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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10
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1answer
6k views

Testing Sharpe Ratio significance

What is the proper way to test the significance of Sharpe Ratios or Information Ratios? The Sharpe Ratios will be based on various equity indices and may have variable look-back periods. One solution ...
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1answer
2k views

Should I use the mean difference or mean ratio for a t-test?

I have a quantitative variable (medication dose) that is paired: dose of medication before surgery and after surgery for 76 patients. I was under the impression that I should calculate the mean of ...
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0answers
319 views

Standard Error of the ratio of Binomial variates

What's the right way to compute the Standard Error of the Mean of the ratio of two random variables that follow a binomial distribution? I asked a similar question here using Weibull distributions ...
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0answers
34 views

Diagram for spotting distributions, like "contradicting" results

Let's say we have two results that are related to each other: Result 1 was a questionnaire about food and had two options "I dislike Cake" and "I like Cake". The result is displayed as a ratio: "1:3"...
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3answers
11k views

How to compare percentages for populations of different sizes?

I have several populations (of people, actually) which vary in size (from 5 to 6000). I would like to visualize the ratio of women vs. men in each of them so that they can be compared. I will get, for ...
5
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1answer
205 views

Standard Error of Ratio of Weibull variates

Assuming that I have 2 distinct random variables that follow a Weibull distribution, what's the standard error* of the ratio of these two random variables? Basically I have $X \sim \text{Weibull}, Y \...
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1answer
74 views

What do these probabilities mean in lay language? A HR of 0.419 means what?

The adjusted hazard ratios (HRs) for dementia were significantly inversely associated with increased daily or total equivalent statin dosage. The HRs for the three tertiles of mean equivalent daily ...
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1answer
679 views

How to measure similarity of two rectangles' ratios? [closed]

I have two rectangles $R_1=(w_1,h_1)$ and $R_2=(w_2,h_2)$ and I would like to check how similar their ratios are. My first naive thought was this: $\Delta=\left|\frac{w_1}{h_1}-\frac{w_2}{h_2}\right|$....
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1answer
2k views

Fractional polynomials in PHREG procedure

For regression analysis by fractional polynomials i used the PHREG procedure in SAS. But it didn't give any Hazard Ratio values. Is it normal or any mistake in my code? ...
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2answers
599 views

Weighting CTR ratios based on reliability of the data

This is my dataset: PageID Hits ClickThroughs CTR 1 1000 400 40% 2 10 8 80% I'm trying to calculate click-...
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0answers
54 views

Why is my average CTR different from my overall CTR?

Here's some sample data: ...
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514 views

Distribution of ratio of Poisson distributed random variables

I am currently reading a paper and puzzling about a certain statement. I have a ratio $\frac{\hat\alpha_{T+1}}{\hat\alpha_{T}}=\frac{H_{T-4}+...+H_{T}}{H_{T-3}+...+H_{T+1}}\left(\frac{D_{T-3}+...+...
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1answer
2k views

If X/Y has the same distribution as Z, is it true that X has the same distribution as YZ?

Let X, Y and Z be three independent random variables. If X/Y has the same distribution as Z, is it true that X has the same distribution as YZ?
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90 views

How to analyse the ratio of two continuous variables sampled repeatedly over time

I am measuring reproductive hormones in dolphins over time to look at seasonal changes. The sample type (respiratory vapour) that I am using suffers from variable water dilution that cannot easily be ...
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2answers
274 views

Interactions - using ratio of variables

I have 3 variables, colony size, colony age and growth rate (colony size/age). I am interested to predict various other properties ($y$) of a colony using these 3 variables; $y = a_1 \text{ size} + ...
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2answers
855 views

Hypothesis testing of two standard mortality ratios

Probably this is an easy question, but I don’t seem to find an answer. The standard mortality ratio (SMR) is defined as “the ratio of actual number of deaths in the group under study to the expected ...
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0answers
28 views

Are there any approximation for ratios of factorials (and other similar high-precision ratios with rounding issues?) [duplicate]

I was wondering if there is some mathematical approximation for calculating the ratios of factorials. I don't mean a shortcut to deriving the factorial results through a means like Stirling's Formula, ...
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1answer
12k views

How do I interpret a variance ratio test in Stata?

