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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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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
22 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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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
35 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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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
40 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
34 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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1answer
33 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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29 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
60 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
33 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
101 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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11 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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16 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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2answers
883 views

Calculate variance without calculating the mean

Can we calculate the variance without using the mean as the 'base' point?
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18 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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8 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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111 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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29 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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2answers
76 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
35 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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0answers
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
34 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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19 views

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
23 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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1answer
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 ...
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2answers
125 views

Cauchy distribution: R code [closed]

Generate 1000 sets of numbers from the Cauchy distribution. Do this for set size 2, 5, 10 and 20. Compute the median of each set. Find the distribution of the medians, for each set size. How do I ...
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24 views

Best estimator for the variance of the empirical median

Let $X_i$ be $n=2k+1$ IID continuous random variables with distribution function $F$ and quantile function $F^{-1}$. Let $m$ be their empirical median. It is well known that: If the $X_i$ were ...
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34 views

Mean and variance of the median estimator [duplicate]

We are given an i.i.d sample of size n, $X_{1},...,X_{2}$. We also know that for all i, $EX_{i}=\mu,Var{X_{i}}=\sigma^{2}$. Let us define $\hat{X}_{median}$ as the median of these samples: $\hat{X}...
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1answer
420 views

Calculate Median Value of Likert Scale data

I have a dataset in a Likert Scale: strongly agree, agree, neutral, disagree, strongly disagree (see attached). (i) Is there an online calculator that can used to calculate the Median for each item ...
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1answer
57 views

Welch t-test using the median and MAD

Can the Welch t-test be used with the median and MAD instead of mean and variance? I think outliers are causing problems and the median places less weight on extreme outliers. I'm using this to test ...
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20 views

Is there a standard way to write row-wise median in matrix notation?

The background: I have estimated N time series models, each having the same coefficients. From each of the models i have a column vector of the coefficients: $(\alpha_{i,0},\alpha_{i,1},\alpha_{i,2}...
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0answers
25 views

Median versus Harmonic Mean As Log Normal Data Summary

I have a set of data that follows a lognormal distribution (it is fixed-distance, variable-speed situation https://stats.stackexchange.com/a/23130/55305). I am trying to summarize the data in a single ...
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66 views

Standard error of median small sample

I tried to find this question but what I've found provides answers for normal distributions and large sample sizes. I'm analyzing some data from an experiment with different groups. Each group has ...
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1answer
475 views

Median of Rayleigh Distribution

I am not sure how to solve the following problem: The probability density function of the Rayleigh distribution is, $\ f(x;α) = \frac{x}{α^2} e^\frac{-x^2}{2α^2}, x ≥ 0, $ where α is the scale ...
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1answer
36 views

Pros and cons of using a median version for measuring dispersion?

If a data set is in the presence of some outliers, then the sample average could not be a "fair" measure of the centrality of that data set. Instead, the sample median could be a better choice. ...
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1answer
22 views

Why does the formula for the median assume continous classes (grouped data)?

I was working through problems of the median (grouped data). I encountered a problem where the classes were not continuous, and my textbook said that I needed to make them continuous since the median ...
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1answer
47 views

Which cumulative distribution of F(X) is equal to the cumulative distribution of its sample median (as sample statistics)

We consider random sampling from a population in which the variable of interest $X$ has some cumulative distribution $F$. Next, we consider a simple random sample of size $n, X_1,\ldots,X_n,$ which ...
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2answers
63 views

$\mathbb{E}[\min (X_{1:n}) + \max(X_{1:n})]/2 = \mathbb{E}[\text{median}(X_{1:n})]$?

Say $X$ is continuous random variable, and we have $n$ iid samples, denoted as $X_{1:n}$. Then can we say the following $$\mathbb{E}[\min (X_{1:n}) + \max(X_{1:n})]/2 = \mathbb{E}[\mathrm{median}(X_{...
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3answers
2k views

Is there more than one “median” formula?

In my work, when individuals refer to the "mean" value of a data set, they're typically referring to the arithmetic mean (i.e. "average", or "expected value"). If I provided the geometric mean, people ...
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5answers
95 views

can you report both a mean and a median for same variable

I have a variable that is not normally distributed. The two groups are statistically significantly different using a non-parametric test. However, they do not "look" different when reporting the ...
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0answers
11 views

Independent samples design where groups are statistically different at baseline

I have a dataset wherein 2 independent groups received either treatment or placebo using the following 5-session design: Session 1: Baseline (no treatment for either group) Session 2: GroupA=...
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0answers
22 views

When is it better to exclude outliers and calculate the mean of the data instead of using the median?

I already searched on when to use the mean and median and I often see that median might be better than mean when the data is skewed, ordinal, include outliers, etc.. even tho, this might not be always ...
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0answers
587 views

Parallel trend assumption in difference-in-differences

I want to run a difference in difference model to evaluate the impact of a policy change using panel data with 30 individuals in the control group and 35 individuals in the treatment group. When ...
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2answers
38 views

Effects of exclusion on averages

Given a set of data points, if a single point which is above/below the average is excluded, can it be said that the new average will surely decrease/increase? What if the average is the median instead ...
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1answer
82 views

Effect of adding and removing data on variance

Consider a set of distinct numbers. After removing both the max and the min from the set and adding the median to the set, the set of numbers obviously becomes less dispersed and the variance should ...
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1answer
89 views

What is the maximum entropy distribution given the median (instead of the mean)?

Given that the median seems to be a more robust statistic than the mean/average, I was wondering if there is a solution of the maximum entropy distribution given the median (or the median and some ...