Questions tagged [variance]
The expected squared deviation of a random variable from its mean; or, the average squared deviation of data about their mean.
4,351 questions
3
votes
0
answers
39
views
Is the variance the only well behaved functional of its kind?
I seems to be known to everybody except students who take introductory statistics courses that the reason why standard deviation rather than mean absolute deviation is used is that the variance of the ...
- 13.1k
2
votes
2
answers
87
views
Interpreting Shapley values for variance decomposition?
I trained a SVM multiple regression model and want to know how much each feature contributes to the prediction variance (quantified by the RMSE). I got the Shapley values for each feature on data from ...
- 209
1
vote
1
answer
50
views
Vector direction of individual clusters after PCA
Suppose I have two multi-dimensional population samples - $A$ and $B$.
I hypothesise that $\mathbb{E}[A]$ and $\mathbb{E}[B]$ are orthogonal in this high-dimensional space.
To test this hypothesis, I ...
- 127
0
votes
1
answer
35
views
In linear regression, what changes when you use robust standard errors to overcome non-constant variance?
In my first course on linear regression, I learned the 4 basic assumptions that every textbook teaches: linearity, independence, homoscedasticity, and normality. However, I recently learned about ...
- 411
1
vote
0
answers
25
views
Spatial and temporal variance partitioning with missing values
I have a gridded dataset indexed by time and space, represented as a $m \times n$ array. I'm following along with Eq. 10 in this paper to partition the variance in this data over space and time. ...
- 11
0
votes
0
answers
20
views
Does a fully deterministic Pocock & Simon minimization affect variance estimation and inference validity (ignoring selection bias)?
I have a question about covariate-adaptive allocation in clinical trials.
Suppose we use a Pocock and Simon minimization procedure without any random component: that is, a fully deterministic ...
1
vote
0
answers
46
views
Deriving effective sample size and effective residual error from random-effects model in meta-analysis
I am performing a meta-analysis between two cohorts. I want to aggregate the estimates I obtained across a series of variables for each cohort.
I know that two main models are used in meta-analysis: ...
- 267
1
vote
0
answers
64
views
Is there a way to simplify this online calculation of the adjusted Fisher-Pearson standardized moment coefficient
I am working with an accelerometer on a project where I am calculating the angles between the vertical line and the accelerometer and the horizontal line and the accelerometer (something similar as ...
- 143
0
votes
0
answers
77
views
Sum of Squares and partial $R^2$ in robust multiple regression
I would like to obtain estimates of the variance explained by each predictor in multiple regression using robust linear regression (for instance with the R function ...
- 267
2
votes
0
answers
90
views
Variance of the average treatment effect using the unit-level variances of the potential outcomes
I'm reading Chapter 19 of Imbens and Rubin (2015), which is on the estimation of variance for estimators of treatment effects. They discuss using the variance of each sample/unit's potential outcomes ...
- 105
3
votes
1
answer
241
views
Standard deviation - which formula?
I teach maths and statistics at a secondary school in Glasgow, and am wondering what variance formula users think applies best to Q4 of this years National 5 Maths exam (see https://www.sqa.org.uk/...
3
votes
1
answer
84
views
Lower bound for MSE, based on sample mean and variance
Short question: For two unknown samples $A$ and $B$ of size $n$, if only their sample mean and sample variances are known, what can be said about $MSE(A,B)$ ?
Long version: To be more precise, I ...
- 41
3
votes
3
answers
487
views
Is it possible to identify this residual pattern as heteroscedastic or homoscedastic?
Plotting data onto a scatterplot from the U.S. Department of Transportation shows that there is a clear positive linear relationship between % of drivers under age 21 and fatal incidents per 1000 ...
- 31
8
votes
1
answer
1k
views
If I remove the point in a dataset which is furthest from the mean, does the sample variance automatically decrease, or at least not increase?
I guess the question fit in the title. It seems to me that it should be the case, but I don't see the proof.
It also seems to me to possibly depend on which definition of variance we use, in other ...
- 137
1
vote
0
answers
40
views
How to calculate the variance proportion explained by fixed and random variables in model?
I aim to determine the relative percentage of variance explained by each fixed and random variable in a linear mixed-effects model, such as: lmer(Y ~ A + B + C + (1|D)) (R syntax).
I've reviewed ...
- 63