# 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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391 views

### What does a ratio of PDFs mean?

In searching for an answer I came across this about the pdf/cdf ratio but I would like to know if there is any meaning, name or supporting theory relating to the ratio of two pdf values, the numerator ...
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 ...
59 views

### Expectation of ratio between product of gaussian r.v.'s and generalized gamma r.v

Given \begin{equation}\label{eq:definition_of_z} \begin{split} \textbf{Z} = \left[\begin{array}{cccc} {z}_{11} & {z}_{12} & \cdots & {z}_{1P} \\ {z}_{21} & {z}_{22} & \cdots & {...
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### Confidence interval of ratio of successes

Suppose there are 100 observations of a binary outcome variable, and that 35 of them are successes. To calculate the 95% conf interval for the number of successes I have used prop.test(35,100) in R (...
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### Is it meaningful to take difference between two ratio?

Assume we are investigating a simplified satisfaction survey data, where the outcome is binary: satisfied and not satisfied. We have two years data with ~10K samples for each year. Is the ratio ...
449 views

### Propagating asymmetric and large errors in a ratio

I'm currently trying to propagate the errors of two values: $A=143^{+28.6}_{-26.6}$ , $B=19^{+10.9}_{-8.7}$ $\rightarrow$ $B/A = 0.133^{+?}_{-?}$ Both values A and B (#counts) are derived from a ...
121 views

### Comparing two sets of ratios

I am trying to choose the most appropriate test to use for comparison of two sets of ratios, with several replicates. My data set is the number of male and female offspring, in two different ...
354 views

### Expectation of the ratio between Beta and Gamma random variables

Given \begin{equation}\label{eq:definition_of_z} \begin{split} \textbf{Z} = \left[\begin{array}{cccc} {z}_{11} & {z}_{12} & \cdots & {z}_{1P} \\ {z}_{21} & {z}_{22} & \cdots & {...
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.
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### GLM for relative growth rates

I have this experimental design: I have two sets of cell lines. One in which I mutated a gene and another in which I didn't and therefore serves as the control. I grow each of these cell lines under ...
1k views

### Ratio of Means or Mean of Ratios? Inference Across Groups

Edit: For the purposes of the bounty, it would suffice to answer my third question below for the statistic $\hat{P}_g$. I have two groups $g \in \{1, 2\}$ and customers $i$ within those groups who ...
753 views

### Distribution of the ratio between two Negative binomial distributions

I'm dealing with some biological data (read counts from gene expression measurements). For each individual we have 2 measurements, which correspond to two different version of the same gene. These ...
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### Regression with a ratio as an independent variable

I'm regressing a response versus a ratio between two measurements as an independent variable. I'm getting a significant positive effect and I'd like to test whether the contribution of the increase in ...
351 views

### Expected value of maximum ratio of n iid normal variables

Suppose $X_1,...,X_n$ are iid from $N(\mu,\sigma^2)$ and let $X_{(i)}$ denote the $i$'th smallest element from $X_1,...,X_n$. How would one be able to upper bound the expected maximum of the ratio ...
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 ...
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### Can I work out the numbers in the groups, based on the results of hazard ratio?

I need to extract data from a paper that report a hazard ratio=0.72, 95% CI=0.57, 0.92, p=0.010. Knowing that the one group that did better had 255 individuals and the other 252. How can I find out ...
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### How to interpret Monte Carlo samples of the ratio of two variables?

My aim is to find the 95% confidence interval of the ratio of two variables for which I have summary statistics. More specifically, I have the prevalence of mothers drinking during their pregnancy (...
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### Ratio symbol in multiple regression

I am running a multiple regression of the following form: Ratio Y = X0 + Ratio X1 + Ratio X2 I was wondering if there would be a symbol I could use for the 'Ratio'? I found a similar type of ...
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### How can I apply a ratio distribution for modelling quantities per hour?

I'm faced with an interesting situation regarding modelling rates of two populations. Say that I collected the following quantity from each of my employees: ...
18 views

### Variability of the reference data and its effect on the transformed values

I conducted a study to compare two different tests at two different ages (children). Based on the previous literature we had hoped that the scores should be better (low score) with age but this was ...
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### Can we take natural log of a variable in ratio form e.g. age dependency ratio? [closed]

I have been through many posts arguing about whether we should use the natural log of a ratio or not. Yet I am still unable to understand the concept completely for I feel even ratios differ from each ...
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### Working with ratios: standardizing problem

I have a dataset, let's say of counts of apples and oranges. I would like to have a metric that equally reflects the ratio of apples to oranges but if I simply use the ratio: apple count + 1 : ...
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?
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### How to compare two incidence ratios statistically- the rate parameter test

I want to compare two standardized incidence ratios (SIR) obtained in stratified analyses. I read in Mocci et al (2013) that they used the rate parameter test and cited the book Statistical models in ...
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I have data from Cox regression which indicates that compared to a baseline condition condition A => has hazard ratio= 2 condition B => has hazard ratio= 6.5 Is it possible to say if condition A and ...
1k views

### Test Statistic for a ratio of regression coefficients?

Please read the problem till the end. It may appear first that this problem was answered in earlier posts, but it is not so. I have read all the related posts. Problem: Suppose I have two data sets (...