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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How to calculate the error on the ratio of a counting experiment?
In an experiment I repeat some task $n$ times and count how often the task completes successfully. This gives the number $m$. Therefore the success ratio is
$$
r = \frac{m}{n}
$$
To calculate the ...
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Confidence interval for ratio between two values without confidence intervals
I have two numeric variables (death rates), each without confidence intervals, and I want to calculate the CI of the ratio between the two values.
I was using the MOVERR method developed by Donner &...
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Weighed average (percentage) depending on the number of facilities in each given region
I have 10 regions with facilities (different number of facilities in each region) that test people for presence of condition A. However, there are also facilities, that were included in the pilot ...
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Regression Model for a Ratio Outcome with Count Variables as Numerator and Denominator
I have a dataset where each row corresponds to a country and contains independent variables such as "per capita income" and "mean education status." Additionally, there are two ...
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Relate ratios to sample size
suppose to have the following situation:
you have a total number of deaths equal to 120. Of them, 20 individuals had cancer. The ratio is 20/120 = 0.16. The total individuals with cancer was 320. How ...
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The mean of ratios as a regression or MLE
I have some data that looks like:
$x_i$
$y_i$
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1000
2001
The current method for forecasting an unseen $y'$ based on a known $x'$ is to estimate it as:
$$\hat y' = \frac{1}{n} \...
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How can I execute power analysis for a ratio metric?
I've looked into the Delta method and it looks tedious. I understand the computational performance gain to help when the dataset is quite large. I only have 200 individuals contributing data, so I ...
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How to calculate SD, SEM, IC95 of a ratio?
I feel like this question has been asked a billion times but none of the answers I read seem to fit my situation, so sorry if it's redundant and I missed it !
Here's my situation :
I have 2 non-paired ...
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Necessary to transform ratios for ANOVA and T-Test?
I am using ANOVA and T-Test to compare wheat grain characteristics between states, agroecological zones, soils, etc.
Most of this data is grain mineral concentrations but some of it is ratios ...
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Should the odds ratio be used to judge incremental information in psychological scales?
I am looking at the incremental validity of the MMPI-A-RF (a psychological instrument) and MACI (another psychological instrument) in the prediction of the DSM code for depression disorders found in ...
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Rationale about the difference between logarithms quocient and ratio? Fold-change?
Following this post I was wondering how to plot or even communicate gene expression using relative quantification, meaning through transformation of cycle threshold values. In my particular experiment,...
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Calculating mean and estimating variance of ratios
I am a biologist with very limited statistics/mathematics background who frequently encounters the same problem when trying to analyse a specific type of data, but would like to finally begin to ...
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Distribution of the ratio of Dirichlet/Gamma variates
It can be seen that the following random variates have the same distribution:
$\frac{X_1 + X_3}{X_2 + X_3}$, where $(X_1, X_2, X_3) \sim \text{Dirichlet} (\alpha_1, \alpha_2, \alpha_3)$
$\frac{Y_1 + ...
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Computation of ratio with Dirichlet distribution
I would like to compute ratio of proportions coming from a Dirichlet distribution. My understanding is that each proportion should be treated as a random variable and therefore I should use Taylor ...
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Relationship between ratio and power in retrospective cohort study
In this study I try to compare two bariatric surgery techniques with respect to their impact on weight loss (Treatment 2= treatment, treatment 1=Control). The ...
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Permutation Test for mean ratio
I am given three vectors of length 11, that represent blood levels of a
hormone measured after placebo, old and new treatment.
...
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Removing Gaussian distribution from mixed ratio distribution
I have a dataset with many ratios gathered from a large group of individuals. Each ratio is between repeated measurements from the same individual. Ratios normalize the concentrations, which vary ...
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Test of statistical significance for equality of two ratios rather than proportions
I have data from two sample surveys done on Maternal Mortality. At each survey, the number of live births and the number of maternal deaths have been recorded. I have calculated the Maternal Mortality ...
