## Solved – Statistical test for normalised data

I am working with culture cells where one dish has been transfected with a scrambled knockdown clone and two dishes which have been transfected with two knockdown clones each knocking down the expression of a single gene. An example of an experiment I have performed is to measure the mitochondrial membrane potential (using a fluorescent … Read more

## Solved – Are two sets of 1-D data are equal, if they have same mean and variance and same size

I have two datasets of size n. They have same mean and variance. Is it possible that they have the same entries as their data? What if I considered variance using L1 norm? EDIT: By L1 norm I mean that, the mean of the deviation with the mean of the data. Best Answer Is it … Read more

## Solved – Why does \$r^2\$ between two variables represent proportion of shared variance

Firstly, I appreciate that discussions about \$r^2\$ generally provoke explanations about \$R^2\$ (i.e., the coefficient of determination in regression). The problem I'm seeking to answer is generalizing that to all instances of correlation between two variables. So, I've been puzzled about shared variance for quite a while. I've had a few explanations offered but they … Read more

## Solved – Understanding the homoscedasticity assumption

I can't understand how this works: \$e\$ is the error term and \$x\$ is the explanatory variable. \$\$Var(e|x) = E(e^2|x) – [E(e|x)]^2\$\$ I know that \$[E(e|x)]^2\$ = 0 because \$E(e|x) = 0\$, and squaring 0 is still 0. So that leaves \$Var(e|x) = E(e^2|x)\$ I am confused on this part. This may be a clearer … Read more

## Solved – Understanding the homoscedasticity assumption

I can't understand how this works: \$e\$ is the error term and \$x\$ is the explanatory variable. \$\$Var(e|x) = E(e^2|x) – [E(e|x)]^2\$\$ I know that \$[E(e|x)]^2\$ = 0 because \$E(e|x) = 0\$, and squaring 0 is still 0. So that leaves \$Var(e|x) = E(e^2|x)\$ I am confused on this part. This may be a clearer … Read more

## Solved – the difference between (bias variance) and (underfitting overfitting)

I think bias and variance are metrics to choose the moderate model complexity(to choose the right model from candidate models), and underfitting and overfitting are metrics to know to what extent has the model leant the data. Am I right? And what is the relationship between them? Best Answer All are metrics to find the … Read more

## Solved – 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: >> var(randn(1),0) %the '0' here tells var to give sample variance ans = 0 >> var(randn(1),1) %the '1' here tells var to give population variance ans = 0 Somehow, the sample variance is not dividing by \$0 … Read more

## Solved – test/technique/method for comparing principal components decompositions between samples

Is there any methodical way to compare the directions, magnitudes, etc of PCA results for different samples drawn from the same population? I'm leaving the nature of the test deliberately vague because I'd like to hear all the various possibilities… e.g. there might be (and I'm speculating here) a test comparing the sizes of the … Read more

## Solved – test/technique/method for comparing principal components decompositions between samples

Is there any methodical way to compare the directions, magnitudes, etc of PCA results for different samples drawn from the same population? I'm leaving the nature of the test deliberately vague because I'd like to hear all the various possibilities… e.g. there might be (and I'm speculating here) a test comparing the sizes of the … Read more

## Solved – Variance of a linear combination of vectors

Let \$A\$ and \$B\$ be two constant matrices and let \$x\$ and \$ y\$ be two random vectors, what is the general formula for \$Var(Ax+By)\$? I know the formula for when \$x\$ and \$y\$ are scalar random variables and \$A\$ and \$B\$ are constants, but what about the matrix case? Best Answer The "variance" of … Read more