Tagged Questions

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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16 views

What are the pros and cons of using median imputation to handle missing value?

I have to choose between median or mean imputation to handle missing values. I feel median imputation will work better because it is a number that is already present in the data set and is less ...
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23 views

Confidence intervals for median

I have a distribution of samples with a small number of values in each one (less than $10$). I have calculated the median for each sample, which I want to compare with a model and obtain the ...
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24 views

Statistical nomenclature: what family does “head” and “tail” - in the sense of data runs belong

If I look at mean, variance, skew and kurtosis they are nth moments. If I look at percentiles, quartiles, and medians they are order statistics. Both work together to make a textbook summary. The ...
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30 views

Comparing medians

I am interested in comparing the medians of a continuous random variable across two groups. One option is to do a chi-square-based median test - in stata run median var, by(group). The other option is ...
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1answer
38 views

Definition of Scale median

Lehmann, in Theory of Point Estimation p.212 (and also on p.169), defines scale median as the solution to: $${E(X)I(X\le c)} = {E(X)I(X\ge c)}$$ given $X$ is a positive random variable, and ...
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20 views

Unique matching for quantiles from one half of the density to a subset of the other half?

I am interested in finding the median absolute distance to quantiles. So, for $Q_\alpha$ the $0 \le \alpha \le 1$ quantile, I would like to find $Q_\gamma^*$ such that $Q_\gamma^*$ satisfies ...
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44 views

What is the multivariate analog of the median?

There is a univariate mean: sum the points and divide by the count. There is a multivariate mean analog - the centroid, a point in a multidimensional space. (1). For the median one sorts the list ...
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1answer
46 views

Median and mode

Consider grouped data with frequencies and more specifically data that are discrete. If I have for example different xi with the same frequencies, what is the right answer: there is no mode or all ...
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17 views

SPSS Bootstrapping Medians - Two Groups Over Time

I am evaluating the effects of two different teaching methods for chest compressions during CPR over time. I have four sets of data: a control and study group compressions per minute on the first day ...
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0answers
13 views

How to quantify the similarity between two samples using quartiles only?

I have several sets of samples I would like to compare. Each set is comprised of two samples, for which I only have the quartiles, min/max values and sample size for each sample. I would like to ...
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1answer
92 views

What is the median of an equally weighted mixture of two Normal Distributions?

Suppose men's heights follow a normal distribution $X \sim \mathcal{N}(\mu_1,\sigma_1^2)$ and women's heights follow a normal distribution $Y \sim \mathcal{N}(\mu_2,\sigma_2^2)$. How can I find the ...
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32 views

Which measure of Central Tendency should I choose for skewed data?

I am trying to find out the best measure of central tendency from a list of data. As a first step, I'm trying to figure out the outliers in my distribution by using the usual Q1,Q3 and IQR formulas. ...
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2answers
58 views

Comparing normal with non-normal

I have two sets of data for setup time of a machine, one is setup time when fixture is running alone, another is when another fixture is running alongside. For fixture running alone the data I ...
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42 views

Find the median individual with observations on multiple variables over time

I have a question regarding the use of median. We collected data concerning disease development on hosts. We gathered the evolution of three variables over time on individuals. Their characteristics: ...
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0answers
14 views

Plotting raw data, but running statistics on log-transformed data

My data is non-normal, I want to show my raw data, in a scientific journal, by median +/- mad, to show the true nature of the data. However, if log-transformed, the data is normal. Can I then ...
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27 views

Bar plot with median +/- median absolute deviation in scientific publication

I know bar plots usually represents mean +/- sem, but if the data is non-normal, is it ok to bar plot median +/- mad? I don't like box plots. Suggestison?
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0answers
18 views

How to project video viewcount based on historicals?

My goal is to create a formula that can give an indication of how a YouTube channel's video will perform in the first 30 days of its lifespan and eliminate viral video / "lightening in a bottle" ...
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1answer
35 views

When to report proportions and when to report median + IQR for ordinal variable

A colleague brought to my attention documentation for a standardised questionnaire which recommended using the median and interquartile range to describe summary variables created by combining ...
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38 views

Find interquartile range of these data

Take these data: 5, 8, 9, 14 R says the interquartile range is 3: ...
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1answer
174 views

Do mean, variance and median exist for a continuous random variable with continuous PDF over the real axis and a well defined CDF?

For a continuous random variable with continuous PDF over the real axis and well defined CDF, are the mean, variance, and median always well defined? Mean and variance do not always exist, e.g. for a ...
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2answers
192 views

Why is the geometric median called the $L_1$ estimator?

My question is simply, why is the geometric median called the $L_1$ estimator? This always reminds of $L_p$ spaces but the distance being minimized in the geometric median's definition isn't $L_1$ but ...
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1answer
23 views

Estimating costs with extreme values

I am trying to estimate health care costs and I was wondering what the standard practice is for extreme values? By extreme values I mean I have a large portion of my costs being zero and a small ...
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44 views

What are the exact assumptions of Mood's Median Test?

