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Questions tagged [mean]

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

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Prove Zero Mean Hypothesis

I have a stochastic process for which I can compute a final outcome that is real valued. I know that the process has a relatively high variance and is costly to obtain more data points. (which I know ...
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0answers
25 views

How should I calculate mean CI - from raw data or mean values?

I have experimenatal data from medical industry. In the experiment 4 observations were weighted, each one 2 times for more precise measurement. As a final weight, a mean from each pair is reported. ...
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1answer
11 views

Repeated measurements descriptive statistics for whole period

I am looking at the number of doctor’s visits over a 10-year period in about 2000 municipalities. Each municipality is assigned to one of five municipality types (e.g. large town, rural community, ..)....
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1answer
33 views

how to combine standard deviations and mean for each group?

I have a table with 10000 rows, each row having 10 columns and their numbers vary from 0 to 80.Now, if I want to compare the mean of these rows.Maybe because of the largeness of one of the numbers in ...
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1answer
16 views

Valid way of determining spread of data

I’m trying to determine a valid method for quantifying the maximum spread of values I can statistically expect to see. I’ve collected 12 sensor values from 12 different sensors. I’ve calculated the ...
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0answers
16 views

Proof that a poisson regression with 2 categorical predictors is the same as each observed mean

I have a poisson regression with 2 categorical predictors to predict\estimate the sales of product $p_i$ on location $j$: $\hat{X}_j(p_i) = e^{\gamma_0 + \alpha_i + \beta_j + \mu_{i,j}}$ It appears ...
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10 views

Combining point prevalence estimates and their confidence intervals

I have some health survey data from multiple years. This includes the estimated prevalence of a flu vaccination in a population, then number of people surveyed, and the high/low confidence intervals. ...
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3answers
65 views

What comes after the geometric mean?

The geometric mean is a multiplicative alternative to the arithmetic mean, which we could call additive mean, thereby calling the geometric mean multiplicative mean. My question is the following: what ...
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1answer
36 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
76 views

Existence of $E(X^2)$ when $X$ has the pdf $f(x)= \frac{1}{(2+x^2)^{3/2}}$

In a competitive exam, I came across an objective question which says Let $X$ be a continuous random variable with the probability density function $$f(x)= \frac{1}{(2+x^2)^{3/2}}\quad,\,-\infty&...
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1answer
24 views

Example of maximum a posteriori that does not match the mean of a marginalized posterior

Given a N-parameter likelihood and prior, I can obtain the marginalized posterior for each parameter through Bayesian MCMC. I can also estimate the maximum a posteriori (MAP) of the N-parameter ...
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1answer
22 views

mean of autoregressive process [closed]

An autoregressive process of order p, AR(p), is of the form $x_t=\phi_1x_{t-1}+...+\phi_px_{t-p}+w_t$ where $x_t$ is stationary, i.e. $E[x_t]=\mu$ for all $t=0,1,2,...$, and $w_t$ is white noise, i.e....
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9 views

How can I calculate confidence for a multiplicative (growth) dataset?

I have a dataset of daily price changes, represented as decimals. Perhaps: 0.5, 1.5, 2.0. That's to say it lost 50%, then it gained 50%, then it gained 100%. I'd like to know how confident I should ...
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1answer
13 views

Detecting significant changes in groups of values over certain ranges of time-series

Below is an example of data output. It represents indicies [y-axis] calculated for 52 weeks in a range of 64 years. Group of 64 years is classified and several years are represented with blue, some ...
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0answers
23 views

how can we differentiate if the mean, variance of a distribution is finite or infinite?

For X with random variable distribution, can anyone please share an example, how can we differentiate if the mean, variance of that distribution is finite or infinite. Is there any easier way to ...
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0answers
27 views

Estimate mean from sample data

Assuming a sufficiently large set of data, is there a formula for "predicting" a mean value with a certain degree of accuracy without calculating the mean for the whole set of data? Example, say I ...
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0answers
44 views

Why that distribution is normal with those parameters?

