Questions tagged [mean]

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

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Mean and standard deviation comparisons

I have datasets (one 1997-2001, another 2020, 2021) with means and standard deviations that I need to compare. Two different dats information (mass and total number). It is expected that I compare ...
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Determining the precision of a range

Supposing that I have 2 measured values which cover a range Y and Z and the actual value "X" is somewhere in the middle. How can I calculate the precision of the range? I expected to ...
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Is there a way to estimate bias in aggregated data?

I have a data set with aggregated data of two study groups. Twenty response variables were recorded for each group and for each response variable, the group size, mean, median, and the 5 and 95 ...
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Changes in overall mean as a consequence of group composition vs. group-wise mean shifts

The mean body size of an entire community might shift due to different mechanisms and as a consequence of e.g. "changes in the relative abundances of different age-classes [...] within the ...
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Understanding the Importance of "Sufficiency" within Statistics

I am trying to better understand what it means to be a "sufficient statistic". "In statistics, a statistic is sufficient with respect to a statistical model and its associated unknown ...
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How does Michaud Resampling improve Mean-Variance Optimization?

Michaud Resampling claims to reduce estimation error through the following process: Step 1. Sample a mean vector and covariance matrix of returns from distribution of both centered at the original (...
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Right way to compute mean and variance

If I take as definition of $a_{lm}$ following a normal distribution with mean equal to zero and $C_\ell=\langle a_{lm}^2 \rangle=\text{Var}(a_{lm})$, and taking the following random variable $Z$ ...
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Convergence in distribution for difference in sample means?

Suppose $X_i, i=1,\ldots, n$ are $i.i.d.$ random variables with mean $\mu_X$ and variance $\sigma^2_X$ $Y_j, j=1,\ldots, m$ are $i.i.d.$ random variables with mean $\mu_Y$ and variance $\sigma^2_Y$ $\...
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How to estimate mean confidence intervals for a sample of a population with the population standard deviation?

First off, this is my first question on stats exchange. So if I mess up or anything, please let me know because I know this website is a lifesaver, and I want to spend more time on it. Recently, I ...
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What is the best way to combine mean and standard errors calculated from the same data set, but with different analysis strategies?

If I have a data set of sample size $N$ and I calculate a mean and standard error from this data set using different approaches -- for example, if I bin the data into groups by some criteria, and ...
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What statistics describe a distribution uniquely and completely? [closed]

I have a very weird and possibly amateurish question. I have a situation where I need to keep track of some activity until some event occurs. I want to store that activity (say, a series of 0s and 1s),...
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Comparing 2 sample means

I'm trying to quantify the difference between two sample means. I'm not sure if I can use the standard two sample t-test. The first sample comes from the difference of two time series (inflation rate ...
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On average what is the norm of a sample from a multivariate normal distribution? [duplicate]

Problem Suppose I sample a multivariate standard normal sample $x \sim N(0, I_d)$ where $d \geq 1$ is the dimension. What is the expected value of the norm of $x$ $$ \mathbb{E}[\|x\|] = ? $$ Using ...
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How can I make an existing time series more volatile?

I have an existing time series that I would like to make more volatile, or more variance. I would like the highs to be higher and the lows to be lower. The time series is somewhat stationary and I ...
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Difference between Hmisc::describe() and base::mean()

I am currently using the function Hmisc::describe() to work on a dataset, but I am a bit confused by the fact that I get different mean results between the mean ...
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Why do 95% confidence intervals contain the unknown population mean 95% of the time?

I am learning about the Central Limit Theorem (CLT) and confidence intervals from this online course. I have learnt that that the CLT states that the theoretical sampling distribution of a sample ...
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How to calculate the distribution of the sample mean of uniform distribution? [duplicate]

I am working on the following question but I'm not sure if my approach is correct. Given that X~U(4,8), I need to find the distribution of the sample mean for a sample size 30. My approach is that ...
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testing whether a sample of the population has a different mean than the population mean

I have a short question regarding testing whether multiple subsample means are different from the population mean. To be specific, I have the full population of the energy consumption per square ...
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Geometric Brownian motion drift estimation problem

Given: $$ d \ln{S_t} = \left( \mu - \frac{\sigma^2}{2} \right)dt+ \sigma dW_t $$ We have that: $$ \mathbb{E}_t[d \ln(S)]=\left( \mu - \frac{\sigma^2}{2} \right)dt $$ $$ \mathbb{V}_t[d \ln(S)]=\sigma^2 ...
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Covariance of the means of $x_t$ and $y_t=(x_t-\bar{x})^2$

Given a sample of a real-valued time series, $x=\{x_t\}_{t=1,...,T}$, let $\bar{x}$ be the sample mean of $x$ and set $y_t=(x_t-\bar{x})^2$. Then, $\bar{y}$ estimates the variance of $x$. Question: ...
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Comparing the mean and spread of two distributions

I am conducting an experiment wherein I am building several (around 6500) regression models. Each model's performance is indicated by the R², RMSE etc and as a result, I have a distribution of these ...
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Mean of ratio, ratio of mean and statistic test

First off, I'm sorry if this has been answered or if the answer seem obvious, but I'm currently stuck and can't really wrap my head around the problem. So here are an example table of my situation (...
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expected value of the sample variance, a strange result

Reading this article (https://arxiv.org/pdf/1812.09384.pdf) I have met an apparently simple result, which however I cannot explain. The result ise the following: given a set of samples $M$, each with $...
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Covariate analysis comparing distributions / means of circular data

Are there publicly available software packages to run an analysis comparing the means or distributions of two samples of circular data with the presence of a covariate? If not, are there ways to ...
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Fourth moment of sum of unit normal distributions, given constraints

Suppose that I have M draws from a unit normal distribution N(0,1). By construction, the sum of the M draws equals zero, and the sum of the squares equals M. Given these constraints, what is the ...
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How is standard error affected by multiplication?

