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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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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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19 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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0answers
11 views

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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0answers
6 views

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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19 views

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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0answers
9 views

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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16 views

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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21 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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0answers
13 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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2answers
45 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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41 views

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) ...
3
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2answers
303 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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0answers
8 views

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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68 views

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
47 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
86 views

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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19 views

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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15 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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38 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
39 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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0answers
11 views

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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0answers
18 views

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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0answers
13 views

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
143 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
32 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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42 views
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1answer
17 views

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
265 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
13 views

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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582 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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0answers
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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0answers
18 views

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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0answers
89 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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19 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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0answers
110 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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15 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
47 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
15 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
21 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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2answers
102 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
152 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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144 views

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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44 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
368 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
150 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. ...
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1answer
81 views

Distribution of ratio between complex Gaussian and Chi-square R.V.s

What would be the distribution of the following ratio? $z = \frac{x_{1}}{|x_{1}|^2 + |x_{2}|^2 + ... + |x_{M}|^2}$ where $x_{i} \sim \mathcal{CN}(0,a), \forall i$ and $a > 1$. As can be seen, the ...
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1answer
422 views

Odds ratio for poisson regression

Can I compute Odds ratio coefficients and their 95% CI from a Poisson regression (GLM) using the exp function? I have an ordinal dependent variable (i.e., a GS of a scale) and some independent ...
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0answers
21 views

What's the difference between ratios as independent variables and absolute numbers as independent variables in regression analysis

In regression analysis (such as multivariate regression or negative binominal regression), if I input ratio (absolute number versus the number of dependent variable) as independent variable, what is ...
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1answer
273 views

What type of statistic should I use to compare two ratios in two groups

I compare mean hounsfield units (HU) in two different levels of the spine (v1, v2) at two different time points (time1, time2) in 50 patients in R. test data: ...
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141 views

Using Index (ratio) for time series analysis

I am doing a multivariate time series analysis. However, one of my time series is the Productivity Index. The time series consist of quarterly data from 1971 to 2015. The index is such that 2010 = 1, ...