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.

Filter by
Sorted by
Tagged with
0 votes
0 answers
11 views

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 ...
user avatar
  • 520
1 vote
0 answers
18 views

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 ...
user avatar
  • 737
0 votes
0 answers
18 views

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): ...
user avatar
  • 1
1 vote
1 answer
31 views

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 ...
user avatar
  • 11
1 vote
0 answers
35 views

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^...
user avatar
  • 1,078
2 votes
1 answer
23 views

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 ...
user avatar
  • 21
0 votes
0 answers
50 views

Ratio Confidence Interval for Proportions

Wondering if Fieller's theorem is used for the 'ratio' value in the compare argument in ...
user avatar
0 votes
0 answers
28 views

Cumulative Distribution function of ratio of 2 correlated gamma distributed random variables

Let $X \sim \Gamma(k_x, \theta_x)$, $Y\sim \Gamma(k_y, \theta_y)$ be correlated with correlation coefficient $\rho$. The shape and scale parameters are different. i.e. $k_x \neq k_y$ and $\theta_x \...
user avatar
1 vote
1 answer
45 views

Why is it called a ratio scale?

Can you provide a simple example that clearly explains- why ratio scale is called ratio scale?
user avatar
  • 145
2 votes
1 answer
93 views

Confidence interval for multiple samples of ratios of counts (in R)

Data and objective I have count data from two groups, A and B, from across multiple samples. I want to estimate the average ratio of A to B across all samples, along with a confidence interval. Issues ...
user avatar
3 votes
1 answer
38 views

Inference on ratio of coefficients

Question: How to construct standard errors and test statistics for a ratio of regression coefficients? Background: I am running the same regression on two related outcomes $$ Y_1 = \alpha_1 + \...
user avatar
  • 253
0 votes
1 answer
33 views

Should you include the ratio of two variables in survival analysis?

Suppose I have the following (Rossi recidivism) dataset: ...
user avatar
2 votes
1 answer
80 views

95 % CI for ratio of variables subject to measurement imprecision

An instrument used for measurements has a known measurement imprecision of $CV = 10 \%$. Thus, if the variable to be measured has a true value $x_{true}$, the range of possible measured values will be ...
user avatar
3 votes
3 answers
113 views

$\mathbb{E} \left[ \frac{X}{c + X} \right]$ for known constant $c > 0$?

In general, describing expectations of ratios of random variables can be tricky. I have a ratio of random variables, but thankfully, it's nicely behaved due to known structure. Specifically, I have a ...
user avatar
0 votes
1 answer
39 views

Calculate power-effect size relationship for difference in difference of proportions

I am trying to conduct power calculations for a "Before-After-Control-Impact" type of study focused on public opinion variables. Ideally, I want to look at the relationship between effect ...
user avatar
0 votes
0 answers
10 views

Estimate minimum sample size for a rolling time-serie percentage

I have to calculate the conversion rate for a web page, defined as CVR = orders / clicks This is an e-commerce web page, so clicks arrives to the web page ...
user avatar
3 votes
1 answer
135 views

Distribution of the ratio of two related chi-square variates

Suppose a binormal population $X_1, X_2 \sim \mathcal{N}(0,\Sigma)$ where $\Sigma$ is obtained from $\sigma^2$ the variance of each item, assumed equal, and $\rho$, the correlation between pairs. We ...
user avatar
2 votes
1 answer
17 views

Comparing ratios with more than than two numbers

I have a specific reference ratio such as 1:2:1 against which I want to compare other ratios. I'd like to know how to rank test ratios like those below in order of how close they are to the reference ...
user avatar
  • 21
4 votes
1 answer
120 views

Calculating a 95% confidence interval without the original dataset

I have been asked to calculate a 95% confidence interval based on the following paper: https://www.nber.org/system/files/working_papers/w26107/w26107.pdf The question reads: Suppose rainfall in the ...
user avatar
  • 53
0 votes
0 answers
18 views

Best way to code ratio of two skewed, heavy-tailed continuous variables with zero values present in denominator?

