# 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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### Is the variance of the mean of a set of independent random variables equal to the average of their respective variances?

I understand that, given a set of iid random variables, the variance of the sum is equal to the sum of the variance. Likewise, I know that the variance of the mean is equal to the variance over n. My ...
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### Do calculate SNR based on mean and stdev need normalization?

How to calculate Signal to Noise Ratio? Is the mean to stdev ratio valid to be used as the basis for calculating SNR? What if a dataset or sample has a value of 0 all then add 1 random value other ...
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### What does the standardized anomaly mean? [closed]

What does the standardized anomaly [(x-mean)/standard deviation] really represent? From Wikipedia, the standardized anomaly (SA) represents the number of standard deviations above or below the mean ...
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### Suppose a normal distribution with min = 0, max = 22, mean = 11. How to calculate the standard deviation? [closed]

Suppose a normal distribution with min = 0, max = 22, mean = 11. How to calculate the standard deviation?
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### Using standard deviation or variance/precision as dependent variable in repeated measures ANOVA

Imagine an experiment with four different conditions in a 2x2 design. Each condition was tested using n trials (approximately equal across conditions). I summarized the continuous outcomes for each ...
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### Confidence interval for standard deviation ($\sigma$)

I‘m trying to find 95% confidence interval for $\sigma$ from a given sample. The sample is: $$n=6 \\40000, 200663, 142690, 48560, 40000, 242628$$ (we know that we’re dealing with normal distribution)...
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### 95% CI for net benefit estimates - use of SD and SE

Can someone please help me to understand the calculation of the certainty of net benefit that is done here: https://bmjopen.bmj.com/content/9/6/e027445. I understood that the net benefit is kind of ...
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### In getting to the standard deviation, why do we square d.f.?

this question is similar to another on this platform, but that one adresses the general question of rooting the variance, while this question is about rooting d.f. - furthermore, that question has an ...
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### Why standard deviation is based on squared value? [duplicate]

Why is not "standard deviation" = $\frac{Σ|X-μ|}{N}$, $μ$ being the mean, and is the formula we know today? This could be considered a philosophical question until you try to connect word &...
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### Linear trans on normal distribution

Let's say a variable fits a ratio measurement level and is also normally distributed (for example, height). Why is it possible to do a linear transformation on such a variable if the only ...
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### Summing multiple standard deviations (repeated measures) [duplicate]

Say a set of 5 participants completed two subtests (A and B). The scores on these subtests can be summed to get a total test score. Here is the dummy data: Participant Subtest A Subtest B Total test ...
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### Rolling z-score or z-score? [closed]

Suppose that we have some time series data, in what context we use rolling z-score and when do we use z-score?
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### Converting dispersion to standard deviation in a beta regression

I'm unsure about the relationship between dispersion estimates (precision^-1) from beta regression models (log link) and the standard deviation. The left panel is from a glmmTMB model ... ...
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### What are the differences between sd of population divided by sqrt of sample size and sd of sample divided by sqrt of sample size?

What are the differences between the standard deviation of a population divided by the square root of the sample size and the standard deviation of a sample divided by the square root of the sample ...
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### How to calculate a standard deviation given a sample proportion of 0? [duplicate]

I'm conducting a meta-analysis, and some of the studies that I have included only report the number of occurrences of the event of interest without an accompanying standard deviation. As such, I am ...
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### When is the bootstrap distribution estimate of the standard deviation better than the sampling distribution estimate?

Consider three ways of estimating the standard deviation of a population: First, we take $N$ samples of size $k$ and compute the standard deviation of this sampling distribution. Multiply by $\sqrt{N}$...
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### How to combine standard deviations from independent samples?

I have a population of 7954 subjects and multiple random samples from it: 1st sample size 2,665 with a standard deviation 1.386 and mean -7.45 2nd sample size 2,399 with std dev 1.53 and mean -7.33 ...
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### Which standard deviation should I use to calculate standardised mean difference from mmrm mean difference?

I have data of an RCT study. It is a two arm study with 3 post-baseline time points. Based on the study design and study objectives, I have ran a MMRM on a continuous outcome variables. The model ...
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### How can I average the variance extracted from different group of samples?

I have groups of samples, where each group has a different number of samples and a different mean. I also know the variance of each group of samples. I would like to compute a sort of "average&...
1 vote
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### Computing mean and standard deviation of a set of time series data

Consider a set of $M$ time series described by $D = \{d^1,\ldots,d^M\}$ where each $d^i$ is a time series of the same length, say $N$. I want to create a plot with the mean time series and the ...
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### Relating mean, standard deviation and area below the graph? [duplicate]

I'm sure this is a very basic question. I have the mean and standard deviation of a normal distribution and am given a percentage, in this case 5%. I need to find out below what 'level' as in number, ...
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### Quantifying variation in noisy distribution

I have plotted ten datasets, each collected over the course of a year. They contain data on charitable donations made by thousands of people over the course of a year, and so have a lot of variability ...
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I am attempting to split a number v into n roughly-equal sized parts. For example, splitting 100 into 4 parts could return <...
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### Question about μ_X̄ and σ_X̄

Is μ_X̄ = The average mean of all sample means, within a population? Is σ_X̄ = The standard deviation of all the sample means, within a population (i.e.: the standard error? Thank you very much
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### How to calculate the mean and standard deviation of a time series spread?

