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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27 views

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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38 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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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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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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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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55 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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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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11 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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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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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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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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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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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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39 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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150 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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51 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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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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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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How best to represent changing risk over time in data set with groups of different duration

Here is an example outline of my dataset: I have 20 shops that are open for a period of time, but the duration is not the same (i.e. some locations are open for 4 years, others are open for 2 months, ...
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Confidence intervals

How do you determine the confidence interval of the quotient of 2 numbers, each of which has its own confidence interval? I have a numerator and denominator. Each has a confidence interval, i.e., the ...
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Proper analysis procedure of paired rate comparisons - ratio or difference?

I have a set of population counts where each row represents a different region, and variables show overall counts and counts/percentages within specific groups/criteria. I am interested in the cross-...
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Can I use Poisson regression to model prevalence ratios if I only have information on events?

I often used Poisson regression models to estimate prevalence ratios. However, in these cases my data contained information on the whole population, including events (1) and non events (0). ...
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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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How does forecast skill score change when seasonality in the forecast quantity is removed?

Given RMSE skill score $s$: \begin{equation}\label{eq:msess} s = 1-\frac{\text{RMSE}(f,x)}{\text{RMSE}(r,x)}, \end{equation} where $f$, $r$, and $x$ are forecasts of interest, reference forecasts, ...
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pearson correlation on ratio

I have a very strange statistical result : I measure the employment rate in 2 different systems and I want to compare the results. The analysis is done for example by school frequented before. ...
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Ratio variables in regression

I am trying to do a regression to find the impact of grants given to schools and the graduation rate. As of now, the current regression model is ...
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Determining difference in vector of coefficients for a model according to likelihood ratio test in SPSS

I have performed logistic regression on my data set designed to explore significant independent variables (IVs) (Age, Gender, disease severity, co-morbidity, etc) associated with all-cause 30 day ...
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107 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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27 views

Likelihood Ratio Tests Hogg

Let $n$ independent trials of an experiment be such that $x_{1},x_{2},...,x_{k}$ are the respective numbers of times that the experiment ends in the mutually exclusive and exhaustive events $A_{1}, A_{...
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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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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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Is there a closed-form solution for ratios of order statistics?

Is there a closed-form solution for the expected value and variance of the ratios between specified order statistics drawn from a large sample from a known parametric distributional family? Actually, ...
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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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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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Comparing Sex Ratios Between Locations

Feel like this should be a pretty simple test to run but am having a major brain fart courtesy of having the holiday off. I have a data set that looks like this: ...
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How to calculate the standard error of ratio of two AUC

Please can anyone help me with this! I hope my explanation is going to be simple: This is the data I have: I only have access to the aggregated data as below. the first column is the time points a ...
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regression with percentage DV and multiple dummy IV

I am running a market analysis about e-mail responses for my marketing class. I have the following data entries: Observations: 400 different sequences of e-mails where sent to different target ...
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Randomization test for comparing ratio estimators

I want to compare two ratio estimators for fisheries data. They are calculated by summing the catch over years divided by the sum of effort over years. One set of data was collected during an open ...
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63 views

Expectation of norm ratio

Suppose $x = (x_0, x_1, \ldots, x_{n-1}) \in \mathbb{R}^{n}$ with $x_{i} \sim \mathrm{Unif}(0, b)$. How can I calculate or estimate $E\left[\left\|x \right\|_{1}/\left\|x \right\|_{2}\right]$? I ...
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Tail probability of minimum to maximum ratio among $n$ i.i.d. half-normal random variables

I have $n$ i.i.d.$\sim\mathcal{N}(0,1)$ random variables $X_1,\cdots,\ X_n$. For my research, I am interested in finding bounds (upper and lower) of the tail probabilities of the ratio $\frac{|X|_{(1)}...
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How to interpret hazard ratios of Cox output?

I'm really struggling to understand how to interpret my R outputs in terms of hazards ratios. I have ran a Cox proportional hazard regression to compare survival between 2 treatment groups (neutron ...
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How to find the sample points that have statistically meaningful large outlier ratios between two values of the point?

As an example application, consider following two properties of Stack Overflow users: reputation and profile view counts. It is expected that for most users those two values will be proportional: ...
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How to optimize ratiometric loss function with variance term in it?

I'm training a neural network (or any ML model with non-convex gradient-based optimization) to predict a continuous outcome variable. Currently, I use the mean squared error loss function, i.e., if $y$...
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Distribution of *conditional* frequencies when frequencies follow a Dirichlet distribution

Context: we have a large number of individuals characterized by two binary traits; call these $T$ with values $\{0,1\}$, and $T'$ with values $\{0',1'\}$. So there are four types of individuals: $00'$,...
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How to calculate whether a disease outcome in a population is by chance or significant?

I have a huge dataset of longitudinal medical records. Each record contains indications for drug and disease. I have been able to calculate the Outcome Rate in the population given a particular drug....
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I am looking for an explanation of inference of results from weighted regression for a ratio of two continous variables.

I am performing a weighted regression for a ratio $R = \frac{Y}{X}$ using $X$ as weights. Y and X are normal and they are not independent. Is it valid to use $X$ as weights? What is the interpretation ...
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What test to use to prove one sample is significantly different

I am studying performance of football teams. I want to prove one team is significantly more successful at home then other teams. I calculate the ratio between points per game at home and points per ...