Questions tagged [median]
The median is the value below which half the data or probability distribution lies - when the sample size is odd, the median is the 'middle' value of an ordered sample.
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Wrong results for (pseudo)median on Wilcoxon paired test in R [closed]
I calculated results for the paired Wilcoxon test, one of which is (pseudo)median.
I tried to reproduce the computation of the ...
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Descriptive Statistics for Zero-Inflated Dataset
Just as titled, I'm curious as to what should you choose to represent a measure of central tendency for a zero-inflated vector or such. My background says go "mean" if normally distributed, &...
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Expected value and variance of median
Suppose $Y|\Lambda\sim U(0,\lambda)$ with $\Lambda \sim U(0,1)$. If there is sample with size $n$ of $Y$ (To simplify, assume $n$ is odd, so $n=2m-1$). How do I calculate the expected value of median (...
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Adjustment for confounders
I have some epidemiological data, relating to the prevalence of obesity at UK local authority level. For the purpose of exploration I want to derive the median obesity prevalence. However, I need to ...
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Is it acceptable to take the mean of a bunch of median values?
I use a Bayesian latent variable model to construct a time series cross-sectional measure of corruption for all countries in the world from 1960 to 2010. For each country-year observation, I obtain a ...
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Can I calculate median survival time and its confidence interval using the Kaplan-Meier curve? I don't have available raw data
I am conducting a meta-analysis to compare the differences between Group A and Group B by measuring the pooled Hazard Ratios (HRs) for the median Progression-Free Survival (PFS) and Overall Survival (...
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"Weighted Median": statistical properties and connection to the sample variance
Suppose we only have the following information:
A set of sample means : $\bar{x_1}$, $\bar{x_2}$ ... $\bar{x_k}$
The sample size used to calculated each sample mean: $n_1$, $n_2$ ....$n_k$
The ...
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Can any quantity be bootstrapped?
Suppose we have the median incomes of 150 different countries (in each country, the median income was calculated on a sample of people) - we don't have the individual incomes of each person in these ...
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Mean of Medians? Median of Means?
This is a question I have wondered about for a long time and have never been able to find a full mathematical explanation behind this.
Suppose there are 100 countries. As an experiment:
We give Person ...
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How do I compare my data with the general population data in SPSS
My purpose is to compare my data with the general population data derived from a published report. I can only extract mean, median, 5th, 95th and 97.5th percentiles from it. Also, My data is non-...
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Is distance from the median instead of from the mean in standard deviation calculation meaningful in case of data with outliers?
I'm borrowing from the idea of Mean of absolute deviation around the median (https://en.wikipedia.org/wiki/Average_absolute_deviation#Mean_absolute_deviation_around_the_median). Would calculating ...
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How to set the age range, median, and mean age
Thank you for reading my question.
I used the clustering method to classify the age of the houses.
This graph show the clustered results.
I should to get the age range, mean age, and median age for ...
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Scaled median shift between two observation when median is close to zero
I'm coming for a computer science background and statistics is not my forte, please bear with me.
I have two revisions $R_1$ and $R_2$ each consisting of around 10000 processes $T_i$ (involving some ...
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Where is the number "0.963" in the paper "Why Isn't Everyone a Bayesian?" by Bradley Efron coming from? [duplicate]
This paper by Bradley Efron (also available here) concerning Bayesian vs. frequentist interpretation of probability contains an example I don't quite understand.
It's on page two in the right column ...
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In R Limma's `normalizeMedianValues` function, why is its operations preceded with a log transformation followed by an exponential transformation?
In the function normalizeMedianValues in the package limma, column counts are normalised such that their column medians are ...
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How can I compare median survival times statistically based on Kaplan Meier curves/Log-rank test
I have a few question concerning the log-rank test and would be glad if anyone can answer these:
First of all I am wondering which benefits one has when plotting KM curves of two groups if one already ...
