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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21 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 ...
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What is the expected value of $\frac{X}{X+Y}$ when $X,Y > 0$?

I've read this question (and suggested links) which poses the same question assuming $X,Y$ are bivariate standard normal. Since the support includes $0$, the expectation does not exist. This makes ...
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38 views

Please help me win my argument! What is an appropriate statistical test to use on Proportional Data?

I recently got into a debate with a friend of mine because I claimed that the 9th circuit court tends to have its rulings overturned at a greater rate than other courts (this is about statistics trust ...
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20 views

I am stuck here at how to find likelihood ratio test of 3 variable of exponential distribution

How can I find the critical region/value for the likelihood ratio test of 3 exponentially distributed variables $u_1,\,u_2,\,u_3$? $ H_0:\,u_1=u_2=u_3 \\ H_1:\,u_1\neq u_2 $ I'm not sure where to go ...
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Ratio Correction

In my study I calculate some ratios. The theoretical background is as follows: There is the effect of Binocular Rivalry, where a different picture is presented to the left eye than to the right eye (...
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18 views

Ratios and proportions as predictors [duplicate]

I am interested in modeling a continuous variable (e.g., second language learners' English proficiency measured in TOEFL scores) as a function of a number of predictors some of which are continuous ...
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29 views

Uncertainty on fraction of a population

I have a sample (let's assume it unbiased) of the US population. The sample size is N and the number of people having a certain feature in the sample is n. I would like to calculate the uncertainty ...
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139 views

Can a ratio of random variables be normal? [duplicate]

For a pair of random variables $Y$ and $Z$, is it possible that their ratio $X:=\frac{Y}{Z}$ is (exactly, not asymptotically) normally distributed? If so, could you offer an example of the ...
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39 views

Ratio Estimator as WLS

Apologies in advance for whatever rules this post breaks. I'm looking at a problem where we're currently using a ratio estimator for a certain survey. $$r = \dfrac{\sum_i{y_i}}{\sum_i{x_i}}$$ This ...
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1answer
36 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-...
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Test if counts in two conditions are significantly different without knowing the population size

The data are counts of cell structures in different (independent) conditions. For N cells per condition, in which N is different for each condition and unknown, the total number of X and Y structures ...
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769 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 ...
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1answer
245 views

Help with log2 transformation of normalized data

I have a dataset that I normalize so that the average equals 1. If I then log2 transform the dataset, should the average of the log2 data equal 0? For example: 1, 1, 1. The average of the dataset is ...
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46 views

Standar Deviation of a ratio of means

First, my question. I have 20 data points of a baseline ($b$) and 20 data points of a faster version ($f$). I currently present $\frac{\bar{b}}{\bar{f}}$ in a bar graph in which I'd like to add error ...
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Is the ratio of two noncentral exponential distribution the logistic distribution?

Is the ratio of two noncentral exponential distribution the logistic distribution? If yes, How to set the parameter of the logistic distribution using the parameters of noncentral exponential ...
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44 views

Expectation and variance notation for ratio of random variables [duplicate]

When we have a ratio of random variables, is their expectation/variance defined in the same way? That is, if we want to write out explicitly $E[\frac{X}{Y}]$ where X and Y are random variables, then ...
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54 views

Calculating Log2 Fold Change from Regression Model

I'm reading through Chapter 8 of Modern Statistics for Modern Biology and I'm having trouble understanding the exact computation that goes into estimating the $log_2$ fold change between 2 conditions. ...
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How do I calculate the standard deviation of a financial ratio

For example, the ATO (assets turnover ratio) is Sales/Total Assets. I have both the means and the averages of the Sales and the Total Assets, but I don't know how to get the standard deviation of the ...
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33 views

Can temperature be both an interval and ratio scale?

I am looking at a set of statistics slides and came across the following question and answer: Quiz: Temperature. What is it, interval scale or ratio scale? Temperature can be seen as both! Interval ...
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20 views

What is the ratio distribution of 2 normal variables that have been divided? [duplicate]

I cannot find the prove for this problem. I know that when $$X \sim N(0, 1)$$ and $$Y \sim N(0, 1)$$are both standard normals and if I divide them I get a Cauchy distribution. But what happens when ...
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14 views

How do I interpret lift in Latent Dirichlet Allocation modeling?

I've found the definition of the image below in this document (Pp 3 / 65 in the whole document). When lambda is = 0, it gives whole relevance weight to the ratio of the term probability given the ...
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1answer
9 views

Testing group differences of submissions and acceptances

I've got a dataset with two outcome measures Count of submissions made by an individual. At least one submission was made by all individuals in the dataset. Count of those submissions that were ...
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66 views

Confidence interval for the ratio of two Gaussian means

I have data set of $\sim\! 125$ points of a certain variable $A$ that goes approx. proportional with variable $B$. The quotient $A/B$ is approx. independent of $B$; however the distribution is not ...
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Help - Expectations and Ratios

I would need your help for a problem I have and I don't know how to solve. I would like to know whether I could prove that : $$E[0.5X/(0.5X+0.25)] = E[0.5(1-X)/(0.5(1-X)+0.25)]$$ knowing that $E[X] =...
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Is this data interval or ratio?

Students at my school can have 0 to n number of absences. We recorded the number of absences of 100 students in Fall 2018 before the intervention. At the beginning of the Fall 2019 school year we ...
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40 views

Confidence Limit for Inference on Ratios

I need to know how to construct a confidence interval on a Ratio which is the number of Incidents per Vehicle, calculated as shown for a schematic example in the image below. As shown in the image, I ...
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Why do we use sample mean in ratio estimator of a population mean?

