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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2
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1answer
830 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
204 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: ...
3
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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
516 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
16k 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, ...
5
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1answer
990 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
145 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
333 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 ...
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3answers
773 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
53 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
48k 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
459 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 ...
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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 ...
11
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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
4k 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
295 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)...
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1answer
334 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
127 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
144 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
371 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 ...
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1answer
2k 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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380 views

Analyzing ratios or numerator/denominator, with weights, measured over time at irregular intervals

I have gathered information on the rate increases allowed by a government regulator over about 17 years. As background, utilities in this area must apply to the regulator if they wish to raise their ...
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4answers
26k views

How to compute the confidence interval of the ratio of two normal means

I want to derive the limits for the $100(1-\alpha)\%$ confidence interval for the ratio of two means. Suppose, $X_1 \sim N(\theta_1, \sigma^2)$ and $X_2 \sim N(\theta_2, \sigma^2)$ being independent, ...
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1answer
1k views

Analysing ratios of variables

Ratios (X/Y, e.g. body mass index) are variables with odd distributions. They have no means or moments (e.g. variances, skewness or kurtosis). Thus, my questions are: How to compare between (or among)...

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