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

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2
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2answers
162 views

What should I do when a confidence interval includes an impossible range of values?

Let's say I'm analyzing the mean number of students per class for a school district. The district has imposed a hard limit on the maximum ratio: there can never be more than 30 students in a class. ...
1
vote
0answers
76 views

Can the proof of the central limit theorem be expressed as the limit of a convolution with an operator

The central limit theorem, as I understand it (engineer, non-statistician), says that the distribution comprised of means of some other reasonably behaved distributions converges to a normal ...
0
votes
1answer
178 views

Regression on means of log-transformed variables

Suppose that I want to study the relationship between two variables $Y$ and $X$ using the linear model $Y \sim X$. Unfortunately, both $Y$ and $X$ are not normally distributed, say they are both ...
0
votes
0answers
2k views

How to report results from Friedman's test including post-hoc results

I have performed comparison of repeated measures for a group using Friedman’s test (K-related-samples test) and additional post-hoc analysis with Wilcoxon signed-rank test and Bonferroni correction. I ...
0
votes
1answer
704 views

How to derive p-value from standard error between two group means?

Data was collected on binary variable and continuous variable. The binary variable represents two groups. Group 1 has a sample size $n_1$ and mean $\mu_1$ on the continuous variable Group 2 has a ...
0
votes
1answer
126 views

Given weighted mean and raw data, derive weights to minimize error

Imagine I have a set of data from an experiment: Observed Measurement 1: 5 Observed Measurement 2: 6 Observed Measurement 3: 7 Observed Measurement 4: 8 Observed Measurement 5: 9 I have a target ...
2
votes
1answer
335 views

Standard deviation of revenue where numbers are only positive

Is there a way for standard deviation to ignore negative numbers? In other words, how can you make it so that 2 or 3 deviations do not extend into negative territory? When looking at a set of only ...
-1
votes
2answers
105 views

can I compare standard deviation and mean?

I hope no question is too simple. I am just learning, and I came across an expression that compared standard deviation and mean of a distribution. I thought that it makes no sense to compare them, ...
1
vote
0answers
460 views

Ordinal data, different scales, comparison between variables

I would appreciate any help you could give me I have ordinal data which I want to standardise in order to compare averages and data spread between variables. I need to standardise since the variables ...
12
votes
4answers
2k views

Is it appropriate to plot the mean in a histogram?

Is it "okay" to add a vertical line to a histogram to visualize the mean value? It seems okay to me, but I've never seen this in textbooks and the likes, so I'm wondering if there's some sort of ...
0
votes
0answers
48 views

Removing data above the mean

I am working with a data set, for which to remove noisy data I take the average of the sample itself and cut anything above that average. What I'm trying to understand here is does this have a name ...
3
votes
1answer
90 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
votes
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 ...
0
votes
2answers
760 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 ...
1
vote
2answers
197 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
176 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
235 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
88 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
170 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
6k 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
241 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
150 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
693 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
870 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
5k 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
256 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
805 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
69 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
671 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
110 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
382 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
628 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
157 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 ...
1
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
391 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
226 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
73 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
674 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
208 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
111 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? ...