Questions tagged [variability]
Variability or dispersion describes how a variable's values are spread out or compressed.
112
questions
61
votes
13
answers
182k
views
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
...
- 779
10
votes
1
answer
1k
views
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 ...
- 5,837
9
votes
1
answer
221
views
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 ...
- 62.3k
9
votes
3
answers
8k
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 ...
- 195
8
votes
1
answer
153
views
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?
- 83
8
votes
1
answer
2k
views
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}...
- 253
6
votes
3
answers
531
views
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 ...
- 173
6
votes
1
answer
10k
views
What exactly is the "proportion of variability explained"?
One often hears to say "more than 70% variability is explained by ..." What exactly is meant by this? Th proportion of the sum of squares (SSE), or mean sum of squares (MSE)? For example in the ...
- 6,033
6
votes
2
answers
476
views
What is the frequentist interpretation of uncertainty vs. variability?
I have been reading Begg, Welsh, and Bratvold (2014), which is an excellent and lucid discussion of the distinction between uncertainty and variability (from a petro/geostatistics perspective). The ...
- 5,183
5
votes
2
answers
7k
views
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 ...
- 173
5
votes
1
answer
8k
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 ...
5
votes
1
answer
679
views
How to compare the variability of two measures from meta analysis?
I have two measures from each of 20 studies. Random-effects meta analysis has been performed for each of the two measures, and for each measure I have two values to indicate data variability, cross-...
- 2,548
5
votes
1
answer
268
views
Informational value of R squared and correlation? [closed]
Taleb has previously undermined the typical interpretation of correlation with regards to the informational value it carries, showing how the uncertainty is reduced in a non-linear fashion.
With ...
- 1,241
4
votes
3
answers
2k
views
How do I compare the repeatability of two sets of experiments with a low number of samples?
I'm investgating the repeatability of an experimental process (actually measuring lift in a wind tunnel), which can be measured using a single number, Q. However, I only have limited access to the ...
- 105
4
votes
1
answer
494
views
How big is "sufficient" sample size?
I am currently doing some tests with some specific parameter settings to characterize a process.
I roughly remember that a widely used rule of thumb for lab tests and whatnot is a sample size of 5 or ...
- 177
4
votes
1
answer
148
views
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 ...
- 171
4
votes
1
answer
269
views
Inter-experimental variation in survival experiment - how to estimate variability?
In my animal experiments, I do survival studies, which generate Kaplan-Meier survival curves for each group, which I then compare with an appropriate log rank test.
My question is: If I have run a ...
- 41
3
votes
1
answer
1k
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, ...
3
votes
1
answer
397
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 ...
- 1,939
3
votes
0
answers
730
views
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 ...
- 589
2
votes
2
answers
1k
views
Are negative Detection Limit for concentrations consistent
We are monitoring Air Quality: essentially concentrations. We collect time series and we periodically calibrate analysers in order to control the process. Knowing the specifications or assessing it ...
- 131
2
votes
2
answers
142
views
How to measure variability of categorical time series?
I have a list of categorical variable time series. For example
A, A, A, A, A, A, A, A, A
A, B, C, A, B, C, C, C, A
A, Z, D, X, Y, T, A, A, F
C, D, C, D, C, D, D, C, C
A, A, A, A, B, A, A, A, A
A, A, ...
- 153
2
votes
2
answers
5k
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 ...
- 919
2
votes
2
answers
2k
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 ...
- 63
2
votes
1
answer
1k
views
Looking for significant variability of categorical data in columns of data frame
I have a data frame with each column contains categorical data: 0,0.5,1,-1
...
- 125
2
votes
1
answer
228
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 ...
- 149
2
votes
1
answer
27
views
Formal language for describing variability of a random experiment
I have a random experiment with its probability space $(\Omega, \cal{F}, P)$ but no random variable defined over it. Is there any formal language for describing the variability of the random ...
- 62.3k
2
votes
1
answer
204
views
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., ...
- 167
2
votes
1
answer
1k
views
Choosing Variance for Gaussian Prior
I'm relatively new to bayesian inference, and was trying to apply a bayesian model in a real-world scenario.
Let me describe the model in brief:
We have $N$ i.i.d. random variables $D =(X_1, X_2, ......
- 305
2
votes
3
answers
116
views
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 ...
- 395
2
votes
3
answers
2k
views
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:
<...
- 91
2
votes
1
answer
304
views
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 ...
- 538
2
votes
1
answer
3k
views
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 ...
- 123
2
votes
1
answer
227
views
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 ...
- 2,424
2
votes
0
answers
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 ...
- 107
2
votes
0
answers
18
views
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 ...
- 21
2
votes
0
answers
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 ...
2
votes
1
answer
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 ...
- 203
2
votes
0
answers
50
views
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, ...
- 1,144
2
votes
0
answers
76
views
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. ...
2
votes
0
answers
57
views
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 ...
- 427
2
votes
0
answers
485
views
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 ...
- 21
2
votes
0
answers
36
views
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 ...
- 21
2
votes
1
answer
57
views
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
3
answers
2k
views
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 ...
- 11
1
vote
3
answers
2k
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 ...
1
vote
2
answers
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.
- 11
1
vote
1
answer
596
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 ...
user163005
1
vote
1
answer
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 ...
- 2,146
1
vote
1
answer
2k
views
Comparing variability of likert scale answers beyond IQR
I am analysing a simple study where users were asked questions on 5-point likert scales. I use interquartile range (IQR) to assess the variability in the answers of the respondents. In particular, I ...
- 2,323