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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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32 views

relationship between expectation of a ratio of random variables and a ratio of expectation of random variables [duplicate]

I know that in general for random variables $X$ and a function $g$ $E[g(X)]\ne g[E(X)]$. I would like to know when the following holds $E_Z\Big[\frac{cov(X,Y|Z)}{var(X|Z)}\Big] = \frac{E_Z[cov(X,Y|Z)]}...
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39 views

Way to test a hypothesis that mean of A is N times greater than mean of B?

I designed an experiment where there are two treatments: A and B. Each subject does both A and B with a randomized order, so it's a within-subject design. For example, the data would look as follows: ...
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65 views

Expresion for Var(X/Y)

I am suggested the following formula and I can't find some reference on this expression : $$\text{Va}r(X/Y)=E(X^2/Y^2)-E^2(X/Y)=\text{Cov}(X^2,1/Y^2)+E(X^2)E(1/Y^2)-(\text{Cov}(X,1/Y)+E(X)E(1/Y))^2$$ ...
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93 views

Ratio between two values with confidence intervals

I have two integer values, each with confidence intervals, and I want to calculate the ratio between the two values. My strategy would be to find all the pairs of integer values within the CIs and ...
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39 views

Mean of ratio, ratio of mean and statistic test

First off, I'm sorry if this has been answered or if the answer seem obvious, but I'm currently stuck and can't really wrap my head around the problem. So here are an example table of my situation (...
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22 views

Is computing the average of a ratio the correct approach, and how to do it with nested data?

In general, is computing the average of a ratio appropriate? And secondly, is the nested model below appropriate for doing this? Here is a data set created from the Iris data that resembles my ...
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14 views

Testing for differences in ratios - biological experiment

Summary - I need a statistical test to compare Ratios of average ratios of presumably normal distributed samples Dear readers, I am planning a biological experiment, but want to make sure I know how ...
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25 views

Is there any form or program that generates prevalence ratio values ​through logistic regression?

When performing a binomial or multinomial logistic regression, odds ratio (OR) values ​​are generated. Is there any form or program that generates a prevalence ratio value instead of OR?
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27 views

What's the distribution of this random variable, and why? [duplicate]

Suppose $S_x\sim\Gamma(n,\theta)$,$S_y\sim\Gamma(m,\theta)$, $S_x$ and $S_y$ are independent. What's the distribution of $T=\frac{S_x}{S_x+S_y}$?
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28 views

Outliers for Ratios

We have a large data set that includes two variables of interest (e.g., X and Y). We were interested in whether there were any outliers in the ratios of these two variables of interest across the ...
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96 views

Expectation and distribution of ratio of correlated Gamma/Chi-square random variables

This question is very similar to: Distribution of the ratio of dependent chi-square random variables But the big difference is what happens when we don't have standard normal variables. I want to ...
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What type of data is human-observed wave height and surface quality?

Currently working on a machine learning algorithm that will predict a "fun factor" attributed to the local beach break 4 times a day by human employees of a local business. The human ...
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Statistical Significance of a Comparison of Percentages

I'm looking at a comparison of percentages pre/during covid and I'm trying to work out how to show if there is a statistical difference between groups. I'm not sure which statistical test to use and/...
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19 views

Alternative to Fisher's exact test when observations are not independent

I have a situation where I was planning to use post-hoc Fisher's exact tests to look for significant differences in the ratios of populations of cell subsets in response to treatments, but I'm ...
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5 views

Calculating significance between ratios made of two means

I am trying to find a test to analyze the significance between ratios of two means. I am doing a study that investigates the expression of a certain protein in the brain following an experiment. I ...
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1answer
38 views

How to use logistic regression with original values from a dependent variable that is a ratio?

I have a dependent variable that is a ratio, i.e. it takes the values between 0 and 1. Some 30% of values are 1s. The dependent variable measures the distribution of funds, i.e. it is calculated just ...
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16 views

What do the covariance and correlation tell me about two values?

I started reading a bit about probabilities and how they are used in investing. When reading about covariance and correlation, I got a bit confused about what they tell me about the two values I ...
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22 views

what is the ratio of a ratio of two variances

I know that the ratio of two variances leads to an F-test but what of the ratio of two variance ratios? Is there are simple comparable result? Essentially I'm looking for the analogue of an ...
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5 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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64 views

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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25 views

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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10 views

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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1answer
55 views

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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54 views

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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38 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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102 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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34 views

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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86 views

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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296 views

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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43 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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41 views

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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20 views

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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39 views

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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11 views

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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12 views

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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30 views

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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34 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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28 views

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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22 views

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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12 views

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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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
26 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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1answer
21 views

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
239 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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29 views

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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1answer
239 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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2answers
130 views

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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1answer
43 views

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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