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

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81 views

Asymmetric confidence intervals on bootstrap estimates

I've performed bootstrapping on my leastsq parameters and now I have a load of data from which I can get the mean and standard deviation for each parameter. Lovely. But when I look at a histogram of ...
0
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0answers
60 views

Calculating the variance of sample mean?

I am working on time series analysis. The book I am using ("Statistics for Long Memory Processes" by Jan Beran) uses a number of measures for process memory and one of them is to graph Sample Mean ...
4
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3answers
577 views

Variance of the sum of a Poisson-distributed random number of (normally distributed) random variables

Suppose I have a fruit stand where I sell oranges. Every day I have an average of $\lambda$ people (Poisson distributed) each buying a normally distributed weight quantity of oranges with mean $\mu$ ...
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0answers
57 views

Proof for mean and variance of a multidimensional half normal distribution

Given a $p$-dimensional random variable $\xi \sim \mathcal{N}\left( 0, I_{p} \right)$ and a $p\times p$ dimensional diagonal matrix $\Lambda$ with diagonal entries $\lambda = \left( ...
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0answers
150 views

Poisson Distribution of a radioactive decay

You have received a radioactive mass that is claimed to have a mean decay rate of at least 1 particle per second. If the mean decay rate is less than 1 per second, you may return the product for a ...
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0answers
86 views

can I compute the product of these two multivariate normal densities in a simple way

I have two multivariate normal densities and I parameterise them by the precision matrix (i.e. the inverse covariance matrix). One of them has a sparse precision matrix and the other one has a simple ...
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1answer
174 views

test for comparing means of two time series [duplicate]

I wonder if there is a test for comparing means of two different time series (both measured at the same person or two different persons)? Would be very glad if someone can help me!
2
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0answers
491 views

Confidence interval for the restricted mean in survival analysis

What is the recommended way of calculating confidence intervals for the restricted mean in survival analysis? Here are some example data, taken from the paper Chris Barker (2009), The Mean, Median, ...
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0answers
66 views

Comparing three means

I'm performing a meta-analysis but I have a question: I'm evaluating three different treatment strategies (A,B,C) for each of those treatment strategies I have around 20 papers describing outcomes. ...
5
votes
1answer
94 views

When estimating population mean, how can one half of the sample mean have lower risk than the sample mean itself?

I read Efron and Morris (1977) Stein's Paradox in Statistics with interest yesterday and stumbled upon the statement that, if and only if the population mean is close to zero, than the risk (mean ...
4
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1answer
73 views

A question on sampling distributions

I once read the following interesting distribution related question: An insurance company identified the 10 safest and 10 least-safe cities from 200 cities in the US based on the mean number ...
0
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1answer
129 views

standard deviation help [duplicate]

A tire manufacturer believes that the tread-life of its snow tires can be described by a normal model with a mean of 32 thousand miles and standard deviation of 2.5 thousand miles. Based on this ...
2
votes
1answer
128 views

Testing whether the mean of a group is different from the mean of the entire sample

I have the mean and standard deviation of a large sample (30k obs) and the mean and std of a subsample (2k obs). The means are percentage figures (i.e. between 0 and 100% and hence not a normal ...
3
votes
1answer
186 views

Why are statistical properties of mode and median difficult to determine?

I have read a book saying that statistical properties of the mode and the median are difficult to determine compared to the mean. I am not entirely sure why is so. Is it correct that because the mean ...
5
votes
2answers
3k views

Calculate the confidence interval for the mean of a beta distribution

Consider a beta distribution for a given set of ratings in [0,1]. After having calculated the mean: $$ \mu = \frac{\alpha}{\alpha+\beta} $$ Is there a way to provide a confidence interval around ...
1
vote
1answer
80 views

What is the expected value E(X), E(Y), Var (X,Y)

Suppose there are three cards labeled with values 1, 2, and 3, and two of them are chosen at random (without replacement). Let the random variable $X$ be the value on the first card chosen, and let ...
1
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1answer
172 views

