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Questions tagged [variability]

Variability or dispersion describes how a variable's values are spread out or compressed.

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Understanding partial autocorrelation (PACF) and variability

A strong positive partial autocorrelation of lag 1 means that an observation is highly correlated with its previous observation whereas a near zero PACF indicates no correlation. Does that mean that ...
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How to calculate the variability of proportions?

I need to find the proper sample size, and I have found formula in the Stanford lectures. But I can’t understand what the “variability” of proportions means in this case. Consider two proportions : ...
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Confidence interval for population variance and chi-square distribution [closed]

At present, i am reading the e-book by Robert L. Mcdonald(Professor of Finance,Northwestern University's Kellogg school of Management) named $"Derivatives Markets" 3rd Edition.$ In that book, I didn'...
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Why we try to capture variability?

I am new to Statistics and I have a Mathematics background. In Statistics, particularly in Linear Regression and Principal Component Analysis (PCA) so far what I have understood is that the main idea ...
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How to test whether variability between subjects (repeated measures) is significant or not?

I have resting state fMRI data of 77 subjects. For each subject, there are (let's say) 10 regions of interest, and for each region, 50 measurements (time-series). I am trying to compare the ...
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Measuring relative variability for variables with different scales II

I'm reformulating this question to see if I might have better luck than OP did at encouraging a response. Consider that you have two univariate datasets at different scales, and need to establish ...
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331 views

Ways of visually comparing variance of data [closed]

I have a dataset containing 8 categories, I now want to visually compare the variance between the categories. The most common approach would be to use box plots or violin plots but I would like to ...
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41 views

Variability of positive and negative values

I'm interested in variability of postural changes in blood pressure. From a lying to standing position, blood pressure can fall or rise. In my dataset, I have 4 measurements of postural changes over ...
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Maximum Possible Variation Ratio

When calculating the maximum possible variation ratio for a variable, what does k represent? Bachman and Paternoster (2017, p. 107) define the variation ratio as: ...
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How do I interpret this PCA plot made in R? [duplicate]

I am very new to PCA, and I understand that principal components 1 and 2 account for most of the variability in my data, but how can I make statements about my variables and their influence on each ...
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intra rater variability

150 raters from 30 different centres inside 10 geographical region (so 3 centres from 10 regions and raters from each centre) grade 10 images twice on an ordinal scale. How can I calculate intra ...
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How do you measure the variation of probabilities over time?

Suppose we have $K$ possible outcomes, and a model that assigns a probability to each of those $K$ outcomes over time $t$. That is, suppose for each time period $t$, we have a set of probabilities $(...
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If we change only one value of a data set, will the mean absolute deviation behave in the same way as standard deviation?

I took the new data as b and the data removed as a and calculated the new mean and used that to find the new mean and deviation in terms of the old. But it gets too complicated and there is no way to ...
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what to say about low variability

I did a survey and 4-point likert scale and most of survey participants responded “Agree” or “Strongly Agree” and that made low variability in the summated scale scores, what can I write for the ...
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20 views

Variability in categorical variables while reducing dimensionality

If a dataset has a variable with categorical values (A, B, C, D, E, F), would converting them to numeric and breaking them down into separate columns (for example, column A that will have 1s for all ...
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Is there any universal criterion for small vs. large variability?

Is there any universal criterion that permits to say that there is small or large variability? For example, I plan to conduct an experiment. I would like to say that if obtain small variability, I ...
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How are mean results on benchmark obtained when training neural networks?

In most neural network papers, networks are trained on a known database where state-of-the-art performance is known ("benchmark"). Whatever metric is chosen to illustrate the network's performance, ...
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What problem or game are variance and standard deviation optimal solutions for?

For a given random variable (or a population, or a stochastic process), mathematical expectation is the answer to a question What point forecast minimizes the expected square loss?. Also, it is the ...
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Account for a factor variability in a logistic GLMM in lme4 [closed]

We did a field study in which we tried to understand which factors significantly explain the probability of a group of animals (5 species in total) crossing through 30 wildlife road-crossing ...
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Good metric for describing relative variation of data

I am measuring the energy consumption and runtime of computer programs and would like to select a subset of the programs that have stable energy / runtimes. Each program is ran 10 times and I measure ...
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28 views

Average variability of small data set

I have data for 300 devices and each device has been tested a different number of times so some devices have 2 data points and some have 8. For example, one device scored 5, 6.5, 6.5, 6, 6, 6 whilst ...
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31 views

Measuring how “changey” a time series is over time

I am currently working with a medical dataset which among other things contains data on usage of certain instruments as well as power levels. I am attempting to monitor how "fidgety" a care provider ...
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270 views

What can be used to evaluate “variance” of samples of categorical data?

