# Questions tagged [variability]

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

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### Mean absolute deviation vs. standard deviation

In the text book "New Comprehensive Mathematics for O Level" by Greer (1983), I see averaged deviation calculated like this: Sum up absolute differences between single values and the mean. Then ...
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### Estimating variability over time

I have a dataset that contains ~7,500 blood tests from ~2,500 individuals. I'm trying to find out if variability in the blood tests increases or decreases with the time between two tests. For ...
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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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### 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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### Why is variability measured relative to a point?

Why are measures of dispersion calculated relative to some central point? Why wouldn't, for instance, all possible non-repeated, pairwise differences in the dataset be a valid measure of spread?
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### Combining sources of uncertainty/variation in a multi-layered linear model

I’m having trouble understanding how to combine parameter uncertainty and interannual variability from various levels in a bootstrapped linear model. Specifically, this model is designed to generate ...
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### What is the best way to estimate the variability of a measurement?

I am trying to capture the variability of a specific measurement. I have 9 measurements from each patient – 3 measurements at 1-hour intervals over 3 consecutive days. So it kinda looks like this: <...
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### How to summarize measurement variability for repeated measures?

I have a data set where different measures are taken repeatedly (3) times for multiple samples, like so: A B C X ... Y ... So, for people X, Y, etc I have ...
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### Measuring intra-observer correlation

We're far from what you'd call expert statisticians, so we'd like to ask some help in an ongoing medical research. We have 60 subjects. A researcher took at least 3 times the measurements of 8 of ...
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### A measure of variability/dispersion that captures only one direction of change

I am conducting a study trying to correlate changes in a biologic parameter (e.g., blood bilirubin concentration) with clinical outcomes (e.g., bleeding). I have found that variability in such ...
242 views

### Using random effects for a between-subjects variable to assess variability in a mixed model

I want to use a mixed model to test random effects for between subject factors. Similar questions have been covered before, with answers that it can be done using lme4. (See here and here for some ...
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### What model to use to evaluate whether the "variability" of one variable is determined by the "variability" of other variables?

I have observations taken for four subjects at a number of points/locations. The data is formatted similarly to as below: I am not directly interested in the impact that a predictor has on the ...
85 views

### Measure for variability of proportional data

I have a list of expected values (E) for the proportions of 20 amino acids in protein sequences.In a particular set of protein sequences these proportions differ from the expected values. In a subset ...
318 views

### 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 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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### 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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### 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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### Parametric (Poisson) Bootstrap

I am trying to estimate population size and I am trying to assess its variability. If the only data I have is on frequencies of encounters and that I know that this frequency follows a Poisson ...
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### Assigning weights in stat evaluation of NFL quarterbacks

I'm doing a statistical analysis of multiple former and current NFL quarterbacks to try to determine who is the best ever. Basically, I'm doing this by evaluating how much better or worse than a ...
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### Estimating if a distribution is significantly less conserved than others when one group is involved.

I am looking at levels of genes in a dataset and want to identify genes that do not vary much in terms of their expression level. While I can do this using the coefficient of correlation, calculating ...
1 vote
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### What's the best method to measure relative variability for non normal data?

I have a set of data that states the volume required each month for the next 12 for 750 raw materials. I would like to determine the variability in the demand for each material, and categorise the ...
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1 vote
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### 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 ...
1 vote
6k views

### How do you interpret the interquartile range?

My data is: Q1: 8.5 Q2: 13 Q3: 17.5 IQR:9. The math problem says to interpret the interquartile range. I have no idea what this means or how to do it.
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1 vote
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### 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 ...
1 vote
222 views

### Variability Analysis for Nominal Variables

I have a very large datasets (billions of observations) made of multiple nominal categorical variables (nominal, not ordinal), and I want to outline the set of variables that accounts for the most ...
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1 vote