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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Proper use of the coefficient of variation

I have a variety of samples, each with a different standard deviation and mean. The coefficient of variation $CV$ = ${\sigma} / {\mu}$ defines the amount of variation in a population or sample around ...
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10 views

Standardizing unbalanced repeated measures data

I have a dataset of height and weight measurements for adult patients in hospital clinic and want to calculate a standardized measure of boy mass index (BMI). For a given pair of measurements, it is ...
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16 views

Nested Standard Deviations

This is a finance question but most of it is statistics related. A few years ago the Chicago Board Options Exchange created the volatility index VIX, which is really just the 30-day standard ...
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51 views

Analytic or sample standard deviation with binomial data

I've been looking for recommendations on whether it's better to use the sample standard deviation (SD) for a binomial distribution or use the analytic SD (or variance). It's for experiments with ...
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21 views

Showing deviation of data on a fixed scale

I'm creating a chart in D3 which shows the Mode from a large (1mil +) dataset; and colors it according to the standard deviation of the dataset. But the issue is that I need to map the range (Red ...
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1answer
56 views

High Standard Deviation for Leave one out cross-validation?

I am using the leave one out cross-validation technique to evaluate my model. If the prediction on the test sample is right the output is 1 otherwise 0. So I have a array of N samples with 0's and 1's ...
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1answer
43 views

Standard Deviation After Subtracting One Mean From Another

I've got two sets of data from some fluorescent cells. The first set is when the cells don't have their fluorescence switched on, but they are still faintly glowing. The second set is when they do ...
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19 views

Figuring out the fixed characters in (for example) a ISBN number

I'm trying to remove positions that contain fixed values from strings of random data. An example is removing the string "ISBN" from a book isbn code without prior knowledge of that being a fixed ...
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23 views

Proper back-transformation of lognormal standard deviation to find confidence intervals around a mean [duplicate]

I want to determine the 95% confidence interval of a mean. I logged-transformed my data in order to achieve a normal distribution. Several observations contained 0, so I changed these to 1 so that ...
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1answer
16 views

How to determinate standard deviation above and below mean classes programatically

I have an array of float from wich I calculate the mean and the standard deviation. The user can specify a number of class varying between 2 and 8. The min and max values of each class is calculated ...
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1answer
37 views

Standard Deviation of an Exponentially-weighted Mean

I wrote a simple function in Python to calculate the exponentially weighted mean: ...
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31 views

How does Standard Deviation (Error) change with sample size change in this scenario. Explanation needed for a nonprofessional

I have this question that I want figured out. A person's Blood pressure was taken 4 times,the mean of these 4 observations came out to be say 120mm of Hg And the SD was 2.5. Now we have taken 4 more ...
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40 views

Sum of Variance or Standard Error?

My end goal is to present the average travel time for a corridor and the standard deviation (or standard error) of that travel time. I'm not sure what to present to be statistically correct, here is ...
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2answers
107 views

Should I use the use the confidence-t or confidence-norm function in Excel?

n=6 (this relates to maximum values of measurements of force (in Newton) when conducting the same process with the same setting of parameters 6 times) There is ...
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15 views

Merge two different plots: one in the X-axis and the other in the Y-axis [migrated]

I have the represented independently these two plots using R: PLOT 1 ...
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1answer
72 views

Marginal effect calculation in Stata

My estimated dynamic GMM model results are as follows. $$Y = -0.009 + 0.009PF + 0.015PS - 0.001(PF\times PS)$$ I want to calculate the marginal effect of $PF$ at $PS$ (min, mean, max), which I can ...
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1answer
37 views

Approximating sample distribution standard deviation

I've seen in video lessons that if the sample size is big enough (n>30) sample distribution standard deviation can be approximated by sample standard deviation. How do we get the sample distribution ...
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2answers
58 views

Calculate confidence interval from point estimate and standard error

Im having a problem with calculating a confidence interval for an incidence rate ratio between two populations. Using PROC STDRATE from SAS, I've obtained the Incidence Rate Ratio (the difference in ...
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35 views

How to convert daily variances to a monthly volatility and then annualize it?

I work out the conditional variance using a GARCH model based on daily returns as follows: ...
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1answer
189 views

Test that two normal distributions have same standard deviation

I have two normal distributions, and I want to test whether they have the same standard deviation, I really don't care about the mean. My idea is: de-mean both of them and then use Kolmogorov-Smirnov ...
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2answers
65 views

Finding the Expected Average Distance from the Maximum given a distribution

For a given sample set $S$ with $N$ individual samples $x_i$, I can easily find the average distance from the maximum by doing something like this: ...
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2answers
39 views

How to obtain the standard deviation from means or confidence interval of the mean difference?

I am trying to calculate the sample size for a new study based on a previous one. The previous study compared means using a t test. I have: the means, the t test result, the confidence interval of ...
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1answer
89 views

The standard normal distribution vs the t-distribution

Given an IID normally distributed sample $X_1,...,X_n$ for $n$ small with mean $\mu$, standard deviation $\sigma$, sample mean $\overline{X}$ and sample standard deviation $s$ (the unbiased estimator ...
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10 views

Standard deviation of multiple root mean square values

I am calculating the R.M.S. of a periodic signal that has a stochastic component to it. For every period I am able to calculate a value for R.M.S. using the following function: $R.M.S. = ...
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2answers
136 views

What does standard deviation tell us in non-normal distribution

In a normal distribution, the 68-95-99.7 rule imparts standard deviation a lot of meaning. But what would standard deviation mean in a non-normal distribution (multimodal or skewed)? Would all data ...
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1answer
33 views

Standard deviation when sample is significant part of population

I know that sample standard deviation and population standard deviation are different, and are used in different cases (first when N>>n, second when N=n). But what when N>n, although not by much? For ...
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3answers
80 views

Confidence interval for poisson distributed data

I'd like to calculate the confidence interval for a variable with a lower bound and I can't seem to figure out how to do so. I've seen several similar posts, but none answered my question, at least ...
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20 views

How to calculate the standard deviation from a normalised value?

