Questions tagged [mean]

The expected value of a random variable; or a location measure for a sample.

731 questions with no upvoted or accepted answers
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503 views

Propensity Score Matching – How do the mechanics lead to a different result than unmatched?

The gist of propensity score matching, as I understand it, is as follows: You want to estimate the average treatment effect (ATE) of a treatment on some outcome. However, if you simply calculate the ...
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187 views

First two moments of the ratio of the geometric mean to the arithmetic mean of Gamma random variables

Let $X_1,\ldots, X_n$ be $n$ uncorrelated random variables from a Gamma distribution with different parameters: $X_i \sim Gamma(k_i, \theta_i)$. What is the distribution of $$ U=\log \left[ \dfrac{\...
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3k views

Confidence interval for the restricted mean in survival analysis

What is the recommended way of calculating confidence intervals for the restricted mean in survival analysis? Here are some example data, taken from the paper Chris Barker (2009), The Mean, Median, ...
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1answer
906 views

Scale of the correlation coefficient: is “r = .40 is twice as strong as r = .20” allowed/correct?

Some people recommend the following procedure to calculate the mean of several correlation coefficients: transform the coefficients by Fisher's $z$ transformation, calculate the mean of that, and ...
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936 views

Asymmetric confidence intervals on bootstrap estimates

I've performed bootstrapping on my leastsq parameters and now I have a load of data from which I can get the mean and standard deviation for each parameter. Lovely. But when I look at a histogram of ...
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963 views

Which normalization method for different units (zero, negative, etc.)

Commonly, normalization of ratings seems to mean adjusting values measured on different scales to a notionally common scale. I have different metrics that measure different performance aspects of a ...
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146 views

How to improve estimation of a deconvolved density

I have the following problem: Y = X + e with Y = Total reaction time (noisy signal) X = selection time (signal) e = discrimination time (noise) I am interestend in the distribution for X and ...
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3answers
143 views

How to represent periodic paired data?

I'm working on paired data, of which absolute values plotted over time, show periodicity with varying peak heights as shown in the following graph: The data represent the absolute distance between ...
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1k 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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444 views

If I want to estimate a population median from a bunch of sample medians, should I use their mean or their median?

Suppose you just have some sample medians, and want to estimate the population median. Assume the samples are random, independent of each other, and of the same size. Should you use the mean or the ...
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87 views

So many ways to calculate the t-statistic - is this the 'super-formula' I need to yield all the different forms?

I've noticed that the formula for the t-statistic takes on a number of forms depending on the nature of the test being performed, i.e.,: one sample independent samples (equal variances) independent ...
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195 views

median and mean of the sample mean of i.i.d. log-normal

Let $y:=\frac1n\sum_{i=1}^n x_i$, where $\{x_i\}_{i=1}^n$ is a set of i.i.d. random variables, and every $x_i$ has a lognormal distribution $x_i \sim\text{Lognormal}(\mu,\sigma^2)$. Let $\text{Med}[y]$...
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1answer
229 views

Population, sample and model

Background: In Statisical Methods by Pfaffenberger and Patterson, they say that "A parameter is a numerical measure of a population characteristic." (p. 306) "A statistic is a numerical measure ...
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69 views

If $\bar{x}$ has a Burr distribution, what is the distribution of $x_{i}$?

If $X=( x_{1},x_{2}, \cdots ,x_{n})$ $x_{i}$s are iid, and $\bar{x}$ has a Burr distribution (https://en.wikipedia.org/wiki/Burr_distribution), what is the distribution of $x_{i}$, $i=1, \cdots ,n$.
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620 views

Expectation and variance of sample mean with random sample size

I have a question regarding sampling where the sample size itself is a random variable. Say I have two sub-populations $A$ and $B$ from which I can sample a real valued random variable with ...
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181 views

The practical use of the lower/upper semivariance adaptation of Chebyshev's inequality for sampled data

The wikipedia article about Chebyshev's inequality also lists a one-sided sharpened variant, based on upper/lower semivariances. It is additionally mentioned there there that "The inequality with the ...
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90 views

Comparison of two means when they are means of means?

