# Questions tagged [weighted-mean]

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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### Simpson's paradox in Freedman, Pisani and Purves book

In this book, there is an example of sex bias in graduate admissions. Major Men Women # applicants % admitted # applicants % admitted A 825 62 108 82 B 560 63 25 68 C 325 37 593 34 D 417 33 375 ...
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### Why can the standard error of the weighted mean be smaller than the standard errors of the individual measurements?

I am combining two independent measurements with their respective standard errors using a weighted mean. The measurements are: It seems counterintuitive to me that the standard error of the weighted ...
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### How do I calculate the weighted average of a 2D data set for a 3D structure?

I have a 2D data array indicating a chemical percentage content (PC) in a chemical droplet. I am trying to calculate the average PC in the droplet. The image of one of these arrays is shown below (the ...
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### Are there coventions on reporting weighted sample sizes?

Suppose I analyze survey data and calculate weighted means. Should I report the sample size if it differs from the unweighted sample size, as would be the case with non-normalized weights? It seems ...
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### Central tendency of survey results and geometric mean

I recently conducted a survey asking users about their music listening habits at different times of day. Here are the results from 6am in the morning: Taking a weighted average, 32.14% seems quite ...
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### Calculating proportion

I have a dataset of 10 people who share the cost of a service at the end of each month. The cost of the service is constant. Is there a fair way to split the cost of the service such that the ...
1 vote
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### Weighted average of covariance matrixes

My issue is as follows: In my model there are 4 different states, which each have a calculated probability of happening. I also have calculated covariance matrixes for my variables in each of these ...
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### Rank clusters based on mean feature value and variance feature value of the cluster

I would like to rank clusters according to their importance. From 113 demand time series data I extract the following 6 features from each time series. "Average Demand", "n95 demand&...
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### Combining velocity measurements which are accurate in different ranges

I am using two different methods to measure velocities, which can be positive, negative or zero. Method A accurately measures low velocities and no velocity, but not highly positive or highly negative ...
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### Comparing means on aggregated data

I'm confused about how to compare means given the following scenario. Suppose a company has stores in 2 countries, CA and US, which each get some number of Customers...
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### How to measure ML model performance across race via area level demographic info

I want to know how my ML model is performing by customer race/ethnicity. The issue is that we do not know our customer's race. We, however, do know zipcode level demographic information. ie) A ...
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### Formula for standardized mean difference in Cobalt package for categorical variables

I am having troubles in understanding the formula in cobalt package used for standardized mean difference calculation in BINARY variables ...
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### PISA scores wrong when computed by regions

I am testing a script in R to work with the PISA data for Spain. I calculate the average maths score as the weighted average with the weights (w_fstuwt) of each of the 5 plausible values and then ...
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### Distribution of Weighted Sample Variance

Say we have $N$ independent Gaussian variables $X_i$, each drawn from a mean-zero Gaussian with variance $\sigma_i^2$, where in this case I assume I know the $\sigma_i^2$. Define the weighted average ...
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### Weighed average (percentage) depending on the number of facilities in each given region

I have 10 regions with facilities (different number of facilities in each region) that test people for presence of condition A. However, there are also facilities, that were included in the pilot ...
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### Customized F1-Score for multi-class classification

Let's consider a multi-class classification problem with 4 classes: 0, 1, 2, and 3 F1-Score 'macro'-averaged is calculated like that: ...
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### Generalizing Inverse Variance Weighting?

Consider a generalization of inverse-variance weighting, where we choose normalized weights $w_i = \dfrac{\sigma_i^{-p}}{W_p}$ for some $p\geq 1$, where $W_p \equiv \sum\sigma_i^{-p}$. Then $p=2$ ...
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### How to iteratively calculate weighted standard error to report alongside a weighted mean

I have a group of individuals for which I would like to report a mean and a weighted error. The data that I observe on a daily basis are two independent $iid$ random variables with unknown ...
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### aggregate variance or standard deviation similarly as weighted mean

Say I have several regions' melon produce data. I wish to measure the variability of melon weight in each area, and summarize these as an overall variability metric accounting for the different sizes ...
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### Recognize extreme weights in inverse probability treatment weighting

I have some doubts about how to recognize if there are extreme weights after balancing my population with inverse probability treatment weighting. For instance, let's look at these results [code at ...
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1 vote
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### Calculating outcomes in IPTW

I have a few questions concerning what to do next after balancing your population with IPTW. This is a code just to have an example: ...
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### Calculating mean rate of change with weights

Say, I have some data on price of goods sold, quantity and location. ...
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### Combining N number of weighted probabilities

I have a question that I thought was simple but I can’t seem to find an answer. Let’s say I have N number of models that will predict a binary event and i have an accuracy assigned to each model, for ...
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### How to get weighted mean with two weighting sources

I have some data on a cyclists distance traveled and hours it took. ...
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### Skewed distributions: choosing the median or average

Goal: To determine whether to use the median or average (or a weighted combination of the two) from a data set based on whether ...
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### Statistical comparison of grand/pooled means (nested, mixed-model, t tests)

My problem: I am comparing the means of means of means in my data set. However, my stats software (GraphPad Prism) doesn't know that these said individual values (the means of means of means) are ...
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### Smoothing time series with Adjusted R2-weighted averages

I have two parameters (a,b) resulting from an exponential estimation of a curve. I have estimated this curve every hour for one month. In other words, I have a total of 720 parameters a and b, and I ...
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### Robust distance weighted mean

Given a data sample $\{x_i\}_1^n$, instead of hard omitting outliers by e.g. trimming, one can form a weighted average where we soft penalize observations out in the tails. \begin{align} \mu = \frac{...
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### distribution of normalized random weights

TL;DR: Given a finite series of positive and iid random variates/weights $w_i$ of known distribution, $(w_1, ... w_n)$, what is the distribution (or at least the exp.val. and variance) of the ...
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### Compare mean of subsamples between groups

I am going to collect quantitative data for two groups that I would like to compare. I have done a two sample t-test on some preliminary data and found a significant difference, but I don't think that ...
1 vote
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### How is the formula for the variance of a weighted mean effect derived? [duplicate]

NOTE: I'm aware that another post covers this from a slightly different angle. But the derivation (of the variance of the weighted mean) in that post does not look the one I give below, and (more ...
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### Help students understand Gaussian Kernel in mean shift segmentation

I am creating a image mean shift segmentation algorithm for a class. So far what I've done is basically Iterate through each point/pixel on the image and with a given bandwidth(radius) calculate the ...
I'm creating a metric which is a weighted average of a parameter $X_i$. Weights themselves are multiplications of $W_i * T_i$. In other words, my metric is something like: \$my\_metric = \frac{\sum_i(...