Questions tagged [mean]

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

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Confidence interval for the sum of 2 binomially distributed variables

$P_1$ and $P_2$ are uncorrelated, binomially distributed variables with success probabilities $p_1 \neq p_2$. Say I measure: $k_1 = 9$ successes out of $n_1 = 10$ trials for $P_1$ and $k_2 = 1000$ ...
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$\mathbb{E}[X^2]\leq k \mathbb{E}[X]^2$, upper bound second moment from first moment

Let $X$ be a non-negative random variable bounded on $[0,1]$. Is it true that $\mathbb{E}[X^2]\leq k \mathbb{E}[X]^2$ for some constant $k$? If not, are there any minimal assumptions on $X$ where this ...
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Conditional and unconditional mean in GARCH(1,1) model

Say I have a stationary time series and want to fit a GARCH(1,1) model. Does this mean that the conditional mean, which is used in GARCH, would always be the same as the unconditional mean of the ...
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Sample mean of subsample appended to original sample [closed]

From an $SRSWOR(n)$ drawn from $N$ units, an $SRSWOR(n_1)$ sub-sample is drawn and added to the original sample. Show that the sample mean based on $(n + n_1)$ units is an unbiased estimator of the ...
Abhilash Saha's user avatar
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Can raw means and estimated marginal means be the same ? And when?

I have read a lot about calculating raw (standard) means and EMM. First are data based (descriptive stats), the latter are model based. I try to learn how to calculate both of them. In my example both ...
Andrzej Andrzej's user avatar
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Decision theory when distributions don't have a first moment? [closed]

Lets say that we are presented with two gambling opportunities and would like to decide between them in a decision-theoretic framework. For gamble 1, the cost is $1$ and the payoff is $X_1$ where $X_1 ...
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How to estimate mean and standard deviation of individual result given a sample of batch results?

I apologize in advance if my title is not well-worded, or if I am using the wrong tags; this is my first time asking a question here. I want to analyze how long it takes for a system in production to ...
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Converting the unit for mean and standard deviation

I have a problem and it's been days and I couldn't find a solution Simply what I want to do for the purpose of a research data, I have the mean and standard deviation of some measurements in diameter ...
Ibrahim Hassan's user avatar
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Standard Deviation and Standard Mean Error of measurement with uncertainties

It is well known that, given a set of $n$ values $Y_1, \cdots, Y_n$, its Sample Standard Deviation is $\sigma = \sqrt{\dfrac{1}{n-1}\sum_{i=1}^n (X_i - \bar{X})}$ and its Standard Mean Error is $\...
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Why is taking the mean RMSE sometimes so far off overall RMSE?

I'm working with a multi-threaded program, which splits a dataset into N chunks, and evaluates some regression model's performance, predicting a score for each item in each chunk. I'm using RMSD as ...
Seán Healy's user avatar
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compare means of lognormal distribution

I have a small set of data that I used to generated a lognormal distribution: ...
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Can I compare two estimates by their sample variance?

For example, to estimate the population mean $\mu$, I am given two sample mean $\bar{x}_1$ and $\bar{x}_2$ from two (independent) data sets of $N_1$ and $N_2$ observations respectively. Without access ...
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Meaning of subscript $n$ in sample mean variable

I am reading Wasserman's All of Statistics. In Chapter 13: Linear and Logistic Regression, when deriving the least square estimates for simple linear regression, we have the data $(Y_1, X_1), \dots,(...
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Deviation between Mean and Median

If I have a mean of 15 and median of 10, is there a term for the difference between these? Can you use this difference of 5 for anything valuable statistically?
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Calculating the mean of different SMRs

I have the SMRs of different local areas. The same reference population was used for the standardization. The local areas were divided into 5 groups (group1, group2,...,group5). I want to know if the ...
Luke's user avatar
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Calculated spread and mean using mean results only

Background: We have a large database of measurement data. The individual data points are actually the mean results of a particular sampling. No further information is available against each data point,...
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What is the intuition behind the single-pass algorithm (Welford's method) for the corrected sum of squares?

The corrected sum of squares is the sum of squares of the deviations of a set of values about its mean. $$ S = \sum_{i=1}^k\space\space(x_i - \bar x)^2 $$ We can calculate the mean in a streaming ...
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Estimating Standard Error of the Mean Across Multiple Samples: Method Selection and Best Practices

I have multiple samples, each of size (n), and I'm exploring different methods to estimate the Standard Error (SE) of the mean. I understand there are several approaches, but I'm seeking insights into ...
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Why regarding mean Average Precision for 50 and for 50 to 95? And can you average different evaluations?

