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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21 views

ANOVA for median and interquartile range

I have 5 samples of different sizes (5000-15000 observations each) from 5 (presumably different) distributions. I need to perform something like ANOVA to test the hypothesis that these distributions ...
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9 views

Is it possible to derive the median of a distribution from the mean and Gini Index?

I have some data on GDP, population, and the Gini index for various countries, and I would like to derive some median metric. To put it more broadly, given the sum $\sum_{i=1}^{n} x_i$ and size $n$ ...
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21 views

Choosing the best aggregation location measure

I'm trying to analyze a granular dataset that is composed as follows: ...
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31 views

If Mann-Whitney U is a median test? Then what the heck is “unpaired pairwise median”?

Header: I am really sorry for the confusing title. I am going to edit it so it fits the responses I get based on Mann Whitney U. So I had this exact question on stack overflow about is the Mann ...
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64 views

When does the sum of the medians = the median of the sum

I have two random variables (say x1 and x2) defined by empirical probability distributions, and would like to calculate the median of their sum. Under what circumstances (in terms of the ...
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180 views

What is a reasonable sample size for median statistics?

I am asking this question because of a recent question on Skeptics.SE and a 2015 study by Duke University and the Federal Reserve Bank of Boston. This question is based on the study. In a Boston ...
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17 views

Random Forest Underperforms Median on Training Set for Toy Regression Problem

I have found that random forests is failing on a toy regression problem. My prior impression of random forests is that it is very robust, so I expected that, on the training set, it should always ...
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24 views

What types of analysis will work on a dataset of medians?

The dataset I currently have is wages for different occupations across different geographical regions, however each observation is a median. For example, a doctor in region A, the wage reported would ...
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14 views

When is variance a better description of spread over IQR? What about mean over median for description of center?

I was reading that IQR and median are a better representation of spread and center when there are outliers and when the distribution is skewed. When is variance a better measure of spread? What about ...
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87 views

What's the best method to measure relative variability for non normal data?

I have a set of data that states the volume required each month for the next 12 for 750 raw materials. I would like to determine the variability in the demand for each material, and categorise the ...
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27 views

calculate the average visits and running days

What do I've got? I have received a huge data from a real estate portal. It contains more than 50 million rows and data for over 10 years. In addition to the rental prices and other parameters (...
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33 views

Median for symmetric distribution

When do the spatial median or the L1-median and the componentwise median coincide ? Does it happen for only a symmetric distribution or other cases too ? Also, are both of them equal to the mean for a ...
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25 views

Bootstrapping a sample of discrete data

I am using the bootstrap to calculate 95% confidence intervals for the median of a population. The data can only take positive integer values. My sample indicates a fair bit of variability, though ...
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25 views

Am I allowed to create a cumulative frequency distribution from non-normally distributed data?

I have data gathered from a circadian rhythm experiment and I like to present this data as a percentile cumulative frequency distribution (CFD%), because I think this is a clean way to present the ...
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77 views

Should I compare the median or mean for my data?

I have a data frame in R that contains the information about 252 freshman university students. ...
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3k views

Why does mean tend be more stable in different samples than median?

Section 1.7.2 of Discovering Statistics Using R by Andy Fields, et all, while listing a virtues of mean vs median, states: ... the mean tends to be stable in different samples. This after ...
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19 views

Point estimator and confidence interval for median and mean [duplicate]

I want to find point estimator and confidence interval for both median and mode of number of samples that we've collected from a number of simulations. What I've done so far is that I found a point ...
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17 views

Testing differences in 5 star rating (Which hotel to choose)

Say, I want to choose a Hotel with the following ratings (1-5) on TripAdvisor. This seemed interesting if the mean for the Hotel with smaller number of votes is bigger than the mean of the hotel with ...
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53 views

Can the Median and mean be “zero”? [closed]

I have a data set with 32 variables. I take the summary of these variables. I found that some of these variables have a Mean or Median equal to zero. Is that Ok? Can I still work with this data set? ...
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49 views

Inference using robust statistics

I'm simulating the overall usage of a cluster using historic deployment data. Due to the nature of the simulation, there are some heavy points (i.e. very low overall usage). As a result, the variance ...
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10 views

Estimating yearly diagnosis rate from multiple studies

I want to estimate yearly diagnosis rates from some 8 studies. Each of the 8 studies contains the following data: $n$ = total number of patients (e.g., 100) $t_{start}$ = start timestamp of the ...
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16 views

Merging categories with small n (or median splits on categorical variables)

I've found a lot of resources on why median splits on continuous variables are generally bad, but I haven't found anything on merging levels from already categorical variables, specifically when some ...
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1answer
26 views

Confidence in Forecasted Median

Suppose I am measuring the time it takes to complete tasks, and I am looking across a year period, say 2019. At the end of the year, I will report on the median time taken across all tasks. Assume ...
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15 views

Median point vs. number of points

I am trying to assign a binary label to a group of 2D points. Essentially I want to know whether or not the group lies mainly within a certain region in 2D space, such as above a line. I've been ...
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1answer
36 views

Expectation of absolute difference between a random variable with its median [closed]

Given a random variable $x \sim p(x)$. Denote $m$ to be the median of x. What is the expected value of $|x-m|$, i.e we would like to compute the following integral: $$\int |x-m| p(x)dx $$
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33 views

Wilcoxon signed rank test - interpretation

I have 6 dependent variables that were measured on a 5 point Likert scale (treated as interval here). I want to test if their means differ significantly from the midpoint 3. As the normality ...
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1answer
46 views

Is my interpretation for Wilcoxon Signed Rank test correct?

