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

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5
votes
1answer
327 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
5k 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
7k 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
190 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
367 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
961 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
626 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
348 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
79 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
322 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
183 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
368 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
589 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
130 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
381 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
204 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
365 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
620 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
121 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
439 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
758 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
353 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
354 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
378 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
464 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
836 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
638 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 ...