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

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3
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1answer
89 views

Distribution family of the mean of iid random variables

Let $X_1,X_2,...,X_n$ be $n$ iid random variables following some distribution family $A$ (beta, gamma, normal, etc.). Does the mean $\bar{X}=\frac{1}{n}\sum{X_i}$ also follow a $A$-like distribution ...
0
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0answers
53 views

Appropriate tests for finding a diffference between the scores of two groups of questions

I am testing whether there is difference between the scores of 2 groups of 12 questions on a Likert-scale questionnaire. Each question from one group has a corresponding question in the other group ...
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2answers
745 views

Mean comparison for statistical significance

I was told to come here by a friend to ask a stats question. I took Social Stats and Methods of Social Research about 4 years ago and to be honest, I don't remember much about it. Now I'm writing a ...
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vote
2answers
195 views

Mean of a function of $K$ Gaussian random variables

Consider $K$ Gaussian random variables $Z_1, Z_2,\ldots,Z_K$ that are mutually independent with $Z_1 \sim \mathcal{N}(\mu,\sigma^2)$ and the remaining random variables $\sim \mathcal{N}(0,\sigma^2)$. ...
0
votes
1answer
169 views

Show that $E(XY) = σ_{XY} + μ_Xμ_Y$?

Let X and Y be two random variables with means $μ_X$ and $μ_Y$ , variances $σ^2_Y$, $σ^2_X$ and covariance $σ_{XY}$ . Show that $E(XY) = σ_{XY} + μ_Xμ_Y$? I tried the Covariance formula with: ...
3
votes
1answer
1k views

How is finding the centroid different from finding the mean?

When performing hierarchical clustering, one can use many metrics to measure the distance between clusters. Two such metrics imply calculation of the centroids and means of data points in the ...
0
votes
1answer
232 views

Plotting means and standard deviations

Does it make sense to look at a scatterplot of means versus standard deviations in terms of looking for outliers or changepoints? So the mean is on the x-axis and the standard deviation is on the ...
1
vote
0answers
86 views

Variance explained for averaged values

I am trying to work out how good my particular model is at explaining some observed data. The problem here is that the observed data takes the form of averaged (mean) values for each of my predictive ...
3
votes
2answers
169 views

Finding mean and standard deviation

Experience raising Labrador puppies revealed that the weight of the puppies at six months follow a normal distribution. The subsequent weights (in pounds) of a small sample of seven six-month puppies ...
5
votes
3answers
5k views

R: Calculating mean and standard error of mean for factors with lm() vs. direct calculation -edited

When dealing with data with factors R can be used to calculate the means for each group with the lm() function. This also gives the standard errors for the estimated means. But this standard error ...
1
vote
1answer
65 views

Average rate versus average period

I am working on a project where I need to do workload balancing, and to see how well my approach is working I want to compute both the average amount of time between requests for a workload and the ...
1
vote
1answer
237 views

Compare means of two groups with a variable that has multiple sub-group

I was unable to understand how to compare multiple mean values in each group. Within the subgroup the mean values influence each other (If one changes, the other changes automatically). I collected ...
2
votes
2answers
132 views

Interpretation of an equation

I'm trying to describe the equation in the attached screenshot in my own words. $\lvert(\overline\chi_1-\overline\chi_2)\rvert > s_1(t_{1 @ 99 \%}) + s_2(t_{2 @ 75 \%})$ The equation tests ...
1
vote
0answers
53 views

Assessing the consistency of an estimator of the average path length of a large network

I have found the following in a network-science article and would like clarification of what the authors are claiming: We observe that the root mean square of the difference between the empirical ...
1
vote
1answer
146 views

Comparing many means in JMP

I'm trying to compare several sets of experiment data, by comparing means. I read there are several different tests such as Each Pair, Student’s t and All Pairs, Tukey HSD, which give different ...
2
votes
1answer
119 views

Normal distribution in R

I am trying to check what is the probability that a new observation is anomalous or not? Suppose I have the following set of observations: ...
0
votes
5answers
648 views

How can I find distribution from mean and variance

If I know the mean and variance of a discrete random variable $\in \{0,1,\dots \}$, How can I find the distribution?
9
votes
5answers
856 views

If not a Poisson, then what distribution is this?