I need help with interpreting output from a Variance Ratio Test in Stata. $f = 1.2988$ (my variance) $\text{Degrees of freedom} = 249, 493$ I have Ho: ratio = 1 as my null Ha: ratio != 1 Am I ...
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1answer
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Risk Ratio (or Prevalence Ratio) in SAS Proc Glimmix

Is it possible to obtain risk ratio in proc glimmix. And if yes, how do I specify the base. E.g base 'male' in variable 'gender'. Below is a template of my model: ...
6
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1answer
855 views

How should I evaluate the expectation of the ratio of two random variables?

Let $A$ and $B$ be random variables and $f(A,B)=\frac{A}{B}$. How should I approximate $E(f(A,B))$? I think a Taylor expansion may be in order, but I am not sure how to fire it off in this function. ...
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2answers
66 views

How can I use ratios to set priors on multinomial probabilities?

I have a vector, $k$, that determines allocation to five pools. I'd like to set priors on these probabilities, and I can provide informative priors on a few of the ratios, e.g.: $$ \frac{k1}{k2} \...
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0answers
270 views

Which kind of mean (harmonic, geometric, arithmetic) is best suited for averaging probability ratios? [closed]

There are a bunch of examples around on how harmonic mean is more suitable for averaging rates, e.g. speed (when the distance is fixed). But what about probability ratios (p(A)/p(B), i.e. how much ...
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1answer
872 views

Does the ratio fallacy apply when calculating a Pearson's correlation between one ratio variable and one absolute variable (no common term)?

Am I committing the ratio fallacy when I calculate the Pearson's correlation between a variable x/y and a variable z, with no common terms? I have found a similar question to mine here but the reader ...
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0answers
215 views

Odds Ratio in 2*3 Table

How can calculate Odds Ratio in 2*3 Table ( Participante [case -control] and marker [genotype])?
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2answers
66 views

Difference in predicted value using two different methods

Take these two vectors: ...
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1answer
90 views

Ideas for ratio estimation (X and Y from different surveys)?

We are trying to estimate the rate of event X per hour exposed to certain activities (e.g. commuting) by combining statistics from two multi-year cross-sectional surveys, one for the denominator and ...
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2answers
2k views

Best distribution to handle a ratio of counts as a response variable

A quick statistics question (apologies for the added biology): I have two sets of counts (for the expression of two different isoforms of a particular gene), and to generate the response variable in ...
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0answers
1k views

Distribution of random vector divided by it's norm

Does anyone know anything about the distribution of a random vector divided by it's norm? More specifically, if we know the distribution of a vector valued random variable $x$, what can we say about ...
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2answers
3k views

Should types of data (nominal/ordinal/interval/ratio) really be considered types of variables?

So for instance here are the definitions that I get from standard text books Variable - characteristic of population or sample. ex. Price of a stock or grade on a test Data - actual ...
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3answers
1k views

Bias of estimating a Ratio?

I would like to know why 1/N * Summation of(y/x) is a worse estimator than average of y divided by average of x. This is in the context of constructing an estimator of a ratio where the ratio would ...
6
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1answer
554 views

Ratio of correlated sample variances (gamma distributed)

for $N$ samples of two correlated random variables $X \sim N\left(0,\sigma_X^2\right)$ and $Y \sim N\left(0, \sigma_Y^2\right)$ with correlation $\rho$, I am analyzing the ratio of the sample ...
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3answers
19k views

What are the issues with using percentage outcome in linear regression?

I have a study where many outcomes are represented like percentages and I'm using multiple linear regressions to asses the effect of some categorical variables on these outcomes. I was wondering, ...
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1answer
1k views

Statistical test to assess differences between two sequencing methods

To asses differences between two DNA sequencing methods (454 and MiSeq) I have made artificial mixtures of different bacteria in the lab (mock communities). An Example might be (numbers are ...
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1answer
151 views

Regressing a ratio on a component of the ratio

Is there anything wrong with regressing a ratio on itself? For example can we regress the log(savings ratio) on log(income) or the log(debt to income) ratio on log(income)? If not, should we use the ...
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1answer
408 views

Problem when using ratio of two Poisson distributed variables?