Mi question is the following. I have two independent 2-dimensional normal distributions with the same mean vector and different covariance matrixes, lets say $X_1 \sim N_2( \mu, C)$ and $X_2 \sim N_2(...
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38 views

Understanding sum of square deviations [duplicate]

Given $X_1...X_n\stackrel{iid}{\sim} N(\mu,\sigma^2)$ and $U=\sum_{i=1}^n (X_i-\overline{X})^2$, why is $U\sim\sigma^2 \chi_{n-1}^2$ ? And what would be the distribution of $V=\sum_{i=1}^n (X_i-\mu)^...
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1answer
66 views

Time varying random variable

I am studying the water surface elevation in the presence of waves, at one location over time $\eta(t)$ as seen in the following figure.           &...
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2answers
63 views

Is “geometric mean” the same as “the first moment of the lognormal distribution”?

I would like to compare the results of two studies, one reporting "geometric mean diameter" and the other one reporting "the first moment of the lognormal size distribution". I am not sure whether the ...
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2answers
30 views

Combining two means and SDs of one group [duplicate]

I have the mean & SD of several different time points, I want to combine them into one mean and SD. Is it possible? Example; At 1 hour; mean=5, SD=1, n=42 At 2 hours; mean=6, SD=3, n=42 and so ...
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2answers
104 views

Calculating the variance of sample, knowing the mean of population

Suppose that I somehow know the mean of the population. And I want to calculate the variance of a sample. Should I subtract population mean or sample mean? Is there any situation in which I should use ...
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0answers
17 views

Can one use parametric regression tests (e.g., Pearson's R2) on summary statistics (that are normal) derived from non-normal data?

Can one use parametric linear regression tests (e.g., Pearson's R2) on summary statistics (e.g., mean and median) that are normal but derived from non-normal data? I am specifically dealing with mean ...
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Test for comparing 4 groups, 18 conditions and 1 numerical variable

I hope I'll manage to make my problem understandable. I've got a data set which contains 4 groups (CG, TG, HG, IG) across 18 conditions (e.g. 18 verbal cues) and 1 numerical variable (the participant'...
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1answer
73 views

What does the author mean in this description about “mean”?

I am reading the book "Intuitive Introductory Statistics" and it has the below paragraph about the mean which I don't understand. For example if you take a series 1,2,3,100 and calculate the mean, it ...
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0answers
26 views

True Mean of an Observation

I have a list of aggregated data with 100 data points. The information I have is the mean and the number of observations used to calculate the mean. Moreover I have the raw data from which the ...
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1answer
52 views

How to interpret interaction dummies of multiple categories and main effect

I have a panel data crosscountry regression with following structure ($y$ as a drug addiction rate of the country, $x$ as number of homeless of the country and $m$ as HIV infection rate of the country)...
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0answers
18 views

Which mean to use to find the average of measurements given in the form of “per period”

Let's say I made several measurements on my gas consumption. 2m^3 per day 1m^3 per day 1.5m^2 per day 2m^3 per day What is the average daily consumption of gas? I can take arithmetic mean and it ...
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1answer
18 views

Statistic to Verify Subsample is Similar to Original Sample?

I have a subsample of data (120 students) that was taken from an original sample of 1,216 students' data. I need to report in my manuscript whether my subsample's key demographics (age, gender ...
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29 views

Standardized differences between means in R?

There is data on a sample of 1,216 students that I'm missing, but I know the means and standard deviation of some key demographics on them. I have a subsample (120 students) with the means and ...
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Measuring Impact of Category of continuous variable: is difference in mean valid way?

Suppose a data set with 5000 observation, measuring height of people from 5 distinct region. Assuming I have theory, which says that the some portion of your height is determined by region you belong ...
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33 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
19 views

Comparing the mean of two Likert scales with only one (no) group

I have data from several Likert Scales which look at how people feel about object a - e. I want to compare the means of these results and see whether people feel differently about object c and object ...
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0answers
11 views

Is harmonic mean of feature importance index a statistically appropriate approach to obtaining most important features across different models?

