# 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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20 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 ...
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 <...
39 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 ...
157 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 ...
24 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 ...
7 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 ...
112 views

### Empirical versus Theoretical Convergence of Ratio of Normal Distributions

I have observed that if you take the ratio of two normal variables distributed as $N(1, \sigma) / N(1, \sigma)$, empirically this ratio distribution approaches normality as sigma approaches 0 (shown ...
509 views

### Weighting CTR ratios based on reliability of the data

This is my dataset: PageID Hits ClickThroughs CTR 1 1000 400 40% 2 10 8 80% I'm trying to calculate click-...
267 views

### Which kind of mean (harmonic, geometric, arithmetic) is best suited for averaging probability ratios? [closed]

There are a bunch of examples around on how harmonic mean is more suitable for averaging rates, e.g. speed (when the distance is fixed). But what about probability ratios (p(A)/p(B), i.e. how much ...
41 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 $Z$ ...
25 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.
33 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 ...
55 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 ...
838 views

### 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 ...
159 views

### How to Handle Zeroes in Ratio of Count Variables

In my discipline, it's common to use the ratio of predators:prey as a proxy for pest control by naturally occurring pest insects and spiders. That means making a ratio of two negative binomial ...
28 views

### 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 $n$: \...
275 views

### How to test whether a ratio is different from one using bootstrap?

I have a dataset including two groups of individuals. I get the median of a measurement (say weight) for each group, say W1 and W2 for group 1 and 2, and then get the ratio of the medians W1/W2. How ...
13 views

### 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.) ...
23 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 ...
913 views

### What is the distribution of the ratio between independent Beta and Gamma random variables?

What would be the distribution of the following equation: $$y = \frac{a}{(a+d)^2}$$ where $a, d$ $\sim$ $\Gamma(M,c)$. Additionally, $a$ and $d$ are independent random variables.
4k views

### Distribution of the ratio of dependent chi-square random variables

Assume that $X = X_1 + X_2+\cdots+ X_n$ where $X_i \sim N(0,\sigma^2)$ are independent. My question is, what distribution does $$Z = \frac{X^2}{X_1^2 + X_2^2 + \cdots + X_n^2}$$ follow? I know ...
165 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 ...
36 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 ...
27 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 ...
1k views

### How to find the sample points that have statistically meaningful large outlier ratios between two values of the point?

As an example application, consider following two properties of Stack Overflow users: reputation and profile view counts. It is expected that for most users those two values will be proportional: high ...
22 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 ...
18 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 (...
944 views

### Uncertainty in a fractional count

What is the uncertainty (68% confidence level) of $N/M$, where $N$ is the number of entries that pass a cut and $M$ is the total number of entries? ($N$ and $M$ are both integers, and I'm interested ...
25 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 $$SE_{SMR} = 1.96 * \frac{\sqrt O}{E}$$ ...
10 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 ...
2k views

### I've heard that ratios or inverses of random variables often are problematic, in not having expectations. Why is that?

The title is the question. I am told that ratios and inverses of random variables often are problematic. What is meant is that expectation often do not exist. Is there a simple, general explication of ...
11 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 ...
289 views

### is there any way to calculate confidence intervals (CI) of a ratio?

I need to calculate a ratio of 2 values and each value has its own 95% confidence intervals. The question is: how can I calculate the 95% confidence intervals of the ratio?
25 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 ...
197 views

### Logistic regression: odds ratio when change in the independent variable values is less than 1 unit

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 ...
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 ...
24 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 ...
183 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-...
26k views

### How to compute the confidence interval of the ratio of two normal means

I want to derive the limits for the $100(1-\alpha)\%$ confidence interval for the ratio of two means. Suppose, $X_1 \sim N(\theta_1, \sigma^2)$ and $X_2 \sim N(\theta_2, \sigma^2)$ being independent, ...
2k 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 ...
339 views

### Problem when using ratio of two Poisson distributed variables?

I have two random variables (X and Y), each of which is Poisson distributed. Can I assume the ratio of both variables (X/Y) to be Poisson distributed as well (for an empirical analysis)? Note that Y ...
21 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. ...
27 views

### 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 ...
62 views

### Pros and cons of using a ratio vs a difference score to compare group means

I plan to collect data from 2 groups of people (Gp_1 and Gp_2), some few hundred people in all. Each person will respond to 100 yes/no tasks, each response yielding both accuracy and reaction time ...
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 ...
32 views

### 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 ...
18 views

### 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 ...
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 ...