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What is the correct interpretation of the Log-Rank test (Kaplan Meier Curves)
I am wondering how to correctly interpret Kaplan Meier Curves, the log-rank test respectively. I calculated a log-rank test to compare two survival curves and got an insignificant p-value from this. ...
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Logistic Regression: Median Imputing vs Mean Imputing
Missing values need to be imputed when performing logistic regression. Missing values are often imputed by the median. The mean is the BLUE (best linear unbiased estimator). But Median is robust to ...
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Salesman Auditor problem: Which mean and median is correct? What is preferred?
Trip
Days
Expenses
Expenses per day
1
0.5
13.50
27
2
2.0
12.00
6
3
3.5
17.50
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1.0
9.00
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9.0
27.00
3
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0.5
9.00
18
7
8.5
17.00
2
Total
25.0
105.00
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Question:
The following data ...
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How to transform t-statistic into a statistic using median and IQR?
I want to calculate similarity between various samples, but I'm limited to only knowing the IQR and medians. I came across a similar problem
here but the top answer states that the newly proposed ...
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How to calculate median and median absolute deviation of data with a function applied?
I have a set of data X containing members xi (these are pixel values). I need to calculate the median and MAD of f(X), where f is a color space transform from linear RGB to sRGB (i.e. f(x) = x^(1/2.2))...
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Overall Average greater than Individual Category averages
I am calculating Gender Pay gap using gross salaries for employees. I'm doing two things to be specific:
Calculate Overall Gender pay gap for all the employees. (Taking all male/female employees to ...
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When is the median-of-means estimator better than the standard mean?
The median-of-means estimator is often given as an alternative way to, given a sequence of IID random variables $X_1,...,X_N$, estimate the expectation value $\mathbb{E}[X]$ (see e.g. these pdf notes ...
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standard error of the median survival time using r
I would like to find the standard error of the median survival time and do some approximation to estimate the density function around the median survival time according to equation (5) of this: http:/...
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Why does one interested in modelling the distribution of median of random samples?
I was reading this article which introduce the families of distribution for the median of an random sample. However, the writer did not state the reason why one is interested in modelling the ...
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Why am I not able to correctly calculate the median survival time for the Weibull distribution?
The survival function for the Weibull distribution is:
$S(t) = exp(-\lambda t^\alpha)$, $\lambda$ = scale parameter, $\alpha$ = shape parameter
If I wanted to calculate the median survival time, I ...
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Why is the pseudomedian better than the median in a Wilcoxon test?
The wilcox.test function in R calculates the pseudomedian and a confidence interval when conf.int=TRUE.
In this question, ...
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Kruskal-Wallis Test - medians are same but result is significant?
I have run a Kruskal Wallis test in my dataset and have a significant overall result (p<<0.001). However, since the medians for my categories are the same, I can't work out the direction of the ...
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Iterated mean as a variant of the quantile function
Suppose you want to compute the 25% quantile of some random variable. You can do this by first computing the median, and then computing the median of everything less than the median. You can repeat ...
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Is my logic about comparing the 70th/90th percentile from two respective datasets correct or is there a proof to do this?
Larry and Tony work for different companies. Larry's salary is the $90th$ percentile of the salaries in his company, and Tony`s salary is the $70th$ percentile of the salaries in his company.
Which ...
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How can I compute the expected value and variance of the 4th power of the sample median?
Given the following parameter estimate, how do I find $E[\hat{a}_{MED}]$ and $Var[\hat{a}_{MED}]$?
\begin{equation}
\label{eq:Estimator_a_Med}
\hat{a}_{MED} = - \left( n_0 \right)^4 \cdot \log(0.5)...
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Should I use the mean or median of my data for queueing models?
I am working on a project with a call center. Long story short, I am analzying the data revolved around the incoming calls to this call center in order to eventually use a queueing model.
A queueing ...
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quantile regression vs mannU (median difference)
I want to compare the medians of an interrupted time series, for example, years 2019-2020 with 2021-2022. The data is not normally distributed and the distribution of the data is not similar.
