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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How to calculate error for data that changes as a function of time

I have a set of data that I would like to calculate an error for. The data is an electrical current from an electrochemical experiment, recorded as a function of time. As the experiment proceeds, the ...
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T-test with large standard deviation

I have performed a two-sample t test. I am comparing census block groups with a bike lane in the vicinity (n = 608) with block groups with no bike lane (n = 453), in terms of a population deprivation ...
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Is there a way to calculate prediction intervals for decision tree or extra trees regression models?

I only see examples of prediction intervals for random forest and linear regressions but do not see much about ensemble models. I'm not sure if my understanding about prediction intervals is correct. ...
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Comparing measurements I got from my study with other ones from other studies

First of all I’m sorry if this sounds dumb! I’m really trying. I’m conducting a study on measuring adrenal glands in sick patients (3 measurements - cranial height, caudal height and length - in both ...
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Estimating volatility (historical volatility), with the aim to understad how volatile recruitment was in the sectors of my dataset [closed]

I have the following hypothtical (reproduciable dataset) and am seekign to understand/estimate how volatile recruitment was for the period 2019-2020 ie estimating volatility in the recruitment sectors ...
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How is the difference between 2 normal distributions a normal distribution? [duplicate]

I've learned that if we sum or subtract 2 normal distributions, the result would be another normal distribution with $\mu=\mu_{1}\pm\mu_{2}$ and $\sigma=\sqrt{\sigma_{1}^2+\sigma_{2}^2}$ https://www....
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Standard deviation on Bimodal data

Standard deviation, whilst it is often used on normal distributions, is it a useful statistic on global temperature, both daily and yearly, given that weight of the data is towards the ends of the ...
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How to correctly analyse a reduction in variance, and a trend towards a desired value over time?

I have a dataset consisting of some integer values collected over a series of five games, and was hoping someone might be able to recommend an appropriate test to determine whether: the interquartile ...
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How to calculate the within-pen standard deviation?

For my research, I am investigating the occurrence of tail biting in pigs. I would like to calculate both the overall standard deviation of all pigs, and the within-pen standard deviation. I am not ...
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Estimate of an observable and its uncertainty from two inconsistent measurments

Suppose two independent experiments are set up to measure the same observable $\mathcal{O}$ in the same way and report two results $$ o_1 \pm \delta o_1^{stat}\pm \delta o_1^{sys}, \quad \quad o_2 \pm ...
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Confidence in a range estimate, and +- 2sigma rule of thumb

It's common to see people report variability in their realized sample through the $\bar{x} \pm 2s$ range, where $\bar{x}$ is the realized mean and $s$ the realized standard deviation estimate in their ...
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Can I make replicates of an herbal extract, three measurements of the content for each replicate and measure the deviation based on the averages?

I made the extraction of flavonoids from a plant in triplicate. For each replicate of the extraction, I measured the total phenolic content in triplicate and averaged this value, as performed in ...
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Estimating Standard Deviation from sample mean, median and quartiles

I've been trying to estimate the standard deviation from a sample with N = 8149. I've seen a few alternatives to perform this and they all use the IQR. Here's the sample data I have: ...
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Estimating the Probability in a statistical analysis

I am carrying out a statistical analysis where I run the simulation (Matlab) 5000 times, to get 5000 results. The objective is to estimate the probability of having a result that is less than or equal ...
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How does APA define "SD"?

(I apologize if this is off-topic. Also, I've read the numerous questions here about standard deviations, but I believe my question is different.) I've read the 7th edition of the Publication Manual ...
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Standard deviation of a computed response

I have the following, mean values of 2 model parameters corresponding standard deviations of those 2 parameters correlation coefficient a computed response a measured response standard deviation of ...
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Sample of Runners - Can the Group Run 2.5 Miles in 20 mins?

I have a dataset where there are 6 runners. Each runner runs as far as they can for 20 mins, and a watcher records their distance (to the nearest 0.1 miles) at certain times, precisely on the minute ...
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Which best model I have to use to calculate standard deviations?

Suppose that I run the same experiment 5 times. Now, suppose that each model of each experiment has the best accuracy in different epochs. For example: Model1: best accuracy after 10 epochs Model2: ...
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Can non-parametric data have mean value and standard deviation?

I understand that for non-parametric data, the probability density function (pdf) cannot be obtained using parameters like (mean value) and (standard deviation), and I understand that we use Kernel ...
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When to calc std dev? Before or after? [closed]

I have a sample which is analysed 5 times. I get an average of these 5 results. I repeat this test in triplicate to give me three answers which I then find an average of. My question: should I use the ...
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covariance of lognormal random variables

I am trying to find the variance of b*log(x+y) - log(x), where x and y are independent and identically distributed lognormal random variables, the range for log(x) and log(y) is negative infinity to ...
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For two data sets with different means but the same standard deviations, would the SD for the data set with a higher mean indicate lower spread?

I understand the actual math, but I don't understand how it makes sense. For example, if I were working with two data sets (ex. below) and one had higher values than the other but the sizes of the ...
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Finite population correction factor for A/B testing

Generally when reading about statistics in A/B testing, most hypothesis tests are done assuming that the distribution of the sample mean follows a normal distribution where the standard deviation is ...
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How to assess the "reliability" of standard errors?

I am studying linear regression and in particular, I am trying to solve an exercise from my book. The model I am focusing on is about wages and education and the text gives me the output of the ...
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Metric to estimate measuring accuracy

I need help/suggestions on which metric/approach to use. I am trying to estimate pointing precision by measuring the offset of the experimentally measured values from the real, theoretical values, ...
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Descriptive statistical metrics of RMSE, MAE and R2 on cross-validation and holdout testing

I've tuned 100 models of each one LASSO (Least Absolute and Selector Operator) and Random Forest regression methods. I mean, to predict a hypothetical dependent variable, I've tuned 100 models for ...
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Estimating the log-space sigma (std) parameter of a lognormal distribution from its regular-space mean and variance

validaters, I've spent a lot of time on this issue and I can't figure it out yet. So, a lognormal distribution is being defined as follow: X=e^(μ + σ Z), where Z is ...
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How to compute standard error if I only have mean percentage and interquartile range and sample size?

