Questions tagged [mean]

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

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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", ...
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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 ...
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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 ...
Ahsan Yousaf's user avatar
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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 (...
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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
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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 ...
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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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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
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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 ...
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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 ...
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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 ...
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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
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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
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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
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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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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 ...
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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 ...
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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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How to establish what distribution to compare my statistic to

Apologies for this poorly titled question, but I've been taking some statistics courses and sometimes when you try to learn too many things in too little time you want to take a step back to check if ...
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How do you fit a normal distribution to this data?

I've calculated the expected frequencies by using the normal distribution chart and the frequencies given in this table. However the sum of the expected frequencies is turning out to be 67 while the ...
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Understanding parameters interaction contrasts in model averaging

I am struggling to understand how parameter interaction contrasts play into model averaging. As I am new to Stack Exchange, I apologize if my question is in the wrong place or incorrectly asked. I ...
artessy's user avatar
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How to find the equal-weight mixture of an infinite set of probability distribution?

For example, the equal weight mixture of $p,q$ is $0.5p+0.5q$ Let $\Delta$ denote the convex hull. CASE1: The equal-weight mixture of the infinite set $\Delta(p,q)$ should be also $0.5p+0.5q$ CASE2: ...
dodo's user avatar
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Normalising series data of variable length

I have a model m which takes as input a starting array of n_input elements which are actually traces of mining processes and ...
Shivam Roy's user avatar
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Mean of probability distributions? [duplicate]

Mean of a random variable $X$ is its expectation. I am interest in the new definition, mean of probability distributions Let $p,q$ be probability density distributions. $0.5p+0.5q$ is the mean ...
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mean and variance

Let X be a discrete random variable such that X = 0 with probability 0.5 and X = 1 with probability 0.5. Let Y be a discrete random variable such that Y = 1 when X = 1 and Y = 0 when X = 0. What is ...
Meera s's user avatar
1 vote
1 answer
33 views

Extreme values affecting mean in regression analysis

I am examining whether there is a difference in reaction time (RT) for 2 different conditions (A and B). Participants complete trials in both conditions. First, I use a linear mixed model to assess ...
SilvaC's user avatar
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4 votes
2 answers
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Why does my bootstrap sampling distribution no resemble the true sampling distribution?

In trying to understand the bootstrap method, I have taken a sample of 11 observations from a Poisson distribution with a mean of two. I have obtained the following sample: Assuming I do not know the ...
hhh3's user avatar
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Mean difference between four groups with

I have four categorical groups (A, B, C, D) each with one mean representing a numerical, skewed variable. The data structure is as follows: ...
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Comparing means of a small sample with non-normally distributed data

I am confused about how best to compare means when the sample is small and they are not normally distributed. I have survey data which measured the mental wellness status of a very small sample of a ...
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Hypothesis testing of normal distribution, unknown mean unknown variance

Suppose that we make measurements of an effect, and we know that the values that we obtain follow a normal distribution. But we don't know the mean nor the variance. The hypothesis is that 95% of the ...
Adrian 's user avatar
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Calculating standard error of the mean for dose response assays when the data in the points is processed?

I am trying to report honest statistics about an experiment. I do not have a statistics background and am unsure how to approach this question. My experiment measures a signal (S) minus background ...
David Kouvchinov's user avatar
3 votes
1 answer
96 views

Is the sample mean an unbiased estimator of population mean in the presence of autocorrelation?

I've seen previous questions here that the sample mean can be considered an unbiased estimator of the population mean. e.g.1, 2. While the examples seem to refer to independent sample points, it seems ...
JMenezes's user avatar
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Is it possible to replace missing data if 50% of total data are missing?

In my study, 40K completed household surveys. However, when we suggested visiting a nearby health center to measure their physical parameters (height, weight, blood pressure, and blood glucose), only ...
Dr bappa's user avatar
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Averaging linear regression model coefficients with different data sources

I am new to model averaging and its not clear on how to use the model average coefficients. I have data from three different data sources, (say A, B, and C) and the linear regression models for the ...
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Best way to compare editions of a running race?

What is the best way to compare performances between editions of the same running event? In this case, distance and elevation varies slightly from year to year. Compare differences between editions ...
Daniel Westergren's user avatar
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For a stochastic system, should we optimize its time average cost or total cost? What is the difference between the two goals?

For a stochastic system, the time average cost like: $ \lim_{T \to \infty}\frac{1}{T}\sum_{t=0}^{T-1}\mathbb{E}\{cost(t)\}$ and total cost like: $ \lim_{T \to \infty}\sum_{t=0}^{T-1}\mathbb{E}\{cost(t)...
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