Statistical Analysis Stack Exchange
Statistical Analysis Stack Exchange

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.

A ratio is a relationship between two numbers indicating how many times the first number contains the second. For example, if a bowl of fruit contains eight oranges and six lemons, then the ratio of oranges to lemons is eight to six (that is, 8:6, which is equivalent to the ratio 4:3). Thus, a ratio can be a fraction as opposed to a whole number.

A ratio is written "a to b" or a:b, or sometimes expressed arithmetically as a quotient of the two. When the two quantities have the same units, as is often the case, their ratio is a dimensionless number.

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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 female children as only females can inherit the…
Mobius Pizza
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I've heard that ratios or inverses of random variables often are problematic, in not having expectations. Why is that?

The title is the question. I am told that ratios and inverses of random variables often are problematic. What is meant is that expectation often do not exist. Is there a simple, general explication of that?
kjetil b halvorsen
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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, the mean ratio $\Gamma = \theta_1/\theta_2$. I…
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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 up on this, leading eventually to Kronmal 1993. I…
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An unbiased estimator of the ratio of two regression coefficients?

Suppose you fit a linear/logistic regression $g(y) = a_0 + a_1\cdot x_1 + a_2\cdot x_2$, with the aim of an unbiased estimate of $\frac{a_1}{a_2}$. You are very confident that both $a_1$ and $a_2$ are very positive relative to the noise in their…
quasi
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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 from here that the ratio of two chi-squared random…
x0dros
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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, since a linear regression assume that the outcome is…
Bakaburg
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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 Cauchy.
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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 rep users attract more attention and therefore…
Ciro Santilli 新疆再教育营六四事件法轮功郝海东
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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 observed values So for a two column report [Name |…
User 42
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Expected value of maximum ratio of n iid normal variables

Suppose $X_1,...,X_n$ are iid from $N(\mu,\sigma^2)$ and let $X_{(i)}$ denote the $i$'th smallest element from $X_1,...,X_n$. How would one be able to upper bound the expected maximum of the ratio between two consecutive elements in $X_{(i)}$? That…
Max
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Given n uniformly distributed r.v's, what is the PDF for one r.v. divided by the sum of all n r.v's?

I'm interested in the following type of case: there are 'n' continuous random variables which must sum to 1. What then would be the PDF for any one individual such variable? So, if $n=3$, then I am interested in the distribution for…
user3593717
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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 that I have seen described simply applies a…
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Expected value of ratio of correlated random variables?

For independent random variables $\alpha$ and $\beta$, is there a closed form expression for $\mathbb E \left[ \frac{\alpha}{\sqrt{\alpha^2 + \beta^2}} \right]$ in terms of the expected values and variances of $\alpha$ and $\beta$? If not, is there…
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Using Fieller's theorem to calculate the confidence interval of a ratio (paired measurements)

If you have two means (with their own confidence intervals) and want to represent them as a ratio, how do calculate the confidence interval for the ratio? An answer that was given to me, mentions Fieller's theorem, which enables you to compute a…
Marc
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