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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mean\medians as data points in two way repeated measures ANOVA

I have a table with 12 columns each regarding one combination of three (2X2X3) diffrent conditions in an experiment. Each row (25) represent a subject that did the experiment. Each data point in the ...
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515 views

Is there a formula for computing median?

Is there an equivalent of the mean formula: \begin{equation} \mathrm{mean} = \cfrac{1}{N} \sum_{i=1}^{N} X_i \end{equation} for median?
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83 views

Find data and confidence “ellipses” (regions?) for a bivariate median?

I'm wondering about ways to compute data and confidence ellipses around a bivariate median. For example, I can easily compute a data ellipse or a confidence ellipse for the bivariate mean of the ...
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1answer
52 views

How to prove that medians were swapped?

I have two independed samples: df and df8. The first sample df includes points at the data1 and at the data2. These points were earned in an experimental group (n1=20). The second sample df8 includes ...
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6 views

Limitations of dividing the median of one arm in K-M analysis with the hazard ratio to get a “smoothened” estimation of the median of the other arm?

I am not statistician but use statistic measures in my work in regulatory medicine. A commonly used outcome measure in medicine is median survival by Kaplan-Meier (K-M) analysis. It sometimes happens ...
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1answer
31 views

Mann-Whitney test W statistics

Below is Mann-Whitney test result from Minitab. At the end of result, there is no p-value but "Cannot reject since W is < 363.0". What does it mean? I cannot ...
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4 views

Employment Term Likelihood

I have research information advising the median employment term for an executive is 4.8 years.I need to know what is the % likelihood of an executive staying for 5 years+- thanks for help
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3answers
911 views

If the mean and median underestimate the true central tendency, why use them?

In skewed distributions, both the mean and the median can easily underestimate or overestimate the true central tendency. For example, have a look at this violin plot: The median is shown here in ...
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11 views

Variability of the reference data and its effect on the transformed values

I conducted a study to compare two different tests at two different ages (children). Based on the previous literature we had hoped that the scores should be better (low score) with age but this was ...
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1answer
50 views

Calculate median for count data

I've got data that looks like this: ...
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1answer
914 views

How to calculate the median of a pdf

I'm new to statistics and I'm struggling to solve a question from an assignment. I have a probability density function and I need to calculate its median Here is the function: $$f(x) = 2xe^{-x^2}, ...
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30 views

Should I treat my data as ordinal or interval?

I conducted a survey where I asked respondents how much they reduced their financial overhead, based on the following options: 0% (coded as 0 in my dataset) 1-10% (coded as 1) 11-25% (coded as 2, ...
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28 views

Is the sample mean a better point estimate of the population median than the sample median?

A beginner's question to check I've understood correctly. A basic stats textbook says: "The variance of the sampling distribution of the median is greater than that of the sampling distribution of ...
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8 views

Collapse FDR value of probes detecting the same gene

I'm very new in Microarray analysis, so I hope my question wouldn't be too irritating to you all. I have pre-processed and filtered my microarray datasets and perform differential expression analysis. ...
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1answer
13 views

What is the difference between a median and a population/sample median?

If I have an order statistic, I can rank them from smallest to largest like $$X_{(1)}, X_{(2)},...,X_{(n)}$$ and there will be some median $X_{m}$. But I can also have some distribution $f(x)$ ...
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21 views

Best way to calculate a specific median

I have a strange question about calculating median. Context : I have a listing with people who subscribe to an insurance : They subscribe from DATE A to DATE B (at date B, they leave because they ...
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1answer
16 views

alternative way to compute or infer median from survival curve

I have used the survival package in R to generate survival plots. However for one of my sub groups, the graph does not fall below 0.5 survival. Good news for ...
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215 views

Explaining Mean, Median, Mode in Layman's Terms

How would you explain the concept of mean, median, and mode of a list of numbers and why they are important to somebody with only basic arithmetic skills? Let's not mention skewness, CLT, central ...
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16 views

Confidence interval for the median - continued

I have a set of values $x_i\quad i=1,…,N$ of which I can calculate the median M. Each $x_i$ has an error $\delta x_i$. The $x_i$ values are the result of a maximum likelyhood estimation and their ...
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1answer
45 views

How to compute difference in location computed in Mann-Whitney-test?

I would like to reproduce the results of the Wilcoxon-Mann-Whitney-test in R wilcox.test(x,y,paired=FALSE, conf.int=TRUE. I succeed to get the W-value but didn't ...
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13 views

Calculating mean and maximum with open ended bins

I am using excel and I need to work out the average lives of machinery as well as the maximum life. However all I have is the number of machines over ten years and the number of machines under 10 ...
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1answer
29 views

How does one find the sample median of for a group of iid random variables with Laplace distribution?

I know a median is $$\frac{1}{2} = \int_{-\infty}^{\mu} f(x)dx$$ I understand how to solve this for simple distributions. However, I am learning how to do it for iid samples, which I haven't done ...
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463 views

Confidence interval for the median

I have a set of values ${x_i}, i=1, \dots ,N$ of which I calculate the median M. I was wondering how I could calculate the error on this estimation. On the net I found that it can be calculated as ...
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1answer
78 views

How much sense does median of one number make?

Median of one number = the number itself. I am calculating the median price sq ft of properties of different areas based on the different data entries I have got that include their ID, area and ...
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25 views

When the dependent variable is Median Time of a specific event, have we to use Quantile Regression or OLS Regression works well?

