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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Testing for significance where results are expressed as a ratio to an in group control
I originally asked this question in the biology stack exchange site, but realise that it might be more relevant here in the stats site:
I have a large dataset that represents a library of yeast ...
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Monte Carlo simulations and Jensen’s inequality in cost-effectiveness analysis: point estimates vs. expected values of simulations
In cost-effectiveness analysis, we use a cost-effectiveness ratio: effect/cost. Because it is a ratio, calculating and representing uncertainty around it is not straightforward. We can use Monte Carlo ...
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Ratio of Normal pdf to cdf
I want to show that
$$\Bigl\lvert \frac{\phi(a)}{\Phi(a)} - \frac{\phi(b)}{\Phi(b)} \Bigr\rvert \leq |a-b|$$
where $\phi$ is the standard normal pdf, and $\Phi$ is the standard normal cdf.
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Average of ratios - out of all possible combinations [closed]
I have a very dummy question :)
I have two variables, $X$ and $Y$, observed independently. I want to know the estimate of ratio, $Z=X/Y$, using average of ratios.
Can I calculate all possible ...
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The distribution followed by the number obtained by dividing coefficient a1 by the other coefficients a2 in multiple regression
Given the following multiple regression model.
$$
y\sim N(a_0+a_1x_1+a_2x_2,\sigma)
$$
where $y$ is the response variable, $N(\mu,\sigma)$ is the normal distribution following the mean as $\mu$ and ...
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What statistics to use compare many (dependent) ratios
I'm trying to compare the cellular subpopulations of the thymus of transgenic mice. I identify the cells with flow cytometry, and I get results similar to this:
Cell type
Mouse strain 1
Mouse strain ...
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Addressing Scaling Bias in Panel Data Analysis
I am running an (unbalanced) panel data analysis, where the dependent variable is, $fixed\ cost\ (per\ ha)$ for an agricultural firm $i$ in period $t$. The explanatory variables are the hectares per ...
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How to test the difference between two adverse impact ratios?
Let's define the adverse impact ratio as the hiring rate of minority candidates divided by the hiring rate of white candidates. (So the adverse impact ratio is the ratio of two ratios.)
I calculated ...
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Inferences on ratio of branch means in randomized experiment
It's generally well known that the difference of means is an unbiased estimator of the Average Treatment Effect in randomized experiments: $\mathbb{E}[Y|A=1]-\mathbb{E}[Y|A=0]$ is unbiased for $\...
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What is the pdf of the integral of a gaussian process and of the ratio of two gaussian variables?
I need to evaluate the moment functions of a zero mean gaussian process that constitutes the mathematical model of the seismic ground acceleration during an earthquake.
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Poisson regressions in ratio: why is the counterpart not significant?
I am not a statistician and have limited knowledge about the underlying mathematics behind models but I am curious about something I found. I have count data, something like this: out of 150 words in ...
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Comparing ratios of independent means by calculating SE difference – applicable?
I am conducting a study comparing the ratio of a mean number of vocalizations to the mean number of individuals across three treatments. For each treatment, I have the mean number of vocalizations (...
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What weight to use for using NAMCS and NHAMCS together?
I am interested in analyzing the total prescription of aspirin in NAMCS and NHAMCS (https://www.cdc.gov/nchs/ahcd/index.htm) during a given year for all visits. NAMCS and NHAMCS each had a weight and ...
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How to construct confidence intervals for difference of means in logs
I have estimated an OLS model and a Negative binomial model of ln housing search (ln S) per unit (for instance, the average number of visitors per house or bidders per house) as a function of ...
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Ratio of Normal Distributions [duplicate]
Suppose I have two independent random variables, $X \sim N(\mu_1,\sigma_1^2)$ and $Y \sim N(\mu_2,\sigma_2^2)$ with $\mu_1,\mu_2 > 0$.
How can I compute/estimate
$$ \mathbb{E}\left[\left\lvert \...
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Converting Risk Ratios to Odds Ratio in case-crossover trial for meta-analysis
I am doing a meta-analyss of case crossover & time series studies.
so the problem is some studies have reported the RRs, & I need ORs. The data I have is not enough which is
-Total sample size ...
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Does taking the ratio of Empirical Distributions (histogram bins) show their differences?