I ran a wilcoxon signed rank test on paired samples where the outcome variable was a test score. The samples were paired by as siblings (younger and older sibling). I have a problem interpreting the ...
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1answer
36 views

Can you compare the mean of one data set with the median of another?

I’m having an argument with another numerically literate person. We both saw a news site state that under no circumstances should you compare the median of one set with the mean of another. It’s ...
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46 views

Pseudo median from Wilcoxon signed rank test larger than sample median?

I am left wondering, why I can be in a situation where the pseudo median (population estimator) of a Wilcoxon signed rank test, can be larger than the simple differences between sample medians? I am ...
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16 views

Wilcoxon rank signed test, paired or non-paired test?

I have been trying to figure out, whether or not I should use a paired or a non-paired test. My question comes from the fact, that I am trying to get the pseudo median, in order to say that SBP is [x] ...
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41 views

Random Forest Regression: More trees are not necessarily better

This doesn't answer my question, and neither does this. Problem I've been experimenting with random forests. I have 30 or so input features and one very right-skewed response. I've noticed that ...
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2answers
87 views

Wilcoxon signed rank test, getting a numerical media difference instead of p-value?

I have been running the Wilcoxon signed rank test, where my output is a p-value. Now, the p-value interpretation I am confident in, but I read in a paper that the authors reported the: The Wilcoxon ...
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1answer
35 views

Asymptotic distribution of median estimator when density doesn't exist

We know that when density(say $f$) exists at the median(say $\theta$) then the median estimator(say $\hat{\theta_n}$) has the following property $$ \sqrt n(\hat{\theta_n}-\theta) \to^d N(0,1/\{4f(\...
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1answer
233 views

Why median is NA for some of the group outcomes in survival analysis?

I'm trying to do survival analysis using the Followup information, patient_vital_status and the expression of gene. I'm using like below: ...
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11 views

Real (not rounded) Lower and Upper limits of groups of frequency distribution and Median for infinitely continuous data

From here on page 5: https://www.pbarrett.net/techpapers/percentiles.pdf So how can both be correct – yet seem to be more appropriate under different conditions? The clue is spread throughout the ...
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12 views

With few respondents on a 1 to 10 scale, is it better to use a weighted mean or the median?

I have survey data where ~20 respondents replied to some questions on a scale of 1 to 10. For the most part, none of the distributions are Gaussian. A set of questions look to find out a participants ...
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17 views

Are median values numeric or ordinal?

I'm trying to set up the input data that I'd feed into my DL model and for the simplicity, I'm thinking of plugging in only the min/max/average values of the original data. (This is necessary for my ...
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940 views

Calculate variance without calculating the mean

Can we calculate the variance without using the mean as the 'base' point?
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20 views

Paired Wilcoxon signed rank test-compare median

I have been comparing driving behavior before and after a technological intervention for a specific group of people. My data is far from normal hence I have used paired Wilcoxon signed rank test. If ...
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9 views

Median of demeaned variables and fixed effects

I have observations of the profit $y_{it}$ for several firms, noted $i$, over time $t$. For each firm, I compute the mean of $y$ over the years and call it: $\bar{y_i}$. Then I substract this firm-...
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189 views

modified z score

I am using Modified Z-Score to find out outliers on a time series data on exit rate for a website. N = 1131. Based on last 3 years daily data (1096 values), i am finding out outliers for the ...
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38 views

Measures of central tendency for right-skewed size distributions

Suppose we are looking at a right-skewed size distribution such as the distributions of income, casualty losses, or flood sizes, and we want to look at some alternative measures to jointly represent ...
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124 views

Median Absolute Deviation

How median Absolute deviation is immune to outliers? R2 or coefficient of determination is affected by outliers. And how this MAD is going to remove that constraint?
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1answer
38 views

What is the ideal population size so that its median is a representative statistical measure? [closed]

I am perfoming a robust z-score analysis to remove trends of temporal evolution of a certain variable so that I can compare different years. It is robust because there are outliers. My data is ...
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27 views

Statistically determining the median of a data set via quantiles of a sample

I was thinking of algorithms for statistically determining the median of a large data set. To estimate the complexity of my idea I need the following Probability: I have a dataset $\left\{x_i \right\}...
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1answer
37 views

Sufficient conditions for equal marginal medians

Let $X, Y$ be dependent random variables taking values on the same set (either a finite set, an interval or the real line). I'd like to know if there's any condition on $P(Y|X)$ which ensures that $$\...
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Confidence on the median for a weighted empirical distribution

I have observation data $x_1, \dots, x_n$ with associated positive weights $w_1, \dots, w_n$ such that $\sum_i w_i = 1$, representing a "weighted" empirical distribution with CDF $$ \hat{F}(x) = \sum_{...
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1answer
24 views

Help with psychological research for my dissertation?

1) Is median split effective to divide participants in 2 groups considering their scores on a scale? I am using PECK scale (Personal experience checlist) and i need to divide participants into minimum ...
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1answer
25 views

Analyzing/visualizing tightly grouped discrete results

I've been having a very hard time finding a good representation (visual or analytical) for lots of data points on a very small, discrete scale. e.g. given a set of results from 1 to 5 in increments of ...
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44 views

Name of mean- or median-like values?

Consider the data points $x_i \in \mathbb R$ for $i=1,\ldots,n$ as well as following definition: $$\hat x_c := \underset{{r\in \mathbb R}}{\operatorname{argmin}}\sum_i \vert r - x_i \vert^c $$ This ...