I am asked to make a regression model and the dependent variable is Median Time of a specific event. I think I can consider the Median Time of that event as a random variable and therefore the ...
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32 views

Calculating median for different subsets and sample sizes

I have a basic question about calculating median. The database I'm using contains registered records of criminals and the number of committed crimes per year each has committed in country X. Based on ...
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1answer
45 views

Calculating Median of Different Data Groups?

Bear with me here. I'm a newbie at this. Let's say we have this data : ...
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380 views

Is there a reliable nonparametric confidence interval for the mean of a skewed distribution?

Very skewed distributions such as the log-normal do not result in accurate bootstrap confidence intervals. Here is an example showing that the left and right tail areas are far from the ideal 0.025 ...
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240 views

When the Median Absolute Deviation (MAD) is zero

Suppose my data look like the following: (10, 10, 10, 10, 10, 0) Would it be possible to remove an outlier in this distribution using the median absolute deviation? Of course, you wouldn't need to ...
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1answer
24 views

Reducing density of outliers

I have a dataset with right skewed data. It represent frequency of candidates vs their TTB (which is essentially the number of days) Now the TTB values less than 14 or so are possible. But not ...
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1answer
71 views

Why is the 95% CI for the median supposed to be $±1.57*IQR/\sqrt{N}$?

In various sources (see e.g. here), the following formula is given for confidence interval for median (especially for the purpose of drawing notches on box-and-whisker plots): $$ 95\%\ CI_{\rm ...
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1answer
81 views

Why use a “truncated mean” (aka “trimmed mean”)?

NB: In this post, I will use the abbreviation $TM_P$ to stand for a symmetric truncated (or trimmed) mean that discards the largest and smallest $P/2$ percent of the data. In fact, for concreteness I ...
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57 views

(CDF Quantile) Understanding an example from a swirl lesson

I need to understand an explanation from a swirl() lesson in course "Statistical Inference", menu option "Probability2". At 76% of completion, there is a question: "The quantile v of a CDF is the ...
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1answer
22 views

Probability of median of numbers in a range

how to calculate the probability that median of 3 random numbers from 0 to n, that are not in [0.2n, 0.8n] ? I think it should me P(2 numbers < 0.2n) + P(2 numbers > 0.8n) + P(all numbers < 0.2n ...
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28 views

Does the asymptotic distribution of sample median follow from statistical functionals?

I know that if $F_n$ is the empirical distribution function and $F$ is the true distribution function, then, with $T$ being any statistical functional (satisfying the von-Mises derivative conditions), ...
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31 views

Statistical analysis on daily data

I have a number of data points that I am trying to extract a meaningful pattern from (or derive an equation that could then be predictive). I am trying to find a correlation (?) between RANK and DAILY ...
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30 views

median split procedure reference

Is there any reference that I might use when I mention the median split method in a paper? i.e. turning a continuous variable into a categorical one by splitting a sample into 2 (above and below the ...
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16 views

Theil–Sen estimator in R with more than one variable? [duplicate]

Can Theil-Sen be defined for multiple linear regression? If so, is there an implementation in R for it? I simply want a formula a~b+c, but the package ...
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24 views

Effectiveness of Median

New to this board and hoping this question is something easy to describe. I am working on a project that look at median cycle times of emergency department patients length of stay. Across a quarter, ...
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1answer
28 views

Filtered Data for Median - strange?

I am looking at a legacy process for work. We look at corporate budget data. The data is composed of annual budgets for different major categories for different corporate regions. The upper management ...
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1answer
98 views

Using the median for calculating Variance

I have a 1-D random variable which is extremely skewed. In order to normalize this distribution, I want to use the median rather than the mean. my question is this: can I calculate the variance of the ...
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254 views

Comparison of medians in samples with unequal variance, size and shape

What am I trying to do and how does my data look? I am trying to perform some comparisons of medians of groups of data that, most often than not, are not-normally distributed. In some cases I am ...
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26 views

How many min & max values to remove?

I imaging that the following problem is quite common, so there should be recommendations what to do. I've got multiple measurements of a certain value. Let's order these measurements: ...
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1answer
263 views

Can I get the parameters of a lognormal distribution from the sample mean & median?

I have the mean and median values for a sample drawn from a lognormal distribution. Note that this is not the mean and median of the logs of the variable, though I can of course calculate the logs of ...
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45 views

cleaning outliers based on MAD but if MAD == 0.0 then clean by STD?

I'm trying to clean outliers from my features by the following univariate method: calculate median for each feature, and nullify values that are far from it by more than 3*MAD (median absolute ...
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15 views

Is there any reason not to model group medians with a plain regression model?

Consider the Boston Housing dataset, in which the intended target/response $Y$ is actually a group median. Are there any objections to modeling this group median with a standard regression model, in ...
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49 views

bootstrapped standard error to make inference about difference of means

I have a variable showing individual wages and a categorical variable of their race (Hispanic, Asian, etc). After getting their means, medians and their respective standard errors for each group ...
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67 views

Combining sets of medians and their deviation measures

Suppose I have the following sets of estimates : $S_i = \{ (m_1,d_1), (m_1,d_1), \ldots (m_{N_i},d_{N_i}) \}, i = 1,2,\ldots P $. In each set, an ordered pair corresponds to median of a set of ...
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21 views

Recalculating mean, median, std dev and confidence interval after updating sample

I am working on an application which gets rolling samples of World of Warcraft auctions every two hours. The auctions contain, among other data: item ID (will be used to group auctions before ...
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57 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 ...