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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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How can I calculate $\mu_x/\mu_y$ using Jackknife?

I have difficulties in calculating confidence interval using Jackknife. Suppose that I have two independent samples and I do not know both their population distributions. I understand how to ...
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1answer
20 views

Test for ratio of variances across multiple groups

I am looking for a statistical test for whether the ratio of variances vary significantly among groups. I have 100 groups, each with ~50 A individuals and ~50 B individuals (n varies somewhat between ...
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Is there a closed-form solution for ratios of order statistics?

Is there a closed-form solution for the expected value and variance of the ratios between specified order statistics drawn from a large sample from a known parametric distributional family? Actually, ...
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Which test should I use to predict a ratio from multilevel, time series data?

Thanks in advance for any help you can provide - I've done as much research as possible but I think it'll become obvious I'm somewhat unfamiliar with statistics. Let's say that you've noticed that ...
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Help understanding this admissions statement!

The statement reads: "applicants invited to interview will be based on the z scores of their MCAT total score percentile and their GPA combined in a 2:3 ratio." From what I understand is that GPA ...
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1answer
35 views

Comparing Sex Ratios Between Locations

Feel like this should be a pretty simple test to run but am having a major brain fart courtesy of having the holiday off. I have a data set that looks like this: ...
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How to calculate the standard error of ratio of two AUC

Please can anyone help me with this! I hope my explanation is going to be simple: This is the data I have: I only have access to the aggregated data as below. the first column is the time points a ...
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regression with percentage DV and multiple dummy IV

I am running a market analysis about e-mail responses for my marketing class. I have the following data entries: Observations: 400 different sequences of e-mails where sent to different target ...
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Randomization test for comparing ratio estimators

I want to compare two ratio estimators for fisheries data. They are calculated by summing the catch over years divided by the sum of effort over years. One set of data was collected during an open ...
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1answer
39 views

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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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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3answers
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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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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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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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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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47 views

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
325 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
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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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20 views

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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47 views

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
41 views

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
159 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
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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
291 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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805 views

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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25 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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133 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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38 views

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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1answer
140 views

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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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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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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22 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!