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

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23 views

Using more measurements of lower quality or just the one with the best quality?

I am currently trying to analyze some pupillometry data. The device I use gives me X and Y measurements of the pupil area (from which I compute the total area via $A = \pi \times ...
3
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133 views

Better estimator of expected sum than mean

I am trying to find the optimal estimator for the maximal expected $\Sigma X_i$ where $X_i$ is sampled from an unknown distribution which is chosen to be maximal. To clarify and simplify, there are ...
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7 views

Comparing the means of correlations based on different size of sub-correlations

I would like to compare the mean correlation of two different sample groups: I had two groups of teachers who were judging their students' performance. One group of real teachers (N=10) judged on ...
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0answers
68 views

Largest eigenvalue of this random 2x2 matrix

Consider four random complex vectors $\mu_i$ of length $K$ whose entries are drawn from the complex normal distribution $\mathcal{CN}(\mathbf{0},\mathbb{1})$ centered in zero and of unit variance. ...
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2answers
1k views

How to calculate Estimated Arithmetic Mean for a lognormal distribution

I have been tasked to program functions from some Excel sheet into a asp.net app so it can be shared to my colleagues via a web interface. However, I am stuck on one thing. I have a set of variables ...
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35 views

Estimation of Noise Level in the High-Throughput Cancer Data

Assume that I have made a coverage log ratios signal by dividing the coverage data coming from a tumour sample over the reference sample and then taking the log2 of this division. My question is: ...
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1answer
49 views

Timeseries: Find points deviating from the mean

I haven't done much time-series modelling at all and now I have a dataset which screams "time series" at me and now I am hunting for a model. The data: Imagine a video watched by ~400 people, 100 ...
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1answer
68 views

$E(X_1| \overline X ) = \overline X$, the sample mean

Let $X_1, X_2, ..., X_n$ be a random iid sample from a population with mean $\theta$. Now I am wondering about the intuition behind $E(X_1| \overline X ) = \overline X$, the sample mean. If we just ...
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60 views

How to calculate mean on group statistics

How can I calculate the mean of the first schema? I don't have the individual values of the sample. Std. Deviation (B) is 0.6441.
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1answer
155 views

Why do means&error bars in an ANOVA graph depend on the factors and covariates that define it?

I have a mixed-model design with between-subjects factors Group (treatment, control) and Difficulty (easy, hard), and within-subjects factor Timepoint (pre, post). I want to use my statistical package ...
3
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1answer
308 views

Question about standard deviation and central limit theorem

I have a quick question about the central limit theorem. Lets say I measure some value that comes from an arbitrary distribution N times and I repeat this M times. I understand that if I calculcate ...
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1answer
137 views

Estimating a distribution based on three percentiles and a mean

I have a set of percentiles the 10-th, 50-th and 90-th. Furthermore I have the mean value. I am trying to reconstruct the underlying distribution. The question is similar to Estimating a ...
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0answers
22 views

Symmetry of a distribution

I have received a sample, summarized by a frequency table with groups (i.e. 1-7, 7-10, 10-13, 13-16, etc...) I calculated the mean and median, both were around 15, the mean was 15.3, the median 15.6. ...
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45 views

Adding mean and standard deviation to each other

I make a certain measurement and I would like to arrive at a single descriptive number that would give me an idea of both the average value of the measurement, as well as the deviation from the mean. ...
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2answers
345 views

Shouldn't a weighted t-test and a weighted linear regression yield the same standard error on the estimated mean?

I have a vector of values and a vector of the reciprocal of their standard error. I'd like to estimate their mean and the standard error on the mean. At first I used linear regression using the ...
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26 views

Testing equality of mean vectors

Which is the best method to test equality of mean vectors say that of age, height, weight and BMI of 150 men and women?
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69 views

Is one-way ANOVA appropriate for comparing differences in (calendar) monthly means?

