All Questions
4,885 questions
7
votes
3
answers
1k
views
How do extreme values scale with sample size?
Assume I have a random vector $X = \{x_1, x_2, ..., x_N\}$, composed of i.i.d. binomially distributed values. If it would simplify the problem substantially, we can approximate them as normally ...
- 8,879
6
votes
1
answer
483
views
Quantile extrapolation?
Suppose you wanted to estimate the $q$ quantile of a distribution by observing $n$ independent draws from that distribution, but with $q < \frac{1}{n}$. What methods are available, and for what ...
- 15k
6
votes
1
answer
2k
views
What is the prediction error while using deming regression (weighted total least squares)
Deming Regression is a regression technique taking into account uncertainty in both the explanatory and dependent variable.
Although I have found some interesting references on the calculation of ...
- 203
3
votes
1
answer
182
views
Basics of extreme values / high-water marks?
With real-valued $X_1, X_2, \ldots$, define
$Max_n := \max(X_1,\ldots,X_n)$ record value or high-water mark
$NextMax_n :=$ the next greater high water, $Max_{n+m} > Max_n$
$Up_n := NextMax_n - ...
- 3,297
40
votes
2
answers
59k
views
Variance of a function of one random variable
Lets say we have random variable $X$ with known variance and mean. The question is: what is the variance of $f(X)$ for some given function f. The only general method that I'm aware of is the delta ...
- 4,034
4
votes
2
answers
249
views
Calculating $\operatorname{Var}\left\{(\hat{m}-m)^2\right\}$ for a univariate normal distribution
Suppose $\hat{m} = \frac{1}{N}\sum_{i=1}^{N}(X_i)$ where $X_i \sim N(m,\sigma)$.
Are the following steps correct?
\begin{align}\operatorname{Var}\left\{(\hat{m}-m)^2\right\} &= \mathrm E\left\{(\...
- 1,003
1
vote
1
answer
883
views
Determining variance of meta-analysis log-response ratio generated from fitted curve
I'm working on a meta-analysis and have generated a quirky question for which I'm at a bit of a loss. The MA is for a large set of factorial experiments. Calculating the Log Response Ratio (LRR) and ...
- 1,025
37
votes
2
answers
8k
views
Distributions other than the normal where mean and variance are independent
I was wondering if there are any distributions besides the normal where the mean and variance are independent of each other (or in other words, where the variance is not a function of the mean).
- 17.9k
64
votes
7
answers
29k
views
Intuitive explanation of the bias-variance tradeoff?
I am looking for an intuitive explanation of the bias-variance tradeoff, both in general and specifically in the context of linear regression.
- 5,621
17
votes
2
answers
12k
views
What is the precise definition of a "Heywood Case"?
I had been using the term "Heywood Case" somewhat informally to refer to situations where an online, 'finite response' iteratively updated estimate of the variance became negative due to numerical ...
- 15k
8
votes
3
answers
4k
views
How should one define the sample variance for scalar input?
I was horrified to find recently that Matlab returns $0$ for the sample variance of a scalar input:
...
- 15k
9
votes
2
answers
8k
views
Microsoft Excel formula for variance
According to Microsoft Excel Help:
VAR uses the following formula:
where x is the sample mean
AVERAGE(number1,number2,…) and n is
the sample size.
Shouldn't it be n, rather than n - 1, in the ...
- 837
12
votes
2
answers
8k
views
How to parameterize the ratio of two normally distributed variables, or the inverse of one?
Problem:
I am parameterizing distributions for use as a priors and data in a Bayesian meta-analysis. The data are provided in the literature as summary statistics, almost exclusively assumed to be ...
- 7,270
5
votes
2
answers
836
views
Is there an analytical expression for the distribution of the max of a normal k sample?
For example:
k <- 100
R <- 10000
max.g <- numeric(R)
for(i in 1:R) max.g [i] <- max(rnorm(k))
hist(max.g) # We can see it's right tailed...
I ...
- 21.9k
4
votes
1
answer
327
views
Given sample size, group means, and misc. post-hoc range statistics, can you suggest a good way to estimate variance through simulation?
I previously asked this question about the validity of my solutions for for $SE$ given $n$, $\bar{X_i}$ and summary statistics from post-hoc multiple comparisons such as Fisher's $LSD$ and Tukey's $...
- 7,270
5
votes
1
answer
2k
views
Normalizing or detrending groups of samples
How do I detrend or normalize multiple series of data so that I can inter-compare between the series?
Specifics below may not be appropriate for this forum. Please let me know and I can remove or re-...
- 175
11
votes
3
answers
4k
views
Are these formulas for transforming P, LSD, MSD, HSD, CI, to SE as an exact or inflated/conservative estimate of $\hat{\sigma}$ correct?