Would ...
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Why is median not a sufficient statistic? [duplicate]
Suppose a random sample of $n$ variables from $N(\mu,1)$, $n$ odd. The sample median is $M=X_{(n+1)/2}$, the order statistic of the middle of the distribution.
How to prove that sample median is not a ...
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Mean of bootstrapped medians
I have a large set (10^6) of very small sets (5-10 entries) of numbers. For each of them, I want to compute a sensible average measure. An example might be this:
$$
x = [-2, 5, -1, 3, 100]
$$
Because ...
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Compare ARE of mean and median
I have followed some lectures on the internet on asymptotic relative efficiency. When I had calculated the relative efficiency $ARE(median, mean)$ than my result was $ARE(median, mean)=\frac{2}{\pi}\...
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What is the appropriate test to compare median wages?
I am trying to find a test to compare how median wages have changed for college graduates after graduating. I am comparing the median wages for individuals based on the programs they graduated from (...
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Statistical Tests Comparing Median Wages [duplicate]
I am trying to find a statistical test that will compare the medians of two columns. When I try have searched around I have found the wilcox.test function in R, however, I have read mixed ...
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Fitting an arbitrary distribution to a given mean/mode/median
Given some combination of mean/mode/median, how would I go about generating a distribution that can fit an arbitrary combination?
For cases where mean = mode = median, I would just use a normal ...
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Why is the median of an even number of samples the arithmetic mean?
When calculating the median for an even number of samples, we sort the samples and take the arithmetic mean of the two in the middle.
This seems quite arbitrary - it assumes the best way to ...
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Is the median preserved for any strictly monotonic mapping?
Problem
Let $X\sim f_X$, where $f_X$ is the probability density function of $X$. Let $g: \mathbb{R} \to \mathbb{R}$ a strictly monotonic (decreasing or increasing) mapping. I aim to prove or disprove:
...
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Is the ratio of medians a good approximation of the median of ratios?
For two random variables $X$ and $Y$, does it hold that the median of $\frac{X}{Y}$ is approximately equal to the median of $X$ divided by the median of $Y$:
$$
F_{X/Y}^{-1}(0.5) \approx \frac{F_{X}^{-...
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OLS model assumptions for ML [closed]
hey i'm a beginner in data science, started working on the familiar "Boston" dataset ,and i tried to fit a multiple linear regression model to predict the "median house price " , ...
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Sum of medians or median of sums
I am estimating the total consumption of a community of species.
I have a dataset of total consumption for a given species based on population density and average energetic needs. This is related to ...
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Equivalent of $E[(a-X)^2] = E[(a-E(X))^2] + Var(X)$ for $E[|a-X|]$ and $med(X)$?
The minimzer of the MSE $E[(a-X)^2]$ is $a=E(X)$, and the MSE can be decomposed into $E[(a-X)^2] = E[(a-E(X))^2] + Var(X)$.
I am wondering whether there exists a similar expression th MAE $E[|a-X|]$ ...
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Fast Median Estimation: figure out the proof of correctness and error calculation
I found the Yuval Shavitt's FAME algorithm but I can't figure out the proof of correctness and how to calculate the median error. It would also be interesting to compare this with the case of ...
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Creating a reference group to have equal sample sizes for Wilcoxon signed rank test
I am analyzing three years' worth of data. For some descriptive analysis, I want to know if there is a difference in the median between, $year_1$ and $year_2$ compared to $year_3$. To do this, I ...
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Comparing median of groups within many clusters
I have the gender composition for thousands of boards (there is no sampling involved. The data set contains all boards). Boards are consisted of different number of male and female directors. So, to ...
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Comparing averages of non normal distributions
I want to compare the daily average revenue of a promotion period (7 days) of a business with the daily average of the rest of the year.
So, sample 1 has 7 data points, whereas sample 2 has 300 data ...
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