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How to address Simpson's paradox when aggregating ratios?
I have a table of means and ns from several studies comparing x and y groups. I've also computed the ratio of the means for each ...
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How to choose between simple random sampling at psu level vs one-stage random sampling?
Say I am measuring barrels of oil drilled per persons in a population.
I can sample at the county level. I randomly sample counties all with equal probability. Our total samples is $N$, the total ...
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Correlation of a ratio formed by two highly correlated random variables
Let´s consider 4 random variables: $Num_1$ and $Den_1$ and $Num_2$ and $Den_2$.
$Num_1$ and $Den_1$ are highly correlated, as well as $Num_2$ and $Den_2$.
Moreover, $Num_1$ and $Num_2$ are also highly ...
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Expectation of ratio of 2 Normal(0,1) with one shifted [duplicate]
I have the following random variables $X$ ann $Y$ following respectively $N(0,b)$ and $N(0,c)$
$Z=\dfrac{(X+a)}{Y}$ with $a$ a real number.
What's the expectation of Z, i.e $E(Z)$ ?
UPDATE : sorry for ...
user226073
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What is the difference between the quotient of two ratios and the difference between the same two ratios?
A commonly used measure of industrial competitive advantage is the location quotient, which compares the local concentration of an industry to the concentration of the same industry in a larger (...
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Justification for normalization in a ratio scale data
Without loss of generality, I asked a group of participants $X=\{x_1,x_2,\ldots ,x_m\}$ to give scores in a $L$-point ratio scale $0,\ldots,l$ to different items $C=\{c_1,c_2,\ldots ,c_n\}$ based on ...
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NAs in Ratio Data in addition to "real" zeros
I have created a ratio dataset - representing the number of rejections/total number of applications. There are some instances in which none of the applications will have been rejected, resulting in a ...
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For semi-supervised learning, is more pseudolabels always better than less pseudolabels?
Let's say I have a labeled dataset $L$ and unlabeled dataset $U$, where $U \gg L$. Suppose I focus on a subset of $U$ called $u$ and generate a subset of $u$ I'll call $u_L$ that consists of ...
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The regression model of the ratio of two linear combination sharing same weight
If We have two varible $X$ and $Y$ that can be modelled by $X = \sum w_i x_i$ and $Y = \sum w_i y_i$ ($x_i$ and $y_i$ are already known), and we have the observation about $R_j = X_j/Y_j$, $j$ for ...
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Should the variable of interest always be placed in the numerator when creating predictive ratios?
Background:
I do research in medical imaging. In a current study I am analyzing a measured variable from images that may predict prognosis/survival. Studies of potential imaging survival predictors ...
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Are ratios and percentages univariate or multivariate?
Edited
I'm working on an anomaly detection project where I have a set of independent variables and dependent variables. As I have ratio and percentage data, I want to know how to document ratios and ...
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Use of ratio of means effect measure and estimation of variance from mean of ratios
I am running a meta-analysis where we are using the ratio of means (RoM) effect measure as the data we are using compare the two sides of the body (i.e. left and right). All RoM calculations are ...
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Which regression models are appropriate for (ratios of) two different but dependent counts?
Consider a variable Y which is the ratio of the frequencies of two words/concepty (f,g) in a text: Y = f/g. Since the texts do not have equal length, the denominator when calculating the percentage of ...
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Weighting Ratio Data?
I am conducting an Interrupted Time Series Analysis on ratio data (number of applications refused/total number of applications). Data is modelled using a binomial logit regression (see below):
...
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Find UMVUE of Ratio of two parametric functions
Let T be UMVUE of $g(\theta)$ and S be UMVUE of $h(\theta)$.
Is there any way to find UMVUE of ratio of $g(\theta)$ and $h(\theta)$ i.e
, $g(\theta)/h(\theta)$?
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How to calculate expected value of within-cluster variance
I have a one-stage cluster sample with $K$ clusters. For $i=1,...,K$, the $i_{th}$ cluster contains $n_i$ units ($X_{ij}$, $j = 1,...,n_i$) with mean $\mu_i$ and variance $\sigma_i$.
