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

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4
votes
2answers
750 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
67 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
649 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
106 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
365 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
611 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
1k 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
145 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
16 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
377 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
208 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
603 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
1k views

Finding mean when class sizes are unequal

A class teacher has the following absentee record of students: ...
1
vote
1answer
180 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
203 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
144 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
97 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
661 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
583 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
255 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
79 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
675 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
874 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
128 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
155 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? ...
1
vote
1answer
141 views

Find the mean and variance of $U_1 + U_2$

Let $Y_1, Y_2, Y_3$ be i.i.d continuous random variables. For $i = 1, 2$ define $U_i$ as $U_i=1$ if $Y_{i+1} > Y_i,$ $=0$ ,otherwise Find the mean and variance of $U_1 + U_2$ I can't find the ...
1
vote
2answers
955 views

What is the correct SD to use to get a 95% CI for skewed data?

Let $X = [94, 10, 100, 100, 16, 14, 100, 100, 70, 88, 100, 100, 12, 100, 100, 58, 32, 100, 32, 36, 98, 0, 100, 100, 100]$ where $X$ are students' scores (between 0 and 100), and note many full marks! ...
12
votes
2answers
4k views

How do I calculate a confidence interval for the mean of a log-normal data set?

I've heard/seen in several places that you can transform the data set into something that is normal-distributed by taking the logarithm of each sample, calculate the confidence interval for the ...
3
votes
1answer
78 views

Finding a linear relationship without linear model

(If this doesn't make sense it is because I am inexperienced at statistics) Assume I have a broad universe of actions $A$ I could pursue, and for each $a_i \in A$ there is an associated ...
0
votes
2answers
667 views

Two sample t-test vs regression

I would like to examine the difference in forecast error between year 1 and 2. The descriptive statistics show that the mean of forecast error is higher in Year 2 but the median is lower. Under what ...
6
votes
1answer
227 views

What could “directional mean” be in this context?

I have some reasonable idea of what directional means are in the context of spatial statistics, but I am stumped by this use of the term in the methods section of this computational biology paper ...
31
votes
3answers
10k views

Difference between standard error and standard deviation

I'm a beginner in statistics. I'm struggling to understand the difference between the standard error and the standard deviation. How are they different and why do you need to measure standard error? ...
5
votes
1answer
4k views

How to draw mean, median and mode lines in R that end at density?

I have drawn a skewed distribution, using these commands: ...
1
vote
1answer
418 views

How to best represent median proportions using stacked bar charts?

I have a large dataset with several responses about an organization's labour costs. I would like to represent this data graphically. Typically what we do is provide a stacked bar chart (using R) of ...
2
votes
1answer
3k views

Kurtosis/4th central moment in terms of mean and variance

Is it possible to express the kurtosis $\kappa$, or the 4th central moment $\mu_4$, of a random variable $X$ in terms of its mean $\mu = E(X)$ and variance $\sigma^2 = Var(X)$ only, without having to ...
31
votes
6answers
4k views

Is Amazon's “average rating” misleading?

If I understand correctly, book ratings on a 1-5 scale are Likert scores. That is, a 3 for me may not necessarily be a 3 for someone else. It's an ordinal scale IMO. One shouldn't really average ...
5
votes
1answer
350 views

How to combine values based on standard errors?

Let's assume we have two means with corresponding standard errors. mean_1 = 3.75, se_1 = 0.64 mean_2 = 2.90, se_2 = 0.94 I would like to average the means and ...
11
votes
2answers
6k views

How should one interpret the comparison of means from different sample sizes?

Take the case of book ratings on a website. Book A is rated by 10,000 people with an average rating of 4.25 and the variance $\sigma = 0.5$. Similarly Book B is rated by 100 people and has a rating of ...
3
votes
5answers
8k views

Likert scale question divided into different group. How to calculate mean of different group?

I want to do a survey to determine how satisfied the (16) employees are with the company training program. The survey has 30 questions, each using a 5 point Likert scale for responses. The questions ...
2
votes
1answer
197 views

Is it typical for group means of composite z-scores to have means with values of the same magnitude but opposite signs?

I developed a composite score by converting four items to z-scores, then I summed up the z-scores to form a composite measure. However, when I've calculated means to compare finding for two ...
8
votes
1answer
417 views

Expected log value of noncentral exponential distribution

Suppose $X$ is non-central exponentially distributed with location $k$ and rate $\lambda$. Then, what is $E(\log(X))$. I know that for $k=0$, the answer is $-\log(\lambda) - \gamma$ where $\gamma$ ...
1
vote
2answers
1k views

How to assess accuracy of phone GPS in measuring distances?

I am a complete stranger to statistics (apart from mandatory courses in college), but lately I ran into an interesting real-world scenario. Recently I started jogging. I take my GPS phone with me to ...
2
votes
1answer
745 views

How to combine subsets consisting of mean, variance, confidence, and number of sampled points used?

I have a data set that has been divided into $n$ data subsets. I am sampling from each of these subsets and getting a tuple consisting of mean, variance, confidence and number of sampled points used. ...
3
votes
1answer
389 views

R limma voom function mean-variance trend

I am using the limma package in R to do some analysis on a count data matrix. I use the voom function and that normally creates a plot with the mean variance trend line in it. Now I created also a ...
1
vote
3answers
292 views

Confusion regarding the confidence interval

I have some confusion regarding confidence interval. I was going through this link http://www.stat.yale.edu/Courses/1997-98/101/confint.htm It has something like this: Suppose a student ...
1
vote
0answers
135 views

What is the correct way of estimating the proportion of individuals in a population from a count of their individual parts?

My original question was going to be : How do you estimate the proportion of species in a population from count data of their individual body parts, provided that you can identify each part as ...
0
votes
1answer
87 views

Mean-reversion for random process

I moedelled following ARIMA Process which I also smoothed. abc1 <- (arima.sim(n = 1400, list(ar = c(0.3, 0.2, 0.15, 0.1, 0.1, 0.1)), sd = sqrt(0.5))) plot(abc1) abc2 <- SMA(abc1, n=360) ...
2
votes
2answers
338 views

Does the samples mean and the histogram mean have to be the same?

I'm reading this book. Here, he gives me a method for calculating the mean: Here he introduces a new method of calculating the mean through histogram: He says that now we will count and index the ...