Questions tagged [standard-deviation]

Standard deviation is the square root of the variance of a random variable, an estimator thereof, or a similar measure of the spread of a batch of data.

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Does linear discriminant analysis expands or only rotate?

Assume that we have two classes, $X$ and $Y$ and we find the mean $X_\mu$ and $Y_\mu$ and variance $X_\sigma$ and $Y_\sigma$. With that, we could use linear discriminant analysis to expend the ...
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Testing for regression coefficient equal to 0

I usually take a look at the diagonal elements of the matrix $(X'X)^{-1}$ and the $MSE$ in order to determine the standard deviation of the regression coefficients. I encountered a problem from a ...
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Standard deviation and 90% of observations [closed]

The time of changing tires is normal distributed. In changing of 25 tires was found out that mean is equal to 15 min and the variance is equal to 25. In which interval is standrad deviation of 90% of ...
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what is the difference between Standard error of the means vs Sampling error?

I am confused after learning about the different terms. I understood Standard error of the means to be the Standard Deviation of the sample means, whilst Sampling error is the Standard Deviation ...
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Calculate Standard Deviation of hour

I have standard deviation for each 15 min of that hour so can i calculate the standard deviation of that hour using this 4 standard deviation values ? Reason Standard deviation of each 15 min is ...
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How can I determine the optimal binning system for a continuous variable in Python?

I've got two columns of data - a continuous variable that I'd like to treat as a categorical variable (i.e. bin it up), and a metric I want to measure by bin. Let's say the first column is income and ...
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174 views

Appropriate estimation of standard deviation for a sample of proportions

I am working with some bird mortality data across 9 years of surveys and have run up against a problem estimating the standard deviation. Across the 9 years, survival estimates were .47,.60,.36,.58,....
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How can I calculate the standard error of measurement (SEM) for crossed data that were repeated once?

I have acquired the responses of 10 persons that rated 15 items twice. All persons rated all 15 items. (10x15, rows=participants and columns=items). I have calculated the test retest reliability of ...
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For binomial success / fail data, how to calculate if the time since last success is out of the normal range

Struggling to figure this out. I have data sets that are essentially ObjectId, Date, Pass/Fail (1/0) The data is normally daily. What I want to figure out is IF the number of days since the last ...
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Determine when a value has stabilized

Q: Given a set of data points, what is the best way to determine when the value has stabilized? I have sales data for multiple products since their launch and want to find the place where their demand ...
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Why use n-1 in the sample variance when random tests show little differences between a "n-1 standard deviation" and a "n standard deviation"? [duplicate]

I generated random tests to calculate standard deviations of populations and samples using both n-1 and n for the denominator of the variance formula with datasets like [5,20,25... numbers between 5-...
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Standard deviation of estimated parameters in Monte carlo simulation

I am new to Monte Carlo simulation and have a question. What is the connection between the standard errors of the estimates that we normally get from a regression and standard deviation of sampling ...
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Derivation of pair-wise relationships expression of βyx.z and σyx.z

I'm reading Linear Models: A Useful “Microscope” for Causal Analysis. In the article, when discussing the beta coefficient and standard error of partial correlation, the auther mentioned "express ...
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Standard Deviations of Detrended Data vs Original Data

I'am interested to know the opinion on this matter. I have Data of a Financial Security. The goal is to view the Standard Deviations levels of the data to possibly see patterns of behavior of the ...
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F-test for time series

I have a problem and I'm not sure how should I approach it. So I have a time series with a autocorrelation, but without any seasonality. And I notice that standard deviation increases after some ...
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Given a mean and standard deviation how to find sample size?

Given a mean of $5.60$ and a standard deviation of $0.13$ is there a way of finding out how many individual values produced this mean and what those values were?
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Why are there two ways to calculate the standard deviation of a binary variable?

I've always been told that the standard deviation of a binary variable is sqrt(npq). However, there also appears to be a different way to calculate it: ...
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What does the skewness, when converted to the units of the data, represent?

I have calculated the skewness of my data. I was wondering what the skewness, when converted to the units of the data, represents in non-mathematical (biological?) terms? For instance, I know that the ...
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Confused when to use Population vs Sample standard deviation in engineering testing

When I run an test for something (say 10 trials) and want to find the standard deviation of all 10 trials, I am getting confused if I should use the sample or population standard deviation. My initial ...
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Calculating the Standard Deviation of Estimates from a Uniform Distribution

I was looking at this question on Sufficient Statistics and the Uniform Distribution: https://math.stackexchange.com/questions/1359183/why-should-we-care-about-sufficient-statistics In this question, ...
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Why should we use 16-50-84 percentile instead of $\mu$ and $\sigma$ to characterize sampling results such as MCMC

Can someone explain why we should use the 16-50-84 percentile rather than mean and standard deviation to characterize the average and uncertainties of the sampling results, such as MCMC (the Markov ...
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Utilizing the Standard Deviation of a Sample Size of Three (3)

I have been arguing with co-workers today regarding the use of the standard deviation with a sample size of three (3). We do reverse engineering, and obtain samples to measure and duplicate. My ...
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How many samples are needed to justify a given standard deviation?

Context: Someone was asking about individuals with measured IQ above 200. My intuition is that there is not a sufficiently large population of people to justify measurements of scores well past 200. ...
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Confidence intervals around functions of estimated parameters

Suppose I estimate the following model, $$ y = \hat{\beta_0} + \hat{\beta_1} X_1 + \hat{\beta_2} X_2\ , $$ and am additionally interested in the quantity $$ \gamma = \sqrt{\beta_0^2 - 4\beta_1\...
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Variance of Total Value of Sample

Say we have a normally distributed population with mean of 1000 and standard deviation of 10, of which I am taking a sample of 100. My question is what would be the expected standard deviation of ...
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STD of response change of linear regression

Let's suppose I have a single predictor linear dependence: $y = kx+b + \epsilon$. A linear regression was performed on the available data and we have the estimates of $\epsilon$, $k$ and $\sigma_k$. ...
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Does skewness decrease standard deviation ceteris paribus?