I've trained 16 different models on similar biological datasets to predict the occurrence of a specific disease (the target) from ~18000 biological super-pathways (features). Each dataset has the same ...
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31 views

What is the correct formula for Bayesian update for normal distribution with known variance [duplicate]

As question title states, I'm interesting in Bayesian update of normally distributed data with known variance. I compared three sources and they seems to contradict each other. I use some kind of ...
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27 views

What do my mean and standard deviation tell me?

I have American State level unemployment rates in 3 waves of longitudinal data. When I describe unemployment rates for my descriptive table I get the following: ...
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1answer
24 views

Hypothesis Testing For Two Sample Mean Proportion

We've two samples of size n_1 and n_2 from two different normally distributed populations. We don't know their population means ...
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1answer
69 views

Confidence interval for $\sigma^2$

I started with any distribution and underwent the CLT on $\sqrt{n}(\widehat{\sigma}^2 - \sigma^2)$ where $$ \widehat{\sigma}^2 = \frac{1}{n}\sum_{i=1}^n (X_i - \mu)^2 $$ is a sample mean of $\sigma^2$...
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0answers
29 views

Compare Two Means Without Underlying Observations in R?

I have limited information with which to compare two means, is it still possible in R? We have a group of students (1,000 students) about whom we have mean and standard deviation information, and we ...
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1answer
40 views

Two Means, Different Sample Size, How to Compare Using R?

There is a sample of a student population (1,000 individuals) and from these, some were selected for an experiment (230 individuals). Now I need to compare the average of the original population to ...
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0answers
25 views

FIsher's LSD test is appropriate for restricted mean comparisons

Suppose that we perform two way ANOVA with interactions, with factors $A$ and $B$ with three level each $A_{1},A_{2},A_{3}$ and $B_{1},B_{2},B_{3}$. We know that Fisher's LSD test is used for ...
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2answers
68 views

How can I calculate the mean of the cube of random variable that follows chi-square distribuion?

If $X + 1 \sim \chi^2_{1}$, what is the mean of the cube of $X$? I'm confused between raw moment and central moment. My idea is, since the mean of $X$ is 0, I should calculate the raw moment. ...
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1answer
48 views

Log transformation to generate random number producing NA's

I am trying to generate a random values using log distribution. The reason for using log-distribution is keep the values positive. ...
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1answer
146 views

Proving Asymptotic distribution of $\sqrt n( \widehat\sigma^2 -\sigma^2)$

I am looking at trying to derive an expression for the asymptotic distribution. We have $X_1,\ldots, X_n$ i.i.d $N(\mu, σ^2)$. So we have defined $\hat \sigma^2 = \frac 1n \sum_{i=1}^n(X_i-\mu)^2$. (...
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1answer
42 views

Can mean,standard deviation of different populations be similar?

Sorry for the dumb question. Perhaps this is too obvious but i don't see it. Will appreciate any help. We're analyzing a gene expression dataset of 64 autistic individuals vs 82 normally developed ...
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9 views

How do I relativize a subtraction of two associated variables by the mean difference of the respective variables?

I have a dataset from soil samples, i.e. their carbon content. I sampled soil from a flowerstrips (FS) and to each sample I sampled soil from an adjacent arable (AF) field. Hypothetically, I do a t-...
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1answer
46 views

Taylor expansion for random variables

Let $X_n$ and $Y_n$ be random variables such that $X_n-Y_n\overset{p}{\longrightarrow}0$ as $n\rightarrow\infty$. Let $f(.)$ is a differentiable function. Is the following correct? $f(X_n) = f(Y_n) + ...
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1answer
42 views

Robust analogues of Mean, CV and Skewness

I need to characterize the mean, CV and skewness of my observed data (it is gamma-like distributed). This data is an artifact (outliers) enriched, so I decide to use robust statistics: median, ...
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1answer
19 views

Significance of Difference in arithmetic means

We characterized two social group through utilizing a 4 point likert scale and arithmetic means for 32 questions separated in 4 groups and 4 subgroups as our professor advised, we look at the ...
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1answer
37 views

Mean and variance of probability density with multidimensional indicator function

I encountered the following question while studying machine learning: We are asked to calculate mean and covariance of a given probability density function $$p(x) = \frac{1}{16} \cdot 1_{0 \leq x_1 ...