I'm modeling the ratio of total medical cost in one 12 month period and the subsequent 12 month period (total_medical_cost_ratio = post_total_medical_cost/pre_total_medical_cost). The data is skewed, ...
user avatar
  • 4,514
0 votes
0 answers
17 views

Forecasting of ratios that need to addup to 100% [duplicate]

I intend to forecast 'shares' or ratios independently that need to add up to 100% . How can I do this especially when there are >2 ratios to predict. e.g. share of mdot, share of desktop and sahre ...
user avatar
0 votes
1 answer
22 views

Confidence interval of sum of voting percentages in a poll

I've been looking at wikipedia poll data results for the incoming french presidential election (https://fr.wikipedia.org/wiki/Liste_de_sondages_sur_l%27%C3%A9lection_pr%C3%A9sidentielle_fran%C3%...
user avatar
  • 13
1 vote
0 answers
54 views

Correlations with Ratios

I've been running an analysis whereby I've been creating ratios of two variables (e.g. A/B) and then correlating them to a third variable (variable C). These correlations have proved to be quite ...
user avatar
  • 11
0 votes
1 answer
11 views

If an attribute has ranges as its possible values, is that attribute a numerical attribute or a categorical (ordinal categorical) attribute

For example if I ask for someone's age, but instead of them being able to enter any natural number their responses are cropped and saved into bins such as "1-10" and "11-20" etc. ...
user avatar
0 votes
1 answer
27 views

What is the distribution of the ratio of two independent variables, each subject to Rayleigh distribution with different standard deviation?

I am trying to find what is the distribution of the ratio of two independent Rayleigh random variables, each of which has different standard deviation.
user avatar
0 votes
0 answers
46 views

How to perform inverse ratio transformation?

This is partly a "how to" question and partly "is this correct". I have a variable that is the ratio of two variables (ratio=a/b). Similar to as shown below in R: ...
user avatar
0 votes
0 answers
51 views

emmeans - joint effects of interaction terms

I would like to see the joint effects of an interaction term. I tried joint_tests() but it gives f ratios. However, I would prefer Incidence Rate Ratios (IRR) because the rest of my results section ...
user avatar
  • 51
0 votes
0 answers
26 views

How to find the standard deviation of a ratio?

I have means from two dependent datasets (leg length [A] and arm length [B]). I do not have raw values for these datasets, but do have N, median, 10th/90th percentiles, and standard deviation. I would ...
user avatar
0 votes
0 answers
33 views

relationship between expectation of a ratio of random variables and a ratio of expectation of random variables [duplicate]

I know that in general for random variables $X$ and a function $g$ $E[g(X)]\ne g[E(X)]$. I would like to know when the following holds $E_Z\Big[\frac{cov(X,Y|Z)}{var(X|Z)}\Big] = \frac{E_Z[cov(X,Y|Z)]}...
user avatar
0 votes
1 answer
49 views

Way to test a hypothesis that mean of A is N times greater than mean of B?

I designed an experiment where there are two treatments: A and B. Each subject does both A and B with a randomized order, so it's a within-subject design. For example, the data would look as follows: ...
user avatar
0 votes
1 answer
88 views

Expresion for Var(X/Y)

I am suggested the following formula and I can't find some reference on this expression : $$\text{Va}r(X/Y)=E(X^2/Y^2)-E^2(X/Y)=\text{Cov}(X^2,1/Y^2)+E(X^2)E(1/Y^2)-(\text{Cov}(X,1/Y)+E(X)E(1/Y))^2$$ ...
user avatar
2 votes
1 answer
144 views

Ratio between two values with confidence intervals

I have two integer values, each with confidence intervals, and I want to calculate the ratio between the two values. My strategy would be to find all the pairs of integer values within the CIs and ...
user avatar
  • 117
0 votes
1 answer
44 views

Mean of ratio, ratio of mean and statistic test

First off, I'm sorry if this has been answered or if the answer seem obvious, but I'm currently stuck and can't really wrap my head around the problem. So here are an example table of my situation (...
user avatar
1 vote
1 answer
26 views

Is computing the average of a ratio the correct approach, and how to do it with nested data?

In general, is computing the average of a ratio appropriate? And secondly, is the nested model below appropriate for doing this? Here is a data set created from the Iris data that resembles my ...
user avatar
0 votes
0 answers
16 views

Testing for differences in ratios - biological experiment

Summary - I need a statistical test to compare Ratios of average ratios of presumably normal distributed samples Dear readers, I am planning a biological experiment, but want to make sure I know how ...
user avatar
2 votes
1 answer
35 views

Is there any form or program that generates prevalence ratio values ​through logistic regression?

