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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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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How to introduce a weighted percentage?

We wanted to know the knowledge of people about how to eat fruits. For this we provided a party and invited 1000 people. There were 3 kind of fruits on the tables. Banana, orange and melon. If ...
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150 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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62 views

Weighted mean formula for two groups of unequal size

I am very confused with the weighted mean formula. Wikipedia lists the formula as $\bar{x} = \frac{\sum_{i=1}^{n} w_{i}x_{i}}{\sum_{i=1}^{n} w_{i}}$. The article also includes a basic numerical ...
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P-values of weighted means and weighted standard deviations

I have a lot of data like this: control: 0/12 0/14 0/12 and case: 104/111 94/108 36/57 and when I use arithmetic means and unbiased sample variance, I get mean1 = 0.000000 mean2=0.816049 ...
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22 views

Standard deviation for weighted sum of normal distributions

I have 2 normally distributed random variable $H_0$ and $H_1$, which are combined to give the weighted distribution $H$ as follows: $H_0 \sim N(\mu_0, \sigma_0)$ $H_1 \sim N(\mu_1, \sigma_1)$ $$f_H ...
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21 views

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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11 views

Weighted sample mean and variance - asking for references and details

I found this wiki page which tells how to compute the weights to get a BLUE for the mean from correlated observation, assuming the correlation is known. What I'm asking is: Some references (books) ...
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26 views

Weighting data for a valid analysis

I'm analysing road safety data. I have counts for the number of accidents that occur on different roads: ...
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6 views

How does PSPP handle weighting

In an answer to a related question regarding the statistical program SPSS it is stated that the program handles weighting just by repeating an observation x times (where x is the weighting factor). ...
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26 views

Calculating the Title odds

Given a set of expected values within an event. How do you calculate the probability of each of them occuring the most? i.e. Who will win the league? total goals scored in a season , given expected ...
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41 views

Weighted arithmetic mean's alternative for ranking items

I have a Blog post ranking algorithm which has 5 factors which are considered for calculating final score. I have predefined input range according to which i decide score of a factor. e.g. Factor : ...
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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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413 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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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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26 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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8 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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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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25 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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23 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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47 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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57 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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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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45 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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164 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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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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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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54 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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43 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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57 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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67 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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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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101 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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62 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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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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56 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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21 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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122 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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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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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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58 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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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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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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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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104 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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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 ...