To estimate the population mean of a parameter, one of the estimators we can use is the ratio estimator: $$\hat{\mu_{y}} = \frac{\bar{y}}{\bar{x}} \mu_{x}$$, where we use the ratio estimate $$\frac{\...
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141 views

Probability that one positive random variable is greater than another independent and identically distributed positive random variable

Suppose I have the following random variables $X_{0} \sim f(x)$ and $X_{1} \sim f(x)$ are independent. I want to know the probability that $X_{0} > X_{1}$. So I think I want to find: $$ P(X_{0}>...
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53 views

How to calculate confidence interval of sales lift?

I have tried to calculate the confidence interval of sales lift based on cross penetration data, but can't find out how. Say I have a cross penetration matrix of products A-D and a survey on 100 ...
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17 views

Including ratios as features in machine learning algorithms [duplicate]

Assume that body mass index (BMI) is a good predictor for early death which we are trying to model using a host of different algorithms. A colleague posed the following to me: would it be better to ...
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2answers
200 views

Ratio Measurement Scale and Absolute Zero

Levels of measurement are: Nominal, ordinal, interval and ratio. What happens when the absolute zero of a data set using the ratio scale is a negative number? I.E when the absolute zero is -25,000? ...
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141 views

Coefficient of Ratio + Ratio of Coefficients: Inconsistency

I have regression results about the effect of a treatment on two outcome variables, $N$ and $D$. The coefficient on $N$ is positive. The coefficient on $D$ is negative. These results suggest that ...
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14 views

How to standardize fertility ratio?

I would like to know how to calculate the standardized ratio of an indirect fertility ratio, the Child-Women Ratio (CWR) from samples of a population census. What I have read about, is that the ...
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1answer
41 views

Is there a better way to graph a ratio over time than directly graphing the ratio?

I want to compare how effective two potential solutions are, and I have "scores" for each solution such that I can graph the effectiveness of each solution over time by graphing the scores vs time for ...
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9 views

Generalization of finding the minimum win/loss ratio to qualify for playoffs

Imagine a sports season with 'x' players, and y weeks of play such that 'y' and 'x' are positive integers, 'x' is an even number and 'y'<'x'. During each week of the season, 'x'/2 matches will be ...
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45 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 ...
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36 views

A fair ratio for sorting

Say I own a business and people submit products to be sold on my shop. Before they can be displayed on my store, the items will need to undergo review. Over time I accumulated data which consists of ...
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1answer
61 views

Ratio as independent variable for logistic regression

I am trying to model the association between "previous 2 year history of no shows for consult (independent variable)" with current no shows (dependent variable) using a logistic regression model. The ...
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79 views

How to Calculate O/E ratio with Confidence Interval and P-Value for clustering risk factor

I am working with 5 risk factor all these risk factors are also consider as cluster. For each risk factor's observed value obtained from interview. For 5 risk factor 32 combinations are created, ...
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Estimating a ratio which is not in 0-1

I am trying to find future projections of "Mortality to Incidence Ratio" (MIR) using a number of variables. I checked for Binomial (quasibinomial) (although MIR is not a count ratio) and Beta ...
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481 views

How to interpret incidence rate ratio?

I ran a negative binomial model and then decided to also calculate incidence rate ratio but I am not sure if I understand the ratios correctly. My dependent variable is the number of individuals who ...
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1answer
61 views

A simple question from ANOVA

As per definition of $F$ statistic, $F= \frac{MST}{MSE}$ where MST and MSE denote mean square due to treatment and error respectively. From this definition of $F$ am I right in saying that $F$ ...
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92 views

When to choose difference versus log ratio for expressing variables relatively?

Oftentimes I wish to express one time series (say) relative to a second one. The two obvious candidate approaches are to take their difference or their ratio. Whereas the difference is symmetric with ...
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28 views

Understanding ratio variable meaning

I have a ratio variable - women's income : men's income, women in the numerator and men in the denominator. This variable is intended to measure income disparity between women and men. In a logistic ...
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24 views

Creating a Weighted Ratio Based On Size of Customer

I am attempting to created a weighted ratio/score for customers based on the number of support tickets they have entered in a time period against the number of units they have in service with us. ...
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1answer
133 views

Cox's Proportional Hazard coefficients clarification

I'd like a clarification about the Cox proportional hazard coefficients reported on this page. For example, doesn't the hazard ratio (HR) for gender in that ...
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48 views

How can I calculate $\mu_x/\mu_y$ using Jackknife?

I have difficulties in calculating confidence interval using Jackknife. Suppose that I have two independent samples and I do not know both their population distributions. I understand how to ...
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1answer
33 views

Test for ratio of variances across multiple groups

I am looking for a statistical test for whether the ratio of variances vary significantly among groups. I have 100 groups, each with ~50 A individuals and ~50 B individuals (n varies somewhat between ...
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Which test should I use to predict a ratio from multilevel, time series data?

Thanks in advance for any help you can provide - I've done as much research as possible but I think it'll become obvious I'm somewhat unfamiliar with statistics. Let's say that you've noticed that ...
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50 views

Help understanding this admissions statement!

The statement reads: "applicants invited to interview will be based on the z scores of their MCAT total score percentile and their GPA combined in a 2:3 ratio." From what I understand is that GPA ...

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