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

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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
20 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
7k 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
42 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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1answer
15 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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1answer
27 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
142 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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0answers
72 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
700 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
98 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
559 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
77 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
90 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 ...
4
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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 ...
0
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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 ...
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1answer
55 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
139 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 ...
0
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0answers
43 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' ...
3
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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 ...
0
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1answer
104 views

$E(\overline{x})$ vs $E(x)$?

If I have a problem down to $$k(E(x^2) - E(x)^2) = E(\overline{x}^2) - E(\overline{x})^2$$ ...can I say $k = 1$? $X$ has an unbiased mean and a variance. Each $x$ in $X$ is independent. Or is it ...
12
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1answer
3k views

How can a distribution have infinite mean and variance?

It would be appreciated if the following examples could be given: A distribution with infinite mean and infinite variance. A distribution with infinite mean and finite variance. A distribution with ...
0
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1answer
149 views

Find minimum number of batteries to last a week with 95% probability given mean and sd of lifetime

A TA needs a very important program on his computer but his power cable is missing. Luckily, he happens to have 100 batteries lying around and a contraption that can store batteries to use one at a ...
2
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1answer
99 views

fraction of geometric means versus fraction of arithmetic means

Ideally, I would like to know the fraction of the mean of $x$ over the sum of the mean of $x$ and the mean of $y$: $$\text{Fraction of interest} = \frac{\bar{x}}{\bar{x}+\bar{y}}$$ where $$\bar{x} = ...
2
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1answer
200 views

Finding the cluster centers in kernel k-means clustering

I think this is the most easily understood topic in Kernel K Means Clustering. But assuming that I am not an expert in Machine Learning, can someone tell me how does someone calculate Kernel K means ...
5
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1answer
156 views

Was the math/statistics application in this article correct?

I don't know high level math or statistics and wanted to ask about the math in a recent online article. The website 'TheMarySue.com' has an article saying: ON AVERAGE, THE TOP WOMEN-LED FILMS OF ...
7
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1answer
289 views

Do the mean and the variance always exist for exponential family distributions?

Assume a scalar random variable $X$ belongs to a vector-parameter exponential family with p.d.f. $$ f_X(x|\boldsymbol \theta) = h(x) \exp\left(\sum_{i=1}^s \eta_i({\boldsymbol \theta}) T_i(x) - ...
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1answer
384 views

Confidence interval does not include 0, but Wilcoxon test is sgnificant

I've created an error plot with CI 95% to visualize the difference (post test - pre test) between achieved scores. n = 64 Judging from the confidence intervals one could conclude that there's is ...
13
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3answers
3k views

What are the relative merits of Winsorizing vs. Trimming data?

Winsorizing data means to replace the extreme values of a data set with a certain percentile value from each end, while Trimming or Truncating involves removing those extreme values. I always see ...
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1answer
28 views

Creating a translated sample by subtracting mode

Consider a sample $x_1,...,x_n$ which we will call the original sample. To create a translated sample $x_1+c,...,x_n+c$, we add a constant $c$ to each sample point. Let $y_i=x_i+c, ...
2
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2answers
65 views

Padding a matrix - effect on statistical analyses

I have the time-series data for a lot of stocks from their specific groups (market indices), and I would like to perform some quantitative tests on them as a group. Let's say for example I have 30 ...
1
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1answer
55 views

Is it ok to compute statistics on t-values?

Background I have a population in which my dependent variable is binary with a highly-skewed distribution: Very few records are 1 (doers), most records are 0 (non-doers). I'm using logistic ...
3
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1answer
330 views

Arithmetic vs Geometric Mean

There are verbal suggestions everywhere on when one should use a geometric average or when an arithmetic average should be preferred, but I can't find any formal statistical treatment of this ...
3
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1answer
78 views

Summarising simulations on a transformed parameter

Let $\theta > 0$ be some model parameter for which properties (bias, ...) of an estimate are studied via simulations. For a given data set, an estimate $\hat{\theta}_i$ of $\theta$ can be ...
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1answer
262 views

Calculating Confidence Interval

How would one go solving for this? You are told that a 95% CI for expected lead content when traffic flow is 15, based on a sample of n = 12 observations, is (468.1, 591.7). Calculate a CI with ...
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1answer
63 views

What can be inferred when multivariable ordinary least squares and quantile (median) regression yield differing results?

There lies information in a discrepancy of the (unconditional) mean and median. For example, if the median is larger than the mean, the distribution must be left-skewed. Does this kind of inference ...
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2answers
4k views

In left skewed data, what is the relationship between mean and median?

I think the median $\leq$ mean. Is this the case?
7
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1answer
114 views

Coverage Proof of Confidence Intervals

The confidence interval for the mean of a random variable $Y$ has coverage $1-\alpha$ which I am trying to show. Starting from $$\widehat{E(Y)} - ...
2
votes
1answer
90 views

Advantages of bootstrapping when calculating mean

I'm a statistically incompetent social scientist who is very much out of my depth... I'm using R to analyse a data set, which is a 1% sample of a population showing cancer rates across 20 regions. ...
2
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1answer
161 views

comparing means between different studies

In a questionnaire, I have asked some Likert scale questions. These questions were asked to the same population 6 years ago in another study. I only have the mean scores and standard deviation of the ...
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1answer
117 views

Is the bootstrap estimate of the mean biased when a single extreme value is in the sample?

My sample includes $n$ random observations, while $n-1$ of these observations are in the range (0-1) there is also one observation that gets very high value. For example, a sample of prices where ...
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2answers
46 views

Can you have constant mean across samples with different distributions?

This might be a stupid question - but can data samples have constant means even if they are from different distributions?
3
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1answer
178 views

Taylor expansion to contain sample mean, sample variance, sample skewness, and sample kurtosis

I have the following expression: $$\frac{1}{p} \ln\left(1+\frac{p^1}{1!n}\sum_{i=1}^n x_i + \frac{p^2}{2!n} \sum_{i=1}^n x_i^2 + \frac{p^3}{3!n} \sum_{i=1}^n x_i^3 + \frac{p^4}{4!n} \sum_{i=1}^n ...
0
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1answer
46 views

Changing a multivariate Gaussian along a dimension

I have a multivariate Gaussian parameterised by a mean vector $\mu$ and a precision matrix $\Sigma$. Now, I want to set the Gaussian along a given dimension $i$ to a point mass i.e. I set the ...
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0answers
4k views

When is a sample proportion p hat instead of x bar

I just started my first statistics class and am not majoring in statistics so sorry if this sounds like a beginner question and also sorry if my language is incorrect. (feel free to correct me.) I ...
5
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0answers
98 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
67 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 ...