For a given probability distribution, probability mass must sum to 1, thus by increasing a parameter corresponding to skewness do you shift probability away from the second central moment (variance) ...
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RMSE estimation from model accuracy and RMSE of dependent variable

Given the two variables/measurements, which were used for building up the model (Random forest regressor), I would like to estimate an RMSE of the predictor variable/measurement against the "real&...
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Why square the difference instead of taking the absolute value in standard deviation?

In the definition of standard deviation, why do we have to square the difference from the mean to get the mean (E) and take the square root back at the end? Can't we just simply take the absolute ...
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511 views

How can I calculate SD when displaying data as a percentage?

Hypothetically, I am trying to make a graph representing the abundance of 4 species in a quadrat. I want to display this as a % of the total number each species represents. Here is an example dataset: ...
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What does standard deviation mean in this case?

Suppose that someone was collecting samples and he was trying to estimate the average amount of money people spend on purchasing fast food meals. The calculated mean was USD 50 and the standard ...
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How to get the estimated means and standard deviations of two overlapping circular normal distributions?

I have the following plot: Overlapping circular normal distributions I would like to estimate the means and standard deviations of the apparent overlapping normal distributions. This is slightly ...
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What is the difference between population standard deviation, sample standard deviation, and standard error?

Sorry for the rudimentary question, but I just want to make sure I understand everything well conceptually. I understand how we get the standard deviation of a population. My questions are as follows: ...
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What does correlation formula really tell you?

The formula for correlation coefficient is as follows: $$\begin{align}\mathrm{corr} \left(\vec x, \vec y\right) = \frac{1}{n} \sum_{i=1}^n \frac{\left(x_i-\bar x\right)}{\sigma_x} \cdot \frac{\left(...
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Confidence interval without sample size, only variance?

Suppose we have an estimate ($\bar{y}$) and want to generate a confidence interval. However, we only have the variance of the sampling distribution ($v$) - and not the $\text{n}$. Instead of: $$ CI(\...
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How can I compare the standard deviation of the dependent variable?

How can I compare the standard deviation of the dependent variable? Is a lower number better between regressions, i.e. in one model its 0.2 does this mean it the dependent variable is more predictable ...
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How to calculate standard deviation for estimated marginal means calculated after a GEE model in R

I have an unbalanced longitudinal dataset that looks at the effects of diagnostic tests on costs over time. First, I run a GEE using geeglm from geepack package ...
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Statistics question: Why is the standard error, which is calculated from 1 sample, a good approximation for the spread of many hypothetical means?

I'm re-learning statistics and got confused by the idea of taking the standard error from 1 sample's worth of data (standard deviation of sample divided by the square root of sample size, i.e. $\frac{...
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Finding the error variance

I have the following model with 23 observations (n = 23): $Y_{i}=\beta_{1}+\beta_{2} X_{2 i}+\beta_{3} X_{3 i}+\varepsilon_{i}$ and the following information which is available in the form of ...
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Statistical issue : When sum a signal (here $C_\ell$ from Legendre) depending of a variable (here $\ell$), Must we sum Shot Noise for each "$\ell$"?

In an Astrophysics context but actually needing statistical point of view, I am going to explain my issue : From Lengendre spherical harmonics, we have a quantity noted "$C_\ell$ depending on ...
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Ways to show stability in array of numbers between 0-1

I have some results from algorithms that return mean squared error values between 0-1. One of these algorithms shows much more stable results, and I want to show that with e.g., standard deviation or ...
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1 Sigma Error Brings Specificity > 1

I am running a classification model on some medical images. When calculating the specificity, we get a value very close to one and then when the 1 sigma standard deviation is calculated its range ...
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What does the term "instantaneous variance" mean?

What does "instantaneous variance" mean physically - is it just the real, equilibrium variance of a distribution? I know there is this question Difference between instantaneous and long term variance ...
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Calculating standard deviation from log-normal distribution confidence intervals

I have the results of a meta-analysis of 10 studies that reports a combined random effects odds ratio (computed using Woolf's method) and 95% confidence interval of an event happening in one group ...
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Average of standard deviations

I have two sets of data Set 1: 0.051, 0.047, 0.044, 0.049, 0.043, 0.048, and 0.042. Using Excel, the average is 0.046286 and the Std Dev is 0.003352 Set 2: 0.051, 0.046, 0.053, 0.047, 0.047, 0.048, ...
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What happens when you try to find standard deviation of a (non-truncated) cauchy distribution? [duplicate]

I have read that this doesn't work, but I do not understand exactly why. Please can someone explain.
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How to find the standard deviation of a ratio?

I have means from two dependent datasets (leg length [A] and arm length [B]). I do not have raw values for these datasets, but do have N, median, 10th/90th percentiles, and standard deviation. I would ...
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Calculate the standard error of the difference between two independent proportions

Here's the question: A survey of 500 males and 700 females showed that 132 males and 226 females agreed with a particular statement. Use this information to calculate the proportions of males and ...
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35 views

Which SD to use in z-test for proportion in population

Background: I am testing the prediction ability of games in a league season and as a naive approach would like to check if the proportion of correctly predicted games is > 0.5 and statistically ...
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Comparing two or more time series using statistical measurements

I wanted to know if there were any statistical measures to measure two or more time series. For example, this is my overall time series Q1 2000 Q2 2000 Q3 2000 Q4 2000 Q1 2001 Q2 2001 Q3 2001 Q4 2001 ...

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