Basic algebra question regarding properties of the summation operator

I admit that my algebra is rusty. Can someone please explain how the middle part of the top equation is transformed to the middle part of the bottom equation (both are highlighted in black).
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3answers
137 views

Statistical comparisons between large data sets

Currently, I am looking for the correct (or suitable) statistical method to compare 4 very large datasets (n = 31 million each), that are based on an experiment where a continuous variable was ...
2
votes
0answers
112 views

Mean interval estimation when data are not binomial

When a set of data are binomial I have a lot of methods available to me (Wilson score interval, Wilson score interval with continuity correction, Jeffreys interval, Clopper-Pearson interval, ...
6
votes
1answer
583 views

Example of “real life” use of Bayesian inference on $\mu$ from a normal distribution?

A classic example for students, when teaching Bayesian statistics, is to make inference on the mean parameter $\mu$ of a normal distribution, when it has a prior normal distribution. I would like to ...
3
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3answers
3k views

Hypothesis test for difference in medians among more than two samples

Question The test scores of three groups of people are saved as separate vectors in R. ...
3
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2answers
135 views

Does the regression line tell anything about mean

I am trying to find the association of BMI on the age at onset of hypertension in diabetes vs non-diabetes patients. Or in other words, does diabetes (if the patient is already diabetic before the ...
2
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0answers
40 views

Can I use bayesian estimation for Linear Discriminant Analysis?

I was studying classification algorithm , LDA (Linear Discriminant Analysis). In this, we have to estimate the mean and variance of predictors, given a particular class. Can I use Bayesian estimation ...
5
votes
2answers
198 views

What to do with my data?

I'm quite new here so please excuse me if this isn't a suitable question. I'm developing a site for students to allow them to upload their virtual transcripts (grade report) to our site and allow us ...
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2answers
194 views

average length of stay in hospital calculation

I need to calculate the average LOS (Length Of Stay) over 15 years. My formula is the following: ...
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0answers
163 views

Arithmetic mean and Gini index in a grouped distribution

In the following table is represented the relative frequency distribution of 100 families related to the class of annual income (in thousands of dollars): ...
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1answer
212 views

Is median better than mean for reporting on website speed

Whilst I understand why median can be a better metric than mean in certain circumstances (e.g. you're creating/marketing a ...
1
vote
1answer
879 views

Simple Average Method, calculating moving average and moving variance, how can I say if stationary or not?

Lets say I have a sample data (here is just 10 numbers, in real I have about 10000 measurement results). Then, I want to check if the data is stationary or not using Simple Average Method. For ...
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0answers
137 views

Should the mean of the bootstrapped distribution always be asymptotically equal to the sample estimate?

Suppose I bootstrap the distribution of the sample mean. Normally, one would use the mean of the bootstrapped distribution as point estimate of the parameter and the s.d. as its standard error. The ...
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2answers
724 views

When combining p values, why not just averaging?

I recently learned about Fisher's method to combine p-values. This is based on the fact that p-value under the null follows a uniform distribution, and that $$-2\sum_{i=1}^n{\log X_i} \sim \chi^2(2n), ...
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1answer
95 views

Comparing the mean of two non-random sub-groups

Students are assigned to group A or B based on two aspects: a grade from an exam and an evaluation of their teacher. Students with both a high grade and a positive evaluation get into group A, other ...
6
votes
1answer
192 views

Is it possible to combine the F-test and t-test to test for differences in both the variance and the mean?