I have data for solute export by month (monthly mean values with year aggregated so that n=12), in one-way ANOVA the groups should be independent. A month of high solute export will probably lead to ...
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0answers
60 views

Probability that a sample mean is between two values using Central Limit Theorem

Mean is $2.707$, standard deviation is $.049$, sample of $35$ is drawn from the population. What is the probability that the mean price for the sample was between $2.683$ and $2.716$? It was suggested ...
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1answer
209 views

Variance of sample mean for dependent samples

Suppose I have two discrete independant random variables $X$ and $Y$, and that I'm interested in the expected value of the random variable $W$, where: $$ W= \text{sign}(X-Y). $$ So, W is 1 if ...
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1answer
106 views

Standard error of mean

I am learning statistical analysis, and am now confused about calculating the standard error of the mean. My dataset looks like.. Condition A: ...
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147 views

necessary condition for the existence of the posterior mean

I wonder if there exists results relating properties of the prior and the likelihood to the existence of the posterior mean (or more generally to the posterior moments). Any hint or sufficiant ...
2
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1answer
50 views

One-sample median test:: Signrank seems unsuitable

I have some data on successive bets made by customers. I want to see whether there is a statistically significant change in bet stake with each subsequent bet. The data is skewed, so I have ...
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0answers
39 views

Estimating the mean from knowing the first n largest values

There is a sample of n values that are the first n largest values of a population. Is there a way of getting any statistic such as mean or dispersion from such piece of information provided that the ...
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1answer
94 views

Sum of products in an expected value

A box contains $n$ balls numbered from 1 to $n$. Suppose you take a ball at a time, putting it back on the box, until you pick a ball twice. How many balls are you expected to take from the box? Let ...
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2answers
129 views

alternative formulas for standard error of a difference between two means?

I have a question that seems basic but I found two alternative answers online so I thought that I should ask for advice. I have an experiment where each subject makes decisions about target words in ...
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1answer
1k views

How to combine sample means and sample variances?

Given a set of data, assumed normally distributed from 1 to 19. And two subsets of that data, one with the numbers below 10, and one with the numbers above: ...
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1answer
63 views

Given the distribution of a variable X, what is the distribution of f(X)?

Suppose I know the mean and standard deviation of a (roughly) normally distributed variable x. Is there any way for me to calculate the mean and standard deviation of f(x)? The particular problem I ...
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21 views

Can I average samples in nested factor within-subject design if samples are from the same condition?

This question relates to one of my other questions: Split plot with nested factors ANOVA in R . I have subjects taking an experiment, where I have different ...
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1answer
51 views

How to analyse data from different subjects?

DESIGN: I have 4 laboratory mice (= 4 subjects). My factor is a condition with 5 levels ...
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0answers
21 views

Estimate normal distribution mean given standard deviation and samples [duplicate]

I have samples from normal distributions with the same mean but different standard deviations. I know the corresponding standard deviation for each sample. Is there a way to more accurately estimate ...
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1answer
76 views

I want to estimate the mean of a variable. I would like to reduce the SE by controlling for the noise introduced by another second variable

I have a data set with two variables, V1 and V2. V1 is a continuous variable, whereas V2 is a binary variable. I would like to estimate the mean of V1. V2 is known to be adding error to V1 (V2 being ...
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4answers
9k views

Should the mean be used when data are skewed?

Often introductory applied statistics texts distinguish the mean from the median (often in the the context of descriptive statistics and motivating the summarization of central tendency using the ...
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1answer
45 views

Regression and link function

Suppose we have $E (\log (Y)) = a+bx $ vs $\log (E (Y)) = a+bx $. Can $\exp (b) $ in both cases be interpreted as a geometric mean?
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16 views

What is the confidence interval if I compute the total number of bits based on the average number of bits in sampled bins?