If I only have the sample size, average percentage and interquartile range, how could I compute the standard error? I can make an example about the percentage. It is like testing each of the kids in ...
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Standard Deviation of normal distribution transformation - Wilcox book explanation

I started reading the book of Rand Wilcox "Introduction to Robust Estimation and Hypothesis testing" (4th Edition). In the first chapter of the book, it is written: Let $X$ be a standard ...
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How to find 95% CI of CI of Mean?

We know that the 95% confidence interval around the population mean is calculated as x̄ ± 1.96* σ/√n, where x̄ is the sample mean, σ is the sample standard deviation and n is the sample size. On the ...
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Variance of the sum of N correlated random variables with equal variance [duplicate]

According to this Wikipedia article, In general, the variance of the sum of $n$ variables is the sum of their covariances. So if the variables have equal variance ${\sigma}^2$ and the average ...
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Get Standard Deviation and Variance of log 10 data in Excel

In Excel, my data is between 0.000001 and 0.005 and treated as "logarithmic" so I transformed by log 10 (log10(x)) which are all negative. The Excel Var.P() and Stdev.p() functions can only ...
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Posterior standard deviation, from normal sample with discrete prior

Suppose the sample $(7,2,6,12,10,9)$ is well approximated by a normal distribution with mean $\mu$ and standard deviation $6$. Use the discrete prior distribution $(8,9,10,11)$ of possible values for $...
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standard deviations for mean vs for predictions

I work in finance and wanted to ask a quick question regarding standard deviation of data sets. I have collected data sets over the last 10 years and would like to use them to make a prediction for ...
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Difference of differences

Let's take a series: A: a1 a2 a3 ... an Let's say the standard deviation of the above series is S1 Now let's create B = b1 b2 ... bn such that bx = ax+1 - ax The standard deviation of B = S2 Similarly ...
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Using standard deviation to calculate Control Limits for Individual Control Chart

To compute the control limits using the 3 sigma rule, the standard deviation is usually approximated by the formula: $\sigma=\frac{\overline{MR}}{1.128}$, where $\overline{MR}$ is the average of all ...
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Using s to estimate $\sigma$ when finding the sample size in confidence interval questions

I am trying to learn sample confidence interval for $\mu$ , in this topic , there is a subtopic which is finding the sample size. I know that if $\sigma$ is given (standard deviation of population) , ...
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understanding the Central Limit Theorem with different sample size

I'm trying to understanding the standard deviation of the sampling distribution from the Central Limit Theorem. $\bar{X}\rightarrow (\mu ,\frac{\sigma^{2} }{n})$ I can understand from a mathematical ...
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standard deviation impact on regression coefficients

I'm not sure if I'm asking this correctly, but I'll give it a shot: If I have two independent variables (A and B), which each vary from 1 to 5, and have the same correlation with a dependent variable ...
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How do I calculate the mean and SD of change using mean and SD of baseline and follow up results?

I need mean and standard deviation of change from baseline to follow-up for inclusion in a meta-analysis. Some papers present the findings as baseline mean, SD and follow-up mean, SD for both groups. ...
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How to get the standard deviation when summing down a category with multiple independent observations?

I am not sure how to handle calculating the standard deviation in my situation. Four researchers (i.e., R1, R2, R3, and R4) are taking independent measurements of the same variable—the time that a ...
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Rescaling for Imputation under the normal linear model

I am currently working through Stef van Buuren's book Flexible Imputation of Missing Data and I am currently at Chapter 3.2: https://stefvanbuuren.name/fimd/sec-linearnormal.html. The setup consists ...
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Follow-up to "Standard deviation of standard deviation"

This question asks about a way to calculate the standard deviation of a standard deviation. The answer with most votes derives a formula for an unbiased estimator of $\text{SD}[s]$, which confuses me ...
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Standard Error on the Mean for Asymmetric Distributions

Gaussian - symmetric case: consider a statistically independent sample of N observations from a normal distribution.The mean (loc) of the population is the results on which you would like to make a ...
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what does it mean that the coefficient of variation equals 100%

I am taking a Probability and Statistics course. We know that: coefficient of variation = (standard deviation / mean) * 100% Geometrically, what does it mean that the coefficient of variation = 100%...
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What is the combined standard deviation of Poisson photon shot noise and Gaussian read noise?

On various image sensor web sites (e.g., https://www.thorlabs.com/newgrouppage9.cfm?objectgroup_id=10773, https://www.microscopyu.com/tutorials/ccd-signal-to-noise-ratio you'll see something to the ...
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Calculating the SD for the z-test

The following picture, taken from some lecture notes, shows a very strange formula for calculating the SD, that I have never come accross. Can somebody explain how this formula yields the SD, even ...
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A measure of variability/dispersion that captures only one direction of change

I am conducting a study trying to correlate changes in a biologic parameter (e.g., blood bilirubin concentration) with clinical outcomes (e.g., bleeding). I have found that variability in such ...
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Whats the best representation of variables with large uncertainty

When express results with uncertainty it's common that sometimes these uncertainty pass the limit allowed of the variable. For example, training a classificator model with an expected accuracy we ...
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Hypothesis testing and standard deviations away from the mean

A vice chancellor believes that at her university (UoX) graduates on average have higher salaries that the overall graduate population in the UK. She knows that the average salary of all graduates in ...
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