I have checked with various sources, but I'm still puzzled: 1) What are the exact assumptions of Mood's Median Test? 2) Is homogenity of variance needed for both groups or is the same shape criterion ...
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2answers
105 views

Estimating the time for completing a sequence of actions

In short: suppose I have observations for times taken to do some action. I want to estimate, how long will it take to complete a sequence of actions. The estimate should minimize the mean absolute ...
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2answers
47 views

Obtaining error bars for a difference

I have a pair of data sets, and I want to know whether the medians of these two sets differ significantly. I've calculated the median of each set and subtracted them from each other. How can I ...
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0answers
16 views

Regression of a dataset using median

I have a dataset containing (x,y) information from the years 1985–2013. The x data is the pick number and the y data is performance. Each year has 60 (x,y) data points. When looking at my data for ...
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54 views

Standard error on median for exponential distribution

I am trying to find the standard error on the median, $\sigma_\tilde{x}$, for a sample, $X_i$, of a population whose pdf could be modelled as $\lambda e^{-\lambda x} $ if normalized. To make sure we ...
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19 views

Symmetry of a distribution

I have received a sample, summarized by a frequency table with groups (i.e. 1-7, 7-10, 10-13, 13-16, etc...) I calculated the mean and median, both were around 15, the mean was 15.3, the median 15.6. ...
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1answer
47 views

Estimate median from mean, std dev, and/or range

I have easy access to the the mean, standard deviation and min/max values for a variable. I also have the number of elements used to compute those values. The data is real numbers with an absolute ...
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39 views

confidence interval using median

I have a model where time is the response variable. I'd like to generate confidence intervals for the estimates. I have established that the error in the estimation is roughly normally distributed (it ...
3
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1answer
113 views

Online estimation of quartiles without storing observations

I need to compute quartiles (Q1,median and Q3) in real-time on a large set of data without storing the observations. I first tried the P square algorithm (Jain/Chlamtac) but I was no satisfied ...
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1answer
51 views

How to get the median of Z=f(x,y)?

Defining $Z=f(x,y)$ in interval $[q,1][q,1]$,$x,y$ are all i.i.d. uniform. I know that, if $f(x,y)$ is non-increasing or non-decreasing for both $x$ and $y$, the median of $z$ is $f((1-q)/2,(1-q)/2)$. ...
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1answer
172 views

One sample median test: Wilcoxon, sign test or chi squared

I would like to understand the differences between these tests for one sample median test and when to use each of them. I have been searching information and this is what I got so far: Sign test ...
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27 views

One-sample median test:: Signrank seems unsuitable

I have some data on successive bets made by customers. I want to see whether there is a statistically significant change in bet stake with each subsequent bet. The data is skewed, so I have ...
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1answer
60 views

How to calculate median absolute deviation in a cross validation scenario?

In a cross validation scenario "leave one out" I want to measure how the estimated continuous variable fits with the observed variable. I learned from Wikipedia that the Median absolute deviation ...
3
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1answer
64 views

Multistage sampling for Population Median

Has there been any research done on how to estimate the population median using multistage sampling? Simple random sampling is not possible in my case I would really like to use something like ...
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4answers
2k views

Should the mean be used when data are skewed?

Often introductory applied statistics texts distinguish the mean from the median (often in the the context of descriptive statistics and motivating the summarization of central tendency using the ...
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1answer
88 views

Simulate the distribution of the median

I have done part(a); now I need to do part(b): I want to simulate the distribution of the median $M$ using R. I don't know how to work it out. And for part(c), do I need to use R as well? This is ...
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1answer
65 views

What is the sample-size range for which the median should be preferred to the mean as a measure of central tendency? And why?

I have firing-rate data for neurons ranging from 40-60 in number for various experimental groups. I've seen both mean and median being used in the literature, but without much explanation for the ...
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2answers
66 views

Paired t-test of medians

I need to run an inferential test on some large data where the individual data points have a heavily skewed distribution. I'm considering doing a paired t-test across a number of days comparing the ...
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0answers
16 views

Should I take mean or median to compare short-term and long-term observation?

I have a finite set A of discrete values and I have a packet flow (computer networking) where each packet is assigned with a value from A. I want to determine if it is possible to predict the ...
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1answer
129 views

K-medians, formula to compute the median

If you are running K-medians, and your distance metric is the L1 norm, how do you derive that the center of each centroid is the median of the data points assigned to it? Second, how do you compute ...
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2answers
130 views

Prior Gamma distribution: Select appropriate alpha given beta and median

I am trying to programatically select a prior distribution from the Gamma family of distributions. The primary criteria that I need to satisfy is that the median of the distribution should be a given ...
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1answer
44 views

What can be inferred when multivariable ordinary least squares and quantile (median) regression yield differing results?

There lies information in a discrepancy of the (unconditional) mean and median. For example, if the median is larger than the mean, the distribution must be left-skewed. Does this kind of inference ...
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1k views

In left skewed data, what is the relationship between mean and median?

I found this question on the open MOOC from Stanford, however the answer is not present. I think the median $\leq$ mean. Is this the case?
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61 views

Determine number of runs is significant at 5% level of significance

I have the following question to answer: The total thickness X of the four pads of 36 half-ring (H-R) mounts for aircraft engines, taken periodically from the production line, were found to be ...
6
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1answer
175 views

Prove that distribution of sample median (for even sample) is symmetric

Let $\mathbf{X}=(X_1,X_2,\ldots,X_{2k})$ be a sample from normal distribution $\mathcal{N}(0,1)$. Prove that distribution of sample median (for even sample) is symmetric around 0. $me(\mathbf{X}) = ...
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2answers
150 views

Given independence, is the median of a product equal to the product of the medians?

Question: Assume $X$ and $Y$ are independent random variables. Is $Median(XY) = Median(X) \cdot Median(Y)$? If so, how would one prove this? If not, what conditions would be sufficient for this ...
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33 views

Creating a model to interpret numerical scores

Good morning/afternoon everyone, first of all thanks to all of you for the valuable insights provided. I will be oulining here my current challenge, trying to provide as much detail as possible. ...
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1answer
161 views

Why are statistical properties of mode and median difficult to determine?

I have read a book saying that statistical properties of the mode and the median are difficult to determine compared to the mean. I am not entirely sure why is so. Is it correct that because the mean ...