Let's say I want to estimate the total number N marbles among M sacks of marbles. The marbles are assumed to be normally distributed. I can't count them all, so I decide to sample S sacks. I get ...
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30 views

how to find probability of uniformity of data

I was working on image processing where I have some list of pixel value eg:-[5,2,5,2,4,2,4,2,2,2] so I found mean as 3 and variance as 1.77778 My question is how to find the probability of data been ...
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1answer
155 views

Estimating an overall summary statistic (mean) for a value reported by ten published studies

Background I am writing a systematic review and meta-analysis of the association of exposure to X with the outcome Y. I have identified ten studies that report on this subject. This will be a ...
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77 views

analysis of non-normal data

I collected some data on a species of goose called Brent Goose over the winter. A csv file of the data can be downloaded from Dropbox or imported straight into R with this code: ...
2
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1answer
757 views

Calculating scale mean from item means

I'm working on a review paper and need to collect the means and standard deviations of a given measure (such as a measure of depression) from papers of interest. However, some authors report means and ...
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0answers
110 views

'mean' of logit-normal distribution

$ X \sim N(\mu,\sigma^2) $ $ Y = \frac{\exp(X)}{1+\exp(X)} $ Y has a logit-normal distribution. When I have a correct estimate of the mean, say $\bar{Y}$, of the logit-normal distribution, how can ...
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3answers
634 views

Standard deviation of several measurements with uncertainties

I have two 2 hours of GPS data with a sampling rate of 1 Hz (7200 measurements). The data are given in the form $(X, X_\sigma, Y, Y_\sigma, Z, Z_\sigma)$, where $N_\sigma$ is the measurement ...
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1answer
1k views

PCA on non-centered data [duplicate]

How does the mean influence PCA? What happens if I use PCA on data with a mean $\ne0$?
2
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1answer
83 views

How to convert mean and standard deviation to a single meaningful and quantifiable value?

I look at mean and standard deviation of various map like data and each give meaningful information but sometimes they provide different information. For example, let's take states in a country. One ...
2
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2answers
94 views

Bivariate Normal Distribution Mean

$X$ and $Y$ have bivariate normal distribution and have joint pdf \begin{equation*} f\left( x,y\right) =a\exp \left( \frac{-1}{2}\omega \right) ,\text{where }% \omega =6x^{2}+12y^{2}-16xy-8x+24 ...
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2answers
256 views

Expected sum of money

There is a little problem in the working on this one I have encountered recently. Here it goes: Starting off with \$100, when you toss a coin, if there is a tail, you will get \$10 and lose $10 if it ...
3
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1answer
84 views

How to find the probability that a random sample of 10 points out of 52 points of data will have a mean close to the total mean?

I have a data set that consists of 52 weeks of data. I want to find the probability that any 10 weeks of data within the set of 52 weeks is close to the mean of the total 52 weeks. Close meaning ...
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0answers
50 views

Standard mean and deviation

A company supplies specialized high-tensile pins to a customer.It uses an automatic lathe to produce the pins.Due to factors such as vibration, temperature and wear and tear, the lengths of pins are ...
1
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1answer
56 views

How to make sense of 6mo worth of weight loss data?

-I have ~6mo of data that contains daily weight/caloric intake & #carbs/fats/proteins. I'm trying to figure out a way to make sense of the data. It's not a perfect experiment so there are other ...
1
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1answer
158 views

What is the sample-size range for which the median should be preferred to the mean as a measure of central tendency? And why?

I have firing-rate data for neurons ranging from 40-60 in number for various experimental groups. I've seen both mean and median being used in the literature, but without much explanation for the ...
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0answers
45 views

Which is the correct mean?

My colleague and I disagree on the following data, and the calculation of the mean: Given $n$ respondents, each respondent has three chances to score a hoop at basketball. A respondent has 'hooped' ...
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2answers
1k views

Overdispersion in logistic regression

I'm trying to get a handle on the concept of overdispersion in logistic regression. I've read that overdispersion is when observed variance of a response variable is greater than would be expected ...