in Clustered Data Using Stata

I already asked this question on the statalist but have not received any comments on this issue yet. So I am going to post it here too. I am concerned with the following problem. Suppose my data ...
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2answers
38 views

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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26 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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44 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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62 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
48 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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32 views

Weighted mean: Inverse of individual values's confidence interval as weight?

This seems to be a very basic question, however I could not find a satisfactory answer throughout the web, yet. I have, say, N values, whose I know the N respectives 95% confidence intervals (said ...
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22 views

Combining several variances, obtained from weighted mean and moving average

I have three questions 1: Can variances for different mean calculations be combined to obtain the combined variance? \begin{equation} S = \sqrt{s_1^2 +s_2^2 + s_3^2} \end{equation} 2: When using ...
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33 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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12 views

Weighted Standard Deviation [duplicate]

I got a problem calculating a weighted standard deviation for a municipality and its precipitation on various landcover types (LC). I got the mean values of precipitation for several days for each ...
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8 views

Determining overall score based on several scores in the past

I'm one of the captains of my school math club (http://lhsmath.org), and I'm looking for insight into how to determine the overall competitive math ability of a person based on a number of past tryout ...
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1answer
30 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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26 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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67 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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91 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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29 views

Weighted mean and covariance

I have a variable $O$, depending on two other variables $x$, $y$ as $O=\frac{x}{y}$. I have several measurement (each one with its uncertainty) of $x$ and $y$ and for both of them I have computed a ...
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13 views

Outlier detection in weighted time series

Given a set of observations $X _n = \{x_1, \dots, x_n\}$, and a new observation $x_{n+1}$, we aim to find whether $x_{n+1}$ is outlier. One approach to solve this problem is to check whether ...
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68 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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1answer
58 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
28 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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70 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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1answer
17 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 ...
3
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1answer
136 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
212 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
155 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
107 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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28 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
103 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
207 views

Weighted average of measurements with unequal errors

Suppose I have the numbers below. Consider them as results of some measurement. ...
2
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1answer
499 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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222 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, ...