If I have some measure, suppose the difference of two means, and then I multiply it by 100; how will the standard errors be affected? Will they be multiplied too? or will they be completely different?
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Likert data and Likert scales - ordinal or interval?

I was reading up on the use of Likert scales and how to analyse data. I found this bit of text confusing: To properly analyze Likert data, one must understand the measurement scale represented by ...
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How to find mean of multivariate normal distribution when holding a variable constant? [duplicate]

I wanted to know if there is a way to calculate the mean of a multivariate normal distribution when a certain variable is held constant. For example, if I had a continuous bivariate normal ...
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How to construct the confidence band for a timebased sample of n individuals

Let $X^{(i)}(t)$ be some measurement at time $t$ for individual $i$. Let $\bar{X}(t) = \frac{1}{n} \sum_{i=1}^n X^{(i)}(t)$ be the mean of the individuals at time $t$. Let $\bar{X}_{t_0} = \frac{1}{T}\...
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Mean, Median, Mode of Log Normal Distribution

Let $Y$ be Log-Normal with parameters $\mu$ and $\sigma^{2}$. So $Y=e^{x}$ with $X \sim \mathcal{N}\left(\mu, \sigma^{2}\right)$. Which of the following statements is correct? (A) The median of $Y$ is ...
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how to test variance of sample mean for very skewed distribution?

The underlying distribution is not known explicitly but rather inferred from a sample of around 10 million cases. It represents the cost of something and after normalizing the mean to 1 it has the ...
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confused about unbiasedness of sample mean

Recently, in a different thread, I was convinced by others ( after claiming that they were wrong ) that the sample mean is unbiased for the mean of its underlying distribution. But the case of the chi-...
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Interpretation of emmeans table

I have a question about emmeans Variables are A = {a1, a2, a3}, B= {b1, b2}, C = {c1, c2} Model ~ A+B+C+A * B+A * C+C * B One of research questions: Is there an effect of C on a1, a2 und a3 (A)? And ...
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Error (SD) on means of multiple binned datasets?

I manipulate a few datasets and wondering what would be appropriate when calculating the error (standard deviation mostly) Lets say I have 3 datasets (A,B,C) with ranges 1:1000. These datasets are ...
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Is it possible to take the mean of a time series when it is not stationary?

Many guides, when determining the mean of a time series $X_{t}$, assumes that $X_{t}$ must be stationary before calculating $\hat{\mu}=\frac{1}{T}\sum_{i=1}^{T} x_{i}$. But consider the following ...
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confidence intervals for mean values of time series observations

There is the data set of uniform time series: $$x_{1,t},x_{2,t},..., x_{m,t}$$ $$t = \overline{1,n}$$ I want to build a new "average" ts. I can do this by calculating the average for each ...
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Estimation of coefficients of variables x when the sum of the x is equal to y

I'm a new beginner in learning statistics, and I have an issue with the estimation of coefficients. To begin with, let's suppose I have 3 observations and 4 explanatory variables: First observation: y=...
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Finding The Central Tendency From A List Of Averages

Say you have data on the average food consumed per type of animal for a 30 day period. Not the total amount of food itself, but the averages per day per that type of animal. Also assume the number of ...
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Means of Transformed versus Untransformed Data Don't Match

I am doing an ANOVA analysis, and to correct for normality, I used a log transformation on the response variable, RATING. I am trying to display some summary statistics. When I find the means of ...
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Implications of using the mean of the max as a predictor in regression

What are the implications of using a predictor which has been aggregated twice (the mean of a set of max's) as a variable in a regression analysis? I'm performing a regression on the panel dataset: <...
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Comparing means of two samples: anything I'm missing?

I'm hoping for a gut-check from someone with more formal stats education than I to tell me if my proposed approach makes sense or if I'm overlooking anything. I have a survey database where each ...
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Calculate a normal average from uniform samples

Ok, this feels like it should be pretty basic, but maybe I'm missing the right terminology to google this. Suppose I have a (non-analytical) function $f(x)$ that I have evaluated for a large number of ...
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Estimated marginal means with emmeans

I have a mixed linear model, for example, Model <- Values ~ A + B + C + (1 | id) + A:B + A:C + B:C I wanted to do analysis with "emmeans" a.k.a estimated marginal means, so I used these ...
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How do I test for significant differences given only means and standard error?

I'm in a situation where I have two (equally long) lists of means, with sample sizes and stderr for each mean. The variance for these means are all variable and different, and so are the sample sizes. ...
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What are the tradeoffs of using the generalized $f$-median?

The generalized f-mean is a generalization of multiple estimators, and even generalizes the generalized mean. For some invertible function $f$, and $k$-dimensional vector, it is given as: $$M_f(\vec{x}...
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Problem in finding a non-parametric confidence interval for median and mean using Frank Harrell approach when we have more than two categories

These days I am looking for a good estimation for the mean and median difference confidence interval when I have categorical variables with more than two levels using the Kruskal test, Here Dr. Frank ...
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Example distribution where 74% of probability is above the mean

Watching Why You Should Want Driverless Cars On Roads Now, at 8:14 Derek Muller claims: Surveys show 74 % of people believe they are above average drivers. This claim motivates my question, but some ...
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Bootstrapped mean always almost identical to sample mean?

I'm running a simple bootstrapping experiment with the following code ...
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How to calculate within group average of Principal Component Analysis (PCA) scores

am working with a set of population survey data interviewing individuals nested within different levels (households, districts etc.) I am looking to reduce some variables into principal components so ...

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