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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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Combining Variation and Uncertainty from Replicate measurements

I have 3 measurements from 3 independent experiments {m_1, m_2, m_3}. I have another 3 measurements that are used to scale the m measurements {n_1, n_2, n_3} from the same experiment (different from m)...
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Calculating the mean and standard deviation from a normal distribution [duplicate]

I am interested in methods for finding the mean and standard deviation of a normal distribution. It is inspired by the following question that is part of the A-level maths course in England. The ...
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Robust estimation of standard deviation using relatively small sample taken from a Gaussian distribution

I'm sure this question was asked before, but I don't seem to be able to find a convincing answer. If there is a relatively small set (say 3<n<20) of observations of a quantity that is assumed to ...
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How to measure standard deviation for a power test

I have a "so dumb I'm embarrassed" question about calculating power. Suppose a paper tells me, in "Table 1", that the standard deviation of $y$ is 0.8. And then it reports an ...
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Calculate standard deviation

I'm studying an ecological community comprising three samples, each representing different habitats within the community. Within each sample, I've conducted three replicates, summing nine replicates ...
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What is the standard deviation/uncertainty of a single observation in a meta-analysis?

I am running a simulation with parameters based on an existing random-effects meta-analysis. I would like to draw individual patients in the treatment group from a normal distribution with µ=the ...
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Calculating the uncertainty of a very complicated variable

You have taken $N \gg 1$ measurements of a group of variables $V$. You want to estimate the value of a quantity $\mu$ that can be estimated from these variables. Fortunately you have a formula $\mu(V)$...
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Calculating true/population standard deviation from bootstrap standard deviation/standard error

I am using the coffee_ratings dataset to do a proof-of-concept calculation to estimate the population (i.e., coffee_ratings) ...
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What makes the difference between the Mean Absolute Deviation (AAD) and Standard Deviation of a distrubution constant?

We can see very nicely in the normal distribution that the relationship between the mean absolute deviation and standard deviation is a constant ratio (by sqrt(2/pi)). What is it that gives a ...
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Standard deviation of the mean for biased coin with all heads for first $N$ trials

Imagine that we have a biased coin but we only have $N$ trials to determine how much it is biased towards heads (we are resource limited in how many trials we can conduct). Say we assign a value of $0$...
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Standard deviation of an autocorrelated time series

Given a time series of log returns $R_t$ with significant autocorrelation up to $k$ lags, what is the formula for the standard deviation of $R_t$ that accounts for this autocorrelation? I've seen the ...
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Normalization of time-series data with time-varying variance

I'm building a neural network (CNN) model for a regression problem with time-series data. Both input and output are multi-variate zero-mean timeseries data with time-varying variance. Currently, I am ...
P. Leibner's user avatar
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How can I calculate the standard deviation when knowing the P10, P25, P75, P90, mean and median? [duplicate]

I'm trying to find the standard deviation from some simulated task duration results. The results provided the following: Mean - 430 Median - 374 P10 - 371.8 P25 - 372.4 P75 - 440.5 P90 - 588.6 From my ...
Firas Ahmad's user avatar
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3 answers
102 views

How to estimate mean and standard deviation of individual result given a sample of batch results?

I apologize in advance if my title is not well-worded, or if I am using the wrong tags; this is my first time asking a question here. I want to analyze how long it takes for a system in production to ...
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Converting the unit for mean and standard deviation

I have a problem and it's been days and I couldn't find a solution Simply what I want to do for the purpose of a research data, I have the mean and standard deviation of some measurements in diameter ...
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Standard Deviation and Standard Mean Error of measurement with uncertainties

It is well known that, given a set of $n$ values $Y_1, \cdots, Y_n$, its Sample Standard Deviation is $\sigma = \sqrt{\dfrac{1}{n-1}\sum_{i=1}^n (X_i - \bar{X})}$ and its Standard Mean Error is $\...
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results of a regression predictor

I have a neural network trained to predict values from timeseries. the target (which is hopefully to be predicted by NN) is always in range 0.0~1.0, and has these statistic features: ...
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Which error bars to use when comparing only two subjects when many replicates?

