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 ...
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1answer
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 ...
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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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34 views

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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1answer
43 views

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 ...
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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 ...
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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 ...
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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 & {...
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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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103 views

Ratio of correlated vectors is uncorrelated?

Having an issue wrapping my head around a problem today. I have 4 vectors: $A, B, X$ and $Y$. $A$ is linearly correlated to $X$ with an $R^2$ of ~0.93, and $B$ is linearly correlated to $Y$ with an $...
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719 views

T-test or Z-test of two proportions?

We did an intervention to reduce the frequency of use of a certain type of treatment and now I want to compare the data pre vs post intervention. For each month I have the number of treatments per ...
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93 views

Linear regression with ratio as response variable submitted to sampling uncertainty

I have a ratio as a response variable (typically in (0,1) ) which is the result of repeated measurement of a population satisfying a criteria over the total population for the time period. The thing ...
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2answers
233 views

What is the difference between controlling by dividing by a variable, and inserting it as a predictor?

I have a dataset, based on forum conversations, with the following variables: count of emotional words count of cognitive words ...
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137 views

Is the ratio between two correlated time series significant?

I have the following two correlated seasonal time series for the same time period: ...
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1answer
43 views

How can I perform a t test in R that tests the mean difference from a target ratio?

In my data I have a ratio that aims to be 5:1. To test how close the mean difference is between the ratios in my data (of 10 items) and the ideal 5:1 ratio I carried out the following t test. ...
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1k views

Expected value of ratio of correlated random variables?

For independent random variables $\alpha$ and $\beta$, is there a closed form expression for $\mathbb E \left[ \frac{\alpha}{\sqrt{\alpha^2 + \beta^2}} \right]$ in terms of the expected values and ...
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1answer
555 views

How to calculate standard error of the ratio of two complements (e.g., sex ratio)?

If a dataset tells me the sex of every individual (F or M), I can calculate the percent female (0.55) and the relevant standard error (0.005). I can also calculate the percent male (0.45) and the ...
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1answer
134 views

Instrumental variable regression with endogenous ratio variable

I want to estimate the following regression: $y_t=a+bx_t+e_t$ where $x_t$ is an endogenous ratio variable, i.e., continuous values bound between 0 and 1 and $y_t$ is a continuous variable. I want ...
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1answer
250 views

Judging the quality of a statistical model for a percentage

I have a data set with multiple predictors, and a single response variable which is a percentage, thus is bounded between 0 and 100. I cannot share the dataset unfortunately. I would like to build a ...
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1answer
1k views

standard deviation of the reciprocal of a ratio

I have a sample mean ratio of 16 (as in, 16 male to 1 female) and a standard error of 2 (sample size is 10, normal distribution). I want to find the mean and standard deviation (not error this time) ...
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3k views

Ratios as independent variables cause outlieres

If you include Ratios as Independent Variables in a regression or classification problem I often face many outliers. This is a big problem when the ratios can take on bounded values such as $\frac{...
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265 views

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 ...
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1answer
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 ...
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1answer
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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246 views

Distribution of percent difference of two normal variables

I have two performance measures in a given experiment that I know to be approximately normally distributed: $X_1\sim \mathcal{N}\left(\mu_1,\sigma_1^2\right)$ $X_2\sim \mathcal{N}\left(\mu_2,\...
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1answer
576 views

An unbiased estimator of the ratio of two regression coefficients?

Suppose you fit a linear/logistic regression $g(y) = a_0 + a_1\cdot x_1 + a_2\cdot x_2$, with the aim of an unbiased estimate of $\frac{a_1}{a_2}$. You are very confident that both $a_1$ and $a_2$ ...
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75 views

Hypothesis testing in the comparison of two Gaussian ratio distributions

tldr: This question summarizes mine in a more concise way I am struggling with this seemingly trivial question that goes as followed: The data are time points at which 50% of my yeast culture has ...
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1answer
283 views

Regression on fractional data

I'm writing a piece of research into the death rate of minorities on tv shows, as there's been a lot of outcry over the deaths of queer women in media but very little actual analysis on the topic. I'...
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1answer
62 views

Observed/Expected rate correlates with Expected rate - A Flaw?

I am trying to finish my thesis, in which I investigated the association between different hospital characteristics and (numerous)patient outcomes, using multivariable regression models. One of the ...
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61 views

Test if two binomial number of successes are statistically different from each other

I'm looking to compare two groups and their number of successes (on a hit/miss task) to see whether the difference is statistically significant. This is similar but slightly different to a comparison ...
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42 views

Is a Poisson model appropriate when the response are Poisson rate parameters

I am familiar with modelling count data with Poisson regression, for example for count responses $Y_i$ which are random variables with distribution $\operatorname{Pois}(\mu_i)$ with means $\mu_i$ such ...
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2answers
2k views

how to compare ratios in R

I have 10 samples which has males and females. I want to check whether the sex ratios in any of these sample are significantly different from other. Can someone please help me what test can I use in R ...
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965 views

If my goal is to test the absolute change of the ratios, can I compare the ratios directly without log transformation?

Ratios (e.g. $Z$=$Y$/$X$) are frequently used (e.g. fold-changes in mRNA or protein expression, body mass index [BMI], etc.). Many people advise that variables coded as ratios (e.g. fold-change) ...
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1answer
54 views

Estimator for E[A]/E[B]^2

I have 2 random variables $A$ and $B$, with unknown means (denoted $\overline A$ and $\overline B$), and I take $n$ samples $\{<A_i,B_i>|i=1..n\}$. If I want to estimate $\overline A/\overline B^...
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2answers
2k views

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 ...
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1answer
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 ...
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2answers
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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1answer
35 views

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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1answer
161 views

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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89 views

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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1answer
43 views

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: ...
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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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3k views

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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3answers
100 views

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 : ...
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2answers
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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1answer
984 views

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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1answer
1k views

Are hazard ratios additive?

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 ...
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1answer
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 (...
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1answer
30 views

reference for valid rates, ratios, normalization, etc

I'm compiling a list of valid ratios that can be used in analysis. For example, # of sub population / # of population, amount by sub population / number in sub population, etc... I'm having trouble ...
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298 views

Which test for fold changes (where controls are always 1)

I have some data, where I have 3 separate biological groups which grow at different rates. If I treat them all with X, I see an increase in growth. If I look at the absolute numbers then there is very ...