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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Averaging and comparing mean values across studies

I am having a statistical problem that falls into two parts: (!) I have several literature reports on studies that have investigated the effect of drug "A" on a particular laboratory parameter. Some ...
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50 views

Meta analysis across studies with multiple response measures

I'm trying to do a meta analysis across a bunch of bird playback studies. Thanks to help on a previous post here I'm fairly certain I need to use inverse variance weighting (maybe with the 'meta' ...
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7 views

Estimating variance or coefficient of variation for population given total and count for four segments of population

My goal is to estimate the coefficient of variation for a population, but the data we have been given is very limited. All we have is the total and count for four segments of the population. The ...
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6 views

Time weighted variables

anyone please help... Variables: *Independent variable: BP in followup *Dependent variable: Change in Glucose/year (ordinal: low:<-10/year, moderate: -10/year to 10/year, high: >10/year) Time: ...
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Average Difference of Averages

I'm looking at the gender pay gap across the UK using some data from the ONS. The data is released as mean and median gross pay by sex by local authority area. Figures for England as a whole are also ...
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31 views

Proving that weighted probabilities lie in the range 0 to 1

How to prove that: $$P_{avg} = \dfrac{w_{1}P_{A} + w_{2}P_{B} + w_{3}P_{C}}{w_{1} + w_{2} + w_{3}}$$ lies between 0 and 1, where $P_{i}$ corresponds to probability scores and $w_{j}$ are real ...
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1answer
20 views

Averaging results from different experiments where errors may be underestimated

Let's say we have three different published results that measure the same physical quantity $x$ using completely different methods. Experiment 1 says $x=100\pm0.1$, Experiment 2 says $x=102\pm0.2$, ...
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19 views

Sampling distribution of the *weighted* mean

I'm wondering if someone could send me a book reference about the sampling distribution of the weighted mean, I have found some information in wikipedia, however, I'm needing a more complete and ...
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1answer
41 views

Permissible to use survey data in generating sampling weights?

Summary: Can I use non-population information (e.g. representative proportions from another survey) when calculating sampling weights? If so how might one account for the sampling error? I'm ...
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1answer
54 views

learning shared weights

I have a classification problem with 100 variables measured during 5 conditions, so 500 features. Some conditions are more informative than others, so I would like to have a learner that learns ...
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1answer
52 views

Is this equation a mean value?

I met the following equation. $b=\frac{\sum_{i=1}^{N}x_i^2 }{\sum_{i=1}^{N}x_i }$, $0<x_i<1$ $x_i$ are probabilities. Is it a kind of mean value? It seems that it is used as a mean value ...
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144 views

Confidence interval for a weighted mean of proportions

I am doing an experiment in which I measure success or failure of a series of $k$ trials, yielding a proportion $P$. I repeat the experiment several times, yielding a set of $N$ proportions: $P_1, ...
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33 views

Weighting results in a Likert survey

I have very little (i.e. high school level) stats training, so forgive me if anything in here doesn't make sense. A team at my work has performed a training exercise for about 250 employees and has ...
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73 views

Understanding simple weighted average

This is a really dumb question but I can't seem to return anything useful from Google. The basic question is: Why is the weighted average of the column that is the "weight" different than it's mean? ...
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10 views

Is there a way to calculated weighted mean with two weights associated with each value?

If there are n values with 2 weights w1 and w2 associated with each, is there a way to use both w1 and w2 to calculate the weighted mean?
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1answer
39 views

Weighted median

I'd like to compute a median of measurements taken from a population with 3 subgroups, A, B, and C. I'd like to the median to be "weighted", in the sense that each of the groups should have equal ...
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31 views

Calculating a cubic mean value which summarizes conditions with different probabilities

I am not sure how to calculate a 'typical' cubic mean load (CML, where L=load=force) given CML values for various conditions which have different probabilities of occurrence. The conditions are ...
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38 views

Hypothesis test for 2 Weighted Means

I was trying to compare pairs of medical cost from several customized groups. The medical cost is adjusted by age and gender distribution in the sample. The resulting per member medical cost in each ...
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1answer
53 views

How to get weighted summaries of survey responses in R

I am analysing survey data. Since my demographic categories are discrete I can summarise responses within demographics using prop.table. However, I would also like ...
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36 views

Gradient of a sum of indicators

EDITED w.r.t. whuber's comment: Say I have a function $\mathbb R^n \rightarrow \mathbb R$: $$f(w_1,\ldots,w_n) = \frac{n^-\sum_{i\in I^-}w_ix_i}{n^+\sum_{i\in I^+}w_ix_i}$$ with fixed $x_i\in\mathbb ...
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1answer
73 views

Weighted median of a portfolio

I need to calculate weighted median return for a portfolio (using MATLAB). There is information available online: MATLAB Central/rates&weights and Excel/note 4+4+4+7+7/5 logic How would you ...
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1answer
44 views

Comparing retention rates with differing sample sizes

I'm looking to compare the retention rate of people who attended an event and those who did not. The list of those who did not (70) is significantly larger than those who have (28). Here is an ...
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64 views

Okay to use oneway ANOVA to compare these 3 group proportions from aggregated dataset?

My situation: I am assessing outcomes of a university course redesign. One of the goals of the redesign project was to increase successful course completion, as measured by a decrease in the course ...
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42 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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18 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
155 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
111 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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108 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
29 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
47 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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105 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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32 views
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42 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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91 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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16 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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45 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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61 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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133 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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147 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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168 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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166 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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71 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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31 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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78 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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68 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
61 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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45 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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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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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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136 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 ...