When performing a binomial or multinomial logistic regression, odds ratio (OR) values ​​are generated. Is there any form or program that generates a prevalence ratio value instead of OR?
user avatar
0 votes
0 answers
30 views

What's the distribution of this random variable, and why? [duplicate]

Suppose $S_x\sim\Gamma(n,\theta)$,$S_y\sim\Gamma(m,\theta)$, $S_x$ and $S_y$ are independent. What's the distribution of $T=\frac{S_x}{S_x+S_y}$?
user avatar
  • 1,734
0 votes
0 answers
43 views

Outliers for Ratios

We have a large data set that includes two variables of interest (e.g., X and Y). We were interested in whether there were any outliers in the ratios of these two variables of interest across the ...
user avatar
  • 1
1 vote
1 answer
153 views

Expectation and distribution of ratio of correlated Gamma/Chi-square random variables

This question is very similar to: Distribution of the ratio of dependent chi-square random variables But the big difference is what happens when we don't have standard normal variables. I want to ...
user avatar
  • 291
2 votes
0 answers
30 views

Statistical Significance of a Comparison of Percentages

I'm looking at a comparison of percentages pre/during covid and I'm trying to work out how to show if there is a statistical difference between groups. I'm not sure which statistical test to use and/...
user avatar
1 vote
0 answers
8 views

Calculating significance between ratios made of two means

I am trying to find a test to analyze the significance between ratios of two means. I am doing a study that investigates the expression of a certain protein in the brain following an experiment. I ...
user avatar
1 vote
1 answer
55 views

How to use logistic regression with original values from a dependent variable that is a ratio?

I have a dependent variable that is a ratio, i.e. it takes the values between 0 and 1. Some 30% of values are 1s. The dependent variable measures the distribution of funds, i.e. it is calculated just ...
user avatar
  • 331
1 vote
0 answers
17 views

What do the covariance and correlation tell me about two values?

I started reading a bit about probabilities and how they are used in investing. When reading about covariance and correlation, I got a bit confused about what they tell me about the two values I ...
user avatar
  • 11
1 vote
0 answers
22 views

what is the ratio of a ratio of two variances

I know that the ratio of two variances leads to an F-test but what of the ratio of two variance ratios? Is there are simple comparable result? Essentially I'm looking for the analogue of an ...
user avatar
  • 343
2 votes
1 answer
230 views

Can ratio data have negative values?

I get the concept of a "true zero" value, but I'm not sure why this implies that there cannot be any negative values—at least that's what most sources say that I found only, with only few ...
user avatar
  • 125
2 votes
1 answer
125 views

When is the ratio of two normals approximately normal?

Suppose that $X \sim N(\mu_1,\sigma_1)$ and $Y \sim N(\mu_2,\sigma_2)$ are two independent normal random variables. Define $Z = X/Y$. I noticed that there are some cases where the distribution of $Z$ ...
user avatar
  • 23
0 votes
0 answers
177 views

Proof that ratio of normal distributions is Cauchy [duplicate]

I recall that the ratio of 2 independent standard normal random variables follows a Cauchy distribution, but I don't recall if there is a proof for this.
user avatar
  • 53.3k
0 votes
1 answer
44 views

How to account for population sizes when comparing percentages (not CI)?

Let me articulate my line of thought. Imagine that you're working for the ministry of transportation. We compare two countries. One country is significantly bigger than the other – for example we ...
user avatar
2 votes
1 answer
230 views

Expected Value of the Ratio of Independent Variables, E(X/(X+Y)) [duplicate]

If $X$ and $Y$ are independent random variables, is the following true? Is there an easy way to show this? $$E\left[\frac{X}{X+Y}\right]=\frac{E[X]}{E[{X+Y}]}=\frac{E[X]}{E[X]+E[Y]}$$ If this is not ...
user avatar
1 vote
0 answers
31 views

How to prove that sample-based covariances of sample errors $E[(\bar x-\bar X)^r(\bar y-\bar Y)^s]$ tend to zero with increasing sample size?

Within the context of sample-based ratio estimators (i.e., sampling without replacement), this article here stated that the covariances of sample biases tend to zero with increasing sample size $n$: \...
user avatar
  • 481

1
2 3 4 5
7