I have two vectors "$A$" and "$B$". Each vector contains multiple mean values derived from observations. The two vectors are subsets of a sample that has been categorized into five vectors. All ...
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75 views

Combining apples and pears to form a single comparator

(I am not a statistician, so this might seem a dumb question, but I need your expert help!) I have data that looks like this: ...
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1k views

Should the mean of the bootstrapped distribution always be asymptotically equal to the sample estimate?

Suppose I bootstrap the distribution of the sample mean. Normally, one would use the mean of the bootstrapped distribution as point estimate of the parameter and the s.d. as its standard error. The ...
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1k views

Model averaging - models with different covariates

I have run models using negative binomial glm.nb() in R and have 3 top models with really close AIC (<2). I was thinking about doing a model averaging using ...
4
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225 views

Backing out the standard deviation from information on baseline mean/s.d., and coefficient mean/s.d

I am trying to run a power calculation for a randomized control trial. For this I need a mean and standard deviation for our 'baseline'. There are papers out there which would have a mean and standard ...
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37 views

Average of ongoing durations

Suppose I run a community center and I want to find the average length of time that someone is a rec center member. It is straightforward to do this with people who have already cancelled their ...
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67 views

How to find 1-year population average with intermittent series data

I have performance review data and scores (ranging from 1 to 4) for employees of a company. I need to show the company average over the past year. However, the employees were only ever reviewed for a ...
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9k views

What does a squared coefficient of variation signify?

The coefficient of variation is defined as the ratio of S.D to mean, a dimensionless number which on multiplication by 100 gives the percentage of dispersion with mean. But when we square this ...
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195 views

Set of data and averaging/standard deviation

I have a set of data (positive real numbers < 1) in five categories. My aim is to show that the data in the last category is bigger than the other categories for a range of examples (the data set), ...
4
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1answer
67 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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37 views

How many samples are needed to distinguish the means of two distributions?

In a paper on Multi Armed Bandits, I came across the following statement: This generalizes the well-known fact that one needs of order $\frac{1}{\Delta^2}$ samples to differentiate the means of two ...
3
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1answer
37 views

Communicating aggregate percentage changes in data without exposing individual contributors

So i have a dataset that tracks widget production from 100 different factories, each individually owned and highly competitive. Each line contains the factory name, the date of production, and the # ...
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28 views

How to set up contrasts in a linear regression models that involve averaging over levels of another factor?

For simplicity, assume we have a linear model which looks like this: Outcome = beta0 + beta1*Treatment + beta2*Time + beta3*Treatment*Time + error where ...
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70 views

Is it dangerous to take the mean of ratio measurements?

I'm going through a Computer Architecture course and in one of the lectures they mention that when measuring the difference in runtime performance between two systems, using for example multiple ...
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107 views

What is the proper method for calculating the Coefficient of Variation of a rate?

I have been asked to evaluate the variation between movement rates of fish within different systems (rates are in km/day). I have between 25-100 samples in each system. I understand that when ...
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115 views

Sample mean vs population mean

I was provided with the following: $X_1,\ldots,X_5$ are independent random samples from a distribution with mean $5$ and standard deviation $3$. Then I was asked to find the mean and standard ...
3
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449 views

Threshold value for Cluster after document similarity

I have N documents. I have found out cosine similarity between all documents. T = (N*(N-1)/2) Because docSim between a document with itself is 1. Now, I have one query and I want to find out all ...
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166 views

Bootstrapping A Mean: What is the significance (if any) of a converging mean for n iterations?