Background
I have two Empirical distributions, both derived from social media data.
The first represents a broad sample of ~4.8 million posts and the number of followers each post author has. The ...
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How do I take this ratio of two means, then normalize according to another mean while maintaining a correct measure of spread?
I have been trying to figure out how to correctly calculate the standard deviation for the ratio of two protein expressions as measured by ELISA, so that I may then run a hypothesis test, similar to ...
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Confidence interval of a relative difference
I know the size, empirical mean and empirical variance of two samples $X_1$ and $X_2$, but I don't know the values. How can I calculate the bounds of a confidence interval of the relative difference ...
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Reweighting hazard ratios
Assume I have two populations (pop 1 and pop 2). I also have three treatments (A, B, C).
In population 1, I have $HR_{A vs B}$
In population 2, I have $HR_{A vs B}$ and $HR_{C vs B}$
When I want to ...
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Expectation and Variance of two sets
In genomics, you have an input control (I) and a treatment (T) where then you determine the ratio T/I. You perform multiple replicates for each but the number of replicates is not always the same. ...
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Tests for comparing ratio data from independent samples
The data are from an international study comparing participants' perceptions of how much more corporate CEOs make compared to unskilled workers (median ratios are used because mean ratios did not pass ...
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Testing change in ratios
I do not know how to perform this statistical test. I have a proportion of a bodily liquid substance, and I am interested in the ratio with respect to another. For instance, ratio of water (20l) and ...
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What would be the most appropriate distance metric for percentage/ratio data?
I have a matrix where each row is an observation (i), each column is a feature (j), and each value is the ratio the feature j is complete in observation i. That is, the values are floats that range ...
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Contribution of a single value in a Division of Sums
I need to isolate contribution of a single entity in a Division of Sums as shown below. For example, find the contribution of variable a in the following: (a 1 + b ...
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Relationship between Ratio of expectation squared vs ratio of squared expection
I have these pair of numbers
$ (a, b) = (\frac{4}{9}, \frac{1}{9}) $ and $(c, d) = (\frac{1}{2}, \frac{1}{6}) $.
Note that - (a, b) are pair of numbers which represent $((E(e_1))^2, (E(e_2))^2) $ and (...
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Estimating ratio of regression coefficients
What is the best method of estimating a ratio of regression coefficients $\beta_1/\beta_2$ under the usual assumptions / in practice? I have two relatively well approximated signals $X_1, X_2$ and ...
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Convert β to odds ratio?
I would like to convert β-values into odds ratios. It is about table 1 on page 5 in the article
„A revised inventory of Adverse Childhood Experiences“
https://www.semanticscholar.org/paper/A-revised-...
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What is the variance on the ratio of dependent random variables
I have the data on thousands of emission lines such as the one shown in the figure below. A single emission line covers $N$ pixels (11 in this example). Because the data come from counting photons, $...
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Ratio of random variables and the expected ratio of the average
Suppose I have the following random variables $X_1, X_2, Y_1, Y_2$, their support is the natural numbers. $X_1$ and $Y_1$ as well as $X_2$ and $Y_2$ are not independent.
I am given that $E(X_1/Y_1 ) \...
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How to choose theta θ thresholds for ocat family in mgcv package. (ordinal regression)
I have a dependent variable named "FGR" which represents a ratio and takes values between 0 and +Inf. The histogram plot below illustrates the distribution of FGR, excluding +Infinite values
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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}
$$
To calculate the ...
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Confidence interval for ratio between two values without confidence intervals
I have two numeric variables (death rates), each without confidence intervals, and I want to calculate the CI of the ratio between the two values.
I was using the MOVERR method developed by Donner &...
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Weighed average (percentage) depending on the number of facilities in each given region
I have 10 regions with facilities (different number of facilities in each region) that test people for presence of condition A. However, there are also facilities, that were included in the pilot ...
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Regression Model for a Ratio Outcome with Count Variables as Numerator and Denominator
I have a dataset where each row corresponds to a country and contains independent variables such as "per capita income" and "mean education status." Additionally, there are two ...
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The mean of ratios as a regression or MLE
I have some data that looks like:
$x_i$
$y_i$
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The current method for forecasting an unseen $y'$ based on a known $x'$ is to estimate it as:
$$\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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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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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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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 ...
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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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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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