Background
I am conducting a meta-analysis that includes previously published data. Often, differences between treatments are reported with P-values, least significant differences (LSD), and other ...
11
votes
2
answers
8k
views
When to use (non)parametric test of homoscedasticity assumption?
If one is testing assumption of homoscedasticity, parametric (Bartlett Test of Homogeneity of Variances, bartlett.test) and non-parametric (Figner-Killeen Test of ...
- 3,748
8
votes
2
answers
4k
views
Pitman's test of equality of variance and testing for regression to the mean: am I doing the right thing?
I have 2560 paired observations from an experiment in which participants provided two ratings for a set of objects, at two different points in time. Half of the objects in the set had the value of an ...
- 3,472
31
votes
6
answers
4k
views
Test for finite variance?
Is it possible to test for finiteness (or existence) of the variance of a random variable given a sample? As a null, either {the variance exists and is finite} or {the variance does not exist/is ...
- 15k
4
votes
2
answers
1k
views
Determining the "variability" of a benchmark
I have a software benchmark which is quite noisy. I am trying to for the bugs which are causing the noise, and I need to be able to measure it somehow.
The benchmark is comprised of a number of ...
- 141
6
votes
3
answers
2k
views
Might be an unbalanced within subjects repeated measures?
I ran a within subjects repeated measures experiment, where the independent variable had 3 levels. The dependent variable is a measure of correctness and is recorded as either correct / incorrect. ...
- 63
7
votes
2
answers
3k
views
Using bootstrap for glm coefficients variance estimation (in R)
I am fitting a GLM model (in R), and would like to get an estimation of the variability of the coefficients estimated by the model.
If I understand it correctly the method to use in such a case is ...
- 21.9k
7
votes
1
answer
2k
views
Tangency portfolio in R
I am trying to solve for an efficient portfolio in R. How do I translate my constraints for a tangency point for 2 risky asset portfolio, and a given risk free rate to R solve.QP function? So ...
- 2,799
5
votes
2
answers
575
views
Using mixed effects modelling to estimate and compare variability
Say I observe two groups of 10 people, measuring some quantity 100 times in each person. There will presumably be some variability across these 100 measures in each person. Can I use mixed effects ...
- 14k
9
votes
3
answers
10k
views
What is the expected MINIMUM value drawn from a uniform distribution between 0 and 1 after n trials?
Assume you draw a uniformly distributed random number between 0 and 1 n times. How would one go about calculating the expected minimum number drawn after n trials?
In addition, how would one go ...
- 597
25
votes
3
answers
14k
views
Coefficient of Determination ($r^2$): I have never fully grasped the interpretation
I want to fully grasp the notion of $r^2$ describing the amount of variation between variables. Every web explanation is a bit mechanical and obtuse. I want to "get" the concept, not just mechanically ...
- 3,017
4
votes
3
answers
2k
views
How many measurements are needed to 'baseline' a measurement?
When we are monitoring movements of structures we normally install monitoring points onto the structure before we do any work which might cause movement. This gives us chance to take a few readings ...
- 607
5
votes
6
answers
969
views
Basic question regarding variance and stdev of a sample
Suppose there is a very big (infinite?) population of normally distributed values with unknown mean and variance.
Suppose also that we have a sample, S, of n values from the entire population. We can ...
- 113
6
votes
2
answers
233
views
How to tell if something happened in a data set which monitors a value over time
I have a data set where a series of measurements are being taken each week. In general the data set shows a +/- 1mm change each week with a mean measurement staying at about 0mm. In plotting the data ...
- 607
54
votes
8
answers
39k
views
When conducting a t-test why would one prefer to assume (or test for) equal variances rather than always use a Welch approximation of the df?
It seems like when the assumption of homogeneity of variance is met that the results from a Welch adjusted t-test and a standard t-test are approximately the same. Why not simply always use the Welch ...
- 19k
50
votes
5
answers
430k
views
What is the difference between a population and a sample?
What is the difference between a population and a sample? What common variables and statistics are used for each one, and how do those relate to each other?
- 2,318
4
votes
1
answer
826
views
Variance components
I have a set of $N$ bodies, which is a random sample from a population whose mean and variance I want to estimate. A property of each body is being measured $m_i$ times ($m_i>1$) and different for ...
- 113
9
votes
4
answers
855
views
Why is the average of the highest value from 100 draws from a normal distribution different from the 98th percentile of the normal distribution?
Why is the average of the highest value from 100 draws from a normal distribution different from the 98% percentile of the normal distribution? It seems that by definition that they should be the ...
- 19k
83
votes
3
answers
105k
views
How is the minimum of a set of IID random variables distributed?
If $X_1, ..., X_n$ are independent identically-distributed random variables, what can be said about the distribution of $\min(X_1, ..., X_n)$ in general?
- 941