I would like to test $H_{0} :$ $\mu_{1} = \mu_{2}, \ \sigma_{1}^{2} = \sigma_{2}^{2}$ vs $H_{0} :$ $\mu_{1} \neq \mu_{2}, \ \sigma_{1}^{2} \neq \sigma_{2}^{2}$Is there a test statistic that would ...
22
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7answers
2k views

Replacing outliers with mean

This question was asked by my friend who is not internet savvy. I've no statistics background and I've been searching around internet for this question. The question is : is it possible to replace ...
2
votes
2answers
178 views

Finding the mean of a Gaussian distributed random variable given the variance

I have a Gaussian distributed random variable $X$ with known variance $\sigma^2$. Given that I know $P(X\geq t)=m$, how can I find the mean of the random variable?
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0answers
48 views

Comparing two means

I have a question on comparing means and I would be really thankful if you could help... I have a data set that contains responses from a questionnaire (so one group only, N=216). The questionnaire ...
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1answer
73 views

What statistical test should I use for this situation?

I've got three groups A,B,C. Each has a different number of records and I have calculated the mean for each group. Now I want to know if these means are equal or not? What statistical test should I be ...
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0answers
17 views

Tests if means between factors are significantly different

After performing a factor analysis and grouping a set of 20+ questions into 3 different factors, we can then calculate a mean, std dev etc for each of these sets of questions or in other words, per ...
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0answers
29 views

Is the mean of n independent Bernoulli random variables normal? [duplicate]

I'm trying to figure out the difference between an A/B split test and an ANOVA test and I came across this article. It suggests that the mean of $n$ independent Bernoulli random variables is normally ...
0
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0answers
81 views

anova, t-test, linear models: run on individual data points or per-person means?

The format of my studies is testing 10 individuals in 5 conditions 100 times per condition (this is a behavioral test) - resulting in around 5000 raw data points. I am currently using 3 statistical ...
2
votes
2answers
127 views

What is the appropriate test for comparing means?

I have a case and control group, both of which had a blood sugar level tested multiple times over 48 hours. I took the mean of the levels for each person and then calculated the mean of the means ...
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0answers
27 views

How to scale a variable to a specific mean and standard deviation [duplicate]

This may be a dumb question, and I'm certain I should know this, but let's say I have one variable that has a known metric (e.g., variable A has a mean of .7 and standard deviation of .3). How do I ...
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0answers
47 views

determining probability of spatial pattern metric greater than some instance

Let's say I have a grid of cells from a satellite image that take on the value of 0 or 1, with 1 being forest. There are many spatial pattern metrics that measure things about this pattern such as ...
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1answer
949 views

Meaning of standard deviation of the mean difference

I'm trying to understand the meaning of stating the standard deviation (SD) of the mean difference (MD) [or otherwise called the absolute mean difference]. This is for a paper I'm writing up where ...
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3answers
5k views

Comparing means with unequal variance and very different sample sizes

I am trying to compare the means of the same variable between men and women. This is the statistics: ...
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1answer
251 views

how to Normalize data(with noise) into 0-1 range good scale in mean and variance?

i have a matrix data. Perhaps some data in one cluster and another in some cluster. data scale is between [0-1000](just example). and i want to normalize into [0-1] and good in mean and variance. it ...
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0answers
145 views

Reliability standard via relative standard error for computer science or randomized algorithms

I am performing experiments on randomized algorithms, and want to do it scientifically sound. What relative standard error of mean (RSEM) is acceptable? I know that often RSEM<30% or RSEM<25% ...
5
votes
3answers
207 views

Why do they call it “sampling distribution of the sample mean”?

Ok, I understand that there is a true population mean and one that I get from the sample. It is different for every sample and, thus, I can build the distribution of the sample means. I arrive at a ...
2
votes
2answers
276 views

When is the median more affected by sampling error than the mean?

I'm writing a paper on making probability estimates, and it's been asserted to me that I should take the median of the estimates given by my participants, rather than the mean. I've been told I should ...
0
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0answers
41 views

Mean and Covariance of Office Hours

I have a homework assignment with the following question. I've attempted to solve the problems and my answers are below, but I feel like they are incorrect, and have no idea how to check. I would be ...
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1answer
41 views

Inferring an unmeasured value

Suppose we have a table of finishing times for an number of 100 metre races where each competition has a different mix of entrants. We suspect that some races are slower than others due to, say, a ...