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Questions tagged [mean]

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

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Independent Sample Power Analysis With Unequal Means

I am running a test with two groups that have equal sample sizes (33 per group) but very unequal means - control group: 28,000 vs test group: 80,000. I am trying to determine the required sample ...
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1answer
96 views

Mean and variance of $\tan(\mathcal{N}(\mu,\,\sigma^{2}))$

How could we find the mean and variance of $\tan(\theta )$ if $\theta \sim \mathcal{N}(\mu,\,\sigma^{2})$?
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9 views

Correct order for computing standard error of the mean of means

Good afternoon, I read some related questions but there is still some things I can't quite wrap my head around. Let's say I want to average some time series over X subjects, Y channels, and, ...
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1answer
26 views

Estimate mean of a population with multiple samples when the individual sample mean is biased

I am working with datasets of grades going ~15 years back for different classes. I am trying to determine if there is a difference in the average grade for odd years compared to even years. There is a ...
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2answers
42 views

R and mean value of random variable

This question might be a bit naive. According to theory the mean value of a r.v. is the sum of the value times the pdf. I try to test this in R. I am using the following code: ...
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0answers
18 views

Meta-analyzing means/SDs from repeated-measures studies

I'm working on a meta analysis of prospective studies assessing changes to mental health in the year following an event. For the purposes of example, say it's the severity of depressive symptoms (...
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23 views

Wilcoxon signed rank test - interpretation

I have 6 dependent variables that were measured on a 5 point Likert scale (treated as interval here). I want to test if their means differ significantly from the midpoint 3. As the normality ...
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1answer
32 views

How to generate mean curve of non-function?

I am currently working on curves generated in tensile tests of polymer specimens. Here, I try to generate a mean curve of five data sets generated at the same composition of the samples. Unfortunately,...
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1answer
33 views

Can you compare the mean of one data set with the median of another?

I’m having an argument with another numerically literate person. We both saw a news site state that under no circumstances should you compare the median of one set with the mean of another. It’s ...
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1answer
20 views

Usage of sample covariance and sample mean

I understand the difference between sample mean/covariance and population mean/covariance and how to calculate them. However, I'm a bit unsure about what happens afterwards. If I only have the sample ...
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3answers
2k views

Using mean length and mean weight to calculate mean BMI?

Is it valid to use mean length ($h$) and mean weight ($w$)) from a given population to calculate mean Body Mass Index ($BMI = \frac{w}{h^2}$) for that population?
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10 views

Calculate mean by decile in Svydesign object

So, I´m working with ENIGH - Database, which stands for ¨National Survey of Household Income and Expenses¨ in Spanish, this is an exercise conducted by the Mexican government and like most surveys of ...
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1answer
47 views

Finding method of moments estimator of $\theta$ in $\Gamma(\theta,\theta)$ distribution

Please refer to the question in image I have tried to find $ E(x) $ but i ended up with $\overline x $ = $\frac{\theta + 1}{\theta} $ which statisfies no option , i also tried to find $ E(x-1)^2 ...
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1answer
23 views

Conditiional probability as mean of gaussian?

I am reading the paper "Tutorial of Variational Auto-Encoder" and I faced the following notation: $$P(z) = \mathcal{N}(z\mid 0,I)$$ $z$ is a latent variable which should have been normal distributed. ...
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1answer
34 views

Which formula for t-test is correct?

When Population variance is unknown and n<30 we use t-test. x=sample mean, u=population mean, s=sample standard deviation, In my book and on many online websites i found t-test formula to be t=(...
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0answers
30 views

Sample mean lognormal variables

Suppose you've got $x_1, ..., x_n$ independant realisation drawn from a $LogNormal(\mu, \sigma^2)$. Could someone explain me why $exp(\mu + 0.5*\sigma^2)$ $\neq$ $\frac{1}{n}(x_1 + ... + x_n)$ ? Here ...
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1answer
27 views

