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.

learn more… | top users | synonyms

0
votes
0answers
6 views

Analytic Hierarchy Process (AHP) - factor weight score

As title mentioned, how to determine the 'scale of relative importance' point for factor weight score? Besides, I have read some example of ahp saying there are 1-9 point, 1-5 point (1,2,3,4,5) and ...
1
vote
0answers
16 views

Constrained regression for binary dependent variable

I would like to discuss the methodology for the following case: I have a data for several patients over several years for 5 factors describing the health of a particular patient. Every factor ...
5
votes
2answers
295 views

What does it mean to say that “the population mean is a single fixed number?”

I am trying to figure out what it means if a population mean value is fixed.
0
votes
0answers
15 views

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 ...
0
votes
1answer
66 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 ...
0
votes
0answers
36 views

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 ...
0
votes
1answer
25 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 ...
1
vote
0answers
12 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) ...
0
votes
0answers
7 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). ...
0
votes
1answer
28 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: ...
0
votes
0answers
27 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 ...
1
vote
0answers
43 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 : ...
0
votes
1answer
23 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 ...
2
votes
3answers
105 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' ...
0
votes
0answers
33 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 ...
0
votes
0answers
9 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: ...
1
vote
0answers
20 views

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 ...
1
vote
2answers
38 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 ...
1
vote
1answer
26 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 $x=102\pm0.2$, ...
0
votes
0answers
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 ...
0
votes
1answer
51 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 ...
0
votes
1answer
60 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 ...
0
votes
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 ...
1
vote
1answer
498 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, ...
0
votes
2answers
49 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 ...
0
votes
2answers
178 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? ...
0
votes
0answers
12 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?
1
vote
1answer
76 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 ...
0
votes
0answers
50 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 ...
0
votes
0answers
68 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 ...
0
votes
1answer
74 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 ...
1
vote
0answers
40 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 ...
1
vote
1answer
106 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 ...
1
vote
1answer
74 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 ...
1
vote
0answers
76 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 ...
1
vote
0answers
59 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 ...
0
votes
0answers
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 ...
7
votes
1answer
260 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 ...
4
votes
2answers
127 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 ...
6
votes
1answer
163 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 ...
0
votes
1answer
30 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 ...
0
votes
1answer
60 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 ...
0
votes
0answers
133 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 ...
0
votes
0answers
110 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 ...
0
votes
1answer
17 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 ...
0
votes
0answers
50 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, ...
1
vote
2answers
67 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. ...
0
votes
0answers
197 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: ...
0
votes
0answers
221 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 ...
0
votes
0answers
184 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 ...