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Questions tagged [ratio]

the quantitative relation between two amounts showing the number of times one value contains or is contained within the other. Mathematically the quotient of one amount by another amount.

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Expectation of norm ratio

Suppose $x = (x_0, x_1, \ldots, x_{n-1}) \in \mathbb{R}^{n}$ with $x_{i} \sim \mathrm{Unif}(0, b)$. How can I calculate or estimate $E\left[\left\|x \right\|_{1}/\left\|x \right\|_{2}\right]$? I ...
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Tail probability of minimum to maximum ratio among $n$ i.i.d. half-normal random variables

I have $n$ i.i.d.$\sim\mathcal{N}(0,1)$ random variables $X_1,\cdots,\ X_n$. For my research, I am interested in finding bounds (upper and lower) of the tail probabilities of the ratio $\frac{|X|_{(1)}...
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How to interpret hazard ratios of Cox output?

I'm really struggling to understand how to interpret my R outputs in terms of hazards ratios. I have ran a Cox proportional hazard regression to compare survival between 2 treatment groups (neutron ...
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How to find the sample points that have statistically meaningful large ratios between two values of the point?

As an example, suppose that I want to find the Stack Overflow users who have a lot of profile views compared to their total reputation. This could indicate that that user has an external source of ...
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22 views

How to optimize ratiometric loss function with variance term in it?

I'm training a neural network (or any ML model with non-convex gradient-based optimization) to predict a continuous outcome variable. Currently, I use the mean squared error loss function, i.e., if $y$...
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70 views

Distribution of *conditional* frequencies when frequencies follow a Dirichlet distribution

Context: we have a large number of individuals characterized by two binary traits; call these $T$ with values $\{0,1\}$, and $T'$ with values $\{0',1'\}$. So there are four types of individuals: $00'$,...
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22 views

Ratio error propagation for dependent, paired variables

I've been struggling for some days with a statistical issue that is beyond my knowledge. Context: I'm studying the volume of cells, as well as their nucleus volume. These cells are categorized in 3 ...
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How can I assess the position of a novel point in among other points

I have data about the nutrient ratio an animal wants to consume and the available nutrient ratio of grasses in it's environment. The data looks like this: The black dots represent plant nutrient ...
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Finding ratios such that two sets of data is mean reverting

I wanted to know how to find the optimal ratio between two variables X & Y with prices x and y, such that when XY is plotted the resultant data set is mean reverting. XY will have the following ...
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How to calculate whether a disease outcome in a population is by chance or significant?

I have a huge dataset of longitudinal medical records. Each record contains indications for drug and disease. I have been able to calculate the Outcome Rate in the population given a particular drug....
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Testing equality of error ratios between two groups of machines

Edited question: I am given measurements of two types of machines. For each machine I have the following measurements: type $T$ (categorical: either A or B), total production $N$ (positive integer), ...
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I am looking for an explanation of inference of results from weighted regression for a ratio of two continous variables.

I am performing a weighted regression for a ratio $R = \frac{Y}{X}$ using $X$ as weights. Y and X are normal and they are not independent. Is it valid to use $X$ as weights? What is the interpretation ...
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34 views

Ratio estimation vs. regression analysis

I would like to know under which assumptions you would prefer one concept to the other. I would like to conduct an analysis of the relation between sales and expenditures in a sample of financial ...
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15 views

Significance of ratio

In an experiment, we have N containers (N=1000), each of which has two compartments ($C_{i,1}$ and $C_{i,2}$ for first and second compartment of the $i$th container). For each container, we have ...
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What test to use to prove one sample is significantly different

I am studying performance of football teams. I want to prove one team is significantly more successful at home then other teams. I calculate the ratio between points per game at home and points per ...
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How to model the ratio of count data between two treatments in R

I have count data (Detections), two treatments (Control and N) and a continuous variable (Amplitude) ...
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2answers
318 views

What is the ratio of a N[0,1] and U[-1/2,1/2]?