I want to plot discrete time measurements made for two subjects, but where many cells were observed for each subject in triplicate. I think the experimental unit is the subject, so I should just get a ...
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What are the units of a binomial variable's standard deviation?

I recall that a standard deviation is in the same units as the random variable, which is useful. However, when deriving the standard deviation of a binomial variable, how do we resolve the units of ...
E. Kaufman's user avatar
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Why intuitively is standard deviation the correct thing to scale to get Central Limit Theorem?

Let me start off by saying I already know all the rigorous formulas, but let me explain why I still feel like something is missing in my understanding. There is no need for any answer going over e.g. ...
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When calculating the sample variance, why do we divide by "n-1" and not "n-2" or "n-0.5"? [duplicate]

When calculating the sample variance we divide by $n-1$ instead of $n$ to correct the bias that results in from using the sample mean instead of the population mean. My question is why do we only ...
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Confusion with effect of averaging on standard deviation

First of all, I was reading a text and stuck with this part: Now regarding the above quote, I want to give two scenarios I made up to make my question clear: Scenario 1: Imagine we take N ...
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I have a significant change in my outcome with the opposite sign in the lead period. Is this an issue?

Suppose I have a negative significant effect of a variable x on y. Also negative significant effect of the lag ie variable L1.x on y . But I get a positive sign significant effect on y in the future ...
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which SD for Cohens D in psychotherapy pre-post study?

I'm reading a study where two groups receive two different psychotherapeutical treatments. The authors calculated Cohens D: 'In addition, we report estimates for Cohen’s d effect sizes as the adjusted ...
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2 answers
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How can I calculate the weight of a study for meta-analysis?

I'm tasked with producing a forest plot for a meta-analysis but I've only been given the risk ratio, sample size and confidence intervals of the necessary studies. I think that I have to find the SE ...
user356816's user avatar
3 votes
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Recreating data variance from the posterior distribution

Recreating data variance from the posterior distribution Take a set of data points $(x, y)$ with (Gaussian) uncertainties $\sigma_y$ on the $y$ coordinate; they are modeled as $y \sim f(x; \alpha) + \...
Jacopo Tissino's user avatar
6 votes
3 answers
900 views

Do 95% Confidence Invervals use +- 1.96 standard error or standard deviation?

I'm trying to calculate the weight of studies for inclusion in a meta analysis as part of homework. I've been given a number of studies and their final results represented as a risk ratio with 95% ...
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Calculating and displaying variation of sub group responses within larger group

I have a question with 3 possible answers (yes, no, unsure), and I have the responses of two groups. Group A and group B. Group A has three sub-groups (A1, A2, A3), Group B has two sub-groups (B1, B2) ...
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Calculate mean and standard deviation of the ratio of two dependent variables

I have an instrument of which I would like to understand the uncertainty on the measurements taken, so that every time that I perform a single measurement, I can apply the error obtained and therefore ...
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Interpreting the coefficients [duplicate]

I am reading a research paper about the effects of exposure to dirty water on test scores. The paper mentions the following: "a 10pp increase in exposure to dirty water reduce test scores by 0....
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Drawing error bars on a position vs time chart where st. dev. is for vectors and not total position

I have the following data for a position versus time analysis. Note that the total distance is just the sum of the mean vector distances. I want to show the error bars on a chart of total distance vs ...
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What are the expected residual standard deviations from each of the fitted models and data-generating process?

I simulate data to be analyzed using a linear mixed-effects model. It is based on an experiment with 2 levels (A and B) of a ...
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converting data from geometric LS mean and confidence intervals to mean and SD

I Hope this letter finds you well. I am conducting a meta-analysis, and some of the studies have reported data in geometric least squares mean and confidence intervals, while others have presented ...
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Converting median absolute deviation to standard deviation

I'm working on some medical research and I'm wondering what is the most straightforward method to convert median and median absolute deviation (MAD) to mean and standard deviation. If anyone has any ...
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3 votes
1 answer
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Why would a production process in an industry know its (population) standard deviation?