I have a stochastic signal, and I'm taking its mean in the canonical way and comparing that with a bootstrapped mean: ...
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0answers
119 views

Confidence bounds on mean of a limited normal distribution

Suppose we are sampling from an underlying normal distribution with mean $\mu$ and variance $\sigma^2$, i.e $\mathcal{N}(\mu, \sigma^2)$. However, whenever we find a sample value that is greater than ...
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248 views

Calculate the average cumulative distribution

I'm looking at some reaction time data for many individuals. So, for example, one individual will have several hundred measurements in the range of [-200 1000] for the reaction time to a stimulus ...
3
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137 views

What is a test that I can use to determine if a time series is first-order stationary?

I need to test that one of the time series in my analysis has a constant mean over time. Is there a standard test I can use to help me determine this? I know that I can use a nonparametric procedure ...
3
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0answers
318 views

Mulitvariate normal truncated conditional expectation

There is three-variable multivariate normal distribution. Denote 3 variables with $X_1$, $X_2$, $X_3$. Let $\mu_i$ be means, and $\sigma_i^2$ variances of respective variables, and let $\Sigma$ be ...
3
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1answer
112 views

Quantitative Location Shifting Detection for Run-Sequence Plot

I am trying to complement a Run-Sequence Plot by some quantitative metric to validate that a dataset has a fixed location. Since the Run-Sequence Plot will be used in the early phases of Exploratory ...
3
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0answers
34 views

Test for participant subgroups in gradual means shift

In an experiment with 44 participants I have measured the response time for a set of stimuli, where the response could be a or b. The means of the two responses do not differ significantly (783.3 vs ...
3
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0answers
287 views

Two sample differences between percentage means with negative percentages

Hello to everyone and thank you for all the help you've already unknowingly provided to me in the past. I have a group of percentages around zero that are grouped into two categories, and I wanted to ...
3
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0answers
4k views

Averaging z scores when doing a “group by”

I have a dataset where each row is an hourly measurement of certain fields (columns). For each column I then add another column that is its respective z score relative to the entire population. If I ...
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0answers
68 views

Estimating the mean from knowing the first n largest values

There is a sample of n values that are the first n largest values of a population. Is there a way of getting any statistic such as mean or dispersion from such piece of information provided that the ...
3
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0answers
249 views

How do I forecast a timeseries of data using GARCH(1,1)?

I'm new to GARCH, but I've got daily data of TV Ratings. I've been trying to forecast this for future, and a quick background - the data is non-stationary, has high seasonality (weekly, monthly & ...
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0answers
62 views

Statistical properties of a 3D field from spatial averages at different scales

I'm trying to estimate the statistical properties of a 3D vector field (the magnetic field vector in the solar atmosphere) over a 2D field of view from observations. I will neglect for the moment that ...
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0answers
23 views

How to compute/estimate the probability of the mean value of a number of x results of a classification NN?

I use a neural network to classify the sentiment of some news articles per day, regarding a specific topic. Possible results are $[1,2,3,4,5]$ (1=very negative, ..., 5 = very positive). Using one ...
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0answers
25 views

Slutsky's theorem applied to a sample mean conditional on a Bernoulli variable?

Let $(Z_{i},Y_{2i})$, $i=1,2,\ldots,N$ be iid random vectors, where $Y_{2i}$ is the outcome vector and $Z_{i}\sim\operatorname{Bernoulli}(\delta)$. Assume that $E(Y_{2i}|Z_{i})=\mu_{2}+\beta Z_{i}$ ...
2
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1answer
29 views

Combining Estimates with Actual Values

I am exploring stature (living height), calculated from arm and leg bones, from an archaeological sample. Unfortunately, there are very few complete bones that can be measured and entered into the ...
2
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0answers
23 views

How can I estimate the distribution of sizes if I sample from the tails of that distribution?

Let’s say I have an insect farm and they lay down a lot of eggs, which I collect in a cup. Now I want to study the size distribution of those eggs, but there’s a problem: The younger eggs, which are ...
2
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1answer
37 views

What situations using median is not recommeneded?

I was recently asked this question in an interview about when/where not to use median. I know median has some limitations such as it requires ordered list of numbers. But I am not sure if there is any ...

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