I have come across a problem where I can reasonably assume that the numerator is a uniform distribution of the type U[-a,a], i.e., centered on zero, and the denominator is N[0,b]. This seems to be ...
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How to interpret log(ratio b/w 2 variables) coefficient in a regression framework?

I am struggling to interpret the coefficient of an independent variable in OLS regression equation. The (simplified) equation is of the form: $\Delta Y = \alpha + \beta \ln(\frac{GDP_{2000}}{GDP_{...
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DV is a Fractional Response Variable. General assistance is appreciated

I have the model found in the image below, where the DV 'BEVMarketshare' is a ratio bound to 0. Observations for the DV range anywhere from 6.13 e^-5 to 0.029. Straight to the point... I've got the ...
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1answer
48 views

Logistic regression with independent variable values less than 1

I have one independent variable which has values less than 1, and want to see how the odds of having a disease change when the independent variable increase by 0.1. I ran a binary logistic regression ...
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1answer
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How to find the expectation $\mathbb{E} \left[ \frac{|h|^4}{|h+w|^2} \right]$?

Given the independent and complex Gaussian random variables $h$ and $w$, how does one can find the following expectation? $$\mathbb{E} \left[ \frac{|h|^4}{|h+w|^2} \right] = \int_{\mathbb{C}}\...
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Rates Data Analysis

I'm currently working on incidents data; for each cause I have a rate (nbr incidents divided by the number of car trip aggregated on 1 day for each car). I have this for 4 days. The goal is to check ...
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Negative variance with ratio and regression estimators

Considering multivariate stratified sampling for two study variables $y_1$,$y_2$ and two auxiliary variables $x_1$,$x_2$ with specific correlation, I generated populations for four strata with ...
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How to compare multiple ratios to test for significant differences

Please forgive my ignorance. I have return rates of a molecule (quantity returned per hour, determined from 4 time points) from compound x from 3 separate microcosms (n=3) and return rates of ...
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1answer
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Convergence rate of the ratio of two normal distributions?

I am interested in the behaviour of $\log \frac{\Phi(A-x)}{\Phi(B-x)}$, when ${x\rightarrow -\infty}$ and $\Phi$ is the normal cumulative distribution function, $A<B$, and $A,B\in {\mathbb R}$. It ...
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Interpreting the odds ratio for a proportion type regression coefficient - confidence intervals

So, while this post answers the question of how to obtain the odds ratio for intervals within a proportion variable, I was wondering is it possible to obtain confidence intervals for an interval in ...
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Which test to use to compare the ratio of groups within a population over time

I don't think a question close to this has been asked here yet, sorry if that is the case. I have tested the effect of four different levels of a toxic substance on populations, each with four ...
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Likelihood that two ratios are manifestations of the same underlying pattern

In a sample of 100 languages, 10 are found that display pattern A and none are found that display pattern Ā (the complementary pattern to A). Someone claims that pattern A/Ā is a special case of ...
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3answers
151 views

Generating identically-distributed random variables with a constraint

Is there a way to generate identically-distributed random variables (eg $x_1,x_2,x_3,x_4$) with the following constraint: $\frac{x_1*x_2}{x_3*x_4} ≡ 1$ $x \in (0,1)$ Please note that simply ...
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1answer
36 views

Calculating p-values for ratios of binomial variables

I have a problem that I will express in 2 ways: a math-y way and a biology way. Hopefully this will make it more clear. Math-y way: I have N observations of a pair of binomial variables, call them ...
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1answer
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how to interpret ratios between different units?

