# 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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### Relationship between std dev of difference of 2 random samples of a distribution and the std dev of the distribution

I am studying the analytical variance of a clinical test. In published work I observed two things: 1) when looking at a particular patient, the std dev of repeated replicates was 11.5 points. 2) when ...
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### Robustness analysis using Monte Carlo

Using a mathematical model, I have estimated some system parameters using Kalman filter. Now I have to verify whether the proposed system is robust against uncertainties. I have estimated data and ...
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### Standard deviation of symmetric data

Within my field a recent study suggested to use the symmetric properties of certain image datasets to improve signal to noise ratio (SNR). I will spare you the details, but in the end one can get a ... 7 views

### Detect anomaly in seasonal, but not normally distributed data using standard deviation in relation to difference between predicted and actual data

I'm reading an article that suggests using the following formula to detect anomalies in the number of HTTP requests received by a server. | http_requests_rate - http_requests_prediction | / ...
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### Can I calculate a standard deviation for the mean of a sample including data points from different populations

Lets say I have 200 data points from a distribution with standard deviation 4.2, and 50 data points from a distribution with standard deviation 3.5. Can I calculate the standard deviation for the ...
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### What is the variable v in this case? Is it standard deviation or variance?

The code below is from an example on the scikit-learn website for plotting the Gaussians of a GMM as ellipses. However, I don't know whether the final definition of the variable ...
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### Standard Deviation Question, annual policy amounts

I don't understand the answer to standard deviation question below, and hoping someone can help me understand it. I would have though it would have been sqrt(3000*81^2), not sure why the mean comes in....
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### Wrapped normal distribution variance from angle between two multivariate normal distributions

Suppose there are two 2-d multivariate normal distributions , as in the image below: There is no correlation between the x and y components in the distributions, and the variance for each dimension ...
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### When to use standard deviation versus standard error in linear error propagation

I have a question about linear error propagation. Let's say that I want to use an equation to calculate n, where n = (PV)/(RT) (eq.1) I only take one measurement of P, and one measurement of T, but I ...
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### Interpret bell curve, calculate 95th percentile value

I have data showing the distribution of a given metric across a population. The data is broken up into increments, with values for the 90th 97.5th and 99th percentiles. How can I interpret this data ...
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### Can we use Standard Deviation for feature selection?

I am working on the House Price Prediction dataset on Kaggle and am trying to identify the good features for our price predictions. For numerical variables, I have gone with a high correlation with ...
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### Transform to Normal...or is there a better distribution for this case?

I'm not sure whether the right approach here is to transform to Normal or if there's another distribution that perfectly fits the data. What I'm trying to analyze is payroll data each pay period for a ...
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### Is there a test to show that your RMSE is sufficently small for a dataset?

I am currently experimenting with some machine learning, which is going well. However, I am curious if there is a way to show that the $RMSE$ I am achieving is sufficiently small enough for the data ... 1 vote
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### How is t-test on non-normal distribution justified?

I have heard that when the sample size n is large enough, we can apply the t-test to non-normal distribution due to the CLT. But as far as I can see, the CLT only justify the normality of the sample ...
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### Finding standard devition of unknown but non-normal distribution

I have a sample of ~3,000 star systems, and I've found the distribution of a particular parameter. I'd like to find the standard deviation of this distribution, and so I've used the standard ...
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### Calculating mean confidence intervals from a sample with low SEM

Given that: I. The distribution of means of large enough samples converge to a normal distribution (by CLT) II. The Standard Error of the Mean (SEM) of a sample approaches the Standard Deviation (SD) ...
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### Beta estimates outside of -3 to 3

I am performing logistic regression with glmmTMB with random intercepts and random slopes in R, with 5 fixed effects. I have 9 different datasets that I am running through the same model. Before ...
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### Standard deviation of rates normally distributed

I have a sample of observations that are rates. To calculate their average, I must use the harmonic mean. This is not debatable. The distribution of the sample observations is a normal distribution. I ...
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### Why do we use $R^2$ instead of $R$ in linear regression?

$R^2$ equals the "amount of variance explained by the model". However, we rarely use variance in descriptive statistics. We say a sample's weight is 78 ± 13 kg, which is $\bar x$ ± $\sigma$ (...
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### Shortcut for calculating mean and standard deviation of random walk?

I'm trying to follow a blog post and I'm wondering about the following Each step of the sequence independently multiplies by 3/2 or 1/2, each with probability 1/2. Taking logarithms, the sequence has ...
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### Standard deviation in generated data with specified autocorrelation - correction factor?

I want to generate time-series data with specified AR(1) and standard deviation. I am using arima.sim to generate univariate time series. (Ultimately, I want to use ...
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### In what cases would you use a rolling standard deviation instead of a regular standard deviation?

As the question say, I'm curious about this. I understand what standard deviation measures. But I would like to see cases where a rolling standard deviation should be used.
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### How to transform prediction std of gaussian process back to origin

I am looking for a way of rescaling the predictions of my Gaussian Process Model back to the original scale. The data is scaled for training using a ...
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### Comparing values to detect statistically significant difference

I want to compare 2 values to see if there considerable significant different between them. Basically these values comes from 2 credits score bureau providers (score 1 and score 2). The score 3 is ...
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### How to find a decomposition of multivariate X along which y varies the most?

I'm looking for an existing algorithm which carries out the task shown in the title. My use-case in other words: I have a set of continuous independent variables (X) and a continuous dependent ...
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### Propagation of standard error of fit through to the average and standard deviation of replicates

I am using an equation to fit measured data. I have measured multiple replicates for each condition, each of which is then individually fitted to this equation. Once the data are fitted I obtain a ...
1 vote
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### Retrieving standard deviation from glm and glmer

For my thesis I've conducted several GLM's and GLMM's. Now for my report I need standard deviation values, however the summary tables of my models only produce Std error values. ...
1 vote
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### Interpretation of Standard Deviation for different distributions

There are two different populations with unknown distributions but the standard deviation of each of them is known. Can I conclude that the population with higher standard deviation is more spread out ...
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### Formula for standard deviation of a normal distribution from truncated data [closed]

I have some samples taken from a normal distribution of unknown $\mu$ and $\sigma$, and I know someone took away the top and bottom $p$ percent of the original samples ($p$ is known). Is there a ...
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### Calculate standard deviation with only the averages from a number of samples

I am trying to estimate the standard deviation of a population based on 100 samples each with 1,000,000 data points. I have been told it is acceptable to do this using only the average from each of ...
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### Why is standard error of the mean always calculated from the population variance?

The standard error of the mean is often calculated with the formula $\sqrt{\sigma^2 / n}$, which uses population variance (or an estimate of it). However, standard error of the mean is defined as the ...
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### Why Confidence Level 95% is -1.65?

I'm learning about Value at Risk for Investing which got me into statistical questions. Here it's said that For a confidence level of 95%, # of Standard Deviations (σ) = -1.65 x σ And for a confidence ...
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### Is the 'Std. Error' provided by lmer in lme4 actually Standard Deviation?

I have been working with lmer in lme4, and wanted to construct a density curve of the slopes produced by my model (rather than just confidence intervals). The model output of lmer produces a slope, ...
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