I saw a lot of papers using mAP@50 and mAP0:5:95, but in terms of deciding how precise a trained object detection model is, I do not understand why often both values are discussed and shown. Wouldn't ...
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Average of Percents, or Sum Total / Sum Total?

I have some data and need to know the average commission of all the items. For each row, I calculate the percent of items sent out. If I wanted to know, "What is the average commission", ...
BruceWayne's user avatar
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Covariance of Best Linear Unbiased Estimators and arbitrary LUE

I'm working on a problem involving two linear unbiased estimators $T$ and $T'$ of a parameter $\theta$, defined from a sample $\{X_1, \dots, X_n\}$ with mean $\theta$ and finite variance. I aim to ...
Taha Rhaouti's user avatar
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K means clustering of image with k=1 vs mean of all pixels

I have relatively uniformly colored images and I extracted colors using k-means. k means 1 showed the best results for my modeling purposes, k means 2 not so much, and with k-means 3 there ceased to ...
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Calculating $E[(\sum X_i)^4]$

Trying to figure where I'm going wrong with the following. My goal is to calculate var$(\bar X_n^2)$ using $E[(\bar X_n)^4]=\frac{1}{n^4}E[(\sum X_i)^4]$ given that $X_1,...X_n$ are iid with $EX_1=\mu,...
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Confirming my calculation of mean, standard deviation and median for a histogram

Average travel time* for men = 27.2 minutes, women = 23.6 minutes My calculations are the followings: The problem is my calculated mean is 28.4 but chart says 27.2 I calculate the mean with this ...
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Can ANOVAs or Student tests be conducted on any summary statistic at the individual level?

I am wondering if ANOVAs or Student tests can be performed on any summary statistic of performance at the individual level without any effect on type 1 and type 2 error. For example, consider a simple ...
user1363251's user avatar
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In R, why are the results of summary(lm(y~-1))$sigma^2 and mean(y^2) same?

Consider the following data and the model: y <- c(9,3,-2,7,6,12) lm(y~-1) summary(lm(y~-1))$sigma^2 [1] 53.83333 I expected ...
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How does a Random Sample relate to Random Processes and Random Variables?

What is the difference between a Random Sample, Random Variable (RV) and Random Process (RP)? As far as I know, a RV is a mapping from an experimental space to the real numbers and a RP is a mapping ...
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Comparing ratios of independent means by calculating SE difference – applicable?

I am conducting a study comparing the ratio of a mean number of vocalizations to the mean number of individuals across three treatments. For each treatment, I have the mean number of vocalizations (...
Yael Lehnardt's user avatar
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General Expression for the $t$-th difference of conditional means

In econometrics, it is common to work with the difference-in-differences of conditional means. For example, let $Y$ denote a variable of interest and $X_{1}$ and $X_{2}$ denote binary regressors. The ...
Kevin Durant's user avatar
5 votes
1 answer
151 views

What do I do when I *want* to accept the usual null hypothesis?

I have samples from two random variables, and I'm assuming normal distribution with equal variance. I want to show that the distributions have equal means $\mu_1$ and $\mu_2$. The usual two-tailed t-...
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Is this rato between sum of squares beta distributed?

Consider $x_i \sim N(\mu,\sigma)$ I am interested in distribution of the the following statistic (arises from likelyhood ratio test): $$ \frac{ \sum_{n=1}^{n} (x_i - \overline{x})^2 }{ \sum_{n=1}^{n} (...
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Box plots of monthly averaged water flow

I am working with a model that models water flows in a certain area. These flows can be influenced by taking certain measures, resulting in multiple water management scenarios. I would like to compare ...
Nathan's user avatar
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Gaussian posterior/posterior predictive mean [duplicate]

I'm a little confused regarding the difference between the posterior and the posterior predictive distribution. I know that the posterior is a distribution over the parameter, while the posterior ...
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2 answers
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Subtracting the ideal-rank-mean in Wilcoxon rank-sum, what does it do

I am reading Discovering Statistics using R by Andy Field. In the section about how to calculate the rank statistic in MWU, one of the steps is to subtract the mean rank from the sum of ranks. W = sum ...
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Calculate mean and standard deviation of the ratio of two dependent variables

I have an instrument of which I would like to understand the uncertainty on the measurements taken, so that every time that I perform a single measurement, I can apply the error obtained and therefore ...
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Summary statistics (mean and standard error) of split plot nested design- using R

I have a study with a split plot design where every season (wet and dry) we sampled for 3 years at 8 sites. At each site (fixed factor), we have plots (nested within sites) and then we have subplots ...
Veronica's user avatar
2 votes
1 answer
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Is the use of geometric mean for water chemical concentrations appropriate?