I have a problem with calculating and interpreting ratios. My team is suffering from huge data gaps and, therefore, we have no choice but to use all resources we have. I want to calculate how many ...
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1answer
283 views

Direct way of calculating $\mathbb{E} \left[ \frac{\textbf{h}^{H} \textbf{y}\textbf{y}^{H} \textbf{h}}{ \| \textbf{y} \|^{4} } \right]$

Considering the following random vectors: \begin{align} \textbf{h} &= [h_{1}, h_{2}, \ldots, h_{M}]^{T} \sim \mathcal{CN}\left(\textbf{0}_{M},d\textbf{I}_{M \times M}\right), \\[8pt] \textbf{w} &...
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1answer
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model building including very large or very small OR

I am using logistic regression for a binary outcome. When building a multivariate model, is including insignificant univariate variables with OR >0.5 and <1.5 appropriate? And why?
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calculate standard deviation for ratios

I have two groups of intensities I want to compare by calculating the ration and log2 transform to plot as bar plot. I am wondering how to calculate the standard deviation and how to draw it in the ...
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23 views

Chi-squared fit for ratios

I am doing a standard chi-squared parameterisation but the data is only available in ratios not absolute values. My data is in the form $A/X$, $B/X$, $C/X$ etc. and I have error estimates for $A/X$, $...
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Test hypotheses that ratios are different

I have data that shows the number of disease cases in the summer versus the winter for 40 different sites. For example: ...
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113 views

Cox Regression SPSS

I ran some survival analysis in SPSS on data on 2 treatment groups: A, B —versus a control group C Therefore: -compared Treatment A to control group C, i have obtained an exp(B)=1.4 -compared ...
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use ratio as dependent variable in glmm

I have a dataset I am working with to model the proportion of fish caught at length conditioned on the total catch at length. I have paired observations (n=96). The paired observations consist of a ...
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Do random variables follow the same algebraic rules as ordinary numbers?

In the comments on my answer to a recent question about the sum of random variables, I came across a link to the Wikipedia article on the ratio distribution, and noticed the following peculiar claim ...
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17 views

Testing Change in Ratio Over Time

I have ratio data collected at 4 time points in an experiment with 2 treatment groups (drug and placebo). I need to test whether there is a difference in the change over time in this data between the ...
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0answers
48 views

Is it dangerous to take the mean of ratio measurements?

I'm going through a Computer Architecture course and in one of the lectures they mention that when measuring the difference in runtime performance between two systems, using for example multiple ...
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0answers
17 views

Scale invariance, share ratios, and parameter values

In distribution theory, scale-invariant distributions are sometime described popularly in terms of a ratio of ratios, as in "the top 20 percent of the households own 80 percent of the wealth," or "the ...
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1answer
23 views

Logistic regression: computing ratio of OR and confidence interval of the ratio

If I have OR(A vs B) and OR(C vs B), the ratio of the OR is equal to OR(A vs C). But, how to I compute the confidence interval for the ratio of OR? Thank you very much!
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108 views

Correct way to interpret odds ratio

I'm looking at a table of logistic regression results. Specifically, the table shows "Logistic regression model of hypertension status in relation to lead biomarkers in the normative aging study, ...
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1answer
160 views

Meta-Analyzing Dependent Effect Sizes (Log Response Ratios)--Is Averaging Effects An Acceptable Solution?

Given k studies, for each computing a log response ratio $L$ and variance $v$ following the Hegdes et al., 1999 equations: $$L = ln(R) = ln(\bar{X}_{E})- ln(\bar{X}_{C})$$ $$v = \frac{(SD_{E})^2}{n_{...
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What is the variance of log response ratio when adding a constant to the means?

Note: while I asked if is ok or not to add a constant to the log response ratio here, with this question I focus specifically on the formula of the variance of the log response ratio when adding a ...
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51 views

Combine absolute and relative difference into one metric

Imagine we're looking to buy some commodity, say a table, and we want to make a good deal. We know the "true" price of the tables at offer and we're interested in both the absolute price difference ...
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1answer
454 views

Beta regression and regression diagnostics. Do we need to check for normality and other diagnostics?

I have a dependent variable which is a ratio and 0 < y < 1 condition holds. I will apply betareg in Stata but I am not sure what are the diagnostics that are ...
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1answer
152 views

What is the distribution of $x/(x + y)$ for $x$, $y$ independent and normally distributed with mean $0$

What is the distribution of $x/(x + y)$ for independent and normally distributed $x$, $y$ with mean $0$? I'm aware $x/y$ has a Cauchy distribution but I don't know if there is a way to make use of it. ...