I am just starting anew in econometrics, and am presently trying out statistical arbitrage, specifically cointegration. I have stochastic time series data for variables A, B. Engle-Granger testing is ...
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### How to get an overall level of a variable among different studies without original data?

I'm not a statistician, so I'd like to get advice on how to compare different scientific studies. I have the following summarized data about glucose (mg/dL) levels before and after a 6-year medication ...
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### Question about σ_X̄ in a specific formula

In this formula, does σ_X̄ stand for the correction of the standard deviation or for the correction of the standard error? Thank you very much
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### Carrying over the standard deviation across calculations

I have conducted a measurement of sample on an instrument. I thus have the value of my samples, of a blank, and the standard deviation of said blank. I would like to execute operations on the value of ...
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### Why does scale not make mean of 0?

I am using R and I want to scale some data. The code looks like this: ...
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### solving for standard deviation of a difference from an F-test

In an old article (1990s), results are reported where 30 subjects respond to two kinds of words and reaction time in milliseconds (ms) is measured for every response. In an repeated measures analysis ...
1 vote
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### How do we relate RMS and standard deviation for continuous signals?

Because the discrete formula for RMS, $\displaystyle X_{RMS}=\sqrt{{1 \over N}(x^2+x^2+...+x[N]^2)}$, is almost the same as the formula for standard deviation (assuming mean zero), except for a ...
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### Are the variances of two different types of distribution comparable?

If I were to fit two models to the data, one being normally distributed and the other being Weibull distributed, and when the normal distribution was fitted on the data, it had a variance of 2 and the ...
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### Good teaching activities for variability and standardized distributions for undergrad stats

As the question states, I am looking for some warmup activities for teaching undergrads practical examples of variation and standardized distributions. I think the first part is relatively easy to ...
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### Updating a team's REAL ability

I am trying to think of a math appropriate way to describe the “real” talent of a team. This stems from looking at the probabilities of each team winning the Super Bowl. Let me illustrate with a ...
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### How to filter out outliers from dataset? [duplicate]

I am trying to filter out outliers given a data set (maximum of 50 samples). For example: dataSet = (10.0, 10.0, 10.0, 10.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, ...
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### Standard error, standard deviation and error propagation

I measured a quantity 100 times to get 100 measurements denoted as $x_1$, $x_2$, ..., $x_{100}$, with uncertainties as $e_1$, $e_2$, ..., $e_{100}$. Now if I want to report the average of these 100 ...
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### Issue on computing correlation coefficient for two vectors

This is a super trivial question, but for some reason I am stuck and I simply don't get what I am missing/doing wrong. The cosine similarity is defined as followed: I have this dataset, of points ...
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### Role of standard deviation in Bayesian optimization using GP

I am new to GP and BO and I have been playing with the two in a simple 1D context which happens to be practically relevant to what I am working on. Essentially, I am trying to find a peak (modeled as ...
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### What is the distribution and standard deviation of the number of Type I errors in hypothesis testing?

My question is from the book "An introduction to statistical learning" (2nd edition), chapter 13, exercise 2. Suppose that we test m hypotheses, and control the Type I error for each ...
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### Which definition of confidence interval is correct, or are they the same thing?

Wondering 1) which of the two ways of calculating confidence intervals is correct, and 2) if they both are correct, are they the same or different? How do they reconcile? CI = [Coef x1 ± 2*SE(coef x1)...
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### Correlation and standard deviation

If the standard deviation of x, sd(x), increases, the correlation cor(x,y) increases as well. Why? If the standard deviation increases 10%, the correlation increases 10% as well. Why?
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### Can we calculate SD or SEM on percentage data?

[![I have two student populations and the percentages of students calculated based on what grade they obtained. So here, in the image close to 70% obtained grade A. But the 70% is obtained after ...
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### Majority vote method for regression trees when there are two peaks

For the majority vote method in statistical regression trees, I should get the most common occurrence in the data. However, there are two such peaks in the following data: ...
If you only have $y_i = \hat{\beta_0} + \hat{\beta_1} x_i + \hat{\epsilon_i}$ , Then $\hat{\sigma}_{\beta_1} = \sqrt{ \frac{\sum_{i=1}^{n} \hat{\epsilon}_i} {(n-2)(\sum_{i=1}^{n} (x_i-\bar{x}))} }$ ...