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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4 views

Standardized Incidence Ratios - Convert to incidence rates

In a study, 60 cases of cancer were identified for the study population and the SIR was 49.09 with 95% confidence interval of <...
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Can ratio data have negative values?

I get the concept of a "true zero" value, but I'm not sure why this implies that there cannot be any negative values—at least that's what most sources say that I found only, with only few ...
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Variance of ratio of sums

How do I compute the variance of a ratio of sums ? $$ Var\big(\frac{\sum_i X_i}{\sum_j Y_j}\big) $$ I have 2 datasets $X=(X_1,...,X_n)$ with $Y=(Y_1,...,Y_n)$ that I need to compare, and estimate the ...
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Why can negative binomial regression be used to model event rate/count data

It seems negative binomial regression can be used interchangeably with Poisson regression to model event rate? but I don't understand how it works. Poisson distribution is for count data. Poisson ...
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When is the ratio of two normals approximately normal?

Suppose that $X \sim N(\mu_1,\sigma_1)$ and $Y \sim N(\mu_2,\sigma_2)$ are two independent normal random variables. Define $Z = X/Y$. I noticed that there are some cases where the distribution of $Z$ ...
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Proof that ratio of normal distributions is Cauchy [duplicate]

I recall that the ratio of 2 independent standard normal random variables follows a Cauchy distribution, but I don't recall if there is a proof for this.
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32 views

How to account for population sizes when comparing percentages (not CI)?

Let me articulate my line of thought. Imagine that you're working for the ministry of transportation. We compare two countries. One country is significantly bigger than the other – for example we ...
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51 views

Expected Value of the Ratio of Independent Variables, E(X/(X+Y)) [duplicate]

If $X$ and $Y$ are independent random variables, is the following true? Is there an easy way to show this? $$E\left[\frac{X}{X+Y}\right]=\frac{E[X]}{E[{X+Y}]}=\frac{E[X]}{E[X]+E[Y]}$$ If this is not ...
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How to prove that sample-based covariances of sample errors $E[(\bar x-\bar X)^r(\bar y-\bar Y)^s]$ tend to zero with increasing sample size?

Within the context of sample-based ratio estimators (i.e., sampling without replacement), this article here stated that the covariances of sample biases tend to zero with increasing sample size $n$: \...
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Standard Deviation of Ratios/Indices?

Just wanted to hear some thoughts on whether we can calculate standard deviation for observations that are actually disparity indices obtained for each racial group (e.g. White, Black, etc.) ...
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Ratio distribution of variance-gamma distribution and normal distribution

How does one calculate the probability density function of a random variable $Z$, defined as the ratio distribution of a variance-gamma distribution $X$ and a normal distribution $Y$ i.e. $Z=X/Y$? The ...
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Non-central correlated normal ratio - distribution of the ratio of two dependent normally distributed variables

I am currently trying to solve a problem in the context of a Bayesian analysis that concerns normal distributions. The situation is as follows. I have an equation that looks like this, where I know ...
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Distribution of the ratio of a Normal distribution divided by Lognormal distribution

I want to know the distribution (and the moments) of a variable, $Z = X/Y$, where $X\sim \mathcal{N}(\mu_{x}, \sigma^{2}_{x})$, and , $Y\sim \text{Lognormal}(\mu_{y},\sigma_{y})$? Hence, what I want ...
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25 views

Normality of a ratio of random variables

For the context, I am measuring the execution time of a piece of code. I run it $N$ times with different problem sizes, its duration is proportional to the problem size. I am interested in the ...
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Bootstrapping confidence intervals Log Response Ratio

I am a novice with R. I know this is a similar question to https://stackoverflow.com/questions/13053336/bootstrapping-confidence-intervals-and-mean-values-for-log-response-ratio But I have some ...
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Computing probabilistic forecasts for a ratio of two other given forecasts

I have three time series (Revenue, Volume and Price), with Price = Revenue / Volume. I have created probabilistic forecasts for Revenue and Volume and now need to derive a consistent forecast (...
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Confidence interval for Standardized Mortality Ratio

So in a number of places, for example here, I've seen stated without explanation that the standard error of the SMR (at 95% confidence threshold) is simply $$ SE_{SMR} = 1.96 * \frac{\sqrt O}{E} $$ ...
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One way anova on within subject percentage data

I need to conduct a an analysis on a data set consisting of percentages calculated within each subject. Fot example, for subject-1 there are 4 measurements in percentage (20%, 40%, 10%, 30%) for a ...
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What could be a good way to interpret this neurophysiological data?