I'm asking for a pointer for a source of definitive descriptions of what types of data are best summarized by the arithmetic, geometric, and harmonic means. I see regulators apply the geometric mean ...
Rich Shepard's user avatar
3 votes
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Power calculation with multiple techniques and multiple observations per subject

Say I have C algorithms/techniques and N subjects. For each algorithm/technique I make some (variable) number of measurements ...
sudo make install's user avatar
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converting data from geometric LS mean and confidence intervals to mean and SD

I Hope this letter finds you well. I am conducting a meta-analysis, and some of the studies have reported data in geometric least squares mean and confidence intervals, while others have presented ...
user405119's user avatar
1 vote
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Converting median absolute deviation to standard deviation

I'm working on some medical research and I'm wondering what is the most straightforward method to convert median and median absolute deviation (MAD) to mean and standard deviation. If anyone has any ...
Yomna's user avatar
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Does the confidence interval for Poisson rate contain the sample mean?

Let $X_1, X_2, \dots, X_N$ be iid random variables from $Poisson(\lambda)$. The confidence interval for $\lambda$ with confidence level $1-\alpha$ is $$ \frac{1}{2N} \chi^2 \left(\alpha/2; 2 \sum_{i=...
mathslover's user avatar
4 votes
1 answer
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Why is this derivation of the mean of the gamma distribution using the log-partition function incorrect?

I am using this formulation of the exponential family : $$ \large f_{X}(x;\boldsymbol{\eta})=h(x) \exp \left(\boldsymbol{\eta} \cdot \mathbf{T}(x)-A(\boldsymbol{\eta})\right) $$ The gamma distribution ...
Sagnik Taraphdar's user avatar
10 votes
2 answers
606 views

Why is E(θ / (1 - θ)) different than E(θ) / (1 - E(θ))?

I've encountered a problem question: The probability of success for a random variable follows a Beta(5, 3) distribution. The posterior mean is θ = 0.625. The odds of success is defined as θ / (1 - θ)....
alexandrosangeli's user avatar
2 votes
1 answer
56 views

How to aggregate standard errors of multiple test scores?

I have three test scores of a student. The three single scores are generated by an IRT-based test using computer adaptive testing and are reportet with standard error bars. For the report I want to ...
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Can you create an age structure of population, if the age was established using multiple different methods?

I want to analyse a age structure of my sample. However, I was not given the ages themselves and instead had to establish them using multiple methods with various coefficients of determination (not ...
Lucy's user avatar
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3 votes
1 answer
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Standard deviation squared is variance. What is standard error of the mean squared? [closed]

Is it correct to say that there is a sample variance and a mean variance, and their square roots are the standard deviation and the standard error of the mean, respectively?
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Versatility and validity of aggregate algorithm for a multiple criteria decision problem (averaging)

I'm trying to aggregate different variables in multiple scales and distributions. The distributions are not known beforehand, but I want to generate a general statistical value that represents all the ...
gabriel's user avatar
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Optimality criterion for mean estimators

Assume a sample size of $n>5$, a given variance $\sigma^2 > 0$ and a $\delta \in (2e^{-n/4}, 1/2)$. Proof that there exists a distribution with variance $\sigma^2$ such that for any mean ...
MrLCh's user avatar
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Confusion forming prior beliefs

Let's say, for the sake of ease, I have a sample of data that I believe comes from the binomial distribution. Let's say I have 100 observations in my sample. Previous to this experiment, I have ...
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Analysis method for comparison of means in zero-inflated non-paired continuous data

I am currently doing my first project involving a lot of statistics and I've stumbled into a bit of a problem. I am researching if comments from two different subreddits explainlikeimfive (ELI5) and ...
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