The Impact of Multiplying the Dependent and Independent Variables by a Constant

I have a regression model in which the intercept is 0 and the slope is 3. Now I multiply the dependent variable by 10 and independent by 2. I wish to find out what happens to the intercept and slope. ...
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1answer
37 views

Testing whether the means within group are different from each other (R)

My Y variable is binary and takes the values 0 and 1. The same applies for the independent variable X. I've been able to create the means within the group, here: ...
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1answer
32 views

Average of marks in examinations

Is it statistically correct to find out final marks of a student in a paper by taking arithmetic mean only of 4 valuations of a single paper without an answer key, or any rectification measures for ...
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26 views

Maximum Likelihood of Mean Parameter

I am very confused by the language of Questions 1&2 in the following link: http://www.gatsby.ucl.ac.uk/teaching/courses/ml1/asst1.pdf My first question: I'm self teaching myself this material ...
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10 views

Test difference of means between subgroups

I have a collection of N samples from which I have computed all pairwise Euclidean distances. The samples can be divided in 3 distinct subgroups. I want to test if the average distance of groups is ...
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2answers
279 views

Sum of two exponential series with equal means and variances

Assuming $A$ and $B$ are two non-negative real-valued random variables such that $\mathrm{E}(A)=\mathrm{E}(B)$ (equal means) $\mathrm{Var}(A)=\mathrm{Var}(B)<\epsilon$ (equal small variances) is ...
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Newbie wondering about standard deviation and how to detect outliers in new datapoints

So I have a dataset, with the count of records processed per day in each, e.g. | 27th April: 3491 | 28th April: 2058 | 29th April: 9321 | 30th April: 1021 I want to be able to take a new day's count ...
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1answer
15 views

The combined SEM of two averages with SEM

I am looking to calculate the difference in blood flow between the controls and intervention group (dipyridamole) and whether this is significant. The table 2 shows the average blood flow + SEM each ...
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0answers
23 views

Why does the inverse gamma distribution look essentially the same when increasing the variance?

I have a function in R which for a given mean $\mu$ and variance $\sigma^2$, spits out the parameters for the shape, $\alpha$, and rate, $\beta$ of the inverse gamma distribution with that mean and ...
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2answers
63 views

Understanding regression to mean

As far as I can understand regression to mean is that if I make a measurement, say the mean of the test scores of some students, when the measurement is repeated with the same student with same ...
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1answer
28 views

The difference between means in t-test

When the sample size is large, the results tend to be statistically significant even when there is a small difference between the means of two groups. however, sometimes we see the results are not ...
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13 views

Can the range of possible values including the margin of error exceed 100%? [duplicate]

1) I'm working on a sample gotten from users on a website. However, on certain days, the sample size can be as small as 5. As a result, I used the T distribution for my calculations instead of the Z ...
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1answer
32 views

Estimating the population median from a kernel density estimator

I have a 1-d kernel density estimate in the form of two vectors: x_grid is a vector of x-values at which the density function was sampled ...
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0answers
3 views

Aggregate Sentiment and Behaviour Index

I have data of sentiment and behavior based signals for certain stocks. They are based on positive, negative words in a document. How can I aggregate(like an index) those individual signals to ...
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0answers
55 views

Proof that the mean is a complete sufficient statistic and the sample variance is an ancillary statistic

I have $X_1, X_2, ..., X_n $ that are random samples from the single variate $N(\mu,\sigma^2) $. I want to prove that the mean $\bar{X}$ and the sample variance $s_x ^2 = \frac{1}{(n- 1)} \sum_{i=1}^...
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1answer
32 views

How exactly can I get sampling distribution of means for calculation of standard error?

Let's denote population by $ N $ and sample with which I want to make inference about $ N $ denote by $ n $. Let's assume I have already collected $ n $. Now I want to get means for sampling ...
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598 views

Right-skewed distribution with mean equals to mode?

Is it possible to have a right-skewed distribution with mean equal to mode? If so, could you give me some example?
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1answer
156 views

Sample mean is always an optimal estimator of the mean?