We are looking at different combinations of neurophysiological tests, and trying to find out which combinations of variables are best suited for clinical use (diagnosing diabetic polyneuropathy). To ...
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Transitivity of Bayesian inference

For more context about this question, please see my other question. Note that I'm a beginner in Bayesian methods. To recall, I'm trying to estimate the ratio of execution times from two different ...
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30 views

How to properly calculate weighted average when the data is in form of ratio

I had a question related to calculating weighted average, on data example below given definition : Column C = Product Supply Column D = Product Demand Column E = Supply / Demand Column F = Demand ...
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Tolerance Interval from the posterior predictive distribution of a ratio of two Normal distributions

I am trying to calculate a Beta-Gamma Tolerance Interval from the Posterior Predictive Distribution of a log(ratio) of two normal (no close form available). In the minimal R code below, assume ...
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Detect if gaming strategy is better

I collect data about a videogame (think about an ego shooter with kills / deaths etc) Obviously the higher "kills" is and the lower "deaths" is, the better the players result is. ...
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Comparing percentages with different denominators to derive metric

I have read similar question posted here but could not find an answer to match my specific problem. So I have a list of countries and number of POI in each country. For eg. Austria (Total POI) : 100 ...
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How to pull in-sample fitted models towards out-of-sample optimum during training?

A common problem in prediction problems is getting a model fit on in-sample data to predict out-of-sample data with decent accuracy and precision. Assuming that we break a part of the in-sample data ...
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How to estimate the correlation between ratio and ratios' denominator

It is a bilogocal issue. I've got measurements of four skeletal elements, 64 observations in total. I produce the ratios, dividing each element length by the sum of elements (sum size) for each ...
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0 - 1 data with asymptote: Which distribution/type of model

I'm analysing data on degradation over time. Degradation has to be expressed as percent. Therefore I use betaregression. However, we repeated to measured degradation after 100% degradation, therefore ...
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1answer
25 views

How to determine the stand-alone potential of words

I'm working on a multimillion-token corpus of conversational speech trying to determine how words differ in terms of being able to form a complete utterance by themselves. To that end I've computed ...
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Proportionality of discipline incidents between student groups

My goal is to see if one student group has a disproportionate number of discipline incidents relative to the another group/s, to what degree, and with what margin of error. I will be speaking mostly ...
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1answer
116 views

Calculate 95% CI for ratio of odds ratio

How can I calculate the 95% CI for the ratio of two odds ratios, given: OR in test group = OR 21.85 (95% CI 3.08, 155.12) OR in control group = OR 27.15 (95% CI 11.64, 63.31)
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27 views

Modelling ratios that are larger than 1 but might include 0s

I've run across a peculiar issue that I can't seem to wrap my head around: In animal ecology, it is common to measure group sizes (number of animals per observed cluster of animals) in relation to ...
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Empirical Bayes Estimation: Different transformation, fully different results

I would be grateful for some advice regarding the following problems: As I reviewed some empirical papers, I learned that most of them use a relatively small number of observations for performing ...
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144 views

Which GLM to use for analyzing the trend in the sex ratio between different years?

I have data on sex ratios (number of males and the number of females) for 13 years. The samples are independent because they are hunted individuals. I want to see if there is a trend of decreasing or ...
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What is the expected value of $\frac{X}{X+Y}$ when $X,Y > 0$?

