# 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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### Maximum Likelihood of Standard Deviation

I'm trying to get a better understanding about the distribution and uncertainty of the sample standard deviation. Since I'm not a mathematician, I try to compare the math literature with some ...
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### Standard deviation on result of calculation

I'm calculating a value based on experimental data. The calculation is $$k = \frac{a - b}{c} \cdot \frac{1}{T},$$ and $a$, $b$ and $c$ are all measured experimentally, multiple times, with some ...
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### Regression: negative intercept with only positive values [closed]

I'm doing a multiple linear regression on some standard deviation values, but the intercept and the coefficient for many of the predictors are negative. Any ideas on how I should interpret the results?...
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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)...
1 vote
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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 ...
1 vote
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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 ...
1 vote
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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 ...
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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 ...
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### 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 ...
1 vote
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### 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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1 vote
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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....
1 vote
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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 ...
1 vote
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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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### 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 ...
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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 ...
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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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### 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 ...
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### 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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### 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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### 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 ...
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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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### 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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