I know that the ...
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How to calculate the confidence interval around a ratio, when the margin of error is known for the two numbers
I've got this table from the U.S. Census Bureau's American Community Survey. The moe column contains the 90% C.I.
...
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Correct se for mean proportion in a survey with varying number of trials
I am analysing fishing surveys using the survey package. My PSU is the person and I want to obtain estimates of the proportion of successful fishing trips. Each person has a variable number of fishing ...
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Comparing distributions of ratios between two samples
I have a dataset structured something like this - obviously the numbers are exaggerated and I actually have hundreds of observations in each group.
Group 1:
Observation
Number of specific items
Total ...
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Interpreting Significant Interaction Term Odds/Hazard Ratio with Binary Variables
I am running a cox proportional hazards regression with Stata and am having trouble interpreting the interaction term between two binary categorical variables.
For simplicity, here's a summary of the ...
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Ratio of Poisson to sum of Poisson
Let $X$ and $Y$ be independent random variables which follows Poisson distribution with rate $\lambda_1$ and $\lambda_2$ respectively. I would like to know and find (if it is possible) the ...
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Unbiasedness properties of Ratio/Proportion-type estimator
I have a ratio estimator, $\hat{a} = n_1/(n_0+n_1)$, where $n_x$ refers to the frequency of $x$-valued data. Note that, $E(n_0)$ and $E(n_1)$ exists and strictly positive.
Usually, to show an ...
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Best regression model for ratios of a zero-inflated Poisson with a zero-truncated Poisson random variables?
I am working with data in which my dependent variables underlying probability distribution is a ratio of correlated ZTP-ish (ZTP = Zero-Truncated Poisson) random variables $Y = \frac{M}{C}$ with $C \...
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Distribution of the ratio of dependent non-central chi-square random variables
I am working on a problem that is similar to the one discussed in this link. But in my case $X_i \sim \mathcal{N}(1, \sigma^2)$, i.e., $X_i$ is not a zero-mean Gaussian RV. Specifically, I want to ...
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How many more females in different sized populations
Delhi
Mumbai
Males
75
60
Females
125
40
TOTAL
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100
In two cities of Delhi and Mumbai we have different population. I need to know how many females are more in Delhi given that we need to ...
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How do I approach calculating an optimal sample size for injecting mice for triggering an immune response?
Hypothetical: there is a research team tasked with injecting mice aimed at triggering a specific immune response to produce monoclonal antibodies (MAb). Up until now, they've been largely unsuccessful ...
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Approximate p-values for Relative Risk Reduction
I am working on a problem in which I compare the probability of infection within a region before treatment, and again after 5 years of Mass Drug Administration (MDA). Below describes the sampling ...
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Fitting a regression model on bounded data
Typically, in a regression equation, the dependent variable is unbounded i.e. follows normal distribution. But sometimes it may happen that dependent variable is bounded i.e. dependent variable is ...
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Unsure about the interpretation of prevalence ratios
I have a question about the interpretation of prevalence ratios. Assuming we have the following prevalences (I use R syntax):
...
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Confidence interval for a rate ratio
My question is easy, but I really got stuck here ...
Say I have 500 people, among them, 200 likes eating ice cream. Among these 200, 60 likes strawberry ice cream.
So the rate ratio of ice cream vs ...
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Arithmetic with normally-distributed variables
Suppose $x \sim \mathcal N(\mu_x,\sigma_x^2)$ and $y \sim \mathcal N(\mu_y,\sigma_y^2)$ are random variables, and suppose $\mu_y$ is large compared to $\sigma_y$. I want to know about
$$
z=\frac{x}{y^...
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odds ratio for two variants of covid [duplicate]
I need to calculate the odds ratio for mechanical ventilation and death in relation to
different early COVID-19 symptoms for two COVID variants - delta and omicron. How should I do it? I want to ...
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