I have 2 data sets (I have more but for simplicity lets say I have 2). Data 1 0.15239652 0.145848036 0.175981261 Data 2 0.417902092 0.342696648 0.354871141 I ...
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9 views

Combining Standard deviation 3 groups

Is this the correct formula for combining the standard deviations of 3 groups? $$ \sigma = \sqrt{\frac{n_1\sigma_1^2 + n_2 \sigma_2^2+ n_3 \sigma_3^2+ n_1(\mu_1-\mu)^2 ...
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2 views

Structural changes in the observed standard deviation

Supposing to have a stochastic process with known normal distribution N(m,s) we can observe samples from. For quality test purpose, we define a threshold for good/bad samples equal to 3 standard ...
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1answer
133 views

How to calculate SD of sample for one new observation?

In below example, Is it possible to calculate new SD for one additional observation? In a class of 25 students, 24 of them took an exam in class and 1 student took a make-up exam the following ...
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15 views

A method to find the inconsistency or variation in the data

I am running an experiment (it's an image processing experiment) in which I have a set of paper samples, and each sample has a set of lines. For each line in the paper sample, its strength is ...
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39 views

Questions about G*Power

Since I found an insignificant result, I performed a power calculation in G*Power. But I am not entirely sure if I input the right number in some fields. My design is a 2(between Ss) x 2(between Ss) ...
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1answer
23 views

On the connection between SSE and absolute deviation from the centroids

Is there any connection between sum of squared error SSE and the absolute deviation from the centroids after clustering. More formally, I have clustered $T=\{x_i\}, i\in\{1,\ldots,n\}$ and the ...
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1answer
148 views

Question about standard deviation and central limit theorem

I have a quick question about the central limit theorem. Lets say I measure some value that comes from an arbitrary distribution N times and I repeat this M times. I understand that if I calculcate ...
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26 views

Relative importance of variables?

The following output is given: The task is to state, which variables, among thoses that are statistically significnat at 0.05, have the greatest and least relative importance on the fitted model? ...
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1answer
50 views

Determining Whether Values Within One Standard Deviation Meet Some Condition

Suppose I have a set of objects, each of which can take on values within some unknown range, and each of which only has one sample of 50+ values associated with it. The values of each observation is ...
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31 views

Adding mean and standard deviation to each other

I make a certain measurement and I would like to arrive at a single descriptive number that would give me an idea of both the average value of the measurement, as well as the deviation from the mean. ...
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1answer
28 views

How to measure dispersion of a single point within a group of points

Lets say you are given a set of $n$ points and for each one, you want to get a measure of dispersion of its closest $d$ points. So a point far away from others will have a large measure of dispersion ...
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1answer
100 views

Calculating sample size with unknown standard deviation

I'm having troubles with understanding a problem which is basically asking to calculate a sample size (in order to estimate what portion of population has income more than 40K) with ...
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19 views

Regression with standard deviation dependent on predictor?

I got this question of how to deal with a regression model involving a set av predictors. The model wanted was one where the response should be divided by the (non-constant) standard deviation of the ...
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1answer
29 views

What is the likelihood of an observed standard deviation given a known normal distribution?

Given a sample X of size n from a normal distribution $N(\mu,\sigma)$ one can estimate $\sigma$ by $\hat{\sigma}$ from X. Then we know that: ...
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114 views

Standard deviation for a measurement that has two causes of uncertainty

I would like to know how to calculate the standard deviation for a measurement value $x$ when there are two separate sources of uncertainty, 1 and 2, each with known standard deviation, $\sigma_1$ and ...
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1answer
24 views

Use of standard error of the mean when the components are not identically-distributed

Let {$X_1$, ..., $X_n$} be a random sample of size n in which the different elements are measurements drawn from $m$ different populations with different distributions. From the Central Limit Theorem, ...
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2answers
144 views

How do you calculate the standard deviation for Roulette?

I've seen quoted in a number of places that the standard deviation for a 1-number bet on a 38 number Roulette wheel (0, 00, 1, 2, .., 36) is 5.76. I can't seem to find a single source that shows how ...
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1answer
49 views

Standard deviation in Weibull distribution

I've have a script that creates Weibull distributions with a static shape parameter and a variable scale parameter, the scale parameter changing to yield a distribution that meets a specified mean ...
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1answer
43 views

Calculation of sigma with Gaussian distribution

I am looking for a Gaussian function centered in $0$ with $90\%$ of the integral is in $[-10,10]$. From this information, how can I get the value of $\sigma$? I guess we can write $P(|X|<10)=0.9$ ...
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36 views

MCMC Standard error

I need to make a simulation to calculate the integral of a pdf $f(x|D)$ over a region $T$.That is, I need to evaluate $$\int_T f(x|D)\; dx$$ to do this, I just defined the function $g(x)=1$ if $x \in ...
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30 views

MC Standard Error for Metropolis Random-Walk Algorithm

I need to calculate some integrals using MCMC with Metropolis Random-Walk Algorithm. To decide the value I will accept as my integral, I will calculate 5 simulations of MCMC with size 2000, but I ...
2
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1answer
65 views

Standard deviation exceeds maximum value

I am trying to plot data that only has two possible values – 1 (present) or 0 (absent) – clearly not a normal distribution. The ...