Suppose you are drawing samples from a population of categorical variables. Given samples s1 and s2, I want to calculate an index that would tell me how close I am to the ideal situation where all ...
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22 views

Difference of variability and its significance

I am quite new to statistics and I am trying to interpret a result I found in a medical study. Specifically, I want to know what methods they used so I can reproduce those in an analysis of a study of ...
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209 views

comparing time-series variability

I have consecutive measurements of two different phenomena (x and y) on the same subject, giving me a collection of time-series x_ik(t) and y_ik(t), where i is the i-th measurement and k is the k-th ...
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Significance test on interobserver variability

I am pretty new to statistical testing. So here is my (completely revised) problem: I have n observers reading the same m datasets consisting of k parameters. For every parameter $k_i$, I therefore ...
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206 views

Model stability and variability

I am using polynomial regression to predict mean occupancy in a hospital unit using average length of stay (LOS) and arrival rate to the unit. I am using different percentages of training sets to ...
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87 views

Comparing variability of measures across time

I am working with some data where I have measurements for two outputs (Output A and Output B) for 5 participants in an experiment. Each of the 5 participants have both their Output A and Output B ...
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Confidence Interval Widths as Measure for Variability

I would like to know to which degree the width of a confidence interval can be used as a measure of variability of a statistic. For instance, the confidence interval for the mean is given by $[\bar{x}...
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66 views

Accounting for spatial clumping when determining the variability of a sample

I am looking for a way to account for the spatial clumping/clustering/ in my data. My data comes from 50m line transects. For each transect I recorded the grass height at 2m intervals, giving me 25 ...
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67 views

measures of sequential variation

I have psychological data that consists of series of binary choices (e.g., 1001010101) made by research subjects, where 1 and 0 reflect two different options that can be chosen. Are there any known ...
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51 views

Distance between distributions with emphasis on tail

I'm creating PDFs of rainfall observations, and I've got six years of data. I'm trying to see if small changes in some model parameters create PDFs that are significantly different than what I'd ...
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Assumptions on the Levene's test

I'm trying to conduct the Levene's test for 10 non-normal samples to study an eventual heteroscedasticity. I was trying to justify my applying of this test, but I can't find it's clear assumptions. ...
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140 views

When it is a good idea to average data to reduce variability?

I have 4 responses per day from animals, at different points of the day (morning, afternoon, etc). My data is marred by a lot of variability, since the nature of the response is such that while some ...
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Interquartile range exceeds the median

What can one infer about the dispersion of a dataset when the interquartile range exceeds the median? Does this always indicate a large degree of variability? Are there any other summary statements of ...
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What type of statistical test can be used to compare multiple sets of data

I have attached a picture of my data plot to hopefully clarify what I'm trying to do. The data is pH adjustment of samples, the left most grouping is the pH curve of one set of samples with the ...
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181 views

How to compare coefficients of variation for lognormal data?

I want to compare the variability of two log-normal samples. They are being summarized as Coefficient of variations (CVs) and I want to test if one sample's CV is different from the other's. To ...
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73 views

Pairwise distance as measure of variability

This is probably a naive question... Why do we use something like standard deviation to measure variability, as opposed to something based on the difference between all pairs in a sample? In other ...
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740 views

Variance/standard deviation versus interquartile range (IQR)

Variance and interquartile range (IQR) are both measures of variability. But IQR is robust to outliers, whereas variance can be hugely affected by a single observation. Since variance (or standard ...
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How to measure the variability of a set of sets?

I have a set of sets and I want to assign a measure of variability to it. If all member sets are the same (e.g., S0={{a,b},{a,b},{a,b}}), the measure shall be 0. If some members are different (e.g., ...
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Can the variability of this multi-variate categorical data set be computed?

I have a set of Survey responses in the format shown below. I want to provide a mathematical measure of Variability to show "how different" the population is, but I'm not sure how to do so without ...
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Is the variability index valid for the Pareto distribution

The Pareto distribution is defined from the CDF: $$ F^{-1}(p) = \frac{b}{(1 − p)^{1/a}},\ 0 < p < 1, $$ where, $b$ is the scale parameter and $a$ is the shape parameter. In the Gaussian ...
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how to quantify variation in continuous outcome for samples matched on continuous predictor

I have a data consisting of about 2 million cases. Cases are scored on some (overdispersed) predictor we'll call "employee performance." I would like to match or pool cases with the same score or ...
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62 views

Proportion of explained variability of a single level of a variable?

I have a dataset with one dependent variable and several independent categorical variables. I want to explore the amount of variability each of the independent variables explain in the dependent ...
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Variability of the reference data and its effect on the transformed values

I conducted a study to compare two different tests at two different ages (children). Based on the previous literature we had hoped that the scores should be better (low score) with age but this was ...
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4k views

What is the difference between standard error and margin of error and when to use which?

Will someone please explain what the difference is between standard error and margin of error and when to use which? I have not had luck finding a simple explanation on the differences anywhere on the ...
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455 views

Comparing spread (dispersion) between samples

EDIT: This question has been heavily paraphrased and re-asked in a broader, but better way here: Paired comparison of instruments using different measurement samples This is going to be a long one, ...
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115 views

How to test difference in variability with paired data?

I am dealing with what seems to be a very simple problem, but my statistical knowledge is now a bit rusty, and I can't think of any good solution. I tried to cast my problem in a simpler one, hope it ...
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58 views

How do I use PCA to know if two categories are sources of variability?

I have a matrix of values 10000x2 that fall in two categories A and B. I would like to use PCA to know if the categories are large sources of variability. I ran a PCA analysis in R, but I have no ...