How to divide standard deviations?

I am trying to work out the standard deviation of a percentage change. I have the mean baseline value ‘a’ and the mean follow up value ‘b’, along with their standard deviations. Percentage change is: (b-a)/a I am able to calculate the SD of (b-a): The formula for which I obtained from: However, I … Read more

How can a more efficient volatility estimator be used to improve the co-variance matrix?

Using mean-variance, I estimate a co-variance matrix $\Sigma$ to obtain the best weights in my portfolio. However, there are other ways to compute the volatility $\sigma$ than historical standard deviation, for instance using Yang and Zhang estimator. I don’t understand however the link between the vol. estimation and the co-variance matrix. I know that on … Read more

Show that $S_p$ is a biased estimator for the pooled standard deviation

I’ve got this question that I’m really struggling with. we have $X \sim N(\mu_X,\sigma^2)$, $Y \sim N(\mu_Y,\sigma^2)$ $S_X^2=$ $\sum_{i=1}^n (X_i-\overline X) \over (n-1) $, and $S_Y^2=$ $\sum_{i=1}^m (Y_i-\overline Y) \over (m-1) $ The pooled variance is $S_p^2=$ $(n-1)S_X^2+(m-1)S_Y^2\over n+m-2$ we also know that $S_X^2, S_Y^2, S_p^2$ are all unbiased estimators of $\sigma^2$. We want to … Read more

Estimate SD using pass rate and median of large-scale exam

I have a list of medians and pass rates for national exams (scores go from 0 to 100) and need the SD. I do not have access to the individual scores. I am assuming normal distribution. How do estimate the SD knowing only the median and the % of students that passed, i.e. had a … Read more

Combining errors from two groups of measurements

Suppose I have two ways of measuring some quantity, a and b, where each method has its own intrinsic error, σa and σb. I make repeated measurements with each method and produce two samples of data, each having a mean ˆμi and sample standard deviation ˆσi, i∈{a,b}. Each sample also has a standard error of … Read more

Correlation coefficient with standard deviation

I quite often find myself testing hypotheses in which the standard deviation of one (Normally distributed) variable is linked to (the mean of) another variable. I would like to be able to express the strength of this association by means of an index between [-1, 1], similar in spirit to a correlation coefficient. I feel … Read more

Iteratively Compute Mean and Variance on Dataset of Images

Not sure where is it better to ask this question because it is kind of between implementation details and conceptual question. Probably it should be moved somewhere else. I need to normalize images before feeding them into deep learning model. I’ve decided to compute mean and std for the whole dataset and then subtract and … Read more

Test whether the mean value differs significantly from the certified value

The table shows the results (% Ti) of alloy samples containing different certified amounts of titanium and I am asked to for each alloy, test whether the mean value differs significantly from the certified value. I am unsure of which T-test to use for this problem. How do I determine which T-test to use in … Read more

Creating a probability distribution from means and standard deviations

I want to look at an objective measure test to get the probability that a given patient falls under a category, in this case, functional level (K-Level) +==============+==============+===============+===============+===============+===============+ | AMPPRO | K-level | K0-K1 | K2 | K3 | K4 | +==============+==============+===============+===============+===============+===============+ | max score 47 | Mean score | 25 | 34.65 | 40.5 … Read more

Skill-based ranking system with individual performance

I am attempting to rank players in an online game and have successfully used TrueSkill to create a good ranking system however I would like to take it a step further and let individual performance account for some of the rating gained/lost. The major factor I see is that its hard to use individual performance … Read more