I've read this question (and suggested links) which poses the same question assuming $X,Y$ are bivariate standard normal. Since the support includes $0$, the expectation does not exist. This makes ...
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Please help me win my argument! What is an appropriate statistical test to use on Proportional Data?

I recently got into a debate with a friend of mine because I claimed that the 9th circuit court tends to have its rulings overturned at a greater rate than other courts (this is about statistics trust ...
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I am stuck here at how to find likelihood ratio test of 3 variable of exponential distribution

How can I find the critical region/value for the likelihood ratio test of 3 exponentially distributed variables $u_1,\,u_2,\,u_3$? $ H_0:\,u_1=u_2=u_3 \\ H_1:\,u_1\neq u_2 $ I'm not sure where to go ...
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Ratio Correction

In my study I calculate some ratios. The theoretical background is as follows: There is the effect of Binocular Rivalry, where a different picture is presented to the left eye than to the right eye (...
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Ratios and proportions as predictors [duplicate]

I am interested in modeling a continuous variable (e.g., second language learners' English proficiency measured in TOEFL scores) as a function of a number of predictors some of which are continuous ...
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158 views

Can a ratio of random variables be normal? [duplicate]

For a pair of random variables $Y$ and $Z$, is it possible that their ratio $X:=\frac{Y}{Z}$ is (exactly, not asymptotically) normally distributed? If so, could you offer an example of the ...
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Ratio Estimator as WLS

Apologies in advance for whatever rules this post breaks. I'm looking at a problem where we're currently using a ratio estimator for a certain survey. $$r = \dfrac{\sum_i{y_i}}{\sum_i{x_i}}$$ This ...
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153 views

Interpreting logistic regression coefficient of a ratio predictor

I'm fitting a logistic regression model in which my predictor of interest is a ratio of measurements in millimeters. Possible values for this ratio range from 0 to ~2.0, with typical values around 0.9-...
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How to correctly analyze fatality rate and daily deaths of Chinese and Italian COVID-19 outbreak?

This is a strange case of difference in fatality rate between Chinese and Italian covid-19 outbreak. In my knowledge, fatality rate is a ratio between deaths from a certain disease compared to the ...
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Help with log2 transformation of normalized data

I have a dataset that I normalize so that the average equals 1. If I then log2 transform the dataset, should the average of the log2 data equal 0? For example: 1, 1, 1. The average of the dataset is ...
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Standar Deviation of a ratio of means

First, my question. I have 20 data points of a baseline ($b$) and 20 data points of a faster version ($f$). I currently present $\frac{\bar{b}}{\bar{f}}$ in a bar graph in which I'd like to add error ...
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Is the ratio of two noncentral exponential distribution the logistic distribution?

Is the ratio of two noncentral exponential distribution the logistic distribution? If yes, How to set the parameter of the logistic distribution using the parameters of noncentral exponential ...
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Expectation and variance notation for ratio of random variables [duplicate]

When we have a ratio of random variables, is their expectation/variance defined in the same way? That is, if we want to write out explicitly $E[\frac{X}{Y}]$ where X and Y are random variables, then ...
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Can temperature be both an interval and ratio scale?

I am looking at a set of statistics slides and came across the following question and answer: Quiz: Temperature. What is it, interval scale or ratio scale? Temperature can be seen as both! Interval ...
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Testing group differences of submissions and acceptances

I've got a dataset with two outcome measures Count of submissions made by an individual. At least one submission was made by all individuals in the dataset. Count of those submissions that were ...
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Confidence interval for the ratio of two Gaussian means

I have data set of $\sim\! 125$ points of a certain variable $A$ that goes approx. proportional with variable $B$. The quotient $A/B$ is approx. independent of $B$; however the distribution is not ...
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Help - Expectations and Ratios

I would need your help for a problem I have and I don't know how to solve. I would like to know whether I could prove that : $$E[0.5X/(0.5X+0.25)] = E[0.5(1-X)/(0.5(1-X)+0.25)]$$ knowing that $E[X] =...

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