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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57 views

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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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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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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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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55 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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112 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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41 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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134 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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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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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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72 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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322 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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50 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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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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160 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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54 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
36 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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52 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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166 views

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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28 views

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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Pros and cons of using a ratio vs a difference score to compare group means

I plan to collect data from 2 groups of people (Gp_1 and Gp_2), some few hundred people in all. Each person will respond to 100 yes/no tasks, each response yielding both accuracy and reaction time ...
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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: high ...
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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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140 views

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 ...
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How to model the ratio of count data between two treatments in R

I have count data (Detections), two treatments (Control and N) and a continuous variable (Amplitude) ...
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377 views

What is the ratio of a N[0,1] and U[-1/2,1/2]?

I have come across a problem where I can reasonably assume that the numerator is a uniform distribution of the type U[-a,a], i.e., centered on zero, and the denominator is N[0,b]. This seems to be ...
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DV is a Fractional Response Variable. General assistance is appreciated

I have the model found in the image below, where the DV 'BEVMarketshare' is a ratio bound to 0. Observations for the DV range anywhere from 6.13 e^-5 to 0.029. Straight to the point... I've got the ...
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185 views

Logistic regression: odds ratio when change in the independent variable values is less than 1 unit

I have one independent variable which has values less than 1, and want to see how the odds of having a disease change when the independent variable increase by 0.1. I ran a binary logistic regression ...
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1answer
119 views

Confidence interval for event rate

I have a data set where I am counting how many events happen ($N$) over a given duration ($t$), and am defining an event rate as $R=N/t$. What I'm wondering is what $N$ gives me a certain confidence ...
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How to find the expectation $\mathbb{E} \left[ \frac{|h|^4}{|h+w|^2} \right]$?

Given the independent and complex Gaussian random variables $h$ and $w$, how does one can find the following expectation? $$\mathbb{E} \left[ \frac{|h|^4}{|h+w|^2} \right] = \int_{\mathbb{C}}\...
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How to compare multiple ratios to test for significant differences

Please forgive my ignorance. I have return rates of a molecule (quantity returned per hour, determined from 4 time points) from compound x from 3 separate microcosms (n=3) and return rates of ...
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1answer
121 views

Convergence rate of the ratio of two normal distributions?

I am interested in the behaviour of $\log \frac{\Phi(A-x)}{\Phi(B-x)}$, when ${x\rightarrow -\infty}$ and $\Phi$ is the normal cumulative distribution function, $A<B$, and $A,B\in {\mathbb R}$. It ...
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Generating identically-distributed random variables with a constraint

Is there a way to generate identically-distributed random variables (eg $x_1,x_2,x_3,x_4$) with the following constraint: $\frac{x_1*x_2}{x_3*x_4} ≡ 1$ $x \in (0,1)$ Please note that simply ...
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1answer
60 views

Calculating p-values for ratios of binomial variables

I have a problem that I will express in 2 ways: a math-y way and a biology way. Hopefully this will make it more clear. Math-y way: I have N observations of a pair of binomial variables, call them ...
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126 views

Regression of a ratio of two continuous variables (i.e. regressing continuous proportions)

I have data of the following form: ...
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1answer
21 views

how to interpret ratios between different units?

I have a problem with calculating and interpreting ratios. My team is suffering from huge data gaps and, therefore, we have no choice but to use all resources we have. I want to calculate how many ...
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331 views

Direct way of calculating $\mathbb{E} \left[ \frac{\textbf{h}^{H} \textbf{y}\textbf{y}^{H} \textbf{h}}{ \| \textbf{y} \|^{4} } \right]$

Considering the following random vectors: \begin{align} \textbf{h} &= [h_{1}, h_{2}, \ldots, h_{M}]^{T} \sim \mathcal{CN}\left(\textbf{0}_{M},d\textbf{I}_{M \times M}\right), \\[8pt] \textbf{w} &...
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model building including very large or very small OR

I am using logistic regression for a binary outcome. When building a multivariate model, is including insignificant univariate variables with OR >0.5 and <1.5 appropriate? And why?
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Are ratio response variables problematic in linear regression? [duplicate]

Is it problematic to use the ratio of two measurements as a response variables in linear regression? Motivating Example: Modeling Differences My motivation comes from the following understanding of ...
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1k views

calculate standard deviation for ratios

I have two groups of intensities I want to compare by calculating the ration and log2 transform to plot as bar plot. I am wondering how to calculate the standard deviation and how to draw it in the ...
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Test hypotheses that ratios are different

I have data that shows the number of disease cases in the summer versus the winter for 40 different sites. For example: ...