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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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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). ...
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7 views

Outliers odd behaviour

I got a sample of data. I applied a linear correction to it and then I calculate again the mean and standard deviation. The mean and the standard deviation before and after the correction are almost ...
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11 views

Best confidence interval for sample mean of any variable in L2

I was thinking about a very basic matter, and arrived at the conclusion I know a lot less about it than I thought. When people have data $ X_1^N $ sampled i.i.d. from a distribution: $ X_1^N \sim X $,...
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22 views

Understanding Mean Shift Vector

I am reading Agnostic Estimation of Mean and Covariance . On page 5, beginning of Chapter 2, they mention the following: Assuming there is a set $S = S_G \cup S_N$, where $S_G$ is Gaussian data with ...
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How to view the descriptive statistics of two between subjects variables in SPSS? [on hold]

Let me first explain the design of my experiment. I have a mixed factorial design. So the participants are first divided into two groups(NATURE and URBAN). The participants also perform a perception ...
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41 views

How to estimate the mean and variance of a Gaussian distribution variable? [on hold]

I have two variables 2X and 0.5Y, both are independent and follows Gaussian distribution. How to estimate their mean and variance analytically? I want to know their individual mean and variance, then ...
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7 views

Compare means between samples, while controlling for sampling differences - valid to use regression this way?

There are two independent samples of people, drawn from a population of a city at times $t_1$ and $t_2$, a decade apart*. The people were asked rate their preference regarding some question $Q$ on a ...
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30 views

Summation of two Gaussian distributed data with different coefficient of mean and variance

I need some help on Gaussian distribution. i have two dataset, both are identical and independent distributed, but having mean as 2μ_1 and μ_2, same scenario for the variance. How can I add them? ...
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44 views

estimating the mean of constant + noise

(This is almost certainly covered in Statistics 101, but I missed that class..) I have a real-world sampled signal $S[t]$ that is a constant $\hat{S}$ plus some noise $\epsilon[t]$. My goal is to ...
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22 views

Sub-group's contribution to a group's mean

I have a statistics 101 question, which I hope the community can help me with. Is there a statistic that summarises a sub-group's contribution to a group's mean? For example, given the following data: ...
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1answer
52 views

$E[\bar{X^3}]$ of N(μ,1)

Suppose $x_1, x_2, x_3,\ldots, x_n$ i.i.d. Normal(μ , 1) random variables with μ $\in$ $\mathbb{R}$ how can we calculate $E[\bar{X^3}]$
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Clustering data multiple times to get statistics

Suppose I have some data (objects described by a number of variables like diameter, etc...) and that I want to run K-means clustering on it. Suppose now that I run the algorithm multiple times (1) on ...
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99 views

Are i.i.d. random variables always associated with a distribution function? [closed]

It is known that independent and identically distributed (i.i.d.) random variables are mutually independent and each random variable has the same probability distribution as the others. However, is ...
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9 views

Combined Variance of two groups with different sample sizes [duplicate]

I have the mean and standard deviation for Male and Female groups in a study, I'm trying to get the combined mean and standard deviation. The two groups have different N's. I can get the weighted ...
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1answer
58 views

How to estimate the confidence interval of the difference of means?

I have two sets of measurements (repeated measurements of two processes, let's call them $X=\{X_i\}_{0...n}$ and $Y=\{Y_i\}_{0...m}$), and I would like to estimate (with confidence interval) the ...
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8 views

Median of demeaned variables and fixed effects

I have observations of the profit $y_{it}$ for several firms, noted $i$, over time $t$. For each firm, I compute the mean of $y$ over the years and call it: $\bar{y_i}$. Then I substract this firm-...
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20 views

What process could lead to a sampling distribution of the mean that is approximately skew normal

I have a data set representing guest ratings of various hotels. Unfortunately, I don't have access to the ratings given by individual guests, only to the mean guest rating for each particular hotel. ...
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37 views

Prove property of a confidence interval

How does one go about proving the characteristic of a confidence interval that: A 95% confidence interval means if you were to randomly sample the same way 1000 times and create 1000 confidence ...
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18 views

Robust Trimmed Mean Proof

This question arises from the first chapter of "ROBUST LEARNING: INFORMATION THEORY AND ALGORITHMS" by Jacob Steinhardt. Given is the following: there are $\epsilon n$ outliers and $(1-\epsilon)n$ ...
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2answers
29 views

How to calculate Mean adjusted by Covariate?

I need to calculate the mean of a variable, adjusted by another variable. Both variables are ratio scaled. I found this online: https://ideas.repec.org/c/boc/bocode/s344803.html which does what I want,...
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2answers
60 views

What is a mean zero time series?

Is a mean-zero time series simply minusing the average value of the series. Say I have data $Y=1,1,2,2,3,3$ would a mean zero series simply be, $$y=(1-2),(1-2),(2-2),(2-2),(3-2),(3-2)$$ as the mean ...
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Which test should I use to compare three geometric means?

I'm trying to use some test to compare three geometric means of some dataset, to see if there are significant differences. I want to compare A with B, B with C and A with C, but I'm unsure of which ...
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64 views

How to reproduce this algorithm?

