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

learn more… | top users | synonyms

2
votes
1answer
625 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. ...
2
votes
0answers
347 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
259 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
127 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
78 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
319 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 ...
4
votes
2answers
180 views

Problem of “clustering” into most similar groups

I do not think that the following problem can be solved with k-means clustering. I am not sure though. Okay, let me describe the problem. I need to find a way or an algorithm that groups members of a ...
8
votes
3answers
367 views

Mean$\pm$SD or Median$\pm$MAD to summarise a highly skewed variable?

I'm working on highly skewed data, so I'm using the median instead of the mean to summarise the central tendency. I'd like to have a measure of dispersion While I often see people reporting mean ...
2
votes
1answer
207 views

Real data collection with small population

I performed an actual scientific experiment and I was only able to collect 2 data points. I am wondering what kind of statistical method I can use to analyze the data. I performed a similar ...
-3
votes
1answer
83 views

How do I make power computation for testing differnce between two log normal means with R? [closed]

I want to do power computation for testing differnce between two log normal means with R. Can you write using R code? best wishes...
0
votes
1answer
584 views

Beginner's question—Dealing with ordinal data (scoring of a medical effect)

I'm a biology PhD student dealing with ordinal data (scoring of a medical effect: 0–3 points) for the first time and I'm looking for information regarding differences in treating ordinal numbers in ...
0
votes
0answers
129 views

What kind of mean to use for a mix of negative and positive percent values?

I've got a question from a colleague about what sort of mean to use in calculating the average of the deviations of actuals from a forecast, which are in percent. The data look(s) like this: ...
0
votes
1answer
77 views

Mean and SD for distance between occurrences of a given value in sequence drawn at random

Given an infinite sequence of values, selected at random (with replacement) from a set of N values, I choose some value X from the set of values. Then, starting from the first occurrence of X in the ...
1
vote
0answers
2k views

What does a squared coefficient of variation signify?

The coefficient of variation is defined as the ratio of S.D to mean, a dimensionless number which on multiplication by 100 gives the percentage of dispersion with mean. But when we square this ...
0
votes
0answers
64 views

Given a two populations, each split by “categories”, how do I test the hypothesis that the mean is larger in the second population?

The means for each category varies, but my hypothesis is that the second population has a higher mean within each category. The variance of each category is unknown. The example I'm working with is a ...
3
votes
2answers
4k views

Can variance be equal to mean?

I understand that variance can be zero if all data points are equal. Can anybody state an example, where sample variance is equal to sample mean and what - if any - is its significance to ...
3
votes
0answers
377 views

Average of a tail of a normal distribution

I have a sample that is pretty normally distributed with a mean greater 0. Is there any way to get a closed form estimate for the mean of all values that are less than 0? In other words, given a mean, ...
1
vote
2answers
139 views

testing that mean(x) = k with a small sample and unknown distribution of x

Suppose a number of random variables (call them "errors") observed for different "scores". For every score 11 errors have been observed. See the plot below to get the picture: I would like to know ...
0
votes
2answers
202 views

Need help to understand the meaning of this formula

I need help to understand the meaning of the following formula: $$\sum_{i=1}^n\sum_{j\neq i,j=1}^n(x_i-\mu_i)(x_j-\mu_j)c_{ij}$$ where C is positive semidefinite matrix, $\mu_i$ is the mean of ...
2
votes
1answer
363 views

Standard deviation of a cluster

I have a list of (x,y) pairs that form a cluster of points. I was able to find the mean of the cluster, but I'd like to be able to find the standard deviation of the cluster. How can I define the ...
2
votes
2answers
617 views

Significance test for two mean differences? Like a t-test but for comparing differences

I'd like to find out if there is a statistical test that I could use to determine if a mean difference is significantly greater than another mean difference. To determine if one mean is different ...
5
votes
3answers
7k views

Why is the arithmetic mean > median on a histogram skewed to the right?

I am fairly new to statistics. Currently I am into (histograms) medians, arithmetic mean and all the general basics. And I came across the fact/rule that the arithmetic mean is (always) larger than ...
3
votes
1answer
119 views

Why is the expected value of the number of trials before the first success larger than the number of trials with a 50% probability of success?

For a Bernoulli distribution with parameter p, the number of trials with a 50% probability of at least one success is about (1/p) * ln(2). But the expected value of the corresponding geometric ...
3
votes
1answer
35 views

Improving an estimate of mean with observations of sign

Suppose $x_i$ are drawn i.i.d. from a $p$-variate Gaussian, $\mathcal{N}\left(\mu,\Sigma\right)$. Suppose one observes $x_1,x_2,\ldots,x_n$. One also observes $s_{n+1},s_{n+2},\ldots,s_{n+m},$ where ...
1
vote
1answer
5k views

Estimated Marginal Means or means from descriptives?

I'm currently looking at a 2x2 Repeated Measure Anova for an undergrad project but I'm struggling to find information about which means to report. I will be reporting the Within-Subjects Anova,the ...
1
vote
1answer
172 views

How many samples should be taken to capture the mean and variance of the original set with given error?

I have a set $S$ of $N$ real numbers. I wanna calculate the mean $m$ variance $v$ of $S$. But since $N$ is too large, I do not want to use all of the numbers. Instead, I would like to sample $n$ ...
0
votes
1answer
138 views

Geometric mean of two numbers

I need to find the geometric mean of 0 and 600. Would it just be the square root of 600? I know that the formula is $$ \bar x_{\mathrm{GM}} = \left(x_1 x_2 \cdots x_n\right)^{1/n}, $$ but in this ...
3
votes
2answers
436 views

Significance tests

I have two sample means from two different samples. I purport that the true population means are identical. $H_{0}$: $\mu_{1}=\mu_{2}$ and $H_{1}$: $\mu_{1}\ne\mu_{2}$ What significance test would I ...
1
vote
0answers
142 views

How do I test whether differences in populations are significant?