I have a data set containing the number of actions performed by individuals over the course of 7 days. The specific action shouldn't be relevant for this question. Here are some descriptive statistics ...
0
votes
1answer
50 views

What number minimises RMSD between itself and randomly generated numbers?

Let us assume that we have a random number generator given by its probability density function. Now, we need to use this distribution to generate a number that has the following property. It minimises ...
8
votes
2answers
4k views

Mean absolute error OR root mean squared error?

Why use Root Mean Squared Error (RMSE) instead of Mean Absolute Error (MAE)?? Hi I've been investigating the error generated in a calculation - I initially calculated the error as a Root Mean ...
1
vote
2answers
244 views

What's the bar above x called in the sample mean?

What's the bar above x called in the sample mean? Is it a diacritic mark?
0
votes
0answers
46 views

Does the standard scores analysis make sense in the following scenario?

INTRODUCTION I've got an image in grayscale. Say the image is a rectangle with width = 1700 pixels and height = 2338 pixels. The image is light in the middle and dark in the top and bottom edges. The ...
0
votes
0answers
44 views

Comparing tests for staging cancer

I am comparing 4 different tests for the evaluation/identification of cancer. One is a continuous variable yielding cut-off values based on both the mean and the median of 5 consecutive measurements ...
4
votes
2answers
780 views

does it make sense for non-negative data to subtract the mean and divide by the std dev?

It is a very usual procedure to subtract the mean and divide by the standard deviation in a set of data. If we deal with non-negative data, i.e. image, (in [0,1] or [0,255]), does this procedure make ...
0
votes
0answers
68 views

Compare variability in different groups

I have 3 groups with a distribution of samples. I used ANOVA to compare means of these groups and also fetched mean, SD and SEM. I have SD and SEM that varies among groups. How can I compare them so ...
3
votes
1answer
665 views

Maximum likelihood of function of the mean on a restricted parameter space

I've been trying to teach myself some of the fundamentals of statistics by trying to work through old qualifying exams. Here's a problem: Suppose $X_1, \ldots, X_n$ are a random sample from a normal ...
0
votes
1answer
107 views

How to remove individual means and deviations for repeated measures

I currently have a experiment with a within subject design, where I repeatedly measure reaction times (RT). Reaction times for each category of reaction were measures multiple times. However now the ...
2
votes
1answer
376 views

Correlation with binary response and Likert scale response

I have 4 data groups: - 3 groups from a 5-point Likert scale (1 ~ 5) - 1 group is binary (Incorrect/Correct -- converted to 0, 1) I have performed Pearson's r and Spearman's rho with the Likert ...
5
votes
2answers
620 views

What is the equation for combining standardized mean differences across multiple studies?

I am trying to come up with a combined/pooled standardized mean difference for meta-analysis of a dozen or so studies that have the same binary predictive groups and the same continuous outcome ...
2
votes
1answer
2k views

Transform Data to Desired Mean and Standard Deviation

I am looking for a method to transform my dataset from its current mean and standard deviation to a target mean and a target standard deviation. Basically, I want to shrink/expand the dispersion and ...
1
vote
1answer
152 views

How large a variance can be for a discrete random variable whose mean is known?

In following Maximum value of coefficient of variation for bounded data set I come up this question: e.g., Say, $X$ can take integer values from $[0, 20]$ The mean of $X$ is known to be $0.005$ What ...
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vote
0answers
18 views

Best way to characterize slowdown factor

I am currently measuring the execution time of a program I have written, but I am unsure how to represent the results. The program has two modes: normal mode and analysis mode. In analysis mode, it ...
6
votes
2answers
387 views

Central limit theorem with unknown variance

In my experiment I compute the average latency of operations per second. I would like to define N, i.e: how many times do I need to run my experiment to compute a close-to-real average latency? I ...
2
votes
2answers
223 views

Comparing means across sub-groups?