Suppose we have $T_i,i=1..n$ i.i.d. with unknown distribution and we want to estimate $E[T]$. Note that in this setting we are not estimating E[T] as a parameter of a parameter-dependent family of ...
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16 views

Using confidence intervals as sole statistical analysis

I am writing a thesis and have been advised to use 95% CI to determine if i have significance between my data. I have been told to use a scatter plot and place CI as error bars. I am unsure how to ...
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3answers
62 views

Mean and Variance of Continuous Random Variable

I have a problem on my homework about the continuous random variable $y$ where the cdf is $F(y)=\frac{1}{(1+e^{-y})}$. Part a is asking for the pdf which I found to be $\frac{e^y}{(e^y+1)^2}$. Part ...
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1answer
41 views

Find the variance of p-hat

We have not discussed $\hat p$ in my probability and statistics course and a problem involving it is on our hw this week after learning about discrete distributions. The problem states "Let the random ...
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42 views

Lottery with known EV and standard deviation. Probablity of positive ROI after x trials?

Lottery with the following payout table: **Payout** **Frequency** 0x 0.59992 1x 0.34992 5x 0.04982 1000x 0.00035 ...
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1answer
32 views

Why is the sample mean's variance smaller when we're sampling without replacement?

I know that we've to use the correction for finite population, but why do we have to use it? My lecturer said that "Sampling without replacement doesn’t waste information by the chance of finding the ...
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1answer
18 views

Given two insights into the distribution of a normally distribution of data, can I determine the mean?

If I was told, 81% of students have a gpa higher than a 3.0 and 44% of students have a gpa over a 3.5. Assuming the data is normally distributed, how would I go about determining the mean of the ...
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2answers
128 views

What “nice” property of a confidence set is being violated

Suppose that I have $X_{i} \overset{i.i.d.}{\sim} P$ with $E[X_{i}]=\mu$ and $V[X_{i}^{2}] = \sigma^{2}<\infty$. Then by the central limit theorem I know that: \begin{align} \sqrt{n} (\bar{X}_{n} ...
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1answer
43 views

What is the variance of the difference of two means?

I'm trying to express $\mathrm{Var}(\mu_x - \mu_y)$ in terms of $\rho$, $\sigma_x$ and $\sigma_y$, where $\mu$ denotes the mean of the random variable. Firstly:\begin{align*} \mathrm{Var}\left(\sum_{...
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0answers
11 views

With few respondents on a 1 to 10 scale, is it better to use a weighted mean or the median?

I have survey data where ~20 respondents replied to some questions on a scale of 1 to 10. For the most part, none of the distributions are Gaussian. A set of questions look to find out a participants ...
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1answer
18 views

ANOVA: single or combined statements

I want to test a hypothesis that states that country of origin significantly influences the consumers' price perception of electronics 'Made in Country X'. In my data, i have four questions measuring ...
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0answers
17 views

Can someone explain the difference of mean and linear bias in residual analysis?

I am struggling in understand the difference between mean and linear biased. What does it mean the a regression has mean biased or linear biased? How do I interpret it?
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1answer
19 views

Deriving the values of the range around the mean value

This is part of a bigger quantitative reasoning assignment I was working on. My understanding here is that the upper bound and lower bound of the ranges for each of the exercises should be reflected ...
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2answers
857 views

Calculate variance without calculating the mean

Can we calculate the variance without using the mean as the 'base' point?
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5 views

How to calculate summary limits of agreement?

I have made a forest plot including multiple studies assessing agreement using Bland and Altman plots between values measured by two different methods. However, most studies only reported mean ...
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1answer
223 views

What is rolling mean and standard deviation in terms of stationarity?

I would like to know what a rolling mean and rolling S.D means in terms of achieving stationairty concerning a time series? I ran an ADF test and it told me my time series was stationary however, by ...
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1answer
13 views

Comparing data sets of varying sizes

Suppose I want to compare the similarity of 2 data sample sets (a and b). Data set a has 13 data points and data set b has 1000 data points. For each data set, I compute a metric z (like the mean). ...