I can understand why the mean is known. I can understand that in some cases based on historical data, you have a rough idea about the variance/ standard deviation. But inherently when the real world ...
PuneUnited's user avatar
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Conversion of log-transformed SD

In a meta-analysis of some research work, there are many situations in which the literature reported the mean values and their corresponding standard deviations in log-transformed forms. The question ...
Ahmed 's user avatar
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1 answer
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calculating the 95% confidence interval, two approaches generated two different results [duplicate]

I am very puzzled by the two 95%CI results generated from the same normal-distributed dataset from the Monte Carlo method with 10000 simulations. See below figure and statistics of the Monte Carlo ...
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2 votes
2 answers
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Adjusting sd for an ARMA(1,1) simulation given phi and theta

I'd like to generate model an ARMA(1,1) process with a mean of zero and a standard deviation of sigma where I specify the ARMA parameters phi and theta. How can I adjust the value of sigma in the draw ...
user111024's user avatar
1 vote
1 answer
30 views

Regarding squaring the deviations when calculating the standard deviation [duplicate]

I learned that the deviations are squared for a number of reasons. (1) They make all values positive. Otherwise the sum of the deviation would be zero. But why not just take the absolute value of the ...
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4 votes
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Unusual variance measure

I explore centrality measures for graphs and discretized regions. The data array (for given point) is all distances from this point to the boundary of region. At the beginning I used standard ...
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1 vote
1 answer
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Confidence interval for number of an event happening with a known probability

As an example, my problem is something similar to this: Lets say that you open 10 chests and each chest has a 30% chance of having an item. Calculate the confidence interval for the number of items ...
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Stationarity and moving standard deviation

Suppose $\{X_t\}$ is stationary process. We observe a sample of $N$ observations from the process, i.e., $x_1, x_2, ..., x_N$. The stationarity property implies that the distribution doesn't change ...
Sane's user avatar
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2 votes
1 answer
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How do you fit a normal distribution to this data?

I've calculated the expected frequencies by using the normal distribution chart and the frequencies given in this table. However the sum of the expected frequencies is turning out to be 67 while the ...
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3 votes
1 answer
291 views

Are there cases where we need to avoid the usage of IQR?

Let's consider the interquartile range (IQR), the standard deviation (SD) and the mean absolute deviation (MAD). We know that "one of the most common robust measures of scale is the interquartile ...
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Expected deviation between a theoretical discrete probability distribution and the simulated one resulting from a number of trials

Suppose we have seven colors, each associated with a theoretical probability to choose one of them. The probabilities are as follows: red ______ 0.304761904761905 blue _____ 0.304761904761905 yellow ...
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1 answer
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How do I interpret a negative relative standard deviation and a relative standard deviation greater than 100 in this example?

I have the following astronomical data data1vcoord =array([[ 709.4497, 1500.3387, 1573.9434, 292.9126, 930.4643], [1423.7768, 1242.1892, 407.6168, 346.3528, 541.8568]]) data10vcoord=array([[ 718....
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Standard deviation of standard deviation under non-normality

In this post, an unbiased estimator for the standard deviation of the standard deviation under normality is provided. I would be interested in such an estimator without the normality assumption, i.e., ...
Hiro's user avatar
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The variance of data set A is twice that of data set B; does this imply that the dispersion of data set A is twice that of data set B? [duplicate]

If the variance of data set A is 4, and the variance of data set B is 2, can we say that the data in set B is twice as dispersed as the data in set A? If the standard deviation of data set A is twice ...
GuoFeng Wang's user avatar
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Using standard deviation of outcome variable as predictor in multiple linear regression

I am attempting to fit a multiple linear regression equation to a continuous, real-valued outcome variable, $Y$, using a number of predictive variables, $(X_1, X_2, ... X_n)$, i.e., $$ Y = \beta_0 + \...
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Standard error of the mean for a questionnaire?

I have the standard deviations and means of 7 questions of a questionnaire and also the sample size. How can I calculate the standard error of the mean of the total questionnaire? I know SEM is ...
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