I have two random variables (X and Y), each of which is Poisson distributed. Can I assume the ratio of both variables (X/Y) to be Poisson distributed as well (for an empirical analysis)? Note that Y ...
5
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3answers
949 views

median(a)/median(b) not equal median(a/b)

I'm sure this is a very straightforward question but it came up in my work today and I could not think of the reasoning behind it. I had two sets of numeric values (A & B) and was looking at the ...
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0answers
55 views

Appropriate Test? Is there a "t-test" for ratios when large number of data points and multiple runs?

N.B. I only have a very basic statistics background since I am in grade 9 in high school. Any help would be GREATLY appreciated. My Experiment: -Part 1: 2 variables (A and B) were each sampled in my ...
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15answers
49k views

Expected number of ratio of girls vs boys birth

I have came across a question in job interview aptitude test for critical thinking. It is goes something like this: The Zorganian Republic has some very strange customs. Couples only wish to have ...
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1answer
500 views

Multicollinearity if independent variables sum to one?

I am intending to explain the variation in dependent variable Y through a number of ratios that, combined, sum to 1 in each period t Hence, $$ Y_t = \alpha + \...
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3answers
2k views

What is the ratio of uniform and normal distribution?

Let $X$ follow a uniform distribution and $Y$ follow a normal distribution. What can be said about $\frac X Y$? Is there a distribution for it? I found the ratio of two normals with mean zero is ...
3
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0answers
113 views

Appropriate probability distribution for censored ratio data

I have two bacterial markers, I'll just call them X and Y. X codes for virulence, whereas Y just indicates the bacteria is present. Consequently, X will not show up without Y although not all bacteria ...
13
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1answer
4k views

Distribution of the ratio of dependent chi-square random variables

Assume that $ X = X_1 + X_2+\cdots+ X_n $ where $X_i \sim N(0,\sigma^2)$ are independent. My question is, what distribution does $$ Z = \frac{X^2}{X_1^2 + X_2^2 + \cdots + X_n^2}$$ follow? I know ...
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1answer
5k views

How to (properly) analyze the sex ratio

Few weeks ago, I was listening to a "HowToDoScience" lecture. In the section which focused on appropriate statistics in articles the lecturer said: Person who will analyse the sex ratio by the chi-...
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0answers
308 views

Expectation of density ratio of two iid variables

Let $X \sim N(0,1)$ and $Y \sim N(0,1)$ be independent RVs and let $f$ be their density function. I'd like to compute the expectation of the density ratio \begin{align} \mathbb{E}\left[\frac{f(X)}{f(Y)...
4
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1answer
425 views

Ratio that accounts for different sample sizes

I'm trying to get a measure for a set of data that indicates someone's "spam score". Essentially, the higher the spam score, the more likely they are to be spammers. Right now, I'm measuring a person'...
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1answer
130 views

Error propagation on correlated Poisson samples

If I have a set of $n$ tuples ($b_1,b_2,b_3,b_4,x,y,z$), where $b_1, b_2, b_3$ and $b_4$ are counters ruled by $P_1, P_2, P_3$ and $P_4$ Poisson distributions (error on the counters are $\sqrt{b_1}$, ...
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0answers
1k views

Regression to predict probability (responses are only ratios) - what transformation to use?

I am working on a project where the training labels are given to me as a probability value in the range [0,1]. My first approach was to fit a simple linear ridge regression to predict the probability....
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0answers
156 views

Estimation of mean of ratio of empirical distributions

I am trying to estimate the mean of the ratio of two empirical count distributions $f(x)$ and $b(x)$ defined on the limited range $[-1, 1]$ $$ \left<\frac{f(x)}{b(x)}\right> $$ $f(x)$ and $b(x)...
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0answers
395 views

Fieller's Theorem Degrees of Freedom

In a previous question I was trying to figure out how to compute the confidence interval of a ratio. Having come to the conclusion that the correct way to do this is Fieller's Theorem, I realize I'm ...
16
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1answer
3k views

Ratios in Regression, aka Questions on Kronmal

Recently, randomly browsing questions triggered a memory of on off-hand comment from one of my professors a few years back warning about the usage of ratios in regression models. So I started reading ...

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