I'm working on a large database. I want to explore whether certain batch jobs run in more or less time after a change was than they did before the change. There are about 90 distinct batch jobs. They ...
6
votes
3answers
753 views

Crash course in robust mean estimation

I have a bunch (around 1000) of estimates and they are all supposed to be estimates of long-run elasticity. A little more than half of these is estimated using method A and the rest using a method B. ...
2
votes
1answer
2k views

How does the expected value relate to mean, median, etc. in a non-normal distribution?

How does the expected value of a continuous random variable relate to arithmetic mean, median, etc. in a non-normal distribution (eg. skew-normal)? I'm interested in any common/interesting ...
57
votes
4answers
8k views

Which “mean” to use and when?

So we have arithmetic mean (AM), geometric mean (GM) and harmonic mean (HM). Their mathematical formulation is also well known along with their associated stereotypical examples (e.g., Harmonic mean ...
1
vote
2answers
374 views

How to find mean relative differences?

I'm trying to describe mean differences between two populations $x_1$ and $x_2$, which are non-zero and positive. Their distribution is approximately beta with a positive skew. For example, with R: ...
3
votes
1answer
352 views

How to supplement comparing benchmark results (means) with a two-sided t-test?

When comparing two runs (means) of different benchmark tests I use an unpaired two-sample t-test assuming equal variance. The problem I've run into is this often results in the same benchmark test ...
0
votes
1answer
350 views

Deriving ${\rm var}(\overline{X})$ from expected value definition

I want to show ${\rm var}(\overline{X})$ is $\sigma^2/ n$ for $n$ independent random variables each with mean $\mu$ and standard deviation $\sigma$. I would like to show this using: $$ ...
0
votes
1answer
377 views

Mean and standard deviation of Gaussian Distribution

I have some random numbers which are generated from Gaussian Distribution. But I don't know the mean, standard deviation of that distribution. How can I find them using random numbers?
2
votes
2answers
1k views

How to compare the variance of two conditions with different means?

I have a series of vectors, which are measurements from one sample at two time points. First time point: 1.[5,3,2,4,4,3,6,5] (mean=4.000) 2....
5
votes
2answers
267 views

One component in PCA is always the mean vector in two-dimensions but not three

I've been testing PCA via SVD to decompose a simple time series data matrix, $X$. I have two signals $x_1(t)$ and $x_2(t)$ in a data matrix where $M$ rows represents each timepoint sample and each ...
3
votes
2answers
463 views

Calculating sample mean and sample variance on all samples vs distinct subsets

Consider 1000 samples drawn from an unknown distribution. Whats the difference between the following two ways of calculating sample mean and sample variance? find sample mean and sample variance ...
14
votes
3answers
2k views

Maximum value of coefficient of variation for bounded data set

In the discussion following a recent question about whether the standard deviation can exceed the mean, one question was raised briefly but never fully answered. So I am asking it here. Consider a ...
14
votes
8answers
8k views

Can the standard deviation of non-negative data exceed the mean?

I have some triangulated 3D meshes. The statistics for the triangle areas are: Min 0.000 Max 2341.141 Mean 56.317 Std dev 98.720 So, does it mean anything particularly useful about the standard ...
8
votes
2answers
125 views

State of the art method(s) to find zero mean portions of a time series

I have noisy time series which I need to segment into those portions with a zero mean and those portions without a zero mean. Finding the boundaries as accurately as possible is important (clearly ...
8
votes
3answers
832 views

Does a univariate random variable's mean always equal the integral of its quantile function?

I just noticed that integrating a univariate random variable's quantile function (inverse cdf) from p=0 to p=1 produces the variable's mean. I haven't heard of this relationship before now, so I'm ...
0
votes
1answer
634 views

What method to test if the mean is constant?

I have a time series with prices (around 800 prices). I need to test if the mean is constant during all the series. I think I should subdivide the series in groups, but what method do I have to use ...
6
votes
2answers
669 views

Contrasts to ANOVA in R

I need to fit orthogonal contrasts to the following model. See the following example data: ...
2
votes
1answer
139 views

ANOVA or other test for summed data

I would appreciate any suggestions of how to analyse the following dataset. It was suggested that I use ANOVA, but I wanted to check with the community. I have a protein where I have calculated the ...
3
votes
2answers
1k views

Test to prove two means do not have a difference

I have a population that I measure a value from once a day. I then made a change, and continued to measure that same value from the same population. What test could I use to prove that my change did ...
2
votes
1answer
460 views

Is it appropriate to report means and standard deviations for composite scores?

Following the post here, I am wondering if reporting the mean and standard deviation is appropriate when describing a composite score. My composite score is the total of responses on several likert ...
5
votes
2answers
2k views

How to calculate mean and standard deviation of a count variable when the raw data is based on frequency categories?

I asked 312 people how many times they visited their preferred local supermarket in a month The results are as follows: 5% did not visit at all 7% visited once a month 33% visited twice a month 22% ...
4
votes
1answer
1k views

Comparing standard deviations between variables with very different ranges

I have a number of variables for which I want to compare the standard deviations. Each of these variables is actually the data for a particular wavelength of light, and I want to produce a plot ...