I am trying to reproduce one of the algorithms presented in the following paper: Rapid Assessment of Annual Deforestation in the Brazilian Amazon Using MODIS Data The authors provide five different ...
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25 views

Comparing populations with multiple variables

My datasets represent the sales of a company with the phone calls they made to promote the products (some zones have sales but no phone calls). I also have the total population per zone which I Can ...
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1answer
28 views

Difference Between Notation of Two Sample Hypothesis Tests

Does this hypothesis test: H0: μd = 0 H1: μd ≠ 0 Represent the same as this test: H0: μ1 = μ2 H1: μ1 ≠ μ2 Since the first is asking if there is a difference between the true mean of the two ...
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9 views

% variation on 1/x function

My data (X) is the rank position of units sales (y). Eg. x=1 top seller, x=1000 is the 1000th top seller I know that sales number can be estimated by: units(x) = $N_0x^{(-0.5)}$ Now I would ...
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3answers
80 views

can I work out *the* standard deviation from a value given as “+/- 1 standard deviation”

I'm confronted by a table of values: 17.1 (16.6) 18.0 (9.5) 38.1 (22.5) 30.6 (16.7) In the left-hand column we have some mean values. I’m told that the values ...
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9 views

Can a difference between statistical deviations be interpreted as a statistical deviation?

I have a cross-table of three variables (2x2x3 design) and I obtained 7 outcome variables for each condition. Since each condition is not a group of participants but a group of models sample size is ...
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1answer
33 views

Interpretation of Mean Square Error formula

This is a very basic question. I'm looking at a physical problem where one wants to estimate a parameter $\lambda$ of a system. Suppose I perform a measurement on the system. I call the (stochastic) ...
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27 views

Confidence intervals on multiplication of two means with confidence intervals

I have survival probability 0.5 with a confidence interval around it. I have mean number of offspring 15.1 produced with confidence interval around it. I want to find species "fitness" by ...
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1answer
22 views

Comparison of the mean of a binary variable from two independent sets

I have two sets of data, one is akin to high performing companies, and the other contains low performing companies. I want to compare the mean of a binary value. For instance, "CEO has a bachelor ...
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Mean of truncated distribution

Is the mean of a left truncated distribution always greater than equal to the original mean? Or is that only for certain distributions?
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38 views

Statistic metric for groups with different observations

I have this problem and more I read online, more confused I'm getting. So I have 4 (or more) groups with different users (for simplicity I only used small numbers, but I may have 50, 100, 150 and 200 ...
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1answer
41 views

Get a plausible distribution from quartiles and mean

I have the 3 quartiles and the mean of the incomes of a population, I would like to get from those a "regular" distribution, there might be several theoretical solutions but I just need a plausible ...
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27 views

Calculating value of a variable from correlated variables [closed]

I have 4 different variables (3 known and 1 unknown) correlated among each other. Y,Z,W are the known variables and X is the unknown variable. I have calculated the correlation coefficients of ...
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33 views

Mean and Variance of $Z=(X^2+Y^2)^{0.5}$ [closed]

I want to find the mean and variance of $Z=(X^2+Y^2)^{0.5}$ where $X$ and $Y$ are independent with mean $0$ and $Var(X)$ and $Var(Y)$ are not equal.
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Can I rotate groups of angular measurements according to each group mean to test the whole population? [closed]

I have four instances where i measure angular data at 9 locations. Pooling all these data shows that it is not non-uniformly distributed. However, I suspect that the data is correlated across the ...
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19 views

What Mean Should One use for CUSUM change detection?

I'm new to CUSUM and I'm using it to detect change of temperature over time past a certain threshold. My data are daily temperatures from July through October, and I am using 0.5*SD for my C and 5*SD ...
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1answer
17 views

Can I derive category thresholds/intervals when the categories are defined as a set of means with standard deviations?

Imagine you have a set of scores between 0 and 100 ("SUS Scores"). Based on the distribution of hundreds of these scores people have tried to provide adjective "grades" for these scores such as "ok", "...
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14 views

t-test to compare means: Small distances between means source of error?

I am currently conducting a t-test with the following null/alternative hypothesis: mean_a >= mean_b mean_a < mean_b As I failed to reject the null hypothesis I am looking for possible reasons ...
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1answer
16 views

Is it possible to estimate a population mean from a convenience sample?

I have data for which I can compute a sample mean. These samples are certainly not random. Is there any way to make an estimate of the population mean from a single biased sample?
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18 views

Prove Zero Mean Hypothesis

I have a stochastic process for which I can compute a final outcome that is real valued. I know that the process has a relatively high variance and is costly to obtain more data points. (which I know ...
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28 views

How should I calculate mean CI - from raw data or mean values?

I have experimenatal data from medical industry. In the experiment 4 observations were weighted, each one 2 times for more precise measurement. As a final weight, a mean from each pair is reported. ...
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2answers
20 views

Repeated measurements descriptive statistics for whole period

I am looking at the number of doctor’s visits over a 10-year period in about 2000 municipalities. Each municipality is assigned to one of five municipality types (e.g. large town, rural community, ..)....
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1answer
38 views

how to combine standard deviations and mean for each group?

I have a table with 10000 rows, each row having 10 columns and their numbers vary from 0 to 80.Now, if I want to compare the mean of these rows.Maybe because of the largeness of one of the numbers in ...
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1answer
19 views

Valid way of determining spread of data

I’m trying to determine a valid method for quantifying the maximum spread of values I can statistically expect to see. I’ve collected 12 sensor values from 12 different sensors. I’ve calculated the ...
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16 views

Proof that a poisson regression with 2 categorical predictors is the same as each observed mean

I have a poisson regression with 2 categorical predictors to predict\estimate the sales of product $p_i$ on location $j$: $\hat{X}_j(p_i) = e^{\gamma_0 + \alpha_i + \beta_j + \mu_{i,j}}$ It appears ...
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15 views

Combining point prevalence estimates and their confidence intervals

I have some health survey data from multiple years. This includes the estimated prevalence of a flu vaccination in a population, then number of people surveyed, and the high/low confidence intervals. ...
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3answers
82 views

What comes after the geometric mean?

The geometric mean is a multiplicative alternative to the arithmetic mean, which we could call additive mean, thereby calling the geometric mean multiplicative mean. My question is the following: what ...