Bit of a stats newbie question here. I've got about 10,000 rows of data about pupil performance, annotated with school and teacher details, that look as follows: ...
1
vote
1answer
71 views

Estimating conditional mean

Suppose I have a uniform random variable $X$ taking values $\{1,...,n\}$, and two functions $v(X)$ and $w(X)$. I know that $v(X)$ and $w(X)$ are jointly distributed with correlation $\rho$. (And can ...
1
vote
1answer
647 views

How to test whether the difference in difference between means is significantly different? (with example)

Basically I have Four groups (2-by-2) with sample means $\overline{x_{1,A}}$, $\overline{x_{2,A}}$, $\overline{x_{1,B}}$ and $\overline{x_{2,B}}$, standard deviations $s_{1,A}$, $s_{2,A}$, ...
5
votes
2answers
2k views

Finding mean when class sizes are unequal

A class teacher has the following absentee record of students: ...
1
vote
1answer
206 views

An analytical framework for considering the geometric mean

Is there an analytical method of looking at the geometric mean that will allow one to break it down to its various components? The focus of the question is more for financially related returns, but I ...
5
votes
1answer
109 views

nth moment, for 0 < n < 1 or n <0, do they exist?

I am interested in the moments, we have for instance the mean, $\mathrm{E}(X)$ and $\mathrm{E}(X^2)$. What about values like $\mathrm{E}(X^{1.5})$ or $\mathrm{E}(X^{-1})$? Have they been investigated? ...
2
votes
1answer
211 views

How to estimate the probability that the mean of an unknown distribution is over a threshold given small sample size

I am trying to quantify my concerns regarding a proposed incinerator in our community. The company is basing its potential to emit dioxins (a class of chlorinated organic compounds with a reference ...
0
votes
0answers
149 views

Compare independent numeric vectors (means) in R

I am working on R, and have multiple data.frames. They all look like this one: ...
0
votes
1answer
101 views

How do you take a weighted mean where values farther from a given number are weighted less?

Say, I have a vector v = {5,2,8,9,2} I then want a weighted mean where values of v closer to a given number (which could be mean(v), or something else) are weighted more (proportionally). So 5 (or ...
0
votes
1answer
687 views

Sum(XY) in terms of Xbar and Ybar [closed]

If $x$ and $y$ are two series, is there any relation between $\sum{(x,y)}$ that can be expressed in terms of mean of these two. Specifically, I want to know if any sort of relation exists between ...
2
votes
1answer
607 views

What formula is needed to calculate the average adjusted gross income by zip code?

Here is an example of one zip code I'm working on: A00100 is the Adjusted Gross Income (aka AGI), agi_class is the size of the adjusted gross income. This ranges from 1 to 7: ...
0
votes
1answer
265 views

Weighted harmonic mean vs weighted geometric mean [duplicate]

Possible Duplicate: Weighted geometric mean vs Weighted mean I searched for the differences between WHM and WGM. When to use each of them? when not?
2
votes
0answers
80 views

Is ANCOVA proper for my experiment?

I've got a serious problem when trying to analyse the data of my psychological experiment. Here are the details of the experiment: In each trial, subjects were presented with lateralized colored ...
2
votes
1answer
715 views

Harmonic mean with zero value

How does harmonic mean handle zero values? what would the harmonic mean of {3, 4, 5, 0} be since $1/0=\infty$?
2
votes
2answers
926 views

Mean centering for PCA in a 2D array…across rows or cols?

I'm pretty new at this and I'm picking my way through the steps for running PCA on a 2D numpy array. Each subarray represents all pixels of an image (all rows & cols flattened). Example: ...
3
votes
1answer
129 views

Convergence problem

I practiced some problem (not homework) as below. Suppose that $X_1,X_2,\cdots$ are independent and identically distributed real-valued random variables with $E|X_1|=\infty$. Show that ...
0
votes
2answers
157 views

Given a set of data, how can I calculate the equation of the mean line that passes through the data?

I have a set of data that I gathered doing some tests. I plotted it and created a scatter chart. I would like to find the equation of the mean line that goes through these points. How can I do this? ...